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Sample records for nonlinear optimal perturbation

  1. Nonlinear optimal perturbations in a curved pipe

    Science.gov (United States)

    Rinaldi, Enrico; Canton, Jacopo; Marin, Oana; Schanen, Michel; Schlatter, Philipp

    2017-11-01

    We investigate the effect of curvature on transition to turbulence in pipes by comparing optimal perturbations of finite amplitude that maximise their energy growth in a toroidal geometry to the ones calculated in the absence of curvature. Our interest is motivated by the fact that even small curvatures, of the order of d =Rpipe /Rtorus art numerical algorithms, capable of tackling the optimisation problem on large computational domains, coupled to a high-order spectral-element code, which is used to perform direct numerical simulations (DNS) of the full Navier-Stokes and their adjoint equations. Results are compared to the corresponding states in straight pipes and differences in their structure and evolution are discussed. Furthermore, the newly calculated initial conditions are used to identify coherent flow structures that are compared to the ones observed in recent DNS of weakly turbulent and relaminarising flows in the same toroidal geometry.

  2. Optimal perturbations for nonlinear systems using graph-based optimal transport

    Science.gov (United States)

    Grover, Piyush; Elamvazhuthi, Karthik

    2018-06-01

    We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on the phase space to a final measure in finite time. The measure is propagated under system dynamics in between the perturbations via the associated transfer operator. Each perturbation is described by a deterministic map in the measure space that implements a version of Monge-Kantorovich optimal transport with quadratic cost. Hence, the optimal solution minimizes a sum of quadratic costs on phase space transport due to the perturbations applied at specified times. The action of the transport map is approximated by a continuous pseudo-time flow on a graph, resulting in a tractable convex optimization problem. This problem is solved via state-of-the-art solvers to global optimality. We apply this algorithm to a problem of transport between measures supported on two disjoint almost-invariant sets in a chaotic fluid system, and to a finite-time optimal mixing problem by choosing the final measure to be uniform. In both cases, the optimal perturbations are found to exploit the phase space structures, such as lobe dynamics, leading to efficient global transport. As the time-horizon of the problem is increased, the optimal perturbations become increasingly localized. Hence, by combining the transfer operator approach with ideas from the theory of optimal mass transportation, we obtain a discrete-time graph-based algorithm for optimal transport and mixing in nonlinear systems.

  3. Stabilization of Hypersonic Boundary Layers by Linear and Nonlinear Optimal Perturbations

    Science.gov (United States)

    Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

    2017-01-01

    The effect of stationary, finite-amplitude, linear and nonlinear optimal perturbations on the modal disturbance growth in a Mach 6 axisymmetric flow over a 7 deg. half-angle cone with 0:126 mm nose radius and 0:305 m length is investigated. The freestream parameters (M = 6, Re(exp 1) = 18 x 10(exp. 6) /m) are selected to match the flow conditions of a previous experiment in the VKI H3 hypersonic tunnel. Plane-marching parabolized stability equations are used in conjunction with a partial-differential equation based planar eigenvalue analysis to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode and first-mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone; however, subharmonic first-mode instabilities, which are destabilized by the presence of the streaks, do reach N = 6 near the end of the cone. The highest stabilization is observed at streak amplitudes of approximately 20 percent of the freestream velocity. Because the use of initial disturbance profiles based on linear optimal growth theory may yield suboptimal control in the context of nonlinear streaks, the computational predictions are extended to nonlinear optimal growth theory. Results show that by using nonlinearly optimal perturbation leads to slightly enhanced stabilization of plane Mack mode disturbances as well as reduced destabilization of subharmonic first-mode disturbances.

  4. Application of nonlinear nodal diffusion generalized perturbation theory to nuclear fuel reload optimization

    International Nuclear Information System (INIS)

    Maldonado, G.I.; Turinsky, P.J.

    1995-01-01

    The determination of the family of optimum core loading patterns for pressurized water reactors (PWRs) involves the assessment of the core attributes for thousands of candidate loading patterns. For this reason, the computational capability to efficiently and accurately evaluate a reactor core's eigenvalue and power distribution versus burnup using a nodal diffusion generalized perturbation theory (GPT) model is developed. The GPT model is derived from the forward nonlinear iterative nodal expansion method (NEM) to explicitly enable the preservation of the finite difference matrix structure. This key feature considerably simplifies the mathematical formulation of NEM GPT and results in reduced memory storage and CPU time requirements versus the traditional response-matrix approach to NEM. In addition, a treatment within NEM GPT can account for localized nonlinear feedbacks, such as that due to fission product buildup and thermal-hydraulic effects. When compared with a standard nonlinear iterative NEM forward flux solve with feedbacks, the NEM GPT model can execute between 8 and 12 times faster. These developments are implemented within the PWR in-core nuclear fuel management optimization code FORMOSA-P, combining the robustness of its adaptive simulated annealing stochastic optimization algorithm with an NEM GPT neutronics model that efficiently and accurately evaluates core attributes associated with objective functions and constraints of candidate loading patterns

  5. Nonlinear optimization

    CERN Document Server

    Ruszczynski, Andrzej

    2011-01-01

    Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...

  6. PWR in-core nuclear fuel management optimization utilizing nodal (non-linear NEM) generalized perturbation theory

    International Nuclear Information System (INIS)

    Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.

    1993-01-01

    The computational capability of efficiently and accurately evaluate reactor core attributes (i.e., k eff and power distributions as a function of cycle burnup) utilizing a second-order accurate advanced nodal Generalized Perturbation Theory (GPT) model has been developed. The GPT model is derived from the forward non-linear iterative Nodal Expansion Method (NEM) strategy, thereby extending its inherent savings in memory storage and high computational efficiency to also encompass GPT via the preservation of the finite-difference matrix structure. The above development was easily implemented into the existing coarse-mesh finite-difference GPT-based in-core fuel management optimization code FORMOSA-P, thus combining the proven robustness of its adaptive Simulated Annealing (SA) multiple-objective optimization algorithm with a high-fidelity NEM GPT neutronics model to produce a powerful computational tool used to generate families of near-optimum loading patterns for PWRs. (orig.)

  7. Perturbations of normally solvable nonlinear operators, I

    Directory of Open Access Journals (Sweden)

    William O. Ray

    1985-01-01

    Full Text Available Let X and Y be Banach spaces and let ℱ and be Gateaux differentiable mappings from X to Y In this note we study when the operator ℱ+ is surjective for sufficiently small perturbations of a surjective operator ℱ The methods extend previous results in the area of normal solvability for nonlinear operators.

  8. A perturbed martingale approach to global optimization

    Energy Technology Data Exchange (ETDEWEB)

    Sarkar, Saikat [Computational Mechanics Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012 (India); Roy, Debasish, E-mail: royd@civil.iisc.ernet.in [Computational Mechanics Lab, Department of Civil Engineering, Indian Institute of Science, Bangalore 560012 (India); Vasu, Ram Mohan [Department of Instrumentation and Applied Physics, Indian Institute of Science, Bangalore 560012 (India)

    2014-08-01

    A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization. - Highlights: • Evolutionary global optimization is posed as a perturbed martingale problem. • Resulting search via additive updates is a generalization over Gateaux derivatives. • Additional layers of random perturbation help avoid trapping at local extrema. • The approach ensures efficient design space exploration and high accuracy. • The method is numerically assessed via parameter recovery of chaotic oscillators.

  9. Perturbation analysis of nonlinear matrix population models

    Directory of Open Access Journals (Sweden)

    Hal Caswell

    2008-03-01

    Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.

  10. Perturbation Theory for Open Two-Level Nonlinear Quantum Systems

    International Nuclear Information System (INIS)

    Zhang Zhijie; Jiang Dongguang; Wang Wei

    2011-01-01

    Perturbation theory is an important tool in quantum mechanics. In this paper, we extend the traditional perturbation theory to open nonlinear two-level systems, treating decoherence parameter γ as a perturbation. By this virtue, we give a perturbative solution to the master equation, which describes a nonlinear open quantum system. The results show that for small decoherence rate γ, the ratio of the nonlinear rate C to the tunneling coefficient V (i.e., r = C/V) determines the validity of the perturbation theory. For small ratio r, the perturbation theory is valid, otherwise it yields wrong results. (general)

  11. Nonlinearly perturbed semi-Markov processes

    CERN Document Server

    Silvestrov, Dmitrii

    2017-01-01

    The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will cont...

  12. Nonlinear optimal control theory

    CERN Document Server

    Berkovitz, Leonard David

    2012-01-01

    Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also dis

  13. A nonlinear inversion for the velocity background and perturbation models

    KAUST Repository

    Wu, Zedong

    2015-08-19

    Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect diving waves, which is an important source of information for extracting the long wavelength components of the velocity model. Thus, we propose a new optimization problem through breaking the velocity model into the background and the perturbation in the wave equation directly. In this case, the perturbed model is no longer the single scattering model, but includes all scattering. We optimize both components simultaneously, and thus, the objective function is nonlinear with respect to both the background and perturbation. The new introduced w can absorb the non-smooth update of background naturally. Application to the Marmousi model with frequencies that start at 5 Hz shows that this method can converge to the accurate velocity starting from a linearly increasing initial velocity. Application to the SEG2014 demonstrates the versatility of the approach.

  14. de Sitter limit of inflation and nonlinear perturbation theory

    DEFF Research Database (Denmark)

    R. Jarnhus, Philip; Sloth, Martin Snoager

    2007-01-01

    We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gaug...

  15. Perturbation Solutions of the Quintic Duffing Equation with Strong Nonlinearities

    Directory of Open Access Journals (Sweden)

    Mehmet Pakdemirli

    Full Text Available The quintic Duffing equation with strong nonlinearities is considered. Perturbation solutions are constructed using two different techniques: The classical multiple scales method (MS and the newly developed multiple scales Lindstedt Poincare method (MSLP. The validity criteria for admissible solutions are derived. Both approximate solutions are contrasted with the numerical solutions. It is found that MSLP provides compatible solution with the numerical solution for strong nonlinearities whereas MS solution fail to produce physically acceptable solution for large perturbation parameters.

  16. Long wavelength limit of evolution of nonlinear cosmological perturbations

    International Nuclear Information System (INIS)

    Hamazaki, Takashi

    2008-01-01

    In the general matter composition where the multiple scalar fields and the multiple perfect fluids coexist, in the leading order of the gradient expansion, we construct all of the solutions of the nonlinear evolutions of the locally homogeneous universe. From the momentum constraint, we derive the constraints which the solution constants of the locally homogeneous universe must satisfy. We construct the gauge invariant perturbation variables in the arbitrarily higher order nonlinear cosmological perturbation theory around the spatially flat Friedmann-Robertson-Walker universe. We construct the nonlinear long wavelength limit formula representing the long wavelength limit of the evolution of the nonlinear gauge invariant perturbation variables in terms of perturbations of the evolutions of the locally homogeneous universe. By using the long wavelength limit formula, we investigate the evolution of nonlinear cosmological perturbations in the universe dominated by the multiple slow rolling scalar fields with an arbitrary potential. The τ function and the N potential introduced in this paper make it possible to write the evolution of the multiple slow rolling scalar fields with an arbitrary interaction potential and the arbitrarily higher order nonlinear Bardeen parameter at the end of the slow rolling phase analytically. It is shown that the nonlinear parameters such as f NL and g NL are suppressed by the slow rolling expansion parameters.

  17. Controllability for Variational Inequalities of Parabolic Type with Nonlinear Perturbation

    Directory of Open Access Journals (Sweden)

    Jeong Jin-Mun

    2010-01-01

    Full Text Available We deal with the approximate controllability for the nonlinear functional differential equation governed by the variational inequality in Hilbert spaces and present a general theorems under which previous results easily follow. The common research direction is to find conditions on the nonlinear term such that controllability is preserved under perturbation.

  18. Nonlinear singular perturbation problems of arbitrary real orders

    International Nuclear Information System (INIS)

    Bijura, Angelina M.

    2003-10-01

    Higher order asymptotic solutions of singularly perturbed nonlinear fractional integral and derivatives of order 1/2 are investigated. It is particularly shown that whilst certain asymptotic expansions are applied successfully to linear equations and particular nonlinear problems, the standard formal asymptotic expansion is appropriate for the general class of nonlinear equations. This theory is then generalised to the general equation (of order β, 0 < β < 1). (author)

  19. Non-linear perturbations of a spherically collapsing star

    International Nuclear Information System (INIS)

    Brizuela, David

    2009-01-01

    Linear perturbation theory has been a successful tool in General Relativity, and can be considered as complementary to full nonlinear simulations. Going to second and higher perturbative orders improves the approximation and offers a controlled way to analyze the nonlinearities of the theory, though the problem becomes much harder computationally. We present a systematic approach to the treatment of high order metric perturbations, focusing on the scenario of nonspherical perturbations of a dynamical spherical background. It is based on the combination of adapted geometrical variables and the use of efficient computer algebra techniques. After dealing with a number of theoretical issues, like the construction of gauge invariants, we apply the formalism to the particular case of a perfect fluid star surrounded by a vacuum exterior. We describe the regularization of the divergences of the perturbations at null infinity and the matching conditions through the surface of the star.

  20. Nonlinear spherical perturbations in quintessence models of dark energy

    Science.gov (United States)

    Pratap Rajvanshi, Manvendra; Bagla, J. S.

    2018-06-01

    Observations have confirmed the accelerated expansion of the universe. The accelerated expansion can be modelled by invoking a cosmological constant or a dynamical model of dark energy. A key difference between these models is that the equation of state parameter w for dark energy differs from ‑1 in dynamical dark energy (DDE) models. Further, the equation of state parameter is not constant for a general DDE model. Such differences can be probed using the variation of scale factor with time by measuring distances. Another significant difference between the cosmological constant and DDE models is that the latter must cluster. Linear perturbation analysis indicates that perturbations in quintessence models of dark energy do not grow to have a significant amplitude at small length scales. In this paper we study the response of quintessence dark energy to non-linear perturbations in dark matter. We use a fully relativistic model for spherically symmetric perturbations. In this study we focus on thawing models. We find that in response to non-linear perturbations in dark matter, dark energy perturbations grow at a faster rate than expected in linear perturbation theory. We find that dark energy perturbation remains localised and does not diffuse out to larger scales. The dominant drivers of the evolution of dark energy perturbations are the local Hubble flow and a supression of gradients of the scalar field. We also find that the equation of state parameter w changes in response to perturbations in dark matter such that it also becomes a function of position. The variation of w in space is correlated with density contrast for matter. Variation of w and perturbations in dark energy are more pronounced in response to large scale perturbations in matter while the dependence on the amplitude of matter perturbations is much weaker.

  1. Nonlinear PI control of chaotic systems using singular perturbation theory

    International Nuclear Information System (INIS)

    Wang Jiang; Wang Jing; Li Huiyan

    2005-01-01

    In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit

  2. Spike-layer solutions to nonlinear fractional Schrodinger equations with almost optimal nonlinearities

    Directory of Open Access Journals (Sweden)

    Jinmyoung Seok

    2015-07-01

    Full Text Available In this article, we are interested in singularly perturbed nonlinear elliptic problems involving a fractional Laplacian. Under a class of nonlinearity which is believed to be almost optimal, we construct a positive solution which exhibits multiple spikes near any given local minimum components of an exterior potential of the problem.

  3. Perturbation method for periodic solutions of nonlinear jerk equations

    International Nuclear Information System (INIS)

    Hu, H.

    2008-01-01

    A Lindstedt-Poincare type perturbation method with bookkeeping parameters is presented for determining accurate analytical approximate periodic solutions of some third-order (jerk) differential equations with cubic nonlinearities. In the process of the solution, higher-order approximate angular frequencies are obtained by Newton's method. A typical example is given to illustrate the effectiveness and simplicity of the proposed method

  4. Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations

    Directory of Open Access Journals (Sweden)

    Waheed A. Ahmed

    2017-11-01

    Full Text Available Approximate symmetries of a class of perturbed nonlinear wave equations are computed using two newly-developed methods. Invariant solutions associated with the approximate symmetries are constructed for both methods. Symmetries and solutions are compared through discussing the advantages and disadvantages of each method.

  5. Painleve analysis, conservation laws, and symmetry of perturbed nonlinear equations

    International Nuclear Information System (INIS)

    Basak, S.; Chowdhury, A.R.

    1987-01-01

    The authors consider the Lie-Backlund symmetries and conservation laws of a perturbed KdV equation and NLS equation. The arbitrary coefficients of the perturbing terms can be related to the condition of existence of nontrivial LB symmetry generators. When the perturbed KdV equation is subjected to Painleve analysis a la Weiss, it is found that the resonance position changes compared to the unperturbed one. They prove the compatibility of the overdetermined set of equations obtained at the different stages of recursion relations, at least for one branch. All other branches are also indicated and difficulties associated them are discussed considering the perturbation parameter epsilon to be small. They determine the Lax pair for the aforesaid branch through the use of Schwarzian derivative. For the perturbed NLS equation they determine the conservation laws following the approach of Chen and Liu. From the recurrence of these conservation laws a Lax pair is constructed. But the Painleve analysis does not produce a positive answer for the perturbed NLS equation. So here they have two contrasting examples of perturbed nonlinear equations: one passes the Painleve test and its Lax pair can be found from the analysis itself, but the other equation does not meet the criterion of the Painleve test, though its Lax pair is found in another way

  6. EDITORIAL: Non-linear and non-Gaussian cosmological perturbations Non-linear and non-Gaussian cosmological perturbations

    Science.gov (United States)

    Sasaki, Misao; Wands, David

    2010-06-01

    In recent years there has been a resurgence of interest in the study of non-linear perturbations of cosmological models. This has been the result of both theoretical developments and observational advances. New theoretical challenges arise at second and higher order due to mode coupling and the need to develop new gauge-invariant variables beyond first order. In particular, non-linear interactions lead to deviations from a Gaussian distribution of primordial perturbations even if initial vacuum fluctuations are exactly Gaussian. These non-Gaussianities provide an important probe of models for the origin of structure in the very early universe. We now have a detailed picture of the primordial distribution of matter from surveys of the cosmic microwave background, notably NASA's WMAP satellite. The situation will continue to improve with future data from the ESA Planck satellite launched in 2009. To fully exploit these data cosmologists need to extend non-linear cosmological perturbation theory beyond the linear theory that has previously been sufficient on cosmological scales. Another recent development has been the realization that large-scale structure, revealed in high-redshift galaxy surveys, could also be sensitive to non-linearities in the primordial curvature perturbation. This focus section brings together a collection of invited papers which explore several topical issues in this subject. We hope it will be of interest to theoretical physicists and astrophysicists alike interested in understanding and interpreting recent developments in cosmological perturbation theory and models of the early universe. Of course it is only an incomplete snapshot of a rapidly developing field and we hope the reader will be inspired to read further work on the subject and, perhaps, fill in some of the missing pieces. This focus section is dedicated to the memory of Lev Kofman (1957-2009), an enthusiastic pioneer of inflationary cosmology and non-Gaussian perturbations.

  7. Interactive Nonlinear Multiobjective Optimization Methods

    OpenAIRE

    Miettinen, Kaisa; Hakanen, Jussi; Podkopaev, Dmitry

    2016-01-01

    An overview of interactive methods for solving nonlinear multiobjective optimization problems is given. In interactive methods, the decision maker progressively provides preference information so that the most satisfactory Pareto optimal solution can be found for her or his. The basic features of several methods are introduced and some theoretical results are provided. In addition, references to modifications and applications as well as to other methods are indicated. As the...

  8. Formulation of nonlinear chromaticity in circular accelerators by canonical perturbation method

    International Nuclear Information System (INIS)

    Takao, Masaru

    2005-01-01

    The formulation of nonlinear chromaticity in circular accelerators based on the canonical perturbation method is presented. Since the canonical perturbation method directly relates the tune shift to the perturbation Hamiltonian, it greatly simplifies the calculation of the nonlinear chromaticity. The obtained integral representation for nonlinear chromaticity can be systematically extended to higher orders

  9. Nonlinear Optimization with Financial Applications

    CERN Document Server

    Bartholomew-Biggs, Michael

    2005-01-01

    The book introduces the key ideas behind practical nonlinear optimization. Computational finance - an increasingly popular area of mathematics degree programs - is combined here with the study of an important class of numerical techniques. The financial content of the book is designed to be relevant and interesting to specialists. However, this material - which occupies about one-third of the text - is also sufficiently accessible to allow the book to be used on optimization courses of a more general nature. The essentials of most currently popular algorithms are described, and their performan

  10. Application of functional analysis to perturbation theory of differential equations. [nonlinear perturbation of the harmonic oscillator

    Science.gov (United States)

    Bogdan, V. M.; Bond, V. B.

    1980-01-01

    The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

  11. Perturbation theory in nuclear fuel management optimization

    International Nuclear Information System (INIS)

    Ho, L.W.; Rohach, A.F.

    1982-01-01

    Perturbation theory along with a binary fuel shuffling technique is applied to predict the effects of various core configurations and, hence, the optimization of in-core fuel management. The computer code FULMNT has been developed to shuffle the fuel assemblies in search of the lowest possible power peaking factor. An iteration approach is used in the search routine. A two-group diffusion theory method is used to obtain the power distribution for the iterations. A comparison of the results of this method with other methods shows that this approach can save computer time and obtain better power peaking factors. The code also has a burnup capability that can be used to check power peaking throughout the core life

  12. Geometric scaling in ultrahigh energy neutrinos and nonlinear perturbative QCD

    International Nuclear Information System (INIS)

    Machado, Magno V.T.

    2011-01-01

    The ultrahigh energy neutrino cross section is a crucial ingredient in the calculation of the event rate in high energy neutrino telescopes. Currently there are several approaches which predict different behaviors for its magnitude for ultrahigh energies. In this contribution is presented a summary of current predictions based on the non-linear QCD evolution equations, the so-called perturbative saturation physics. In particular, predictions are shown based on the parton saturation approaches and the consequences of geometric scaling property at high energies are discussed. The scaling property allows an analytical computation of the neutrino scattering on nucleon/nucleus at high energies, providing a theoretical parameterization. (author)

  13. Exact non-linear equations for cosmological perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Gong, Jinn-Ouk [Asia Pacific Center for Theoretical Physics, Pohang 37673 (Korea, Republic of); Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 41566 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 34055 (Korea, Republic of); Wu, David Chan Lon; Yoo, Jaiyul, E-mail: jinn-ouk.gong@apctp.org, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: clwu@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch [Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, Universität Zürich, CH-8057 Zürich (Switzerland)

    2017-10-01

    We present a complete set of exact and fully non-linear equations describing all three types of cosmological perturbations—scalar, vector and tensor perturbations. We derive the equations in a thoroughly gauge-ready manner, so that any spatial and temporal gauge conditions can be employed. The equations are completely general without any physical restriction except that we assume a flat homogeneous and isotropic universe as a background. We also comment briefly on the application of our formulation to the non-expanding Minkowski background.

  14. On the non-linear scale of cosmological perturbation theory

    CERN Document Server

    Blas, Diego; Konstandin, Thomas

    2013-01-01

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  15. On the non-linear scale of cosmological perturbation theory

    International Nuclear Information System (INIS)

    Blas, Diego; Garny, Mathias; Konstandin, Thomas

    2013-04-01

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  16. On the non-linear scale of cosmological perturbation theory

    Energy Technology Data Exchange (ETDEWEB)

    Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2013-04-15

    We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

  17. Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method

    KAUST Repository

    Higueras, Inmaculada

    2018-02-14

    Perturbed Runge–Kutta methods (also referred to as downwind Runge–Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge–Kutta counterparts. In this paper we study the question of how to optimally perturb a given method in order to increase the radius of absolute monotonicity (a.m.). We prove that for methods with zero radius of a.m., it is always possible to give a perturbation with positive radius. We first study methods for linear problems and then methods for nonlinear problems. In each case, we prove upper bounds on the radius of a.m., and provide algorithms to compute optimal perturbations. We also provide optimal perturbations for many known methods.

  18. Optimal Monotonicity-Preserving Perturbations of a Given Runge–Kutta Method

    KAUST Repository

    Higueras, Inmaculada; Ketcheson, David I.; Kocsis, Tihamé r A.

    2018-01-01

    Perturbed Runge–Kutta methods (also referred to as downwind Runge–Kutta methods) can guarantee monotonicity preservation under larger step sizes relative to their traditional Runge–Kutta counterparts. In this paper we study the question of how to optimally perturb a given method in order to increase the radius of absolute monotonicity (a.m.). We prove that for methods with zero radius of a.m., it is always possible to give a perturbation with positive radius. We first study methods for linear problems and then methods for nonlinear problems. In each case, we prove upper bounds on the radius of a.m., and provide algorithms to compute optimal perturbations. We also provide optimal perturbations for many known methods.

  19. Non-gaussianity versus nonlinearity of cosmological perturbations.

    Science.gov (United States)

    Verde, L

    2001-06-01

    Following the discovery of the cosmic microwave background, the hot big-bang model has become the standard cosmological model. In this theory, small primordial fluctuations are subsequently amplified by gravity to form the large-scale structure seen today. Different theories for unified models of particle physics, lead to different predictions for the statistical properties of the primordial fluctuations, that can be divided in two classes: gaussian and non-gaussian. Convincing evidence against or for gaussian initial conditions would rule out many scenarios and point us toward a physical theory for the origin of structures. The statistical distribution of cosmological perturbations, as we observe them, can deviate from the gaussian distribution in several different ways. Even if perturbations start off gaussian, nonlinear gravitational evolution can introduce non-gaussian features. Additionally, our knowledge of the Universe comes principally from the study of luminous material such as galaxies, but galaxies might not be faithful tracers of the underlying mass distribution. The relationship between fluctuations in the mass and in the galaxies distribution (bias), is often assumed to be local, but could well be nonlinear. Moreover, galaxy catalogues use the redshift as third spatial coordinate: the resulting redshift-space map of the galaxy distribution is nonlinearly distorted by peculiar velocities. Nonlinear gravitational evolution, biasing, and redshift-space distortion introduce non-gaussianity, even in an initially gaussian fluctuation field. I investigate the statistical tools that allow us, in principle, to disentangle the above different effects, and the observational datasets we require to do so in practice.

  20. Perturbation theory in nuclear fuel management optimization

    International Nuclear Information System (INIS)

    Ho, L.W.

    1981-01-01

    Nuclear in-core fuel management involves all the physical aspects which allow optimal operation of the nuclear fuel within the reactor core. In most nuclear power reactors, fuel loading patterns which have a minimum power peak are economically desirable to allow the reactors to operate at the highest power density and to minimize the possibility of fuel failure. In this study, perturbation theory along with a binary fuel shuffling technique is applied to predict the effects of various core configurations, and hence, the optimization of in-core fuel management. The computer code FULMNT has been developed to shuffle the fuel assemblies in search of the lowest possible power peaking factor. An iteration approach is used in the search routine. A two-group diffusion theory method is used to obtain the power distribution for the iterations. A comparison of the results of this method with other methods shows that this approach can save computer time. The code also has a burnup capability which can be used to check power peaking throughout the core life

  1. Non-perturbative aspects of nonlinear sigma models

    Energy Technology Data Exchange (ETDEWEB)

    Flore, Raphael

    2012-12-07

    The aim of this thesis was the study and further development of non-perturbative methods of quantum field theory by means of their application to nonlinear sigma models. While a large part of the physical phenomena of quantum field theory can be successfully predicted by the perturbation theory, some aspects in the region of large coupling strengths are not definitively understood and require suited non-perturbative methods for its analysis. This thesis is concentrated on two approaches, the numerical treatment of field theories on discrete space-time lattices and the functional renormalization group (FRG) as description of the renormalization flux of effective actions. Considerations of the nonlinear O(N) models have shown that for the correct analysis of the critical properties in the framework of the FRG an approach must be chosen, which contained fourth-derivation orders. For this a covariant formalism was developed, which is based on a background-field expansion and the development of a heat kernel. Apart from a destabilizing coupling the results suggest a nontrivial fixed point and by this a non-perturbative renormalizability of these models. The resulting flow diagrams were finally still compared with the results of a numerical analysis of the renormalization flow by means of the Monte-Carlo renormalization group, and hereby qualitative agreement was found. Furthermore an alternative formulation of the FRG in phase-space coordinates was studied and their consistency tested on simple examples. Beyond this an alternative expansion of the effective action in orders of the canonical momenta was applied to the nonlinear O(N) models with the result of a stable non-trivial fixed point, the critical properties of which however show not the expected N-dependence. By means of the FRG finally still the renormalization of topological operators was studied by means of the winding number of the O(3){approx_equal}CP{sup 1} model. By the generalization of the topological

  2. Non-perturbative aspects of nonlinear sigma models

    International Nuclear Information System (INIS)

    Flore, Raphael

    2012-01-01

    The aim of this thesis was the study and further development of non-perturbative methods of quantum field theory by means of their application to nonlinear sigma models. While a large part of the physical phenomena of quantum field theory can be successfully predicted by the perturbation theory, some aspects in the region of large coupling strengths are not definitively understood and require suited non-perturbative methods for its analysis. This thesis is concentrated on two approaches, the numerical treatment of field theories on discrete space-time lattices and the functional renormalization group (FRG) as description of the renormalization flux of effective actions. Considerations of the nonlinear O(N) models have shown that for the correct analysis of the critical properties in the framework of the FRG an approach must be chosen, which contained fourth-derivation orders. For this a covariant formalism was developed, which is based on a background-field expansion and the development of a heat kernel. Apart from a destabilizing coupling the results suggest a nontrivial fixed point and by this a non-perturbative renormalizability of these models. The resulting flow diagrams were finally still compared with the results of a numerical analysis of the renormalization flow by means of the Monte-Carlo renormalization group, and hereby qualitative agreement was found. Furthermore an alternative formulation of the FRG in phase-space coordinates was studied and their consistency tested on simple examples. Beyond this an alternative expansion of the effective action in orders of the canonical momenta was applied to the nonlinear O(N) models with the result of a stable non-trivial fixed point, the critical properties of which however show not the expected N-dependence. By means of the FRG finally still the renormalization of topological operators was studied by means of the winding number of the O(3)≅CP 1 model. By the generalization of the topological operator and the

  3. Internal wave energy flux from density perturbations in nonlinear stratifications

    Science.gov (United States)

    Lee, Frank M.; Allshouse, Michael R.; Swinney, Harry L.; Morrison, P. J.

    2017-11-01

    Tidal flow over the topography at the bottom of the ocean, whose density varies with depth, generates internal gravity waves that have a significant impact on the energy budget of the ocean. Thus, understanding the energy flux (J = p v) is important, but it is difficult to measure simultaneously the pressure and velocity perturbation fields, p and v . In a previous work, a Green's-function-based method was developed to calculate the instantaneous p, v , and thus J , given a density perturbation field for a constant buoyancy frequency N. Here we extend the previous analytic Green's function work to include nonuniform N profiles, namely the tanh-shaped and linear cases, because background density stratifications that occur in the ocean and some experiments are nonlinear. In addition, we present a finite-difference method for the general case where N has an arbitrary profile. Each method is validated against numerical simulations. The methods we present can be applied to measured density perturbation data by using our MATLAB graphical user interface EnergyFlux. PJM was supported by the U.S. Department of Energy Contract DE-FG05-80ET-53088. HLS and MRA were supported by ONR Grant No. N000141110701.

  4. Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime

    Science.gov (United States)

    Zhu, Ping; Yan, Xingting; Huang, Wenlong

    2017-10-01

    Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

  5. Formal Proofs for Nonlinear Optimization

    Directory of Open Access Journals (Sweden)

    Victor Magron

    2015-01-01

    Full Text Available We present a formally verified global optimization framework. Given a semialgebraic or transcendental function f and a compact semialgebraic domain K, we use the nonlinear maxplus template approximation algorithm to provide a certified lower bound of f over K.This method allows to bound in a modular way some of the constituents of f by suprema of quadratic forms with a well chosen curvature. Thus, we reduce the initial goal to a hierarchy of semialgebraic optimization problems, solved by sums of squares relaxations. Our implementation tool interleaves  semialgebraic approximations with sums of squares witnesses to form certificates. It is interfaced with Coq and thus benefits from the trusted arithmetic available inside the proof assistant. This feature is used to produce, from the certificates, both valid underestimators and lower bounds for each approximated constituent.The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of multivariate transcendental inequalities. We illustrate the performance of our formal framework on some of these inequalities as well as on examples from the global optimization literature.

  6. Nonlinear Modeling of Forced Magnetic Reconnection with Transient Perturbations

    Science.gov (United States)

    Beidler, Matthew T.; Callen, James D.; Hegna, Chris C.; Sovinec, Carl R.

    2017-10-01

    Externally applied 3D magnetic fields in tokamaks can penetrate into the plasma and lead to forced magnetic reconnection, and hence magnetic islands, on resonant surfaces. Analytic theory has been reasonably successful in describing many aspects of this paradigm with regard to describing the time asymptotic-steady state. However, understanding the nonlinear evolution into a low-slip, field-penetrated state, especially how MHD events such as sawteeth and ELMs precipitate this transition, is in its early development. We present nonlinear computations employing the extended-MHD code NIMROD, building on previous work by incorporating a temporally varying external perturbation as a simple model for an MHD event that produces resonant magnetic signals. A parametric series of proof-of-principle computations and accompanying analytical theory characterize the transition into a mode-locked state with an emphasis on detailing the temporal evolution properties. Supported by DOE OFES Grants DE-FG02-92ER54139, DE-FG02-86ER53218, and the U.S. DOE FES Postdoctoral Research program administered by ORISE and managed by ORAU under DOE contract DE-SC0014664.

  7. Perturbation methods and closure approximations in nonlinear systems

    International Nuclear Information System (INIS)

    Dubin, D.H.E.

    1984-01-01

    In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak is considered. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase-space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. In the second section, statistical closure theories are applied to simple dynamical systems. The logistic map is used as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the direct interaction approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodically constraint on a Langevin form of the DIA a new stable closure is developed

  8. Optimal random perturbations for stochastic approximation using a simultaneous perturbation gradient approximation

    DEFF Research Database (Denmark)

    Sadegh, Payman; Spall, J. C.

    1998-01-01

    simultaneous perturbation approximation to the gradient based on loss function measurements. SPSA is based on picking a simultaneous perturbation (random) vector in a Monte Carlo fashion as part of generating the approximation to the gradient. This paper derives the optimal distribution for the Monte Carlo...

  9. On the treatment of nonlinear local feedbacks within advanced nodal generalized perturbation theory

    International Nuclear Information System (INIS)

    Maldonado, G.I.; Turinsky, P.J.; Kropaczek, D.J.

    1993-01-01

    Recent efforts to upgrade the underlying neutronics formulations within the in-core nuclear fuel management optimization code FORMOSA (Ref. 1) have produced two important developments; first, a computationally efficient and second-order-accurate advanced nodal generalized perturbation theory (GPT) model [derived from the nonlinear iterative nodal expansion method (NEM)] for evaluating core attributes (i.e., k eff and power distribution versus cycle burnup), and second, an equally efficient and accurate treatment of local thermal-hydraulic and fission product feedbacks embedded within NEM GPT. The latter development is the focus of this paper

  10. Core design and operation optimization methods based on time-dependent perturbation theory

    International Nuclear Information System (INIS)

    Greenspan, E.

    1983-08-01

    A general approach for the optimization of nuclear reactor core design and operation is outlined; it is based on two cornerstones: a newly developed time-dependent (or burnup-dependent) perturbation theory for nonlinear problems and a succesive iteration technique. The resulting approach is capable of handling realistic reactor models using computational methods of any degree of sophistication desired, while accounting for all the constraints imposed. Three general optimization strategies, different in the way for handling the constraints, are formulated. (author)

  11. On Perturbative Cubic Nonlinear Schrodinger Equations under Complex Nonhomogeneities and Complex Initial Conditions

    Directory of Open Access Journals (Sweden)

    Magdy A. El-Tawil

    2009-01-01

    Full Text Available A perturbing nonlinear Schrodinger equation is studied under general complex nonhomogeneities and complex initial conditions for zero boundary conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the symbolic solution algorithm is tested through computing the possible approximations under truncation procedures. The method of solution is illustrated through case studies and figures.

  12. Analytical Investigation of Beam Deformation Equation using Perturbation, Homotopy Perturbation, Variational Iteration and Optimal Homotopy Asymptotic Methods

    DEFF Research Database (Denmark)

    Farrokhzad, F.; Mowlaee, P.; Barari, Amin

    2011-01-01

    The beam deformation equation has very wide applications in structural engineering. As a differential equation, it has its own problem concerning existence, uniqueness and methods of solutions. Often, original forms of governing differential equations used in engineering problems are simplified...... Method (OHAM). The comparisons of the results reveal that these methods are very effective, convenient and quite accurate to systems of non-linear differential equation......., and this process produces noise in the obtained answers. This paper deals with solution of second order of differential equation governing beam deformation using four analytical approximate methods, namely the Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Optimal Homotopy Asymptotic...

  13. Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schroedinger's equation with Kerr law nonlinearity

    International Nuclear Information System (INIS)

    Zhang Zaiyun; Liu Zhenhai; Miao Xiujin; Chen Yuezhong

    2011-01-01

    In this Letter, we investigate the perturbed nonlinear Schroedinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.

  14. Optimized Perturbation Theory for Wave Functions of Quantum Systems

    International Nuclear Information System (INIS)

    Hatsuda, T.; Tanaka, T.; Kunihiro, T.

    1997-01-01

    The notion of the optimized perturbation, which has been successfully applied to energy eigenvalues, is generalized to treat wave functions of quantum systems. The key ingredient is to construct an envelope of a set of perturbative wave functions. This leads to a condition similar to that obtained from the principle of minimal sensitivity. Applications of the method to the quantum anharmonic oscillator and the double well potential show that uniformly valid wave functions with correct asymptotic behavior are obtained in the first-order optimized perturbation even for strong couplings. copyright 1997 The American Physical Society

  15. A perturbation expansion for the nonlinear Schroedinger equation with application to the influence of nonlinear Landau damping

    International Nuclear Information System (INIS)

    Weiland, J.; Ichikawa, Y.H.; Wilhelmsson, H.

    1977-12-01

    The Bogoliubov-Mitropolsky perturbation method has been applied to the study of a perturbation on soliton solutions to the nonlinear Schroedinger equation. The results are compared to those of Karpman and Maslov using the inverse scattering method and to those by Ott and Sudan on the KdV equation. (auth.)

  16. Introduction to Nonlinear and Global Optimization

    NARCIS (Netherlands)

    Hendrix, E.M.T.; Tóth, B.

    2010-01-01

    This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization

  17. Optimization under uncertainty of parallel nonlinear energy sinks

    Science.gov (United States)

    Boroson, Ethan; Missoum, Samy; Mattei, Pierre-Olivier; Vergez, Christophe

    2017-04-01

    Nonlinear Energy Sinks (NESs) are a promising technique for passively reducing the amplitude of vibrations. Through nonlinear stiffness properties, a NES is able to passively and irreversibly absorb energy. Unlike the traditional Tuned Mass Damper (TMD), NESs do not require a specific tuning and absorb energy over a wider range of frequencies. Nevertheless, they are still only efficient over a limited range of excitations. In order to mitigate this limitation and maximize the efficiency range, this work investigates the optimization of multiple NESs configured in parallel. It is well known that the efficiency of a NES is extremely sensitive to small perturbations in loading conditions or design parameters. In fact, the efficiency of a NES has been shown to be nearly discontinuous in the neighborhood of its activation threshold. For this reason, uncertainties must be taken into account in the design optimization of NESs. In addition, the discontinuities require a specific treatment during the optimization process. In this work, the objective of the optimization is to maximize the expected value of the efficiency of NESs in parallel. The optimization algorithm is able to tackle design variables with uncertainty (e.g., nonlinear stiffness coefficients) as well as aleatory variables such as the initial velocity of the main system. The optimal design of several parallel NES configurations for maximum mean efficiency is investigated. Specifically, NES nonlinear stiffness properties, considered random design variables, are optimized for cases with 1, 2, 3, 4, 5, and 10 NESs in parallel. The distributions of efficiency for the optimal parallel configurations are compared to distributions of efficiencies of non-optimized NESs. It is observed that the optimization enables a sharp increase in the mean value of efficiency while reducing the corresponding variance, thus leading to more robust NES designs.

  18. Optimization for nonlinear inverse problem

    International Nuclear Information System (INIS)

    Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.

    2007-06-01

    The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)

  19. Efficient scattering-angle enrichment for a nonlinear inversion of the background and perturbations components of a velocity model

    KAUST Repository

    Wu, Zedong

    2017-07-04

    Reflection-waveform inversion (RWI) can help us reduce the nonlinearity of the standard full-waveform inversion (FWI) by inverting for the background velocity model using the wave-path of a single scattered wavefield to an image. However, current RWI implementations usually neglect the multi-scattered energy, which will cause some artifacts in the image and the update of the background. To improve existing RWI implementations in taking multi-scattered energy into consideration, we split the velocity model into background and perturbation components, integrate them directly in the wave equation, and formulate a new optimization problem for both components. In this case, the perturbed model is no longer a single-scattering model, but includes all scattering. Through introducing a new cheap implementation of scattering angle enrichment, the separation of the background and perturbation components can be implemented efficiently. We optimize both components simultaneously to produce updates to the velocity model that is nonlinear with respect to both the background and the perturbation. The newly introduced perturbation model can absorb the non-smooth update of the background in a more consistent way. We apply the proposed approach on the Marmousi model with data that contain frequencies starting from 5 Hz to show that this method can converge to an accurate velocity starting from a linearly increasing initial velocity. Also, our proposed method works well when applied to a field data set.

  20. Structural optimization for nonlinear dynamic response

    DEFF Research Database (Denmark)

    Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.

    2015-01-01

    by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance......Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear...... resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...

  1. Contributions of changes in climatology and perturbation and the resulting nonlinearity to regional climate change.

    Science.gov (United States)

    Adachi, Sachiho A; Nishizawa, Seiya; Yoshida, Ryuji; Yamaura, Tsuyoshi; Ando, Kazuto; Yashiro, Hisashi; Kajikawa, Yoshiyuki; Tomita, Hirofumi

    2017-12-20

    Future changes in large-scale climatology and perturbation may have different impacts on regional climate change. It is important to understand the impacts of climatology and perturbation in terms of both thermodynamic and dynamic changes. Although many studies have investigated the influence of climatology changes on regional climate, the significance of perturbation changes is still debated. The nonlinear effect of these two changes is also unknown. We propose a systematic procedure that extracts the influences of three factors: changes in climatology, changes in perturbation and the resulting nonlinear effect. We then demonstrate the usefulness of the procedure, applying it to future changes in precipitation. All three factors have the same degree of influence, especially for extreme rainfall events. Thus, regional climate assessments should consider not only the climatology change but also the perturbation change and their nonlinearity. This procedure can advance interpretations of future regional climates.

  2. Simultaneous Perturbation Particle Swarm Optimization and Its FPGA Implementation

    OpenAIRE

    Maeda, Yutaka; Matsushita, Naoto

    2009-01-01

    In this paper, we presented hardware implementation of the particle swarm optimization algorithm which is combination of the ordinary particle swarm optimization and the simultaneous perturbation method. FPGA is used to realize the system. This algorithm utilizes local information of objective function effectively without lack of advantage of the original particle swarm optimization. Moreover, the FPGA implementation gives higher operation speed effectively using parallelism of the particle s...

  3. Perturbation and characterization of nonlinear processes: Progress report, November 15, 1983-June 1, 1987

    International Nuclear Information System (INIS)

    Swinney, H.L.; Swift, J.

    1987-01-01

    This progress report summarizes the principal accomplishments dealing with perturbation and characterization of nonlinear processes. Topics of research include Lyapunov equations, mutual information and metric entropy, the dimensions, complex dynamics and transition sequences and spatial patterns

  4. Nonlinear 2D arm dynamics in response to continuous and pulse-shaped force perturbations.

    Science.gov (United States)

    Happee, Riender; de Vlugt, Erwin; van Vliet, Bart

    2015-01-01

    Ample evidence exists regarding the nonlinearity of the neuromuscular system but linear models are widely applied to capture postural dynamics. This study quantifies the nonlinearity of human arm postural dynamics applying 2D continuous force perturbations (0.2-40 Hz) inducing three levels of hand displacement (5, 15, 45 mm RMS) followed by force-pulse perturbations inducing large hand displacements (up to 250 mm) in a position task (PT) and a relax task (RT) recording activity of eight shoulder and elbow muscles. The continuous perturbation data were used to analyze the 2D endpoint dynamics in the frequency domain and to identify reflexive and intrinsic parameters of a linear neuromuscular shoulder-elbow model. Subsequently, it was assessed to what extent the large displacements in response to force pulses could be predicted from the 'small amplitude' linear neuromuscular model. Continuous and pulse perturbation responses with varying amplitudes disclosed highly nonlinear effects. In PT, a larger continuous perturbation induced stiffening with a factor of 1.5 attributed to task adaptation evidenced by increased co-contraction and reflexive activity. This task adaptation was even more profound in the pulse responses where reflexes and displacements were strongly affected by the presence and amplitude of preceding continuous perturbations. In RT, a larger continuous perturbation resulted in yielding with a factor of 3.8 attributed to nonlinear mechanical properties as no significant reflexive activity was found. Pulse perturbations always resulted in yielding where a model fitted to the preceding 5-mm continuous perturbations predicted only 37% of the recorded peak displacements in RT and 79% in PT. This demonstrates that linear neuromuscular models, identified using continuous perturbations with small amplitudes, strongly underestimate displacements in pulse-shaped (e.g., impact) loading conditions. The data will be used to validate neuromuscular models including

  5. Performance optimization of queueing systems with perturbation realization

    KAUST Repository

    Xia, Li

    2012-04-01

    After the intensive studies of queueing theory in the past decades, many excellent results in performance analysis have been obtained, and successful examples abound. However, exploring special features of queueing systems directly in performance optimization still seems to be a territory not very well cultivated. Recent progresses of perturbation analysis (PA) and sensitivity-based optimization provide a new perspective of performance optimization of queueing systems. PA utilizes the structural information of queueing systems to efficiently extract the performance sensitivity information from a sample path of system. This paper gives a brief review of PA and performance optimization of queueing systems, focusing on a fundamental concept called perturbation realization factors, which captures the special dynamic feature of a queueing system. With the perturbation realization factors as building blocks, the performance derivative formula and performance difference formula can be obtained. With performance derivatives, gradient-based optimization can be derived, while with performance difference, policy iteration and optimality equations can be derived. These two fundamental formulas provide a foundation for performance optimization of queueing systems from a sensitivity-based point of view. We hope this survey may provide some inspirations on this promising research topic. © 2011 Elsevier B.V. All rights reserved.

  6. Application of linear programming and perturbation theory in optimization of fuel utilization in a nuclear reactor

    International Nuclear Information System (INIS)

    Zavaljevski, N.

    1985-01-01

    Proposed optimization procedure is fast due to application of linear programming. Non-linear constraints which demand iterative application of linear programming are slowing down the calculation. Linearization can be done by different procedures starting from simple empirical rules for fuel in-core management to complicated general perturbation theory with higher order of corrections. A mathematical model was formulated for optimization of improved fuel cycle. A detailed algorithm for determining minimum of fresh fuel at the beginning of each fuel cycle is shown and the problem is linearized by first order perturbation theory and it is optimized by linear programming. Numerical illustration of the proposed method was done for the experimental reactor mostly for saving computer time

  7. Application of homotopy-perturbation method to nonlinear population dynamics models

    International Nuclear Information System (INIS)

    Chowdhury, M.S.H.; Hashim, I.; Abdulaziz, O.

    2007-01-01

    In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)

  8. The non-linear Perron-Frobenius theorem : Perturbations and aggregation

    NARCIS (Netherlands)

    Dietzenbacher, E

    The dominant eigenvalue and the corresponding eigenvector (or Perron vector) of a non-linear eigensystem are considered. We discuss the effects upon these, of perturbations and of aggregation of the underlying mapping. The results are applied to study the sensivity of the outputs in a non-linear

  9. Fully nonlinear and exact perturbations of the Friedmann world model: non-flat background

    Energy Technology Data Exchange (ETDEWEB)

    Noh, Hyerim, E-mail: hr@kasi.ac.kr [Korea Astronomy and Space Science Institute, Daejeon, 305-348 (Korea, Republic of)

    2014-07-01

    We extend the fully non-linear and exact cosmological perturbation equations in a Friedmann background universe to include the background curvature. The perturbation equations are presented in a gauge ready form, so any temporal gauge condition can be adopted freely depending on the problem to be solved. We consider the scalar, and vector perturbations without anisotropic stress. As an application, we analyze the equations in the special case of irrotational zero-pressure fluid in the comoving gauge condition. We also present the fully nonlinear formulation for a minimally coupled scalar field.

  10. Optimal Damping of Perturbations of Moving Thermoelastic Panel

    Science.gov (United States)

    Banichuk, N. V.; Ivanova, S. Yu.

    2018-01-01

    The translational motion of a thermoelastic web subject to transverse vibrations caused by initial perturbations is considered. It is assumed that a web moving with a constant translational velocity is described by the model of a thermoelastic panel simply supported at its ends. The problem of optimal damping of vibrations when applying active transverse actions is formulated. For solving the optimization problem, modern methods developed in control theory for systems with distributed parameters described by partial differential equations are used.

  11. A nonlinear inversion for the velocity background and perturbation models

    KAUST Repository

    Wu, Zedong; Alkhalifah, Tariq Ali

    2015-01-01

    Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect

  12. A study of the application of singular perturbation theory. [development of a real time algorithm for optimal three dimensional aircraft maneuvers

    Science.gov (United States)

    Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.

    1979-01-01

    A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.

  13. Nonlinearities Distribution Homotopy Perturbation Method Applied to Solve Nonlinear Problems: Thomas-Fermi Equation as a Case Study

    Directory of Open Access Journals (Sweden)

    U. Filobello-Nino

    2015-01-01

    Full Text Available We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM. Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.

  14. Bifurcation-based approach reveals synergism and optimal combinatorial perturbation.

    Science.gov (United States)

    Liu, Yanwei; Li, Shanshan; Liu, Zengrong; Wang, Ruiqi

    2016-06-01

    Cells accomplish the process of fate decisions and form terminal lineages through a series of binary choices in which cells switch stable states from one branch to another as the interacting strengths of regulatory factors continuously vary. Various combinatorial effects may occur because almost all regulatory processes are managed in a combinatorial fashion. Combinatorial regulation is crucial for cell fate decisions because it may effectively integrate many different signaling pathways to meet the higher regulation demand during cell development. However, whether the contribution of combinatorial regulation to the state transition is better than that of a single one and if so, what the optimal combination strategy is, seem to be significant issue from the point of view of both biology and mathematics. Using the approaches of combinatorial perturbations and bifurcation analysis, we provide a general framework for the quantitative analysis of synergism in molecular networks. Different from the known methods, the bifurcation-based approach depends only on stable state responses to stimuli because the state transition induced by combinatorial perturbations occurs between stable states. More importantly, an optimal combinatorial perturbation strategy can be determined by investigating the relationship between the bifurcation curve of a synergistic perturbation pair and the level set of a specific objective function. The approach is applied to two models, i.e., a theoretical multistable decision model and a biologically realistic CREB model, to show its validity, although the approach holds for a general class of biological systems.

  15. Nonlinear analysis approximation theory, optimization and applications

    CERN Document Server

    2014-01-01

    Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.

  16. Stochastic Recursive Algorithms for Optimization Simultaneous Perturbation Methods

    CERN Document Server

    Bhatnagar, S; Prashanth, L A

    2013-01-01

    Stochastic Recursive Algorithms for Optimization presents algorithms for constrained and unconstrained optimization and for reinforcement learning. Efficient perturbation approaches form a thread unifying all the algorithms considered. Simultaneous perturbation stochastic approximation and smooth fractional estimators for gradient- and Hessian-based methods are presented. These algorithms: • are easily implemented; • do not require an explicit system model; and • work with real or simulated data. Chapters on their application in service systems, vehicular traffic control and communications networks illustrate this point. The book is self-contained with necessary mathematical results placed in an appendix. The text provides easy-to-use, off-the-shelf algorithms that are given detailed mathematical treatment so the material presented will be of significant interest to practitioners, academic researchers and graduate students alike. The breadth of applications makes the book appropriate for reader from sim...

  17. Connection between perturbation theory, projection-operator techniques, and statistical linearization for nonlinear systems

    International Nuclear Information System (INIS)

    Budgor, A.B.; West, B.J.

    1978-01-01

    We employ the equivalence between Zwanzig's projection-operator formalism and perturbation theory to demonstrate that the approximate-solution technique of statistical linearization for nonlinear stochastic differential equations corresponds to the lowest-order β truncation in both the consolidated perturbation expansions and in the ''mass operator'' of a renormalized Green's function equation. Other consolidated equations can be obtained by selectively modifying this mass operator. We particularize the results of this paper to the Duffing anharmonic oscillator equation

  18. Singular perturbation methods for nonlinear dynamic systems with time delays

    International Nuclear Information System (INIS)

    Hu, H.Y.; Wang, Z.H.

    2009-01-01

    This review article surveys the recent advances in the dynamics and control of time-delay systems, with emphasis on the singular perturbation methods, such as the method of multiple scales, the method of averaging, and two newly developed methods, the energy analysis and the pseudo-oscillator analysis. Some examples are given to demonstrate the advantages of the methods. The comparisons with other methods show that these methods lead to easier computations and higher accurate prediction on the local dynamics of time-delay systems near a Hopf bifurcation.

  19. Influence of asymmetric magnetic perturbation on the nonlinear evolution of double tearing modes

    Science.gov (United States)

    Xiong, G. Z.; Wang, L.; Li, X. Q.; Liu, H. F.; Tang, C. J.; Huang, J.; Zhang, X.; Wang, X. Q.

    2017-06-01

    The effects of asymmetric magnetic perturbation on the triggering and evolution of double tearing modes (DTMs) are investigated using nonlinear magnetohydrodynamics simulations in a slab geometry. We find that for reversed magnetic shear plasmas the resistive reconnection process induced by the initial perturbation at one rational surface can drive a new island at the other rational surface with the same mode number. The four typical states of the mode for the time evolution are found, and include: (i) a linear growth stage; (ii) a linear/nonlinear stable stage; (iii) an interactively driving stage; and (iv) a symmetric DTM stage. These differ from previous simulation results. Moreover, nonlinear DTM growth is found to strongly depend on the asymmetric magnetic perturbation, particularly in the early nonlinear phase. The initial perturbation strength scale of island width suggests that the left island enters into a Sweet-Parker growth process when the right island is sufficiently large to effectively drive the other. These results predict that although externally applied magnetic perturbations can suppress the neoclassical tearing mode they can also trigger new instabilities such as asymmetric DTMs.

  20. Influence of asymmetric magnetic perturbation on the nonlinear evolution of double tearing modes

    International Nuclear Information System (INIS)

    Xiong, G Z; Liu, H F; Huang, J; Wang, X Q; Wang, L; Li, X Q; Tang, C J; Zhang, X

    2017-01-01

    The effects of asymmetric magnetic perturbation on the triggering and evolution of double tearing modes (DTMs) are investigated using nonlinear magnetohydrodynamics simulations in a slab geometry. We find that for reversed magnetic shear plasmas the resistive reconnection process induced by the initial perturbation at one rational surface can drive a new island at the other rational surface with the same mode number. The four typical states of the mode for the time evolution are found, and include: (i) a linear growth stage; (ii) a linear/nonlinear stable stage; (iii) an interactively driving stage; and (iv) a symmetric DTM stage. These differ from previous simulation results. Moreover, nonlinear DTM growth is found to strongly depend on the asymmetric magnetic perturbation, particularly in the early nonlinear phase. The initial perturbation strength scale of island width suggests that the left island enters into a Sweet–Parker growth process when the right island is sufficiently large to effectively drive the other. These results predict that although externally applied magnetic perturbations can suppress the neoclassical tearing mode they can also trigger new instabilities such as asymmetric DTMs. (paper)

  1. Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems

    Directory of Open Access Journals (Sweden)

    Daniel Olvera

    2014-01-01

    Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.

  2. Two-parameter nonlinear spacetime perturbations: gauge transformations and gauge invariance

    International Nuclear Information System (INIS)

    Bruni, Marco; Gualtieri, Leonardo; Sopuerta, Carlos F

    2003-01-01

    An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable theory, so that it is sometime convenient to construct a perturbative formalism based on two (or more) parameters. The study of perturbations of rotating stars is a good example: in this case one can treat the stationary axisymmetric star using a slow rotation approximation (expansion in the angular velocity Ω), so that the background is spherical. Generic perturbations of the rotating star (say parametrized by λ) are then built on top of the axisymmetric perturbations in Ω. Clearly, any interesting physics requires nonlinear perturbations, as at least terms λΩ need to be considered. In this paper, we analyse the gauge dependence of nonlinear perturbations depending on two parameters, derive explicit higher-order gauge transformation rules and define gauge invariance. The formalism is completely general and can be used in different applications of general relativity or any other spacetime theory

  3. Methods for Large-Scale Nonlinear Optimization.

    Science.gov (United States)

    1980-05-01

    STANFORD, CALIFORNIA 94305 METHODS FOR LARGE-SCALE NONLINEAR OPTIMIZATION by Philip E. Gill, Waiter Murray, I Michael A. Saunden, and Masgaret H. Wright...typical iteration can be partitioned so that where B is an m X m basise matrix. This partition effectively divides the vari- ables into three classes... attention is given to the standard of the coding or the documentation. A much better way of obtaining mathematical software is from a software library

  4. Perturbing engine performance measurements to determine optimal engine control settings

    Science.gov (United States)

    Jiang, Li; Lee, Donghoon; Yilmaz, Hakan; Stefanopoulou, Anna

    2014-12-30

    Methods and systems for optimizing a performance of a vehicle engine are provided. The method includes determining an initial value for a first engine control parameter based on one or more detected operating conditions of the vehicle engine, determining a value of an engine performance variable, and artificially perturbing the determined value of the engine performance variable. The initial value for the first engine control parameter is then adjusted based on the perturbed engine performance variable causing the engine performance variable to approach a target engine performance variable. Operation of the vehicle engine is controlled based on the adjusted initial value for the first engine control parameter. These acts are repeated until the engine performance variable approaches the target engine performance variable.

  5. Evolution of nonlinear perturbations inside Einstein-Yang-Mills black holes

    International Nuclear Information System (INIS)

    Donets, E.E.; Tentyukov, M.N.; Tsulaya, M.M.

    1998-01-01

    We present our results on numerical study of evolution of nonlinear perturbations inside spherically symmetric black holes in the SU(2) Einstein-Yang-Mills (EYM) theory. Recent developments demonstrate a new type of the behaviour of the metric for EYM black hole interiors; the generic metric exhibits an infinitely oscillating approach to the singularity, which is a spacelike but not of the mixmaster type. The evolution of various types of spherically symmetric perturbations, propagating from the internal vicinity of the external horizon towards the singularity is investigated in a self-consistent way using an adaptive numerical algorithm. The obtained results give strong numerical evidence in favor of nonlinear stability of the generic EYM black hole interiors. Alternatively, the EYM black hole interiors of S (schwarzschild)-type, which form only a zero measure subset in the space of all internal solutions are found to be unstable and transform to the generic type as perturbations are developed

  6. Fuel management optimization based on generalized perturbation theory

    International Nuclear Information System (INIS)

    White, J.R.; Chapman, D.M.; Biswas, D.

    1986-01-01

    A general methodology for optimization of assembly shuffling and burnable poison (BP) loadings for LWR reload design has been developed. The uniqueness of this approach lies in the coupling of Generalized Perturbation Theory (GPT) methods and standard Integer Programming (IP) techniques. An IP algorithm can simulate the discrete nature of the fuel shuffling and BP loading problems, and the use of GPT sensitivity data provides an efficient means for modeling the behavior of the important core performance parameters. The method is extremely flexible since the choice of objective function and the number and mix of constraints depend only on the ability of GPT to determine the appropriate sensitivity functions

  7. Optimal non-linear health insurance.

    Science.gov (United States)

    Blomqvist, A

    1997-06-01

    Most theoretical and empirical work on efficient health insurance has been based on models with linear insurance schedules (a constant co-insurance parameter). In this paper, dynamic optimization techniques are used to analyse the properties of optimal non-linear insurance schedules in a model similar to one originally considered by Spence and Zeckhauser (American Economic Review, 1971, 61, 380-387) and reminiscent of those that have been used in the literature on optimal income taxation. The results of a preliminary numerical example suggest that the welfare losses from the implicit subsidy to employer-financed health insurance under US tax law may be a good deal smaller than previously estimated using linear models.

  8. Suppression of period-doubling and nonlinear parametric effects in periodically perturbed systems

    International Nuclear Information System (INIS)

    Bryant, P.; Wiesenfeld, K.

    1986-01-01

    We consider the effect on a generic period-doubling bifurcation of a periodic perturbation, whose frequency ω 1 is near the period-doubled frequency ω 0 /2. The perturbation is shown to always suppress the bifurcation, shifting the bifurcation point and stabilizing the behavior at the original bifurcation point. We derive an equation characterizing the response of the system to the perturbation, analysis of which reveals many interesting features of the perturbed bifurcation, including (1) the scaling law relating the shift of the bifurcation point and the amplitude of the perturbation, (2) the characteristics of the system's response as a function of bifurcation parameter, (3) parametric amplification of the perturbation signal including nonlinear effects such as gain saturation and a discontinuity in the response at a critical perturbation amplitude, (4) the effect of the detuning (ω 1 -ω 0 /2) on the bifurcation, and (5) the emergence of a closely spaced set of peaks in the response spectrum. An important application is the use of period-doubling systems as small-signal amplifiers, e.g., the superconducting Josephson parametric amplifier

  9. Optimization of nonlinear wave function parameters

    International Nuclear Information System (INIS)

    Shepard, R.; Minkoff, M.; Chemistry

    2006-01-01

    An energy-based optimization method is presented for our recently developed nonlinear wave function expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions, using the graphical unitary group approach (GUGA). The wave function is expanded in a basis of product functions, allowing application to closed-shell and open-shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational function that depends on a relatively small number of nonlinear parameters called arc factors. The energy-based optimization is formulated in terms of analytic arc factor gradients and orbital-level Hamiltonian matrices that correspond to a specific kind of uncontraction of each of the product basis functions. These orbital-level Hamiltonian matrices give an intuitive representation of the energy in terms of disjoint subsets of the arc factors, they provide for an efficient computation of gradients of the energy with respect to the arc factors, and they allow optimal arc factors to be determined in closed form for subspaces of the full variation problem. Timings for energy and arc factor gradient computations involving expansion spaces of > 10 24 configuration state functions are reported. Preliminary convergence studies and molecular dissociation curves are presented for some small molecules

  10. Quantum perturbation solution of sextic nonlinear oscillator and its classical limit

    International Nuclear Information System (INIS)

    Jafarpour, M.; Ashrafpour, M.

    2000-01-01

    We consider the time evolution of the perturbed coherent states to solve the quantum sex tic nonlinear oscillator, in the framework of time dependent perturbation theory. An appropriate limit, h-bar → 0, (absolute value of α)→ ∞,(absolute value of α )√h-bar fixed, is then taken and the classical Poincare'-Landsat series is retrieved. We observe that a proper renormalization of the amplitude and the frequency is needed, if a meaningful comparison between the quantum and the classical results are to be made

  11. Symbolic-computation study of the perturbed nonlinear Schrodinger model in inhomogeneous optical fibers

    International Nuclear Information System (INIS)

    Tian Bo; Gao Yitian

    2005-01-01

    A realistic, inhomogeneous fiber in the optical communication systems can be described by the perturbed nonlinear Schrodinger model (also named as the normalized nonlinear Schrodinger model with periodically varying coefficients, dispersion managed nonlinear Schrodinger model or nonlinear Schrodinger model with variable coefficients). Hereby, we extend to this model a direct method, perform symbolic computation and obtain two families of the exact, analytic bright-solitonic solutions, with or without the chirp respectively. The parameters addressed include the shape of the bright soliton, soliton amplitude, inverse width of the soliton, chirp, frequency, center of the soliton and center of the phase of the soliton. Of optical and physical interests, we discuss some previously-published special cases of our solutions. Those solutions could help the future studies on the optical communication systems. ms

  12. A discrete homotopy perturbation method for non-linear Schrodinger equation

    Directory of Open Access Journals (Sweden)

    H. A. Wahab

    2015-12-01

    Full Text Available A general analysis is made by homotopy perturbation method while taking the advantages of the initial guess, appearance of the embedding parameter, different choices of the linear operator to the approximated solution to the non-linear Schrodinger equation. We are not dependent upon the Adomian polynomials and find the linear forms of the components without these calculations. The discretised forms of the nonlinear Schrodinger equation allow us whether to apply any numerical technique on the discritisation forms or proceed for perturbation solution of the problem. The discretised forms obtained by constructed homotopy provide the linear parts of the components of the solution series and hence a new discretised form is obtained. The general discretised form for the NLSE allows us to choose any initial guess and the solution in the closed form.

  13. New hybrid non-linear transformations of divergent perturbation series for quadratic Zeeman effects

    International Nuclear Information System (INIS)

    Belkic, D.

    1989-01-01

    The problem of hydrogen atoms in an external uniform magnetic field (quadratic Zeeman effect) is studied by means of perturbation theory. The power series for the ground-state energy in terms of magnetic-field strength B is divergent. Nevertheless, it is possible to induce convergence of this divergent series by applying various non-linear transformations. These transformations of originally divergent perturbation series yield new sequences, which then converge. The induced convergence is, however, quite slow. A new hybrid Shanks-Levin non-linear transform is devised here for accelerating these slowly converging series and sequences. Significant improvement in the convergence rate is obtained. Agreement with the exact results is excellent. (author)

  14. Higher accuracy analytical approximations to a nonlinear oscillator with discontinuity by He's homotopy perturbation method

    International Nuclear Information System (INIS)

    Belendez, A.; Hernandez, A.; Belendez, T.; Neipp, C.; Marquez, A.

    2008-01-01

    He's homotopy perturbation method is used to calculate higher-order approximate periodic solutions of a nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(x). We find He's homotopy perturbation method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions with a maximal relative error for the approximate period of less than 1.56% for all values of oscillation amplitude, while this relative error is 0.30% for the second iteration and as low as 0.057% when the third-order approximation is considered. Comparison of the result obtained using this method with those obtained by different harmonic balance methods reveals that He's homotopy perturbation method is very effective and convenient

  15. Nonlinear dynamics analysis of the human balance control subjected to physical and sensory perturbations.

    Science.gov (United States)

    Ashtiani, Mohammed N; Mahmood-Reza, Azghani

    2017-01-01

    Postural control after applying perturbation involves neural and muscular efforts to limit the center of mass (CoM) motion. Linear dynamical approaches may not unveil all complexities of body efforts. This study was aimed at determining two nonlinear dynamics parameters (fractal dimension (FD) and largest Lyapunov exponent (LLE)) in addition to the linear standing metrics of balance in perturbed stance. Sixteen healthy young males were subjected to sudden rotations of the standing platform. The vision and cognition during the standing were also interfered. Motion capturing was used to measure the lower limb joints and the CoM displacements. The CoM path length as a linear parameter was increased by elimination of vision (pnonlinear metric FD was decreased due to the cognitive loads (pnonlinear metrics of the perturbed stance showed that a combination of them may properly represent the body behavior.

  16. Electromagnetic perturbations of black holes in general relativity coupled to nonlinear electrodynamics

    Science.gov (United States)

    Toshmatov, Bobir; Stuchlík, Zdeněk; Schee, Jan; Ahmedov, Bobomurat

    2018-04-01

    The electromagnetic (EM) perturbations of the black hole solutions in general relativity coupled to nonlinear electrodynamics (NED) are studied for both electrically and magnetically charged black holes, assuming that the EM perturbations do not alter the spacetime geometry. It is shown that the effective potentials of the electrically and magnetically charged black holes related to test perturbative NED EM fields are related to the effective metric governing the photon motion, contrary to the effective potential of the linear electrodynamic (Maxwell) field that is related to the spacetime metric. Consequently, corresponding quasinormal (QN) frequencies differ as well. As a special case, we study new family of the NED black hole solutions which tend in the weak field limit to the Maxwell field, giving the Reissner-Nordström (RN) black hole solution. We compare the NED Maxwellian black hole QN spectra with the RN black hole QN spectra.

  17. Gradient-based optimization in nonlinear structural dynamics

    DEFF Research Database (Denmark)

    Dou, Suguang

    The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider......, frequency stabilization, and disk resonator gyroscope. For advanced design of these structures, it is of considerable value to extend current optimization in linear structural dynamics into nonlinear structural dynamics. In this thesis, we present a framework for modelling, analysis, characterization......, and optimization of nonlinear structural dynamics. In the modelling, nonlinear finite elements are used. In the analysis, nonlinear frequency response and nonlinear normal modes are calculated based on a harmonic balance method with higher-order harmonics. In the characterization, nonlinear modal coupling...

  18. Nu shifts in betatron oscillations from uniform perturbations in the presence of non-linear magnetic guide fields

    International Nuclear Information System (INIS)

    Crebbin, K.C.

    1985-05-01

    Uniform magnetic field perturbations cause a closed orbit distortion in a circular accelerator. If the magnetic guide field is non-linear these perturbations can also cause a Nu shift in the betatron oscillations. Such a shift in radial Nu values has been observed in the Bevalac while studying the low energy resonant extraction system. In the Bevalac, the radial perturbation comes from the quadrants being magnetically about 0.8% longer than 90 0 . The normal effect of this type of perturbation is a radial closed orbit shift and orbit distortion. The Nu shift, associated with this type of perturbation in the presence of a non-linear guide field, is discussed in this paper. A method of handling the non-linear n values is discussed as well as the mechanism for the associated Nu shift. Computer calculations are compared to measurements. 2 refs., 4 figs

  19. COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U

    Energy Technology Data Exchange (ETDEWEB)

    Sun, Y.; Borland, Michael

    2017-06-25

    Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.

  20. Finding a nonlinear lattice with improved integrability using Lie transform perturbation theory

    International Nuclear Information System (INIS)

    Sonnad, Kiran G.; Cary, John R.

    2004-01-01

    A condition for improved dynamic aperture for nonlinear, alternating gradient transport systems is derived using Lie transform perturbation theory. The Lie transform perturbation method is used here to perform averaging over fast oscillations by canonically transforming to slowly oscillating variables. This is first demonstrated for a linear sinusoidal focusing system. This method is then employed to average the dynamics over a lattice period for a nonlinear focusing system, provided by the use of higher order poles such as sextupoles and octupoles along with alternate gradient quadrupoles. Unlike the traditional approach, the higher order focusing is not treated as a perturbation. The Lie transform method is particularly advantageous for such a system where the form of the Hamiltonian is complex. This is because the method exploits the property of canonical invariance of Poisson brackets so that the change of variables is accomplished by just replacing the old ones with the new. The analysis shows the existence of a condition in which the system is azimuthally symmetric in the transformed, slowly oscillating frame. Such a symmetry in the time averaged frame renders the system nearly integrable in the laboratory frame. This condition leads to reduced chaos and improved confinement when compared to a system that is not close to integrability. Numerical calculations of single-particle trajectories and phase space projections of the dynamic aperture performed for a lattice with quadrupoles and sextupoles confirm that this is indeed the case

  1. Nonlinearity Analysis and Parameters Optimization for an Inductive Angle Sensor

    Directory of Open Access Journals (Sweden)

    Lin Ye

    2014-02-01

    Full Text Available Using the finite element method (FEM and particle swarm optimization (PSO, a nonlinearity analysis based on parameter optimization is proposed to design an inductive angle sensor. Due to the structure complexity of the sensor, understanding the influences of structure parameters on the nonlinearity errors is a critical step in designing an effective sensor. Key parameters are selected for the design based on the parameters’ effects on the nonlinearity errors. The finite element method and particle swarm optimization are combined for the sensor design to get the minimal nonlinearity error. In the simulation, the nonlinearity error of the optimized sensor is 0.053% in the angle range from −60° to 60°. A prototype sensor is manufactured and measured experimentally, and the experimental nonlinearity error is 0.081% in the angle range from −60° to 60°.

  2. Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects

    International Nuclear Information System (INIS)

    Hwang, Jai-chan; Noh, Hyerim

    2005-01-01

    We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third- and higher-order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work, we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations, we take the comoving gauge. We discover that the third-order correction terms are of φ v order higher than the second-order terms where φ v is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential, we have δΦ∼(3/5)φ v to the linear order. Therefore, the pure general relativistic effects are of φ v order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear-order gravitational potential (curvature) perturbation strength. From the temperature anisotropy of cosmic microwave background, we have (δT/T)∼(1/3)δΦ∼(1/5)φ v ∼10 -5 . Therefore, our present result reinforces our previous important practical implication that near the current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near (and goes beyond) the horizon

  3. Apparently noninvariant terms of nonlinear sigma models in lattice perturbation theory

    International Nuclear Information System (INIS)

    Harada, Koji; Hattori, Nozomu; Kubo, Hirofumi; Yamamoto, Yuki

    2009-01-01

    Apparently noninvariant terms (ANTs) that appear in loop diagrams for nonlinear sigma models are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to 'pion' fields, we employ lattice regularization, in which everything (including the Jacobian) is well defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the pion fields at one-loop and the Jacobian does not play an important role in generating ANTs.

  4. Comparisons of linear and nonlinear plasma response models for non-axisymmetric perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Turnbull, A. D.; Ferraro, N. M.; Lao, L. L.; Lanctot, M. J. [General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States); Izzo, V. A. [University of California-San Diego, 9500 Gilman Dr., La Jolla, California 92093-0417 (United States); Lazarus, E. A.; Hirshman, S. P. [Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831 (United States); Park, J.-K.; Lazerson, S.; Reiman, A. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451 (United States); Cooper, W. A. [Association Euratom-Confederation Suisse, Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Federale de Lausanne, Lausanne (Switzerland); Liu, Y. Q. [Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB (United Kingdom); Turco, F. [Columbia University, 116th St and Broadway, New York, New York 10027 (United States)

    2013-05-15

    With the installation of non-axisymmetric coil systems on major tokamaks for the purpose of studying the prospects of ELM-free operation, understanding the plasma response to the applied fields is a crucial issue. Application of different response models, using standard tools, to DIII-D discharges with applied non-axisymmetric fields from internal coils, is shown to yield qualitatively different results. The plasma response can be treated as an initial value problem, following the system dynamically from an initial unperturbed state, or from a nearby perturbed equilibrium approach, and using both linear and nonlinear models [A. D. Turnbull, Nucl. Fusion 52, 054016 (2012)]. Criteria are discussed under which each of the approaches can yield a valid response. In the DIII-D cases studied, these criteria show a breakdown in the linear theory despite the small 10{sup −3} relative magnitude of the applied magnetic field perturbations in this case. For nonlinear dynamical evolution simulations to reach a saturated nonlinear steady state, appropriate damping mechanisms need to be provided for each normal mode comprising the response. Other issues arise in the technical construction of perturbed flux surfaces from a displacement and from the presence of near nullspace normal modes. For the nearby equilibrium approach, in the absence of a full 3D equilibrium reconstruction with a controlled comparison, constraints relating the 2D system profiles to the final profiles in the 3D system also need to be imposed to assure accessibility. The magnetic helicity profile has been proposed as an appropriate input to a 3D equilibrium calculation and tests of this show the anticipated qualitative behavior.

  5. Topology optimization of nonlinear optical devices

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard

    2011-01-01

    This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation and an incremen......This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation...... limiter. Here, air, a linear and a nonlinear material are distributed so that the wave transmission displays a strong sensitivity to the amplitude of the incoming wave....

  6. Linear and non-linear amplification of high-mode perturbations at the ablation front in HiPER targets

    Energy Technology Data Exchange (ETDEWEB)

    Olazabal-Loume, M; Breil, J; Hallo, L; Ribeyre, X [CELIA, UMR 5107 Universite Bordeaux 1-CNRS-CEA, 351 cours de la Liberation, 33405 Talence (France); Sanz, J, E-mail: olazabal@celia.u-bordeaux1.f [ETSI Aeronauticos, Universidad Politecnica de Madrid, Madrid 28040 (Spain)

    2011-01-15

    The linear and non-linear sensitivity of the 180 kJ baseline HiPER target to high-mode perturbations, i.e. surface roughness, is addressed using two-dimensional simulations and a complementary analysis by linear and non-linear ablative Rayleigh-Taylor models. Simulations provide an assessment of an early non-linear stage leading to a significant deformation of the ablation surface for modes of maximum linear growth factor. A design using a picket prepulse evidences an improvement in the target stability inducing a delay of the non-linear behavior. Perturbation evolution and shape, evidenced by simulations of the non-linear stage, are analyzed with existing self-consistent non-linear theory.

  7. Nonlinear Waves In A Stenosed Elastic Tube Filled With Viscous Fluid: Forced Perturbed Korteweg-De Vries Equation

    Science.gov (United States)

    Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee

    In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.

  8. Application of modified homotopy perturbation method and amplitude frequency formulation to strongly nonlinear oscillators

    Directory of Open Access Journals (Sweden)

    seyd ghasem enayati

    2017-01-01

    Full Text Available In this paper, two powerful analytical methods known as modified homotopy perturbation method and Amplitude Frequency Formulation called respectively MHPM and AFF, are introduced to derive approximate solutions of a system of ordinary differential equations appear in mechanical applications. These methods convert a difficult problem into a simple one, which can be easily handled. The obtained solutions are compared with numerical fourth order runge-kutta method to show the applicability and accuracy of both MHPM and AFF in solving this sample problem. The results attained in this paper confirm the idea that MHPM and AFF are powerful mathematical tools and they can be applied to linear and nonlinear problems.

  9. A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

    Science.gov (United States)

    Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

    2016-01-01

    This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

  10. Continuous nonlinear optimization for engineering applications in GAMS technology

    CERN Document Server

    Andrei, Neculai

    2017-01-01

    This book presents the theoretical details and computational performances of algorithms used for solving continuous nonlinear optimization applications imbedded in GAMS. Aimed toward scientists and graduate students who utilize optimization methods to model and solve problems in mathematical programming, operations research, business, engineering, and industry, this book enables readers with a background in nonlinear optimization and linear algebra to use GAMS technology to understand and utilize its important capabilities to optimize algorithms for modeling and solving complex, large-scale, continuous nonlinear optimization problems or applications. Beginning with an overview of constrained nonlinear optimization methods, this book moves on to illustrate key aspects of mathematical modeling through modeling technologies based on algebraically oriented modeling languages. Next, the main feature of GAMS, an algebraically oriented language that allows for high-level algebraic representation of mathematical opti...

  11. Transition Delay in Hypersonic Boundary Layers via Optimal Perturbations

    Science.gov (United States)

    Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

    2016-01-01

    The effect of nonlinear optimal streaks on disturbance growth in a Mach 6 axisymmetric flow over a 7deg half-angle cone is investigated in an e ort to expand the range of available techniques for transition control. Plane-marching parabolized stability equations are used to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone, but subharmonic first mode instabilities, which are destabilized by the presence of the streaks, reach N = 6 near the end of the cone. These results suggest a passive flow control strategy of using micro vortex generators to induce streaks that would delay transition in hypersonic boundary layers.

  12. New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

    Science.gov (United States)

    van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, G.; Hogeweij, G. M. D.; Tanaka, K.; Tamura, N.; Zwart, H. J.; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M. R.; LHD Experiment Group

    2017-12-01

    A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by two gyrotrons has been used to directly quantify the amplitude of the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions and also the absence of cubic and higher order components. The non-linear component is analyzed using the Volterra series, which is the non-linear generalization of transfer functions. This allows us to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles where the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles, demonstrating the significant impact that non-linearity can have.

  13. A nonlinear optimal control approach for chaotic finance dynamics

    Science.gov (United States)

    Rigatos, G.; Siano, P.; Loia, V.; Tommasetti, A.; Troisi, O.

    2017-11-01

    A new nonlinear optimal control approach is proposed for stabilization of the dynamics of a chaotic finance model. The dynamic model of the financial system, which expresses interaction between the interest rate, the investment demand, the price exponent and the profit margin, undergoes approximate linearization round local operating points. These local equilibria are defined at each iteration of the control algorithm and consist of the present value of the systems state vector and the last value of the control inputs vector that was exerted on it. The approximate linearization makes use of Taylor series expansion and of the computation of the associated Jacobian matrices. The truncation of higher order terms in the Taylor series expansion is considered to be a modelling error that is compensated by the robustness of the control loop. As the control algorithm runs, the temporary equilibrium is shifted towards the reference trajectory and finally converges to it. The control method needs to compute an H-infinity feedback control law at each iteration, and requires the repetitive solution of an algebraic Riccati equation. Through Lyapunov stability analysis it is shown that an H-infinity tracking performance criterion holds for the control loop. This implies elevated robustness against model approximations and external perturbations. Moreover, under moderate conditions the global asymptotic stability of the control loop is proven.

  14. On a Highly Nonlinear Self-Obstacle Optimal Control Problem

    Energy Technology Data Exchange (ETDEWEB)

    Di Donato, Daniela, E-mail: daniela.didonato@unitn.it [University of Trento, Department of Mathematics (Italy); Mugnai, Dimitri, E-mail: dimitri.mugnai@unipg.it [Università di Perugia, Dipartimento di Matematica e Informatica (Italy)

    2015-10-15

    We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.

  15. Parallel Nonlinear Optimization for Astrodynamic Navigation, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — CU Aerospace proposes the development of a new parallel nonlinear program (NLP) solver software package. NLPs allow the solution of complex optimization problems,...

  16. A Nonlinear Fuel Optimal Reaction Jet Control Law

    National Research Council Canada - National Science Library

    Breitfeller, Eric

    2002-01-01

    We derive a nonlinear fuel optimal attitude control system (ACS) that drives the final state to the desired state according to a cost function that weights the final state angular error relative to the angular rate error...

  17. Optimization of nonlinear controller with an enhanced biogeography approach

    Directory of Open Access Journals (Sweden)

    Mohammed Salem

    2014-07-01

    Full Text Available This paper is dedicated to the optimization of nonlinear controllers basing of an enhanced Biogeography Based Optimization (BBO approach. Indeed, The BBO is combined to a predator and prey model where several predators are used with introduction of a modified migration operator to increase the diversification along the optimization process so as to avoid local optima and reach the optimal solution quickly. The proposed approach is used in tuning the gains of PID controller for nonlinear systems. Simulations are carried out over a Mass spring damper and an inverted pendulum and has given remarkable results when compared to genetic algorithm and BBO.

  18. Nonlinear vibration analysis of a rotor supported by magnetic bearings using homotopy perturbation method

    Directory of Open Access Journals (Sweden)

    Aboozar Heydari

    2017-09-01

    Full Text Available In this paper, the effects of nonlinear forces due to the electromagnetic field of bearing and the unbalancing force on nonlinear vibration behavior of a rotor is investigated. The rotor is modeled as a rigid body that is supported by two magnetic bearings with eight-polar structures. The governing dynamics equations of the system that are coupled nonlinear second order ordinary differential equations (ODEs are derived, and for solving these equations, the homotopy perturbation method (HPM is used. By applying HPM, the possibility of presenting a harmonic semi-analytical solution, is provided. In fact, with equality the coefficient of auxiliary parameter (p, the system of coupled nonlinear second order and non-homogenous differential equations are obtained so that consists of unbalancing effects. By considering some initial condition for displacement and velocity in the horizontal and vertical directions, free vibration analysis is done and next, the forced vibration analysis under the effect of harmonic forces also is investigated. Likewise, various parameters on the vibration behavior of rotor are studied. Changes in amplitude and response phase per excitation frequency are investigated. Results show that by increasing excitation frequency, the motion amplitude is also increases and by passing the critical speed, it decreases. Also it shows that the magnetic bearing system performance is in stable maintenance of rotor. The parameters affecting on vibration behavior, has been studied and by comparison the results with the other references, which have a good precision up to 2nd order of embedding parameter, it implies the accuracy of this method in current research.

  19. Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

    Science.gov (United States)

    Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

    2018-03-01

    In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

  20. Discrete-time inverse optimal control for nonlinear systems

    CERN Document Server

    Sanchez, Edgar N

    2013-01-01

    Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th

  1. Application of Homotopy-Perturbation Method to Nonlinear Ozone Decomposition of the Second Order in Aqueous Solutions Equations

    DEFF Research Database (Denmark)

    Ganji, D.D; Miansari, Mo; B, Ganjavi

    2008-01-01

    In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions are consid......In this paper, homotopy-perturbation method (HPM) is introduced to solve nonlinear equations of ozone decomposition in aqueous solutions. HPM deforms a di¢ cult problem into a simple problem which can be easily solved. The effects of some parameters such as temperature to the solutions...

  2. ROTAX: a nonlinear optimization program by axes rotation method

    International Nuclear Information System (INIS)

    Suzuki, Tadakazu

    1977-09-01

    A nonlinear optimization program employing the axes rotation method has been developed for solving nonlinear problems subject to nonlinear inequality constraints and its stability and convergence efficiency were examined. The axes rotation method is a direct search of the optimum point by rotating the orthogonal coordinate system in a direction giving the minimum objective. The searching direction is rotated freely in multi-dimensional space, so the method is effective for the problems represented with the contours having deep curved valleys. In application of the axes rotation method to the optimization problems subject to nonlinear inequality constraints, an improved version of R.R. Allran and S.E.J. Johnsen's method is used, which deals with a new objective function composed of the original objective and a penalty term to consider the inequality constraints. The program is incorporated in optimization code system SCOOP. (auth.)

  3. Linear perturbations of a self-similar solution of hydrodynamics with non-linear heat conduction

    International Nuclear Information System (INIS)

    Dubois-Boudesocque, Carine

    2000-01-01

    The stability of an ablative flow, where a shock wave is located upstream a thermal front, is of importance in inertial confinement fusion. The present model considers an exact self-similar solution to the hydrodynamic equations with non-linear heat conduction for a semi-infinite slab. For lack of an analytical solution, a high resolution numerical procedure is devised, which couples a finite difference method with a relaxation algorithm using a two-domain pseudo-spectral method. Stability of this solution is studied by introducing linear perturbation method within a Lagrangian-Eulerian framework. The initial and boundary value problem is solved by a splitting of the equations between a hyperbolic system and a parabolic equation. The boundary conditions of the hyperbolic system are treated, in the case of spectral methods, according to Thompson's approach. The parabolic equation is solved by an influence matrix method. These numerical procedures have been tested versus exact solutions. Considering a boundary heat flux perturbation, the space-time evolution of density, velocity and temperature are shown. (author) [fr

  4. Application of He's homotopy perturbation method to conservative truly nonlinear oscillators

    International Nuclear Information System (INIS)

    Belendez, A.; Belendez, T.; Marquez, A.; Neipp, C.

    2008-01-01

    We apply He's homotopy perturbation method to find improved approximate solutions to conservative truly nonlinear oscillators. This approach gives us not only a truly periodic solution but also the period of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters in the case of the cubic oscillator, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. For the second order approximation we have shown that the relative error in the analytical approximate frequency is approximately 0.03% for any parameter values involved. We also compared the analytical approximate solutions and the Fourier series expansion of the exact solution. This has allowed us to compare the coefficients for the different harmonic terms in these solutions. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems

  5. A Linearized Relaxing Algorithm for the Specific Nonlinear Optimization Problem

    Directory of Open Access Journals (Sweden)

    Mio Horai

    2016-01-01

    Full Text Available We propose a new method for the specific nonlinear and nonconvex global optimization problem by using a linear relaxation technique. To simplify the specific nonlinear and nonconvex optimization problem, we transform the problem to the lower linear relaxation form, and we solve the linear relaxation optimization problem by the Branch and Bound Algorithm. Under some reasonable assumptions, the global convergence of the algorithm is certified for the problem. Numerical results show that this method is more efficient than the previous methods.

  6. Optimal Nonlinear Filter for INS Alignment

    Institute of Scientific and Technical Information of China (English)

    赵瑞; 顾启泰

    2002-01-01

    All the methods to handle the inertial navigation system (INS) alignment were sub-optimal in the past. In this paper, particle filtering (PF) as an optimal method is used for solving the problem of INS alignment. A sub-optimal two-step filtering algorithm is presented to improve the real-time performance of PF. The approach combines particle filtering with Kalman filtering (KF). Simulation results illustrate the superior performance of these approaches when compared with extended Kalman filtering (EKF).

  7. Galerkin approximations of nonlinear optimal control problems in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Mickael D. Chekroun

    2017-07-01

    Full Text Available Nonlinear optimal control problems in Hilbert spaces are considered for which we derive approximation theorems for Galerkin approximations. Approximation theorems are available in the literature. The originality of our approach relies on the identification of a set of natural assumptions that allows us to deal with a broad class of nonlinear evolution equations and cost functionals for which we derive convergence of the value functions associated with the optimal control problem of the Galerkin approximations. This convergence result holds for a broad class of nonlinear control strategies as well. In particular, we show that the framework applies to the optimal control of semilinear heat equations posed on a general compact manifold without boundary. The framework is then shown to apply to geoengineering and mitigation of greenhouse gas emissions formulated here in terms of optimal control of energy balance climate models posed on the sphere $\\mathbb{S}^2$.

  8. Introduction to the theory of nonlinear optimization

    CERN Document Server

    Jahn, Johannes

    2007-01-01

    This book serves as an introductory text to optimization theory in normed spaces. The topics of this book are existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook presents fundamentals with particular emphasis on the application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a ba

  9. New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

    NARCIS (Netherlands)

    van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, Gerd; Hogeweij, G.M.D.; Tanaka, K.; Tamura, N.; Zwart, Hans; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M.R.

    2017-01-01

    A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by

  10. Exact Solution of a Faraday's Law Problem that Includes a Nonlinear Term and Its Implication for Perturbation Theory.

    Science.gov (United States)

    Fulcher, Lewis P.

    1979-01-01

    Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)

  11. A new optimization algotithm with application to nonlinear MPC

    Directory of Open Access Journals (Sweden)

    Frode Martinsen

    2005-01-01

    Full Text Available This paper investigates application of SQP optimization algorithm to nonlinear model predictive control. It considers feasible vs. infeasible path methods, sequential vs. simultaneous methods and reduced vs full space methods. A new optimization algorithm coined rFOPT which remains feasibile with respect to inequality constraints is introduced. The suitable choices between these various strategies are assessed informally through a small CSTR case study. The case study also considers the effect various discretization methods have on the optimization problem.

  12. Switching of bound vector solitons for the coupled nonlinear Schrödinger equations with nonhomogenously stochastic perturbations

    International Nuclear Information System (INIS)

    Sun Zhiyuan; Yu Xin; Liu Ying; Gao Yitian

    2012-01-01

    We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.

  13. Switching of bound vector solitons for the coupled nonlinear Schrödinger equations with nonhomogenously stochastic perturbations

    Science.gov (United States)

    Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Ying

    2012-12-01

    We investigate the dynamics of the bound vector solitons (BVSs) for the coupled nonlinear Schrödinger equations with the nonhomogenously stochastic perturbations added on their dispersion terms. Soliton switching (besides soliton breakup) can be observed between the two components of the BVSs. Rate of the maximum switched energy (absolute values) within the fixed propagation distance (about 10 periods of the BVSs) enhances in the sense of statistics when the amplitudes of stochastic perturbations increase. Additionally, it is revealed that the BVSs with enhanced coherence are more robust against the perturbations with nonhomogenous stochasticity. Diagram describing the approximate borders of the splitting and non-splitting areas is also given. Our results might be helpful in dynamics of the BVSs with stochastic noises in nonlinear optical fibers or with stochastic quantum fluctuations in Bose-Einstein condensates.

  14. Optimal beamforming in MIMO systems with HPA nonlinearity

    KAUST Repository

    Qi, Jian

    2010-09-01

    In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance. ©2010 IEEE.

  15. Optimal beamforming in MIMO systems with HPA nonlinearity

    KAUST Repository

    Qi, Jian; Aissa, Sonia

    2010-01-01

    In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance. ©2010 IEEE.

  16. Non-linear programming method in optimization of fast reactors

    International Nuclear Information System (INIS)

    Pavelesku, M.; Dumitresku, Kh.; Adam, S.

    1975-01-01

    Application of the non-linear programming methods on optimization of nuclear materials distribution in fast reactor is discussed. The programming task composition is made on the basis of the reactor calculation dependent on the fuel distribution strategy. As an illustration of this method application the solution of simple example is given. Solution of the non-linear program is done on the basis of the numerical method SUMT. (I.T.)

  17. Conference on High Performance Software for Nonlinear Optimization

    CERN Document Server

    Murli, Almerico; Pardalos, Panos; Toraldo, Gerardo

    1998-01-01

    This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSN097) which was held in Ischia, Italy, in June 1997. The rapid progress of computer technologies, including new parallel architec­ tures, has stimulated a large amount of research devoted to building software environments and defining algorithms able to fully exploit this new computa­ tional power. In some sense, numerical analysis has to conform itself to the new tools. The impact of parallel computing in nonlinear optimization, which had a slow start at the beginning, seems now to increase at a fast rate, and it is reasonable to expect an even greater acceleration in the future. As with the first HPSNO conference, the goal of the HPSN097 conference was to supply a broad overview of the more recent developments and trends in nonlinear optimization, emphasizing the algorithmic and high performance software aspects. Bringing together new computational methodologies with theoretical...

  18. Robust Exponential Synchronization for a Class of Master-Slave Distributed Parameter Systems with Spatially Variable Coefficients and Nonlinear Perturbation

    Directory of Open Access Journals (Sweden)

    Chengdong Yang

    2015-01-01

    Full Text Available This paper addresses the exponential synchronization problem of a class of master-slave distributed parameter systems (DPSs with spatially variable coefficients and spatiotemporally variable nonlinear perturbation, modeled by a couple of semilinear parabolic partial differential equations (PDEs. With a locally Lipschitz constraint, the perturbation is a continuous function of time, space, and system state. Firstly, a sufficient condition for the robust exponential synchronization of the unforced semilinear master-slave PDE systems is investigated for all admissible nonlinear perturbations. Secondly, a robust distributed proportional-spatial derivative (P-sD state feedback controller is desired such that the closed-loop master-slave PDE systems achieve exponential synchronization. Using Lyapunov’s direct method and the technique of integration by parts, the main results of this paper are presented in terms of spatial differential linear matrix inequalities (SDLMIs. Finally, two numerical examples are provided to show the effectiveness of the proposed methods applied to the robust exponential synchronization problem of master-slave PDE systems with nonlinear perturbation.

  19. Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Orain, F.; Bécoulet, M.; Dif-Pradalier, G.; Nardon, E.; Passeron, C.; Latu, G.; Grandgirard, V.; Fil, A.; Ratnani, A. [CEA, IRFM, F-13108 Saint-Paul-Lez-Durance (France); Huijsmans, G. [ITER Organization, Route de Vinon, F-13115 Saint-Paul-Lez-Durance (France); Pamela, S. [IIFS-PIIM. Aix Marseille Université - CNRS, 13397 Marseille Cedex20 (France); Chapman, I.; Kirk, A.; Thornton, A. [EURATOM/CCFE Fusion Association, Culham Science Centre, Oxon OX14 3DB (United Kingdom); Hoelzl, M. [Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching (Germany); Cahyna, P. [Association EURATOM/IPP.CR, Prague (Czech Republic)

    2013-10-15

    The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ≥0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST Double Null Divertor geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.

  20. Expectation propagation for large scale Bayesian inference of non-linear molecular networks from perturbation data.

    Science.gov (United States)

    Narimani, Zahra; Beigy, Hamid; Ahmad, Ashar; Masoudi-Nejad, Ali; Fröhlich, Holger

    2017-01-01

    Inferring the structure of molecular networks from time series protein or gene expression data provides valuable information about the complex biological processes of the cell. Causal network structure inference has been approached using different methods in the past. Most causal network inference techniques, such as Dynamic Bayesian Networks and ordinary differential equations, are limited by their computational complexity and thus make large scale inference infeasible. This is specifically true if a Bayesian framework is applied in order to deal with the unavoidable uncertainty about the correct model. We devise a novel Bayesian network reverse engineering approach using ordinary differential equations with the ability to include non-linearity. Besides modeling arbitrary, possibly combinatorial and time dependent perturbations with unknown targets, one of our main contributions is the use of Expectation Propagation, an algorithm for approximate Bayesian inference over large scale network structures in short computation time. We further explore the possibility of integrating prior knowledge into network inference. We evaluate the proposed model on DREAM4 and DREAM8 data and find it competitive against several state-of-the-art existing network inference methods.

  1. Optimized Adaptive Perturb and Observe Maximum Power Point Tracking Control for Photovoltaic Generation

    Directory of Open Access Journals (Sweden)

    Luigi Piegari

    2015-04-01

    Full Text Available The power extracted from PV arrays is usually maximized using maximum power point tracking algorithms. One of the most widely used techniques is the perturb & observe algorithm, which periodically perturbs the operating point of the PV array, sometime with an adaptive perturbation step, and compares the PV power before and after the perturbation. This paper analyses the most suitable perturbation step to optimize maximum power point tracking performance and suggests a design criterion to select the parameters of the controller. Using this proposed adaptive step, the MPPT perturb & observe algorithm achieves an excellent dynamic response by adapting the perturbation step to the actual operating conditions of the PV array. The proposed algorithm has been validated and tested in a laboratory using a dual input inductor push-pull converter. This particular converter topology is an efficient interface to boost the low voltage of PV arrays and effectively control the power flow when input or output voltages are variable. The experimental results have proved the superiority of the proposed algorithm in comparison of traditional perturb & observe and incremental conductance techniques.

  2. Approaches to the Optimal Nonlinear Analysis of Microcalorimeter Pulses

    Science.gov (United States)

    Fowler, J. W.; Pappas, C. G.; Alpert, B. K.; Doriese, W. B.; O'Neil, G. C.; Ullom, J. N.; Swetz, D. S.

    2018-03-01

    We consider how to analyze microcalorimeter pulses for quantities that are nonlinear in the data, while preserving the signal-to-noise advantages of linear optimal filtering. We successfully apply our chosen approach to compute the electrothermal feedback energy deficit (the "Joule energy") of a pulse, which has been proposed as a linear estimator of the deposited photon energy.

  3. New preconditioned conjugate gradient algorithms for nonlinear unconstrained optimization problems

    International Nuclear Information System (INIS)

    Al-Bayati, A.; Al-Asadi, N.

    1997-01-01

    This paper presents two new predilection conjugate gradient algorithms for nonlinear unconstrained optimization problems and examines their computational performance. Computational experience shows that the new proposed algorithms generally imp lone the efficiency of Nazareth's [13] preconditioned conjugate gradient algorithm. (authors). 16 refs., 1 tab

  4. A higher order depletion perturbation theory with application to in-core fuel management optimization

    International Nuclear Information System (INIS)

    Kropaczek, D.J.; Turinsky, P.J.

    1990-01-01

    Perturbation techniques utilized in reactor analysis have recently been applied in the solution of the in-core nuclear fuel management optimization problem. The use of such methods is motivated by the need to evaluate many times over, the core physics characteristics of loading pattern solutions obtained through an optimization process, which is typically iterative. Perturbation theory provides an efficient alternative to the prohibitively expensive, repetitive solutions of the system few-group neutron diffusion equations required in solving the fuel placement problem. A primary concern in the use of such methods is the control of perturbation errors arising during the fuel shuffling process. First-order accurate models inevitably resort to undue restriction of fuel movement during the optimization process to control these errors. Higher order perturbation theory models have the potential to overcome such limitations, which may result in the identification of local versus global optima. An accurate, computationally efficient reactor physics model based on higher order perturbation theory and geared toward the needs of large-scale in-core fuel management optimization is presented in this paper

  5. Improving Convergence of Iterative Feedback Tuning using Optimal External Perturbations

    DEFF Research Database (Denmark)

    Huusom, Jakob Kjøbsted; Hjalmarsson, Håkon; Poulsen, Niels Kjølstad

    2008-01-01

    Iterative feedback tuning constitutes an attractive control loop tuning method for processes in the absence of sufficient process insight. It is a purely data driven approach to optimization of the loop performance. The standard formulation ensures an unbiased estimate of the loop performance cost...... function gradient, which is used in a search algorithm. A slow rate of convergence of the tuning method is often experienced when tuning for disturbance rejection. This is due to a poor signal to noise ratio in the process data. A method is proposed for increasing the information content in data...

  6. Route Monopolie and Optimal Nonlinear Pricing

    Science.gov (United States)

    Tournut, Jacques

    2003-01-01

    To cope with air traffic growth and congested airports, two solutions are apparent on the supply side: 1) use larger aircraft in the hub and spoke system; or 2) develop new routes through secondary airports. An enlarged route system through secondary airports may increase the proportion of route monopolies in the air transport market.The monopoly optimal non linear pricing policy is well known in the case of one dimension (one instrument, one characteristic) but not in the case of several dimensions. This paper explores the robustness of the one dimensional screening model with respect to increasing the number of instruments and the number of characteristics. The objective of this paper is then to link and fill the gap in both literatures. One of the merits of the screening model has been to show that a great varieD" of economic questions (non linear pricing, product line choice, auction design, income taxation, regulation...) could be handled within the same framework.VCe study a case of non linear pricing (2 instruments (2 routes on which the airline pro_ddes customers with services), 2 characteristics (demand of services on these routes) and two values per characteristic (low and high demand of services on these routes)) and we show that none of the conclusions of the one dimensional analysis remain valid. In particular, upward incentive compatibility constraint may be binding at the optimum. As a consequence, they may be distortion at the top of the distribution. In addition to this, we show that the optimal solution often requires a kind of form of bundling, we explain explicitly distortions and show that it is sometimes optimal for the monopolist to only produce one good (instead of two) or to exclude some buyers from the market. Actually, this means that the monopolist cannot fully apply his monopoly power and is better off selling both goods independently.We then define all the possible solutions in the case of a quadratic cost function for a uniform

  7. Nonlinear adaptive optimization of biomass productivity in continuous bioreactors

    Energy Technology Data Exchange (ETDEWEB)

    Sauvaire, P; Mellichamp, D A; Agrawal, P [California Univ., Santa Barbara, CA (United States). Dept. of Chemical and Nuclear Engineering

    1991-11-01

    A novel on-line adaptive optimization algorithm is developed and applied to continuous biological reactors. The algorithm makes use of a simple nonlinear estimation model that relates either the cell-mass productivity or the cell-mass concentration to the dilution rate. On-line estimation is used to recursively identify the parameters in the nonlinear process model and to periodically calculate and steer the bioreactor to the dilution rate that yields optimum cell-mass productivity. Thus, the algorithm does not require an accurate process model, locates the optimum dilution rate online, and maintains the bioreactors at this optimum condition at all times. The features of the proposed new algorithm are compared with those of other adaptive optimization techniques presented in the literature. A detailed simulation study using three different microbial system models was conducted to illustrate the performance of the optimization algorithms. (orig.).

  8. Development of parallellized higher-order generalized depletion perturbation theory for application in equilibrium cycle optimization

    Energy Technology Data Exchange (ETDEWEB)

    Geemert, R. van E-mail: rene.vangeemert@psi.ch; Hoogenboom, J.E. E-mail: j.e.hoogenboom@iri.tudelft.nl

    2001-09-01

    As nuclear fuel economy is basically a multi-cycle issue, a fair way of evaluating reload patterns is to consider their performance in the case of an equilibrium cycle. The equilibrium cycle associated with a reload pattern is defined as the limit fuel cycle that eventually emerges after multiple successive periodic refueling, each time implementing the same reload scheme. Since the equilibrium cycle is the solution of a reload operation invariance equation, it can in principle be found with sufficient accuracy only by applying an iterative procedure, simulating the emergence of the limit cycle. For a design purpose such as the optimization of reload patterns, in which many different equilibrium cycle perturbations (resulting from many different limited changes in the reload operator) must be evaluated, this requires far too much computational effort. However, for very fast calculation of these many different equilibrium cycle perturbations it is also possible to set up a generalized variational approach. This approach results in an iterative scheme that yields the exact perturbation in the equilibrium cycle solution as well, in an accelerated way. Furthermore, both the solution of the adjoint equations occurring in the perturbation theory formalism and the implementation of the optimization algorithm have been parallellized and executed on a massively parallel machine. The combination of parallellism and generalized perturbation theory offers the opportunity to perform very exhaustive, fast and accurate sampling of the solution space for the equilibrium cycle reload pattern optimization problem.

  9. Dynamic behaviors for a perturbed nonlinear Schrödinger equation with the power-law nonlinearity in a non-Kerr medium

    Science.gov (United States)

    Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong; Liu, De-Yin

    2017-04-01

    Effects of quantic nonlinearity on the propagation of the ultrashort optical pulses in a non-Kerr medium, like an optical fiber, can be described by a perturbed nonlinear Schrödinger equation with the power law nonlinearity, which is studied in this paper from a planar-dynamic-system view point. We obtain the equivalent two-dimensional planar dynamic system of such an equation, for which, according to the bifurcation theory and qualitative theory, phase portraits are given. Through the analysis of those phase portraits, we present the relations among the Hamiltonian, orbits of the dynamic system and types of the analytic solutions. Analytic expressions of the periodic-wave solutions, kink- and bell-shaped solitary-wave solutions are derived, and we find that the periodic-wave solutions can be reduced to the kink- and bell-shaped solitary-wave solutions.

  10. Decentralized DC Microgrid Monitoring and Optimization via Primary Control Perturbations

    Science.gov (United States)

    Angjelichinoski, Marko; Scaglione, Anna; Popovski, Petar; Stefanovic, Cedomir

    2018-06-01

    We treat the emerging power systems with direct current (DC) MicroGrids, characterized with high penetration of power electronic converters. We rely on the power electronics to propose a decentralized solution for autonomous learning of and adaptation to the operating conditions of the DC Mirogrids; the goal is to eliminate the need to rely on an external communication system for such purpose. The solution works within the primary droop control loops and uses only local bus voltage measurements. Each controller is able to estimate (i) the generation capacities of power sources, (ii) the load demands, and (iii) the conductances of the distribution lines. To define a well-conditioned estimation problem, we employ decentralized strategy where the primary droop controllers temporarily switch between operating points in a coordinated manner, following amplitude-modulated training sequences. We study the use of the estimator in a decentralized solution of the Optimal Economic Dispatch problem. The evaluations confirm the usefulness of the proposed solution for autonomous MicroGrid operation.

  11. Optimal Control Strategies in a Two Dimensional Differential Game Using Linear Equation under a Perturbed System

    Directory of Open Access Journals (Sweden)

    Musa Danjuma SHEHU

    2008-06-01

    Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.

  12. Generalized perturbation theory error control within PWR core-loading pattern optimization

    International Nuclear Information System (INIS)

    Imbriani, J.S.; Turinsky, P.J.; Kropaczek, D.J.

    1995-01-01

    The fuel management optimization code FORMOSA-P has been developed to determine the family of near-optimum loading patterns for PWR reactors. The code couples the optimization technique of simulated annealing (SA) with a generalized perturbation theory (GPT) model for evaluating core physics characteristics. To ensure the accuracy of the GPT predictions, as well as to maximize the efficient of the SA search, a GPT error control method has been developed

  13. Constrained Optimization via Stochastic approximation with a simultaneous perturbation gradient approximation

    DEFF Research Database (Denmark)

    Sadegh, Payman

    1997-01-01

    This paper deals with a projection algorithm for stochastic approximation using simultaneous perturbation gradient approximation for optimization under inequality constraints where no direct gradient of the loss function is available and the inequality constraints are given as explicit functions...... of the optimization parameters. It is shown that, under application of the projection algorithm, the parameter iterate converges almost surely to a Kuhn-Tucker point, The procedure is illustrated by a numerical example, (C) 1997 Elsevier Science Ltd....

  14. Higher order generalized perturbation theory for boiling water reactor in-core fuel management optimization

    International Nuclear Information System (INIS)

    Moore, B.R.; Turinsky, P.J.

    1998-01-01

    Boiling water reactor (BWR) loading pattern assessment requires solving the two-group, nodal form of the neutron diffusion equation and drift-flux form of the fluid equations simultaneously because these equation sets are strongly coupled via nonlinear feedback. To reduce the computational burden associated with the calculation of the core attributes (that is, core eigenvalue and thermal margins) of a perturbed BWR loading pattern, the analytical and numerical aspects of a higher order generalized perturbation theory (GPT) method, which correctly addresses the strong nonlinear feedbacks of two-phase flow, have been established. Inclusion of Jacobian information in the definition of the generalized flux adjoints provides for a rapidly convergent iterative method for solution of the power distribution and eigenvalue of a loading pattern perturbed from a reference state. Results show that the computational speedup of GPT compared with conventional forward solution methods demanding consistent accuracy is highly dependent on the number of spatial nodes utilized by the core simulator, varying from superior to inferior performance as the number of nodes increases

  15. New Exact Penalty Functions for Nonlinear Constrained Optimization Problems

    Directory of Open Access Journals (Sweden)

    Bingzhuang Liu

    2014-01-01

    Full Text Available For two kinds of nonlinear constrained optimization problems, we propose two simple penalty functions, respectively, by augmenting the dimension of the primal problem with a variable that controls the weight of the penalty terms. Both of the penalty functions enjoy improved smoothness. Under mild conditions, it can be proved that our penalty functions are both exact in the sense that local minimizers of the associated penalty problem are precisely the local minimizers of the original constrained problem.

  16. Hierarchical optimal control of large-scale nonlinear chemical processes.

    Science.gov (United States)

    Ramezani, Mohammad Hossein; Sadati, Nasser

    2009-01-01

    In this paper, a new approach is presented for optimal control of large-scale chemical processes. In this approach, the chemical process is decomposed into smaller sub-systems at the first level, and a coordinator at the second level, for which a two-level hierarchical control strategy is designed. For this purpose, each sub-system in the first level can be solved separately, by using any conventional optimization algorithm. In the second level, the solutions obtained from the first level are coordinated using a new gradient-type strategy, which is updated by the error of the coordination vector. The proposed algorithm is used to solve the optimal control problem of a complex nonlinear chemical stirred tank reactor (CSTR), where its solution is also compared with the ones obtained using the centralized approach. The simulation results show the efficiency and the capability of the proposed hierarchical approach, in finding the optimal solution, over the centralized method.

  17. Development of a VVER-1000 core loading pattern optimization program based on perturbation theory

    International Nuclear Information System (INIS)

    Hosseini, Mohammad; Vosoughi, Naser

    2012-01-01

    Highlights: ► We use perturbation theory to find an optimum fuel loading pattern in a VVER-1000. ► We provide a software for in-core fuel management optimization. ► We consider two objectives for our method (perturbation theory). ► We show that perturbation theory method is very fast and accurate for optimization. - Abstract: In-core nuclear fuel management is one of the most important concerns in the design of nuclear reactors. Two main goals in core fuel loading pattern design optimization are maximizing the core effective multiplication factor in order to extract the maximum energy, and keeping the local power peaking factor lower than a predetermined value to maintain the fuel integrity. Because of the numerous possible patterns of fuel assemblies in the reactor core, finding the best configuration is so important and challenging. Different techniques for optimization of fuel loading pattern in the reactor core have been introduced by now. In this study, a software is programmed in C language to find an order of the fuel loading pattern of a VVER-1000 reactor core using the perturbation theory. Our optimization method is based on minimizing the radial power peaking factor. The optimization process launches by considering an initial loading pattern and the specifications of the fuel assemblies which are given as the input of the software. The results on a typical VVER-1000 reactor reveal that the method could reach to a pattern with an allowed radial power peaking factor and increases the cycle length 1.1 days, as well.

  18. Quantum dynamical effects as a singular perturbation for observables in open quasi-classical nonlinear mesoscopic systems

    International Nuclear Information System (INIS)

    Berman, G.P.; Borgonovi, F.; Dalvit, D.A.R.

    2009-01-01

    We review our results on a mathematical dynamical theory for observables for open many-body quantum nonlinear bosonic systems for a very general class of Hamiltonians. We show that non-quadratic (nonlinear) terms in a Hamiltonian provide a singular 'quantum' perturbation for observables in some 'mesoscopic' region of parameters. In particular, quantum effects result in secular terms in the dynamical evolution, that grow in time. We argue that even for open quantum nonlinear systems in the deep quasi-classical region, these quantum effects can survive after decoherence and relaxation processes take place. We demonstrate that these quantum effects in open quantum systems can be observed, for example, in the frequency Fourier spectrum of the dynamical observables, or in the corresponding spectral density of noise. Estimates are presented for Bose-Einstein condensates, low temperature mechanical resonators, and nonlinear optical systems prepared in large amplitude coherent states. In particular, we show that for Bose-Einstein condensate systems the characteristic time of deviation of quantum dynamics for observables from the corresponding classical dynamics coincides with the characteristic time-scale of the well-known quantum nonlinear effect of phase diffusion.

  19. Investigation of perturbation techniques for nonlinear difference equations and other related topics: Final technical report

    International Nuclear Information System (INIS)

    Mickens, R.E.

    1986-01-01

    Investigations in mathematical physics are summarized for projects concerning a nonlinear wave equation; a second-order nonlinear difference equation; singular, nonlinear oscillators; and numerical instabilities. All of the results obtained through these research efforts have been presented in seminars and professional meetings and conferences. Further, all of these results have been published in the scientific literature. A list of exact references are given in the appendices to this report

  20. A perturbative approach to mass-generation - the non-linear sigma model

    International Nuclear Information System (INIS)

    Davis, A.C.; Nahm, W.

    1985-01-01

    A calculational scheme is presented to include non-perturbative effects into the perturbation expansion. As an example we use the O(N + 1) sigma model. The scheme uses a natural parametrisation such that the lagrangian can be written in a form normal-ordered with respect to the O(N + 1) symmetric vacuum plus vacuum expectation values, the latter calculated by symmetry alone. Including such expectation values automatically leads to the inclusion of a mass-gap in the perturbation series. (orig.)

  1. The correlation function for density perturbations in an expanding universe. II - Nonlinear theory

    Science.gov (United States)

    Mcclelland, J.; Silk, J.

    1977-01-01

    A formalism is developed to find the two-point and higher-order correlation functions for a given distribution of sizes and shapes of perturbations which are randomly placed in three-dimensional space. The perturbations are described by two parameters such as central density and size, and the two-point correlation function is explicitly related to the luminosity function of groups and clusters of galaxies

  2. Optimal analytic method for the nonlinear Hasegawa-Mima equation

    Science.gov (United States)

    Baxter, Mathew; Van Gorder, Robert A.; Vajravelu, Kuppalapalle

    2014-05-01

    The Hasegawa-Mima equation is a nonlinear partial differential equation that describes the electric potential due to a drift wave in a plasma. In the present paper, we apply the method of homotopy analysis to a slightly more general Hasegawa-Mima equation, which accounts for hyper-viscous damping or viscous dissipation. First, we outline the method for the general initial/boundary value problem over a compact rectangular spatial domain. We use a two-stage method, where both the convergence control parameter and the auxiliary linear operator are optimally selected to minimize the residual error due to the approximation. To do the latter, we consider a family of operators parameterized by a constant which gives the decay rate of the solutions. After outlining the general method, we consider a number of concrete examples in order to demonstrate the utility of this approach. The results enable us to study properties of the initial/boundary value problem for the generalized Hasegawa-Mima equation. In several cases considered, we are able to obtain solutions with extremely small residual errors after relatively few iterations are computed (residual errors on the order of 10-15 are found in multiple cases after only three iterations). The results demonstrate that selecting a parameterized auxiliary linear operator can be extremely useful for minimizing residual errors when used concurrently with the optimal homotopy analysis method, suggesting that this approach can prove useful for a number of nonlinear partial differential equations arising in physics and nonlinear mechanics.

  3. Model parameter-related optimal perturbations and their contributions to El Niño prediction errors

    Science.gov (United States)

    Tao, Ling-Jiang; Gao, Chuan; Zhang, Rong-Hua

    2018-04-01

    Errors in initial conditions and model parameters (MPs) are the main sources that limit the accuracy of ENSO predictions. In addition to exploring the initial error-induced prediction errors, model errors are equally important in determining prediction performance. In this paper, the MP-related optimal errors that can cause prominent error growth in ENSO predictions are investigated using an intermediate coupled model (ICM) and a conditional nonlinear optimal perturbation (CNOP) approach. Two MPs related to the Bjerknes feedback are considered in the CNOP analysis: one involves the SST-surface wind coupling ({α _τ } ), and the other involves the thermocline effect on the SST ({α _{Te}} ). The MP-related optimal perturbations (denoted as CNOP-P) are found uniformly positive and restrained in a small region: the {α _τ } component is mainly concentrated in the central equatorial Pacific, and the {α _{Te}} component is mainly located in the eastern cold tongue region. This kind of CNOP-P enhances the strength of the Bjerknes feedback and induces an El Niño- or La Niña-like error evolution, resulting in an El Niño-like systematic bias in this model. The CNOP-P is also found to play a role in the spring predictability barrier (SPB) for ENSO predictions. Evidently, such error growth is primarily attributed to MP errors in small areas based on the localized distribution of CNOP-P. Further sensitivity experiments firmly indicate that ENSO simulations are sensitive to the representation of SST-surface wind coupling in the central Pacific and to the thermocline effect in the eastern Pacific in the ICM. These results provide guidance and theoretical support for the future improvement in numerical models to reduce the systematic bias and SPB phenomenon in ENSO predictions.

  4. Spin glasses and nonlinear constraints in portfolio optimization

    Energy Technology Data Exchange (ETDEWEB)

    Andrecut, M., E-mail: mircea.andrecut@gmail.com

    2014-01-17

    We discuss the portfolio optimization problem with the obligatory deposits constraint. Recently it has been shown that as a consequence of this nonlinear constraint, the solution consists of an exponentially large number of optimal portfolios, completely different from each other, and extremely sensitive to any changes in the input parameters of the problem, making the concept of rational decision making questionable. Here we reformulate the problem using a quadratic obligatory deposits constraint, and we show that from the physics point of view, finding an optimal portfolio amounts to calculating the mean-field magnetizations of a random Ising model with the constraint of a constant magnetization norm. We show that the model reduces to an eigenproblem, with 2N solutions, where N is the number of assets defining the portfolio. Also, in order to illustrate our results, we present a detailed numerical example of a portfolio of several risky common stocks traded on the Nasdaq Market.

  5. Spin glasses and nonlinear constraints in portfolio optimization

    International Nuclear Information System (INIS)

    Andrecut, M.

    2014-01-01

    We discuss the portfolio optimization problem with the obligatory deposits constraint. Recently it has been shown that as a consequence of this nonlinear constraint, the solution consists of an exponentially large number of optimal portfolios, completely different from each other, and extremely sensitive to any changes in the input parameters of the problem, making the concept of rational decision making questionable. Here we reformulate the problem using a quadratic obligatory deposits constraint, and we show that from the physics point of view, finding an optimal portfolio amounts to calculating the mean-field magnetizations of a random Ising model with the constraint of a constant magnetization norm. We show that the model reduces to an eigenproblem, with 2N solutions, where N is the number of assets defining the portfolio. Also, in order to illustrate our results, we present a detailed numerical example of a portfolio of several risky common stocks traded on the Nasdaq Market.

  6. Stiffness design of geometrically nonlinear structures using topology optimization

    DEFF Research Database (Denmark)

    Buhl, Thomas; Pedersen, Claus B. Wittendorf; Sigmund, Ole

    2000-01-01

    of the objective functions are found with the adjoint method and the optimization problem is solved using the Method of Moving Asymptotes. A filtering scheme is used to obtain checkerboard-free and mesh-independent designs and a continuation approach improves convergence to efficient designs. Different objective......The paper deals with topology optimization of structures undergoing large deformations. The geometrically nonlinear behaviour of the structures are modelled using a total Lagrangian finite element formulation and the equilibrium is found using a Newton-Raphson iterative scheme. The sensitivities...... functions are tested. Minimizing compliance for a fixed load results in degenerated topologies which are very inefficient for smaller or larger loads. The problem of obtaining degenerated "optimal" topologies which only can support the design load is even more pronounced than for structures with linear...

  7. An hp symplectic pseudospectral method for nonlinear optimal control

    Science.gov (United States)

    Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong

    2017-01-01

    An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

  8. Global Optimization of Nonlinear Blend-Scheduling Problems

    Directory of Open Access Journals (Sweden)

    Pedro A. Castillo Castillo

    2017-04-01

    Full Text Available The scheduling of gasoline-blending operations is an important problem in the oil refining industry. This problem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but also non-convex nonlinear behavior, due to the blending of various materials with different quality properties. In this work, a global optimization algorithm is proposed to solve a previously published continuous-time mixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimization, the distribution problem, and several important operational features and constraints. The algorithm employs piecewise McCormick relaxation (PMCR and normalized multiparametric disaggregation technique (NMDT to compute estimates of the global optimum. These techniques partition the domain of one of the variables in a bilinear term and generate convex relaxations for each partition. By increasing the number of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates of the global solution. The algorithm is compared to two commercial global solvers and two heuristic methods by solving four examples from the literature. Results show that the proposed global optimization algorithm performs on par with commercial solvers but is not as fast as heuristic approaches.

  9. Simulation-based optimal Bayesian experimental design for nonlinear systems

    KAUST Repository

    Huan, Xun

    2013-01-01

    The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters.Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter inference problems arising in detailed combustion kinetics. © 2012 Elsevier Inc.

  10. Optimization of Candu fuel management with gradient methods using generalized perturbation theory

    International Nuclear Information System (INIS)

    Chambon, R.; Varin, E.; Rozon, D.

    2005-01-01

    CANDU fuel management problems are solved using time-average representation of the core. Optimization problems based on this representation have been defined in the early nineties. The mathematical programming using the generalized perturbation theory (GPT) that was developed has been implemented in the reactor code DONJON. The use of the augmented Lagrangian (AL) method is presented and evaluated in this paper. This approach is mandatory for new constraint problems. Combined with the classical Lemke method, it proves to be very efficient to reach optimal solution in a very limited number of iterations. (authors)

  11. Optimal Initial Perturbations for Ensemble Prediction of the Madden-Julian Oscillation during Boreal Winter

    Science.gov (United States)

    Ham, Yoo-Geun; Schubert, Siegfried; Chang, Yehui

    2012-01-01

    An initialization strategy, tailored to the prediction of the Madden-Julian oscillation (MJO), is evaluated using the Goddard Earth Observing System Model, version 5 (GEOS-5), coupled general circulation model (CGCM). The approach is based on the empirical singular vectors (ESVs) of a reduced-space statistically determined linear approximation of the full nonlinear CGCM. The initial ESV, extracted using 10 years (1990-99) of boreal winter hindcast data, has zonal wind anomalies over the western Indian Ocean, while the final ESV (at a forecast lead time of 10 days) reflects a propagation of the zonal wind anomalies to the east over the Maritime Continent an evolution that is characteristic of the MJO. A new set of ensemble hindcasts are produced for the boreal winter season from 1990 to 1999 in which the leading ESV provides the initial perturbations. The results are compared with those from a set of control hindcasts generated using random perturbations. It is shown that the ESV-based predictions have a systematically higher bivariate correlation skill in predicting the MJO compared to those using the random perturbations. Furthermore, the improvement in the skill depends on the phase of the MJO. The ESV is particularly effective in increasing the forecast skill during those phases of the MJO in which the control has low skill (with correlations increasing by as much as 0.2 at 20 25-day lead times), as well as during those times in which the MJO is weak.

  12. Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance

    Directory of Open Access Journals (Sweden)

    Ma Ruyun

    2007-01-01

    Full Text Available We study the existence of solutions of nonlinear discrete boundary value problems , , , where is the first eigenvalue of the linear problem , , , satisfies some “asymptotic nonuniform” resonance conditions, and for .

  13. PERTURBATION ESTIMATES FOR THE MAXIMAL SOLUTION OF A NONLINEAR MATRIX EQUATION

    Directory of Open Access Journals (Sweden)

    Vejdi I. Hasanov

    2017-06-01

    Full Text Available In this paper a nonlinear matrix equation is considered. Perturba- tion estimations for the maximal solution of the considered equation are obtained. The results are illustrated by the use of numerical ex- amples.

  14. Non-linear theory of elasticity and optimal design

    CERN Document Server

    Ratner, LW

    2003-01-01

    In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it

  15. Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control

    Energy Technology Data Exchange (ETDEWEB)

    Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au [Macquarie University, Department of Mathematics (Australia); Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au [Flinders University, Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and Mathematics (Australia)

    2015-04-15

    The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.

  16. Robust synchronization analysis in nonlinear stochastic cellular networks with time-varying delays, intracellular perturbations and intercellular noise.

    Science.gov (United States)

    Chen, Po-Wei; Chen, Bor-Sen

    2011-08-01

    Naturally, a cellular network consisted of a large amount of interacting cells is complex. These cells have to be synchronized in order to emerge their phenomena for some biological purposes. However, the inherently stochastic intra and intercellular interactions are noisy and delayed from biochemical processes. In this study, a robust synchronization scheme is proposed for a nonlinear stochastic time-delay coupled cellular network (TdCCN) in spite of the time-varying process delay and intracellular parameter perturbations. Furthermore, a nonlinear stochastic noise filtering ability is also investigated for this synchronized TdCCN against stochastic intercellular and environmental disturbances. Since it is very difficult to solve a robust synchronization problem with the Hamilton-Jacobi inequality (HJI) matrix, a linear matrix inequality (LMI) is employed to solve this problem via the help of a global linearization method. Through this robust synchronization analysis, we can gain a more systemic insight into not only the robust synchronizability but also the noise filtering ability of TdCCN under time-varying process delays, intracellular perturbations and intercellular disturbances. The measures of robustness and noise filtering ability of a synchronized TdCCN have potential application to the designs of neuron transmitters, on-time mass production of biochemical molecules, and synthetic biology. Finally, a benchmark of robust synchronization design in Escherichia coli repressilators is given to confirm the effectiveness of the proposed methods. Copyright © 2011 Elsevier Inc. All rights reserved.

  17. Optimal Linear Responses for Markov Chains and Stochastically Perturbed Dynamical Systems

    Science.gov (United States)

    Antown, Fadi; Dragičević, Davor; Froyland, Gary

    2018-03-01

    The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous, sequential, or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.

  18. A Homotopy-Perturbation analysis of the non-linear contaminant ...

    African Journals Online (AJOL)

    In this research work, a Homotopy-perturbation analysis of a non –linear contaminant flow equation with an initial continuous point source is provided. The equation is characterized by advection, diffusion and adsorption. We assume that the adsorption term is modeled by Freudlich Isotherm. We provide an approximation of ...

  19. Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch

    International Nuclear Information System (INIS)

    Mirus, K.A.

    1998-06-01

    In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Roessler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high-dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses

  20. Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch

    Energy Technology Data Exchange (ETDEWEB)

    Mirus, Kevin A. [Univ. of Wisconsin, Madison, WI (United States)

    1998-01-01

    In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Roessler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high-dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.

  1. Control of nonlinear systems using periodic parametric perturbations with application to a reversed field pinch

    Science.gov (United States)

    Mirus, Kevin Andrew

    In this thesis, the possibility of controlling low- and high-dimensional chaotic systems by periodically driving an accessible system parameter is examined. This method has been carried out on several numerical systems and the MST Reversed Field Pinch. The numerical systems investigated include the logistic equation, the Lorenz equations, the Rossler equations, a coupled lattice of logistic equations, a coupled lattice of Lorenz equations, the Yoshida equations, which model tearing mode fluctuations in a plasma, and a neural net model for magnetic fluctuations on MST. This method was tested on the MST by sinusoidally driving a magnetic flux through the toroidal gap of the device. Numerically, periodic drives were found to be most effective at producing limit cycle behavior or significantly reducing the dimension of the system when the perturbation frequency was near natural frequencies of unstable periodic orbits embedded in the attractor of the unperturbed system. Several different unstable periodic orbits have been stabilized in this way for the low-dimensional numerical systems, sometimes with perturbation amplitudes that were less than 5% of the nominal value of the parameter being perturbed. In high- dimensional systems, limit cycle behavior and significant decreases in the system dimension were also achieved using perturbations with frequencies near the natural unstable periodic orbit frequencies. Results for the MST were not this encouraging, most likely because of an insufficient drive amplitude, the extremely high dimension of the plasma behavior, large amounts of noise, and a lack of stationarity in the transient plasma pulses.

  2. Non-linear and signal energy optimal asymptotic filter design

    Directory of Open Access Journals (Sweden)

    Josef Hrusak

    2003-10-01

    Full Text Available The paper studies some connections between the main results of the well known Wiener-Kalman-Bucy stochastic approach to filtering problems based mainly on the linear stochastic estimation theory and emphasizing the optimality aspects of the achieved results and the classical deterministic frequency domain linear filters such as Chebyshev, Butterworth, Bessel, etc. A new non-stochastic but not necessarily deterministic (possibly non-linear alternative approach called asymptotic filtering based mainly on the concepts of signal power, signal energy and a system equivalence relation plays an important role in the presentation. Filtering error invariance and convergence aspects are emphasized in the approach. It is shown that introducing the signal power as the quantitative measure of energy dissipation makes it possible to achieve reasonable results from the optimality point of view as well. The property of structural energy dissipativeness is one of the most important and fundamental features of resulting filters. Therefore, it is natural to call them asymptotic filters. The notion of the asymptotic filter is carried in the paper as a proper tool in order to unify stochastic and non-stochastic, linear and nonlinear approaches to signal filtering.

  3. Optimal Nonlinear Pricing, Bundling Commodities and Contingent Services

    International Nuclear Information System (INIS)

    Podesta, Marion; Poudou, Jean-Christophe

    2008-01-01

    In this paper, we propose to analyze optimal nonlinear pricing when a firm offers in a bundle a commodity and a contingent service. The paper studies a mechanism design where all private information can be captured in a single scalar variable in a monopoly context. We show that to propose the package for commodity and service is less costly for the consumer, the firm has lower consumers' rent than the situation where it sells their good and contingent service under an independent pricing strategy. In fact, the possibility to use price discrimination via the supply of package is dominated by the fact that it is costly for the consumer to sign two contracts. Bundling energy and a contingent service is a profitable strategy for a energetician monopoly practising optimal nonlinear tariff. We show that the rates of the energy and the contingent service depend to the optional character of the contingent service and depend to the degree of complementarity between commodities and services. (authors)

  4. Asymptotic behaviour of optimal fraction-rational series of the perturbation theory at description of molecular rotational spectra

    International Nuclear Information System (INIS)

    Burenin, A.V.

    1994-01-01

    A possibility is shown of substantial expansion of the choice of asymptotic behaviour of optimal fraction-rational series of the perturbation theory on description of molecular rotational spectra. The expansion permits to hope for substantial improvement of results of using the conception of effective rotational hamiltonian in a fraction-rational form on the description of highly perturbed vibrational states

  5. Optimization and benchmarking of a perturbative Metropolis Monte Carlo quantum mechanics/molecular mechanics program.

    Science.gov (United States)

    Feldt, Jonas; Miranda, Sebastião; Pratas, Frederico; Roma, Nuno; Tomás, Pedro; Mata, Ricardo A

    2017-12-28

    In this work, we present an optimized perturbative quantum mechanics/molecular mechanics (QM/MM) method for use in Metropolis Monte Carlo simulations. The model adopted is particularly tailored for the simulation of molecular systems in solution but can be readily extended to other applications, such as catalysis in enzymatic environments. The electrostatic coupling between the QM and MM systems is simplified by applying perturbation theory to estimate the energy changes caused by a movement in the MM system. This approximation, together with the effective use of GPU acceleration, leads to a negligible added computational cost for the sampling of the environment. Benchmark calculations are carried out to evaluate the impact of the approximations applied and the overall computational performance.

  6. Photon attenuation correction technique in SPECT based on nonlinear optimization

    International Nuclear Information System (INIS)

    Suzuki, Shigehito; Wakabayashi, Misato; Okuyama, Keiichi; Kuwamura, Susumu

    1998-01-01

    Photon attenuation correction in SPECT was made using a nonlinear optimization theory, in which an optimum image is searched so that the sum of square errors between observed and reprojected projection data is minimized. This correction technique consists of optimization and step-width algorithms, which determine at each iteration a pixel-by-pixel directional value of search and its step-width, respectively. We used the conjugate gradient and quasi-Newton methods as the optimization algorithm, and Curry rule and the quadratic function method as the step-width algorithm. Statistical fluctuations in the corrected image due to statistical noise in the emission projection data grew as the iteration increased, depending on the combination of optimization and step-width algorithms. To suppress them, smoothing for directional values was introduced. Computer experiments and clinical applications showed a pronounced reduction in statistical fluctuations of the corrected image for all combinations. Combinations using the conjugate gradient method were superior in noise characteristic and computation time. The use of that method with the quadratic function method was optimum if noise property was regarded as important. (author)

  7. Perturbation theory

    International Nuclear Information System (INIS)

    Bartlett, R.; Kirtman, B.; Davidson, E.R.

    1978-01-01

    After noting some advantages of using perturbation theory some of the various types are related on a chart and described, including many-body nonlinear summations, quartic force-field fit for geometry, fourth-order correlation approximations, and a survey of some recent work. Alternative initial approximations in perturbation theory are also discussed. 25 references

  8. Application of perturbation theory to the non-linear vibration analysis of a string including the bending moment effects

    International Nuclear Information System (INIS)

    Esmaeilzadeh Khadem, S.; Rezaee, M.

    2001-01-01

    In this paper the large amplitude and non-linear vibration of a string is considered. The initial tension, lateral vibration amplitude, diameter and the modulus of elasticity of the string have main effects on its natural frequencies. Increasing the lateral vibration amplitude makes the assumption of constant initial tension invalid. In this case, therefore, it is impossible to use the classical equation of string with small amplitude transverse motion assumption. On the other hand, by increasing the string diameter, the bending moment effect will increase dramatically, and acts as an impressive restoring moment. Considering the effects of the bending moments, the nonlinear equation governing the large amplitude transverse vibration of a string is derived. The time dependent portion of the governing equation has the from of Duff ing equation is solved using the perturbation theory. The results of the analysis are shown in appropriate graphs, and the natural frequencies of the string due to the non-linear factors are compared with the natural frequencies of the linear vibration os a string without bending moment effects

  9. Nonlinear perturbations of systems of partial differential equations with constant coefficients

    Directory of Open Access Journals (Sweden)

    Carmen J. Vanegas

    2000-01-01

    Full Text Available In this article, we show the existence of solutions to boundary-value problems, consisting of nonlinear systems of partial differential equations with constant coefficients. For this purpose, we use the right inverse of an associated operator and a fix point argument. As illustrations, we apply this method to Helmholtz equations and to second order systems of elliptic equations.

  10. Perturbation and characterization of nonlinear processes. Progress report, November 15, 1984-November 14, 1985

    International Nuclear Information System (INIS)

    Swinney, H.L.; Swift, J.

    1985-01-01

    Methods of characterizing nonperiodic processes in nonlinear systems are being developed and tested on low dimensional mathematical models and applied to laboratory data for nonequilibrium systems, particularly the Belousov--Zhabotinskii (BZ) reaction. Methods developed for characterizing dynamical behavior are described first, followed by a discussion of the experimental work

  11. Robust and fast nonlinear optimization of diffusion MRI microstructure models.

    Science.gov (United States)

    Harms, R L; Fritz, F J; Tobisch, A; Goebel, R; Roebroeck, A

    2017-07-15

    Advances in biophysical multi-compartment modeling for diffusion MRI (dMRI) have gained popularity because of greater specificity than DTI in relating the dMRI signal to underlying cellular microstructure. A large range of these diffusion microstructure models have been developed and each of the popular models comes with its own, often different, optimization algorithm, noise model and initialization strategy to estimate its parameter maps. Since data fit, accuracy and precision is hard to verify, this creates additional challenges to comparability and generalization of results from diffusion microstructure models. In addition, non-linear optimization is computationally expensive leading to very long run times, which can be prohibitive in large group or population studies. In this technical note we investigate the performance of several optimization algorithms and initialization strategies over a few of the most popular diffusion microstructure models, including NODDI and CHARMED. We evaluate whether a single well performing optimization approach exists that could be applied to many models and would equate both run time and fit aspects. All models, algorithms and strategies were implemented on the Graphics Processing Unit (GPU) to remove run time constraints, with which we achieve whole brain dataset fits in seconds to minutes. We then evaluated fit, accuracy, precision and run time for different models of differing complexity against three common optimization algorithms and three parameter initialization strategies. Variability of the achieved quality of fit in actual data was evaluated on ten subjects of each of two population studies with a different acquisition protocol. We find that optimization algorithms and multi-step optimization approaches have a considerable influence on performance and stability over subjects and over acquisition protocols. The gradient-free Powell conjugate-direction algorithm was found to outperform other common algorithms in terms of

  12. A small perturbation based optimization approach for the frequency placement of high aspect ratio wings

    Science.gov (United States)

    Goltsch, Mandy

    Design denotes the transformation of an identified need to its physical embodiment in a traditionally iterative approach of trial and error. Conceptual design plays a prominent role but an almost infinite number of possible solutions at the outset of design necessitates fast evaluations. The corresponding practice of empirical equations and low fidelity analyses becomes obsolete in the light of novel concepts. Ever increasing system complexity and resource scarcity mandate new approaches to adequately capture system characteristics. Contemporary concerns in atmospheric science and homeland security created an operational need for unconventional configurations. Unmanned long endurance flight at high altitudes offers a unique showcase for the exploration of new design spaces and the incidental deficit of conceptual modeling and simulation capabilities. Structural and aerodynamic performance requirements necessitate light weight materials and high aspect ratio wings resulting in distinct structural and aeroelastic response characteristics that stand in close correlation with natural vibration modes. The present research effort evolves around the development of an efficient and accurate optimization algorithm for high aspect ratio wings subject to natural frequency constraints. Foundational corner stones are beam dimensional reduction and modal perturbation redesign. Local and global analyses inherent to the former suggest corresponding levels of local and global optimization. The present approach departs from this suggestion. It introduces local level surrogate models to capacitate a methodology that consists of multi level analyses feeding into a single level optimization. The innovative heart of the new algorithm originates in small perturbation theory. A sequence of small perturbation solutions allows the optimizer to make incremental movements within the design space. It enables a directed search that is free of costly gradients. System matrices are decomposed

  13. Optimal Detection of a Localized Perturbation in Random Networks of Integrate-and-Fire Neurons

    Science.gov (United States)

    Bernardi, Davide; Lindner, Benjamin

    2017-06-01

    Experimental and theoretical studies suggest that cortical networks are chaotic and coding relies on averages over large populations. However, there is evidence that rats can respond to the short stimulation of a single cortical cell, a theoretically unexplained fact. We study effects of single-cell stimulation on a large recurrent network of integrate-and-fire neurons and propose a simple way to detect the perturbation. Detection rates obtained from simulations and analytical estimates are similar to experimental response rates if the readout is slightly biased towards specific neurons. Near-optimal detection is attained for a broad range of intermediate values of the mean coupling between neurons.

  14. Nonlinear Burn Control and Operating Point Optimization in ITER

    Science.gov (United States)

    Boyer, Mark; Schuster, Eugenio

    2013-10-01

    Control of the fusion power through regulation of the plasma density and temperature will be essential for achieving and maintaining desired operating points in fusion reactors and burning plasma experiments like ITER. In this work, a volume averaged model for the evolution of the density of energy, deuterium and tritium fuel ions, alpha-particles, and impurity ions is used to synthesize a multi-input multi-output nonlinear feedback controller for stabilizing and modulating the burn condition. Adaptive control techniques are used to account for uncertainty in model parameters, including particle confinement times and recycling rates. The control approach makes use of the different possible methods for altering the fusion power, including adjusting the temperature through auxiliary heating, modulating the density and isotopic mix through fueling, and altering the impurity density through impurity injection. Furthermore, a model-based optimization scheme is proposed to drive the system as close as possible to desired fusion power and temperature references. Constraints are considered in the optimization scheme to ensure that, for example, density and beta limits are avoided, and that optimal operation is achieved even when actuators reach saturation. Supported by the NSF CAREER award program (ECCS-0645086).

  15. ARSTEC, Nonlinear Optimization Program Using Random Search Method

    International Nuclear Information System (INIS)

    Rasmuson, D. M.; Marshall, N. H.

    1979-01-01

    1 - Description of problem or function: The ARSTEC program was written to solve nonlinear, mixed integer, optimization problems. An example of such a problem in the nuclear industry is the allocation of redundant parts in the design of a nuclear power plant to minimize plant unavailability. 2 - Method of solution: The technique used in ARSTEC is the adaptive random search method. The search is started from an arbitrary point in the search region and every time a point that improves the objective function is found, the search region is centered at that new point. 3 - Restrictions on the complexity of the problem: Presently, the maximum number of independent variables allowed is 10. This can be changed by increasing the dimension of the arrays

  16. Robust C subroutines for non-linear optimization

    DEFF Research Database (Denmark)

    Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun

    2004-01-01

    This report presents a package of robust and easy-to-use C subroutines for solving unconstrained and constrained non-linear optimization problems. The intention is that the routines should use the currently best algorithms available. All routines have standardized calls, and the user does not have...... by changing 1 to 0. The present report is a new and updated version of a previous report NI-91-03 with the same title, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated from Fortran to C. The reason for writing the present report is that some...... of the C subroutines have been replaced by more effective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modi ed to some extent. For a description of the original Fortran subroutines see the report [17]. The software...

  17. Robust Homography Estimation Based on Nonlinear Least Squares Optimization

    Directory of Open Access Journals (Sweden)

    Wei Mou

    2014-01-01

    Full Text Available The homography between image pairs is normally estimated by minimizing a suitable cost function given 2D keypoint correspondences. The correspondences are typically established using descriptor distance of keypoints. However, the correspondences are often incorrect due to ambiguous descriptors which can introduce errors into following homography computing step. There have been numerous attempts to filter out these erroneous correspondences, but it is unlikely to always achieve perfect matching. To deal with this problem, we propose a nonlinear least squares optimization approach to compute homography such that false matches have no or little effect on computed homography. Unlike normal homography computation algorithms, our method formulates not only the keypoints’ geometric relationship but also their descriptor similarity into cost function. Moreover, the cost function is parametrized in such a way that incorrect correspondences can be simultaneously identified while the homography is computed. Experiments show that the proposed approach can perform well even with the presence of a large number of outliers.

  18. Stabilization of business cycles of finance agents using nonlinear optimal control

    Science.gov (United States)

    Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

    2017-11-01

    Stabilization of the business cycles of interconnected finance agents is performed with the use of a new nonlinear optimal control method. First, the dynamics of the interacting finance agents and of the associated business cycles is described by a modeled of coupled nonlinear oscillators. Next, this dynamic model undergoes approximate linearization round a temporary operating point which is defined by the present value of the system's state vector and the last value of the control inputs vector that was exerted on it. The linearization procedure is based on Taylor series expansion of the dynamic model and on the computation of Jacobian matrices. The modelling error, which is due to the truncation of higher-order terms in the Taylor series expansion is considered as a disturbance which is compensated by the robustness of the control loop. Next, for the linearized model of the interacting finance agents, an H-infinity feedback controller is designed. The computation of the feedback control gain requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control scheme satisfies an H-infinity tracking performance criterion, which signifies elevated robustness against modelling uncertainty and external perturbations. Moreover, under moderate conditions the global asymptotic stability features of the control loop are proven.

  19. New Delay-Dependent Stability Criteria for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

    Directory of Open Access Journals (Sweden)

    Hamid Reza Karimi

    2009-01-01

    Full Text Available The problem of stability analysis for a class of neutral systems with mixed time-varying neutral, discrete and distributed delays and nonlinear parameter perturbations is addressed. By introducing a novel Lyapunov-Krasovskii functional and combining the descriptor model transformation, the Leibniz-Newton formula, some free-weighting matrices, and a suitable change of variables, new sufficient conditions are established for the stability of the considered system, which are neutral-delay-dependent, discrete-delay-range-dependent, and distributed-delay-dependent. The conditions are presented in terms of linear matrix inequalities (LMIs and can be efficiently solved using convex programming techniques. Two numerical examples are given to illustrate the efficiency of the proposed method.

  20. Exponential L2-L∞ Filtering for a Class of Stochastic System with Mixed Delays and Nonlinear Perturbations

    Directory of Open Access Journals (Sweden)

    Zhaohui Chen

    2013-01-01

    Full Text Available The delay-dependent exponential L2-L∞ performance analysis and filter design are investigated for stochastic systems with mixed delays and nonlinear perturbations. Based on the delay partitioning and integral partitioning technique, an improved delay-dependent sufficient condition for the existence of the L2-L∞ filter is established, by choosing an appropriate Lyapunov-Krasovskii functional and constructing a new integral inequality. The full-order filter design approaches are obtained in terms of linear matrix inequalities (LMIs. By solving the LMIs and using matrix decomposition, the desired filter gains can be obtained, which ensure that the filter error system is exponentially stable with a prescribed L2-L∞ performance γ. Numerical examples are provided to illustrate the effectiveness and significant improvement of the proposed method.

  1. Analytical theory and nonlinear δf perturbative simulations of temperature anisotropy instability in intense charged particle beams

    Directory of Open Access Journals (Sweden)

    Edward A. Startsev

    2003-08-01

    Full Text Available In plasmas with strongly anisotropic distribution functions (T_{∥b}/T_{⊥b}≪1 a Harris-like collective instability may develop if there is sufficient coupling between the transverse and longitudinal degrees of freedom. Such anisotropies develop naturally in accelerators and may lead to a deterioration of beam quality. This paper extends previous numerical studies [E. A. Startsev, R. C. Davidson, and H. Qin, Phys. Plasmas 9, 3138 (2002] of the stability properties of intense non-neutral charged particle beams with large temperature anisotropy (T_{⊥b}≫T_{∥b} to allow for nonaxisymmetric perturbations with ∂/∂θ≠0. The most unstable modes are identified, and their eigenfrequencies, radial mode structure, and nonlinear dynamics are determined. The simulation results clearly show that moderately intense beams with s_{b}=ω[over ^]_{pb}^{2}/2γ_{b}^{2}ω_{β⊥}^{2}≳0.5 are linearly unstable to short-wavelength perturbations with k_{z}^{2}r_{b}^{2}≳1, provided the ratio of longitudinal and transverse temperatures is smaller than some threshold value. Here, ω[over ^]_{pb}^{2}=4πn[over ^]_{b}e_{b}^{2}/γ_{b}m_{b} is the relativistic plasma frequency squared, and ω_{β⊥} is the betatron frequency associated with the applied smooth-focusing field. A theoretical model is developed based on the Vlasov-Maxwell equations which describes the essential features of the linear stages of instability. Both the simulations and the analytical theory predict that the dipole mode (azimuthal mode number m=1 is the most unstable mode. In the nonlinear stage, tails develop in the longitudinal momentum distribution function, and the kinetic instability saturates due to resonant wave-particle interactions.

  2. Propagation of nonlinear shock waves for the generalised Oskolkov equation and its dynamic motions in the presence of an external periodic perturbation

    Science.gov (United States)

    Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid

    2018-06-01

    Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.

  3. Adaptive control for a class of nonlinear complex dynamical systems with uncertain complex parameters and perturbations.

    Directory of Open Access Journals (Sweden)

    Jian Liu

    Full Text Available In this paper, adaptive control is extended from real space to complex space, resulting in a new control scheme for a class of n-dimensional time-dependent strict-feedback complex-variable chaotic (hyperchaotic systems (CVCSs in the presence of uncertain complex parameters and perturbations, which has not been previously reported in the literature. In detail, we have developed a unified framework for designing the adaptive complex scalar controller to ensure this type of CVCSs asymptotically stable and for selecting complex update laws to estimate unknown complex parameters. In particular, combining Lyapunov functions dependent on complex-valued vectors and back-stepping technique, sufficient criteria on stabilization of CVCSs are derived in the sense of Wirtinger calculus in complex space. Finally, numerical simulation is presented to validate our theoretical results.

  4. Adaptive control for a class of nonlinear complex dynamical systems with uncertain complex parameters and perturbations.

    Science.gov (United States)

    Liu, Jian; Liu, Kexin; Liu, Shutang

    2017-01-01

    In this paper, adaptive control is extended from real space to complex space, resulting in a new control scheme for a class of n-dimensional time-dependent strict-feedback complex-variable chaotic (hyperchaotic) systems (CVCSs) in the presence of uncertain complex parameters and perturbations, which has not been previously reported in the literature. In detail, we have developed a unified framework for designing the adaptive complex scalar controller to ensure this type of CVCSs asymptotically stable and for selecting complex update laws to estimate unknown complex parameters. In particular, combining Lyapunov functions dependent on complex-valued vectors and back-stepping technique, sufficient criteria on stabilization of CVCSs are derived in the sense of Wirtinger calculus in complex space. Finally, numerical simulation is presented to validate our theoretical results.

  5. Nonlinear power spectrum from resummed perturbation theory: a leap beyond the BAO scale

    International Nuclear Information System (INIS)

    Anselmi, Stefano; Pietroni, Massimo

    2012-01-01

    A new computational scheme for the nonlinear cosmological matter power spectrum (PS) is presented. Our method is based on evolution equations in time, which can be cast in a form extremely convenient for fast numerical evaluations. A nonlinear PS is obtained in a time comparable to that needed for a simple 1-loop computation, and the numerical implementation is very simple. Our results agree with N-body simulations at the percent level in the BAO range of scales, and at the few-percent level up to k ≅ 1 h/Mpc at z∼>0.5, thereby opening the possibility of applying this tool to scales interesting for weak lensing. We clarify the approximations inherent to this approach as well as its relations to previous ones, such as the Time Renormalization Group, and the multi-point propagator expansion. We discuss possible lines of improvements of the method and its intrinsic limitations by multi streaming at small scales and low redshifts

  6. In-core nuclear fuel management optimization of VVER1000 using perturbation theory

    International Nuclear Information System (INIS)

    Hosseini, Mohammad; Vosoughi, Naser

    2011-01-01

    In-core nuclear fuel management is one of the most important concerns in the design of nuclear reactors. The two main goals in core fuel loading pattern design optimization are maximizing the core effective multiplication factor in order to extract the maximum energy, and keeping the local power peaking factor lower than a predetermined value to maintain fuel integrity. Because of the numerous possible patterns of the fuel assemblies in the reactor core, finding the best configuration is so important and complex. Different methods for optimization of fuel loading pattern in the core have been introduced so far. In this study, a software is programmed in C ⧣ language to find an order of the fuel loading pattern of the VVER-1000 reactor core using the perturbation theory. Our optimization method is based on minimizing the radial power peaking factor. The optimization process lunches by considering the initial loading pattern and the specifications of the fuel assemblies which are given as the input of the software. It shall be noticed that the designed algorithm is performed by just shuffling the fuel assemblies. The obtained results by employing the mentioned method on a typical reactor reveal that this method has a high precision in achieving a pattern with an allowable radial power peaking factor. (author)

  7. Design and optimization of carbon-nanotube-material/dielectric hybrid nonlinear optical waveguides

    International Nuclear Information System (INIS)

    Zhao, Xin; Zheng, Zheng; Lu, Zhiting; Zhu, Jinsong; Zhou, Tao

    2011-01-01

    The nonlinear optical characteristics of highly nonlinear waveguides utilizing carbon nanotube composite materials are investigated theoretically. The extremely high nonlinearity and relatively high loss of the carbon nanotube materials are shown to greatly affect the performance of such waveguides for nonlinear optical applications, in contrast to waveguides using conventional nonlinear materials. Different configurations based on applying the carbon nanotube materials to the popular ridge and buried waveguides are thoroughly studied, and the optimal geometries are derived through simulations. It is shown that, though the nonlinear coefficient is often huge for these waveguides, the loss characteristics can significantly limit the maximum achievable accumulated nonlinearity, e.g. the maximum nonlinear phase shift. Our results suggest that SOI-based high-index-contrast, carbon nanotube cladding waveguides, rather than the currently demonstrated low-contrast waveguides, could hold the promise of achieving significantly higher accumulated nonlinearity

  8. A Study on the Analysis and Optimal Control of Nonlinear Systems via Walsh Function

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Jin Tae; Kim, Tai Hoon; Ahn, Doo Soo [Sungkyunkwan University (Korea); Lee, Myung Kyu [Kyungsung University (Korea)

    2000-07-01

    This paper presents the new adaptive optimal scheme for the nonlinear systems, which is based on the Picard's iterative approximation and fast Walsh transform. It is well known that the Walsh function approach method is very difficult to apply for the analysis and optimal control of nonlinear systems. However, these problems can be easily solved by the improvement of the previous adaptive optimal scheme. The proposes method is easily applicable to the analysis and optimal control of nonlinear systems. (author). 15 refs., 6 figs., 1 tab.

  9. NonLinear Parallel OPtimization Tool, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — CU Aerospace, in partnership with the University of Illinois propose the further development of a new sparse nonlinear programming architecture that exploits...

  10. From Nonlinear Optimization to Convex Optimization through Firefly Algorithm and Indirect Approach with Applications to CAD/CAM

    Directory of Open Access Journals (Sweden)

    Akemi Gálvez

    2013-01-01

    Full Text Available Fitting spline curves to data points is a very important issue in many applied fields. It is also challenging, because these curves typically depend on many continuous variables in a highly interrelated nonlinear way. In general, it is not possible to compute these parameters analytically, so the problem is formulated as a continuous nonlinear optimization problem, for which traditional optimization techniques usually fail. This paper presents a new bioinspired method to tackle this issue. In this method, optimization is performed through a combination of two techniques. Firstly, we apply the indirect approach to the knots, in which they are not initially the subject of optimization but precomputed with a coarse approximation scheme. Secondly, a powerful bioinspired metaheuristic technique, the firefly algorithm, is applied to optimization of data parameterization; then, the knot vector is refined by using De Boor’s method, thus yielding a better approximation to the optimal knot vector. This scheme converts the original nonlinear continuous optimization problem into a convex optimization problem, solved by singular value decomposition. Our method is applied to some illustrative real-world examples from the CAD/CAM field. Our experimental results show that the proposed scheme can solve the original continuous nonlinear optimization problem very efficiently.

  11. A collective variable approach and stabilization for dispersion-managed optical solitons in the quintic complex Ginzburg-Landau equation as perturbations of the nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Fewo, S I; Kenfack-Jiotsa, A; Kofane, T C

    2006-01-01

    With the help of the one-dimensional quintic complex Ginzburg-Landau equation (CGLE) as perturbations of the nonlinear Schroedinger equation (NLSE), we derive the equations of motion of pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fibre optic links. The equations obtained are investigated numerically in order to view the evolution of pulse parameters along the propagation distance, and also to analyse effects of initial amplitude and width on the propagating pulse. Nonlinear gain is shown to be beneficial in stabilizing DM solitons. A fully numerical simulation of the one-dimensional quintic CGLE as perturbations of NLSE finally tests the results of the CV theory. A good agreement is observed between both methods

  12. FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

    Institute of Scientific and Technical Information of China (English)

    朱卫平; 黄黔

    2002-01-01

    In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinearbehaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite elementare expanded by taking root-mean-square value of circumferential strains of the shells as aperturbation parameter. The load steps and the iteration times are not cs arbitrary andunpredictable as in usual nonlinear analysis. Instead, there are certain relations betweenthe load steps and the displacement increments, and no need of iteration for each loadstep. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander' s nonlinear geometric equations of moderate smallrotation are used, and the shell made of more than one material ply is also considered.

  13. Nonlinear dynamic simulation of optimal depletion of crude oil in the lower 48 United States

    International Nuclear Information System (INIS)

    Ruth, M.; Cleveland, C.J.

    1993-01-01

    This study combines the economic theory of optimal resource use with econometric estimates of demand and supply parameters to develop a nonlinear dynamic model of crude oil exploration, development, and production in the lower 48 United States. The model is simulated with the graphical programming language STELLA, for the years 1985 to 2020. The procedure encourages use of economic theory and econometrics in combination with nonlinear dynamic simulation to enhance our understanding of complex interactions present in models of optimal resource use. (author)

  14. Optimization of lift gas allocation in a gas lifted oil field as non-linear optimization problem

    Directory of Open Access Journals (Sweden)

    Roshan Sharma

    2012-01-01

    Full Text Available Proper allocation and distribution of lift gas is necessary for maximizing total oil production from a field with gas lifted oil wells. When the supply of the lift gas is limited, the total available gas should be optimally distributed among the oil wells of the field such that the total production of oil from the field is maximized. This paper describes a non-linear optimization problem with constraints associated with the optimal distribution of the lift gas. A non-linear objective function is developed using a simple dynamic model of the oil field where the decision variables represent the lift gas flow rate set points of each oil well of the field. The lift gas optimization problem is solved using the emph'fmincon' solver found in MATLAB. As an alternative and for verification, hill climbing method is utilized for solving the optimization problem. Using both of these methods, it has been shown that after optimization, the total oil production is increased by about 4. For multiple oil wells sharing lift gas from a common source, a cascade control strategy along with a nonlinear steady state optimizer behaves as a self-optimizing control structure when the total supply of lift gas is assumed to be the only input disturbance present in the process. Simulation results show that repeated optimization performed after the first time optimization under the presence of the input disturbance has no effect in the total oil production.

  15. SYNCHRONIZATION OF HETEROGENEOUS OSCILLATORS UNDER NETWORK MODIFICATIONS: PERTURBATION AND OPTIMIZATION OF THE SYNCHRONY ALIGNMENT FUNCTION

    Science.gov (United States)

    Taylor, Dane; Skardal, Per Sebastian; Sun, Jie

    2016-01-01

    Synchronization is central to many complex systems in engineering physics (e.g., the power-grid, Josephson junction circuits, and electro-chemical oscillators) and biology (e.g., neuronal, circadian, and cardiac rhythms). Despite these widespread applications—for which proper functionality depends sensitively on the extent of synchronization—there remains a lack of understanding for how systems can best evolve and adapt to enhance or inhibit synchronization. We study how network modifications affect the synchronization properties of network-coupled dynamical systems that have heterogeneous node dynamics (e.g., phase oscillators with non-identical frequencies), which is often the case for real-world systems. Our approach relies on a synchrony alignment function (SAF) that quantifies the interplay between heterogeneity of the network and of the oscillators and provides an objective measure for a system’s ability to synchronize. We conduct a spectral perturbation analysis of the SAF for structural network modifications including the addition and removal of edges, which subsequently ranks the edges according to their importance to synchronization. Based on this analysis, we develop gradient-descent algorithms to efficiently solve optimization problems that aim to maximize phase synchronization via network modifications. We support these and other results with numerical experiments. PMID:27872501

  16. Distributed Optimization for a Class of Nonlinear Multiagent Systems With Disturbance Rejection.

    Science.gov (United States)

    Wang, Xinghu; Hong, Yiguang; Ji, Haibo

    2016-07-01

    The paper studies the distributed optimization problem for a class of nonlinear multiagent systems in the presence of external disturbances. To solve the problem, we need to achieve the optimal multiagent consensus based on local cost function information and neighboring information and meanwhile to reject local disturbance signals modeled by an exogenous system. With convex analysis and the internal model approach, we propose a distributed optimization controller for heterogeneous and nonlinear agents in the form of continuous-time minimum-phase systems with unity relative degree. We prove that the proposed design can solve the exact optimization problem with rejecting disturbances.

  17. Estimation of dynamic reactivity using an H∞ optimal filter with a nonlinear term

    International Nuclear Information System (INIS)

    Suzuki, Katsuo; Watanabe, Koiti

    1996-01-01

    A method of nonlinear filtering is applied to the problem of estimating the dynamic reactivity of a nonlinear reactor system. The nonlinear filtering algorithm developed is a simple modification of a linear H ∞ optimal filter with a nonlinear feedback loop added. The linear filter is designed on the basis of a linearized dynamical system model that consists of linearized point reactor kinetic equations and a reactivity state equation driven by a fictitious signal. The latter is artificially introduced to deal with the reactivity as a state variable. The results of the computer simulation show that the nonlinear filtering algorithm can be applied to estimate the dynamic reactivity of the nonlinear reactor system, even under relatively large reactivity disturbances

  18. Optimal Control Problems for Nonlinear Variational Evolution Inequalities

    Directory of Open Access Journals (Sweden)

    Eun-Young Ju

    2013-01-01

    Full Text Available We deal with optimal control problems governed by semilinear parabolic type equations and in particular described by variational inequalities. We will also characterize the optimal controls by giving necessary conditions for optimality by proving the Gâteaux differentiability of solution mapping on control variables.

  19. NonLinear Parallel OPtimization Tool, Phase II

    Data.gov (United States)

    National Aeronautics and Space Administration — The technological advancement proposed is a novel large-scale Noninear Parallel OPtimization Tool (NLPAROPT). This software package will eliminate the computational...

  20. Wavefront optimized nonlinear microscopy of ex vivo human retinas

    Science.gov (United States)

    Gualda, Emilio J.; Bueno, Juan M.; Artal, Pablo

    2010-03-01

    A multiphoton microscope incorporating a Hartmann-Shack (HS) wavefront sensor to control the ultrafast laser beam's wavefront aberrations has been developed. This instrument allowed us to investigate the impact of the laser beam aberrations on two-photon autofluorescence imaging of human retinal tissues. We demonstrated that nonlinear microscopy images are improved when laser beam aberrations are minimized by realigning the laser system cavity while wavefront controlling. Nonlinear signals from several human retinal anatomical features have been detected for the first time, without the need of fixation or staining procedures. Beyond the improved image quality, this approach reduces the required excitation power levels, minimizing the side effects of phototoxicity within the imaged sample. In particular, this may be important to study the physiology and function of the healthy and diseased retina.

  1. Self-optimizing robust nonlinear model predictive control

    NARCIS (Netherlands)

    Lazar, M.; Heemels, W.P.M.H.; Jokic, A.; Thoma, M.; Allgöwer, F.; Morari, M.

    2009-01-01

    This paper presents a novel method for designing robust MPC schemes that are self-optimizing in terms of disturbance attenuation. The method employs convex control Lyapunov functions and disturbance bounds to optimize robustness of the closed-loop system on-line, at each sampling instant - a unique

  2. Non-Linear Transaction Costs Inclusion in Mean-Variance Optimization

    Directory of Open Access Journals (Sweden)

    Christian Johannes Zimmer

    2005-12-01

    Full Text Available In this article we propose a new way to include transaction costs into a mean-variance portfolio optimization. We consider brokerage fees, bid/ask spread and the market impact of the trade. A pragmatic algorithm is proposed, which approximates the optimal portfolio, and we can show that is converges in the absence of restrictions. Using Brazilian financial market data we compare our approximation algorithm with the results of a non-linear optimizer.

  3. Optimization of hardening/softening behavior of plane frame structures using nonlinear normal modes

    DEFF Research Database (Denmark)

    Dou, Suguang; Jensen, Jakob Søndergaard

    2016-01-01

    Devices that exploit essential nonlinear behavior such as hardening/softening and inter-modal coupling effects are increasingly used in engineering and fundamental studies. Based on nonlinear normal modes, we present a gradient-based structural optimization method for tailoring the hardening...... involving plane frame structures where the hardening/softening behavior is qualitatively and quantitatively tuned by simple changes in the geometry of the structures....

  4. A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition

    OpenAIRE

    De Sterck, Hans

    2011-01-01

    A new algorithm is presented for computing a canonical rank-R tensor approximation that has minimal distance to a given tensor in the Frobenius norm, where the canonical rank-R tensor consists of the sum of R rank-one components. Each iteration of the method consists of three steps. In the first step, a tentative new iterate is generated by a stand-alone one-step process, for which we use alternating least squares (ALS). In the second step, an accelerated iterate is generated by a nonlinear g...

  5. Simulation-based optimal Bayesian experimental design for nonlinear systems

    KAUST Repository

    Huan, Xun; Marzouk, Youssef M.

    2013-01-01

    The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical

  6. Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications

    Science.gov (United States)

    2015-06-24

    WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Arizona State University School of Mathematical & Statistical Sciences 901 S...SUPPLEMENTARY NOTES 14. ABSTRACT The major goals of this project were completed: the exact solution of previously unsolved challenging combinatorial optimization... combinatorial optimization problem, the Directional Sensor Problem, was solved in two ways. First, heuristically in an engineering fashion and second, exactly

  7. A Parameter Estimation Method for Nonlinear Systems Based on Improved Boundary Chicken Swarm Optimization

    Directory of Open Access Journals (Sweden)

    Shaolong Chen

    2016-01-01

    Full Text Available Parameter estimation is an important problem in nonlinear system modeling and control. Through constructing an appropriate fitness function, parameter estimation of system could be converted to a multidimensional parameter optimization problem. As a novel swarm intelligence algorithm, chicken swarm optimization (CSO has attracted much attention owing to its good global convergence and robustness. In this paper, a method based on improved boundary chicken swarm optimization (IBCSO is proposed for parameter estimation of nonlinear systems, demonstrated and tested by Lorenz system and a coupling motor system. Furthermore, we have analyzed the influence of time series on the estimation accuracy. Computer simulation results show it is feasible and with desirable performance for parameter estimation of nonlinear systems.

  8. Optimization Formulations for the Maximum Nonlinear Buckling Load of Composite Structures

    DEFF Research Database (Denmark)

    Lindgaard, Esben; Lund, Erik

    2011-01-01

    This paper focuses on criterion functions for gradient based optimization of the buckling load of laminated composite structures considering different types of buckling behaviour. A local criterion is developed, and is, together with a range of local and global criterion functions from literature......, benchmarked on a number of numerical examples of laminated composite structures for the maximization of the buckling load considering fiber angle design variables. The optimization formulations are based on either linear or geometrically nonlinear analysis and formulated as mathematical programming problems...... solved using gradient based techniques. The developed local criterion is formulated such it captures nonlinear effects upon loading and proves useful for both analysis purposes and as a criterion for use in nonlinear buckling optimization. © 2010 Springer-Verlag....

  9. Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

    Science.gov (United States)

    Lan, C. Edward; Ge, Fuying

    1989-01-01

    Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

  10. Complex fluid network optimization and control integrative design based on nonlinear dynamic model

    International Nuclear Information System (INIS)

    Sui, Jinxue; Yang, Li; Hu, Yunan

    2016-01-01

    In view of distribution according to complex fluid network’s needs, this paper proposed one optimization computation method of the nonlinear programming mathematical model based on genetic algorithm. The simulation result shows that the overall energy consumption of the optimized fluid network has a decrease obviously. The control model of the fluid network is established based on nonlinear dynamics. We design the control law based on feedback linearization, take the optimal value by genetic algorithm as the simulation data, can also solve the branch resistance under the optimal value. These resistances can provide technical support and reference for fluid network design and construction, so can realize complex fluid network optimization and control integration design.

  11. Optimal design of geometrically nonlinear shells of revolution with using the mixed finite element method

    Science.gov (United States)

    Stupishin, L. U.; Nikitin, K. E.; Kolesnikov, A. G.

    2018-02-01

    The article is concerned with a methodology of optimal design of geometrically nonlinear (flexible) shells of revolution of minimum weight with strength, stability and strain constraints. The problem of optimal design with constraints is reduced to the problem of unconstrained minimization using the penalty functions method. Stress-strain state of shell is determined within the geometrically nonlinear deformation theory. A special feature of the methodology is the use of a mixed finite-element formulation based on the Galerkin method. Test problems for determining the optimal form and thickness distribution of a shell of minimum weight are considered. The validity of the results obtained using the developed methodology is analyzed, and the efficiency of various optimization algorithms is compared to solve the set problem. The developed methodology has demonstrated the possibility and accuracy of finding the optimal solution.

  12. Galerkin v. discrete-optimal projection in nonlinear model reduction

    Energy Technology Data Exchange (ETDEWEB)

    Carlberg, Kevin Thomas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Barone, Matthew Franklin [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Antil, Harbir [George Mason Univ., Fairfax, VA (United States)

    2015-04-01

    Discrete-optimal model-reduction techniques such as the Gauss{Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible ow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform projection at the time-continuous level, while discrete-optimal techniques do so at the time-discrete level. This work provides a detailed theoretical and experimental comparison of the two techniques for two common classes of time integrators: linear multistep schemes and Runge{Kutta schemes. We present a number of new ndings, including conditions under which the discrete-optimal ROM has a time-continuous representation, conditions under which the two techniques are equivalent, and time-discrete error bounds for the two approaches. Perhaps most surprisingly, we demonstrate both theoretically and experimentally that decreasing the time step does not necessarily decrease the error for the discrete-optimal ROM; instead, the time step should be `matched' to the spectral content of the reduced basis. In numerical experiments carried out on a turbulent compressible- ow problem with over one million unknowns, we show that increasing the time step to an intermediate value decreases both the error and the simulation time of the discrete-optimal reduced-order model by an order of magnitude.

  13. Nonlinear Shaping Architecture Designed with Using Evolutionary Structural Optimization Tools

    Science.gov (United States)

    Januszkiewicz, Krystyna; Banachowicz, Marta

    2017-10-01

    The paper explores the possibilities of using Structural Optimization Tools (ESO) digital tools in an integrated structural and architectural design in response to the current needs geared towards sustainability, combining ecological and economic efficiency. The first part of the paper defines the Evolutionary Structural Optimization tools, which were developed specifically for engineering purposes using finite element analysis as a framework. The development of ESO has led to several incarnations, which are all briefly discussed (Additive ESO, Bi-directional ESO, Extended ESO). The second part presents result of using these tools in structural and architectural design. Actual building projects which involve optimization as a part of the original design process will be presented (Crematorium in Kakamigahara Gifu, Japan, 2006 SANAA“s Learning Centre, EPFL in Lausanne, Switzerland 2008 among others). The conclusion emphasizes that the structural engineering and architectural design mean directing attention to the solutions which are used by Nature, designing works optimally shaped and forming their own environments. Architectural forms never constitute the optimum shape derived through a form-finding process driven only by structural optimization, but rather embody and integrate a multitude of parameters. It might be assumed that there is a similarity between these processes in nature and the presented design methods. Contemporary digital methods make the simulation of such processes possible, and thus enable us to refer back to the empirical methods of previous generations.

  14. Optimal control of nonlinear continuous-time systems in strict-feedback form.

    Science.gov (United States)

    Zargarzadeh, Hassan; Dierks, Travis; Jagannathan, Sarangapani

    2015-10-01

    This paper proposes a novel optimal tracking control scheme for nonlinear continuous-time systems in strict-feedback form with uncertain dynamics. The optimal tracking problem is transformed into an equivalent optimal regulation problem through a feedforward adaptive control input that is generated by modifying the standard backstepping technique. Subsequently, a neural network-based optimal control scheme is introduced to estimate the cost, or value function, over an infinite horizon for the resulting nonlinear continuous-time systems in affine form when the internal dynamics are unknown. The estimated cost function is then used to obtain the optimal feedback control input; therefore, the overall optimal control input for the nonlinear continuous-time system in strict-feedback form includes the feedforward plus the optimal feedback terms. It is shown that the estimated cost function minimizes the Hamilton-Jacobi-Bellman estimation error in a forward-in-time manner without using any value or policy iterations. Finally, optimal output feedback control is introduced through the design of a suitable observer. Lyapunov theory is utilized to show the overall stability of the proposed schemes without requiring an initial admissible controller. Simulation examples are provided to validate the theoretical results.

  15. New Delay-Dependent Robust Exponential Stability Criteria of LPD Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

    Directory of Open Access Journals (Sweden)

    Sirada Pinjai

    2013-01-01

    Full Text Available This paper is concerned with the problem of robust exponential stability for linear parameter-dependent (LPD neutral systems with mixed time-varying delays and nonlinear perturbations. Based on a new parameter-dependent Lyapunov-Krasovskii functional, Leibniz-Newton formula, decomposition technique of coefficient matrix, free-weighting matrices, Cauchy’s inequality, modified version of Jensen’s inequality, model transformation, and linear matrix inequality technique, new delay-dependent robust exponential stability criteria are established in terms of linear matrix inequalities (LMIs. Numerical examples are given to show the effectiveness and less conservativeness of the proposed methods.

  16. Nonlinear Non-convex Optimization of Hydraulic Networks

    DEFF Research Database (Denmark)

    Tahavori, Maryamsadat; Kallesøe, Carsten; Leth, John-Josef

    2013-01-01

    Pressure management in water supply systems is an effective way to reduce the leakage in a system. In this paper, the pressure management and the reduction of power consumption of a water supply system is formulated as an optimization problem. The problem is to minimize the power consumption in p....... They can be used for a general hydraulic networks to optimize the leakage and energy consumption and to satisfy the demands at the end-users. The results in this paper show that the power consumption of the pumps is reduced.......Pressure management in water supply systems is an effective way to reduce the leakage in a system. In this paper, the pressure management and the reduction of power consumption of a water supply system is formulated as an optimization problem. The problem is to minimize the power consumption...

  17. Use Residual Correction Method and Monotone Iterative Technique to Calculate the Upper and Lower Approximate Solutions of Singularly Perturbed Non-linear Boundary Value Problems

    Directory of Open Access Journals (Sweden)

    Chi-Chang Wang

    2013-09-01

    Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.

  18. Optimal Control Of Nonlinear Wave Energy Point Converters

    DEFF Research Database (Denmark)

    Nielsen, Søren R.K.; Zhou, Qiang; Kramer, Morten

    2013-01-01

    idea behind the control strategy is to enforce the stationary velocity response of the absorber into phase with the wave excitation force at any time. The controller is optimal under monochromatic wave excitation. It is demonstrated that the devised causal controller, in plane irregular sea states...

  19. Nonlinear Dynamic Analysis and Optimization of Closed-Form Planetary Gear System

    Directory of Open Access Journals (Sweden)

    Qilin Huang

    2013-01-01

    Full Text Available A nonlinear purely rotational dynamic model of a multistage closed-form planetary gear set formed by two simple planetary stages is proposed in this study. The model includes time-varying mesh stiffness, excitation fluctuation and gear backlash nonlinearities. The nonlinear differential equations of motion are solved numerically using variable step-size Runge-Kutta. In order to obtain function expression of optimization objective, the nonlinear differential equations of motion are solved analytically using harmonic balance method (HBM. Based on the analytical solution of dynamic equations, the optimization mathematical model which aims at minimizing the vibration displacement of the low-speed carrier and the total mass of the gear transmission system is established. The optimization toolbox in MATLAB program is adopted to obtain the optimal solution. A case is studied to demonstrate the effectiveness of the dynamic model and the optimization method. The results show that the dynamic properties of the closed-form planetary gear transmission system have been improved and the total mass of the gear set has been decreased significantly.

  20. Perturbative calculations of flow patterns in free convection between coaxial cylinders. Non-linear temperature dependences of the fluid properties

    International Nuclear Information System (INIS)

    Navarro, J. A.; Madariaga, J. A.; Santamaria, C. M.; Saviron, J. M.

    1980-01-01

    10 refs. Flow pattern calculations in natural convection between two vertical coaxial cylinders are reported. It is assumed trough the paper. that fluid properties, viscosity, thermal conductivity and density, depend no-linearly on temperature and that the aspects (height/radius) ratio of the cylinders is high. Velocity profiles are calculated trough a perturbative scheme and analytic results for the three first perturbation orders are presented. We outline also an iterative method to estimate the perturbations on the flow patterns which arise when a radial composition gradient is established by external forces in a two-component fluid. This procedure, based on semiempirical basis, is applied to gaseous convection. The influence of the molecules gas properties on tho flow is also discussed. (Author) 10 refs

  1. Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

    International Nuclear Information System (INIS)

    Hedrih, K

    2008-01-01

    This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of 'an open a spiral form' of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

  2. Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

    Science.gov (United States)

    Stevanović Hedrih, K.

    2008-02-01

    This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

  3. Optimization of CW Fiber Lasers With Strong Nonlinear Cavity Dynamics

    Science.gov (United States)

    Shtyrina, O. V.; Efremov, S. A.; Yarutkina, I. A.; Skidin, A. S.; Fedoruk, M. P.

    2018-04-01

    In present work the equation for the saturated gain is derived from one-level gain equations describing the energy evolution inside the laser cavity. It is shown how to derive the parameters of the mathematical model from the experimental results. The numerically-estimated energy and spectrum of the signal are in good agreement with the experiment. Also, the optimization of the output energy is performed for a given set of model parameters.

  4. Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers

    Czech Academy of Sciences Publication Activity Database

    Adam, Lukáš; Branda, Martin

    2016-01-01

    Roč. 170, č. 2 (2016), s. 419-436 ISSN 0022-3239 R&D Projects: GA ČR GA15-00735S Institutional support: RVO:67985556 Keywords : Chance constrained programming * Optimality conditions * Regularization * Algorithms * Free MATLAB codes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.289, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/adam-0460909.pdf

  5. Statistical identifiability and convergence evaluation for nonlinear pharmacokinetic models with particle swarm optimization.

    Science.gov (United States)

    Kim, Seongho; Li, Lang

    2014-02-01

    The statistical identifiability of nonlinear pharmacokinetic (PK) models with the Michaelis-Menten (MM) kinetic equation is considered using a global optimization approach, which is particle swarm optimization (PSO). If a model is statistically non-identifiable, the conventional derivative-based estimation approach is often terminated earlier without converging, due to the singularity. To circumvent this difficulty, we develop a derivative-free global optimization algorithm by combining PSO with a derivative-free local optimization algorithm to improve the rate of convergence of PSO. We further propose an efficient approach to not only checking the convergence of estimation but also detecting the identifiability of nonlinear PK models. PK simulation studies demonstrate that the convergence and identifiability of the PK model can be detected efficiently through the proposed approach. The proposed approach is then applied to clinical PK data along with a two-compartmental model. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

  6. Learning-Based Adaptive Optimal Tracking Control of Strict-Feedback Nonlinear Systems.

    Science.gov (United States)

    Gao, Weinan; Jiang, Zhong-Ping; Weinan Gao; Zhong-Ping Jiang; Gao, Weinan; Jiang, Zhong-Ping

    2018-06-01

    This paper proposes a novel data-driven control approach to address the problem of adaptive optimal tracking for a class of nonlinear systems taking the strict-feedback form. Adaptive dynamic programming (ADP) and nonlinear output regulation theories are integrated for the first time to compute an adaptive near-optimal tracker without any a priori knowledge of the system dynamics. Fundamentally different from adaptive optimal stabilization problems, the solution to a Hamilton-Jacobi-Bellman (HJB) equation, not necessarily a positive definite function, cannot be approximated through the existing iterative methods. This paper proposes a novel policy iteration technique for solving positive semidefinite HJB equations with rigorous convergence analysis. A two-phase data-driven learning method is developed and implemented online by ADP. The efficacy of the proposed adaptive optimal tracking control methodology is demonstrated via a Van der Pol oscillator with time-varying exogenous signals.

  7. RCLED Optimization and Nonlinearity Compensation in a Polymer Optical Fiber DMT System

    Directory of Open Access Journals (Sweden)

    Pu Miao

    2016-09-01

    Full Text Available In polymer optical fiber (POF systems, the nonlinear transfer function of the resonant cavity light emitting diode (RCLED drastically degrades the communication performance. After investigating the characteristics of the RCLED nonlinear behavior, an improved digital look-up-table (LUT pre-distorter, based on an adaptive iterative algorithm, is proposed. Additionally, the system parameters, including the bias current, the average electrical power, the LUT size and the step factor are also jointly optimized to achieve a trade-off between the system linearity, reliability and the computational complexity. With the proposed methodology, both the operating point and efficiency of RCLED are enhanced. Moreover, in the practical 50 m POF communication system with the discrete multi-tone (DMT modulation, the bit error rate performance is improved by over 12 dB when RCLED is operating in the nonlinear region. Therefore, the proposed pre-distorter can both resist the nonlinearity and improve the operating point of RCLED.

  8. Nonlinear optimal filter technique for analyzing energy depositions in TES sensors driven into saturation

    Directory of Open Access Journals (Sweden)

    B. Shank

    2014-11-01

    Full Text Available We present a detailed thermal and electrical model of superconducting transition edge sensors (TESs connected to quasiparticle (qp traps, such as the W TESs connected to Al qp traps used for CDMS (Cryogenic Dark Matter Search Ge and Si detectors. We show that this improved model, together with a straightforward time-domain optimal filter, can be used to analyze pulses well into the nonlinear saturation region and reconstruct absorbed energies with optimal energy resolution.

  9. Efficient Output Solution for Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

    Directory of Open Access Journals (Sweden)

    Sie Long Kek

    2015-01-01

    Full Text Available A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.

  10. Approximate solutions of a nonlinear oscillator typified as a mass attached to a stretched elastic wire by the homotopy perturbation method

    International Nuclear Information System (INIS)

    Belendez, A.; Belendez, T.; Neipp, C.; Hernandez, A.; Alvarez, M.L.

    2009-01-01

    The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a system typified as a mass attached to a stretched elastic wire. The restoring force for this oscillator has an irrational term with a parameter λ that characterizes the system (0 ≤ λ ≤ 1). For λ = 1 and small values of x, the restoring force does not have a dominant term proportional to x. We find this perturbation method works very well for the whole range of parameters involved, and excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Only one iteration leads to high accuracy of the solutions and the maximal relative error for the approximate frequency is less than 2.2% for small and large values of oscillation amplitude. This error corresponds to λ = 1, while for λ < 1 the relative error is much lower. For example, its value is as low as 0.062% for λ = 0.5.

  11. Optimization of piezoelectric cantilever energy harvesters including non-linear effects

    International Nuclear Information System (INIS)

    Patel, R; McWilliam, S; Popov, A A

    2014-01-01

    This paper proposes a versatile non-linear model for predicting piezoelectric energy harvester performance. The presented model includes (i) material non-linearity, for both substrate and piezoelectric layers, and (ii) geometric non-linearity incorporated by assuming inextensibility and accurately representing beam curvature. The addition of a sub-model, which utilizes the transfer matrix method to predict eigenfrequencies and eigenvectors for segmented beams, allows for accurate optimization of piezoelectric layer coverage. A validation of the overall theoretical model is performed through experimental testing on both uniform and non-uniform samples manufactured in-house. For the harvester composition used in this work, the magnitude of material non-linearity exhibited by the piezoelectric layer is 35 times greater than that of the substrate layer. It is also observed that material non-linearity, responsible for reductions in resonant frequency with increases in base acceleration, is dominant over geometric non-linearity for standard piezoelectric harvesting devices. Finally, over the tested range, energy loss due to damping is found to increase in a quasi-linear fashion with base acceleration. During an optimization study on piezoelectric layer coverage, results from the developed model were compared with those from a linear model. Unbiased comparisons between harvesters were realized by using devices with identical natural frequencies—created by adjusting the device substrate thickness. Results from three studies, each with a different assumption on mechanical damping variations, are presented. Findings showed that, depending on damping variation, a non-linear model is essential for such optimization studies with each model predicting vastly differing optimum configurations. (paper)

  12. Optimized Wavelength-Tuned Nonlinear Frequency Conversion Using a Liquid Crystal Clad Waveguide

    Science.gov (United States)

    Stephen, Mark A. (Inventor)

    2018-01-01

    An optimized wavelength-tuned nonlinear frequency conversion process using a liquid crystal clad waveguide. The process includes implanting ions on a top surface of a lithium niobate crystal to form an ion implanted lithium niobate layer. The process also includes utilizing a tunable refractive index of a liquid crystal to rapidly change an effective index of the lithium niobate crystal.

  13. Optimized nonlinear inversion of surface-wave dispersion data

    International Nuclear Information System (INIS)

    Raykova, Reneta B.

    2014-01-01

    A new code for inversion of surface wave dispersion data is developed to obtain Earth’s crustal and upper mantle velocity structure. The author developed Optimized Non–Linear Inversion ( ONLI ) software, based on Monte-Carlo search. The values of S–wave velocity VS and thickness h for a number of horizontal homogeneous layers are parameterized. Velocity of P–wave VP and density ρ of relevant layers are calculated by empirical or theoretical relations. ONLI explores parameters space in two modes, selective and full search, and the main innovation of software is evaluation of tested models. Theoretical dispersion curves are calculated if tested model satisfied specific conditions only, reducing considerably the computation time. A number of tests explored impact of parameterization and proved the ability of ONLI approach to deal successfully with non–uniqueness of inversion problem. Key words: Earth’s structure, surface–wave dispersion, non–linear inversion, software

  14. Nonlinear Thermodynamic Analysis and Optimization of a Carnot Engine Cycle

    Directory of Open Access Journals (Sweden)

    Michel Feidt

    2016-06-01

    Full Text Available As part of the efforts to unify the various branches of Irreversible Thermodynamics, the proposed work reconsiders the approach of the Carnot engine taking into account the finite physical dimensions (heat transfer conductances and the finite speed of the piston. The models introduce the irreversibility of the engine by two methods involving different constraints. The first method introduces the irreversibility by a so-called irreversibility ratio in the entropy balance applied to the cycle, while in the second method it is emphasized by the entropy generation rate. Various forms of heat transfer laws are analyzed, but most of the results are given for the case of the linear law. Also, individual cases are studied and reported in order to provide a simple analytical form of the results. The engine model developed allowed a formal optimization using the calculus of variations.

  15. Neural-network-observer-based optimal control for unknown nonlinear systems using adaptive dynamic programming

    Science.gov (United States)

    Liu, Derong; Huang, Yuzhu; Wang, Ding; Wei, Qinglai

    2013-09-01

    In this paper, an observer-based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. First, a neural-network (NN) observer is designed to estimate system states. Then, based on the observed states, a neuro-controller is constructed via ADP method to obtain the optimal control. In this design, two NN structures are used: a three-layer NN is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics, and a critic NN is employed to approximate the value function. The optimal control law is computed using the critic NN and the observer NN. Uniform ultimate boundedness of the closed-loop system is guaranteed. The actor, critic, and observer structures are all implemented in real-time, continuously and simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

  16. Reinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraints

    Science.gov (United States)

    Yang, Xiong; Liu, Derong; Wang, Ding

    2014-03-01

    In this paper, an adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem of constrained-input continuous-time nonlinear systems in the presence of nonlinearities with unknown structures. Two different types of neural networks (NNs) are employed to approximate the Hamilton-Jacobi-Bellman equation. That is, an recurrent NN is constructed to identify the unknown dynamical system, and two feedforward NNs are used as the actor and the critic to approximate the optimal control and the optimal cost, respectively. Based on this framework, the action NN and the critic NN are tuned simultaneously, without the requirement for the knowledge of system drift dynamics. Moreover, by using Lyapunov's direct method, the weights of the action NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. To demonstrate the effectiveness of the present approach, simulation results are illustrated.

  17. Nonlinear dynamics optimization with particle swarm and genetic algorithms for SPEAR3 emittance upgrade

    International Nuclear Information System (INIS)

    Huang, Xiaobiao; Safranek, James

    2014-01-01

    Nonlinear dynamics optimization is carried out for a low emittance upgrade lattice of SPEAR3 in order to improve its dynamic aperture and Touschek lifetime. Two multi-objective optimization algorithms, a genetic algorithm and a particle swarm algorithm, are used for this study. The performance of the two algorithms are compared. The result shows that the particle swarm algorithm converges significantly faster to similar or better solutions than the genetic algorithm and it does not require seeding of good solutions in the initial population. These advantages of the particle swarm algorithm may make it more suitable for many accelerator optimization applications

  18. Nonlinear dynamics optimization with particle swarm and genetic algorithms for SPEAR3 emittance upgrade

    Energy Technology Data Exchange (ETDEWEB)

    Huang, Xiaobiao, E-mail: xiahuang@slac.stanford.edu; Safranek, James

    2014-09-01

    Nonlinear dynamics optimization is carried out for a low emittance upgrade lattice of SPEAR3 in order to improve its dynamic aperture and Touschek lifetime. Two multi-objective optimization algorithms, a genetic algorithm and a particle swarm algorithm, are used for this study. The performance of the two algorithms are compared. The result shows that the particle swarm algorithm converges significantly faster to similar or better solutions than the genetic algorithm and it does not require seeding of good solutions in the initial population. These advantages of the particle swarm algorithm may make it more suitable for many accelerator optimization applications.

  19. Digital-Control-Based Approximation of Optimal Wave Disturbances Attenuation for Nonlinear Offshore Platforms

    Directory of Open Access Journals (Sweden)

    Xiao-Fang Zhong

    2017-12-01

    Full Text Available The irregular wave disturbance attenuation problem for jacket-type offshore platforms involving the nonlinear characteristics is studied. The main contribution is that a digital-control-based approximation of optimal wave disturbances attenuation controller (AOWDAC is proposed based on iteration control theory, which consists of a feedback item of offshore state, a feedforward item of wave force and a nonlinear compensated component with iterative sequences. More specifically, by discussing the discrete model of nonlinear offshore platform subject to wave forces generated from the Joint North Sea Wave Project (JONSWAP wave spectrum and linearized wave theory, the original wave disturbances attenuation problem is formulated as the nonlinear two-point-boundary-value (TPBV problem. By introducing two vector sequences of system states and nonlinear compensated item, the solution of introduced nonlinear TPBV problem is obtained. Then, a numerical algorithm is designed to realize the feasibility of AOWDAC based on the deviation of performance index between the adjacent iteration processes. Finally, applied the proposed AOWDAC to a jacket-type offshore platform in Bohai Bay, the vibration amplitudes of the displacement and the velocity, and the required energy consumption can be reduced significantly.

  20. Efficient scattering-angle enrichment for a nonlinear inversion of the background and perturbations components of a velocity model

    KAUST Repository

    Wu, Zedong; Alkhalifah, Tariq Ali

    2017-01-01

    Reflection-waveform inversion (RWI) can help us reduce the nonlinearity of the standard full-waveform inversion (FWI) by inverting for the background velocity model using the wave-path of a single scattered wavefield to an image. However, current

  1. Vibrational quasi-degenerate perturbation theory with optimized coordinates: applications to ethylene and trans-1,3-butadiene.

    Science.gov (United States)

    Yagi, Kiyoshi; Otaki, Hiroki

    2014-02-28

    A perturbative extension to optimized coordinate vibrational self-consistent field (oc-VSCF) is proposed based on the quasi-degenerate perturbation theory (QDPT). A scheme to construct the degenerate space (P space) is developed, which incorporates degenerate configurations and alleviates the divergence of perturbative expansion due to localized coordinates in oc-VSCF (e.g., local O-H stretching modes of water). An efficient configuration selection scheme is also implemented, which screens out the Hamiltonian matrix element between the P space configuration (p) and the complementary Q space configuration (q) based on a difference in their quantum numbers (λpq = ∑s|ps - qs|). It is demonstrated that the second-order vibrational QDPT based on optimized coordinates (oc-VQDPT2) smoothly converges with respect to the order of the mode coupling, and outperforms the conventional one based on normal coordinates. Furthermore, an improved, fast algorithm is developed for optimizing the coordinates. First, the minimization of the VSCF energy is conducted in a restricted parameter space, in which only a portion of pairs of coordinates is selectively transformed. A rational index is devised for this purpose, which identifies the important coordinate pairs to mix from others that may remain unchanged based on the magnitude of harmonic coupling induced by the transformation. Second, a cubic force field (CFF) is employed in place of a quartic force field, which bypasses intensive procedures that arise due to the presence of the fourth-order force constants. It is found that oc-VSCF based on CFF together with the pair selection scheme yields the coordinates similar in character to the conventional ones such that the final vibrational energy is affected very little while gaining an order of magnitude acceleration. The proposed method is applied to ethylene and trans-1,3-butadiene. An accurate, multi-resolution potential, which combines the MP2 and coupled-cluster with singles

  2. Vibrational quasi-degenerate perturbation theory with optimized coordinates: Applications to ethylene and trans-1,3-butadiene

    Energy Technology Data Exchange (ETDEWEB)

    Yagi, Kiyoshi, E-mail: kiyoshi.yagi@riken.jp; Otaki, Hiroki [Theoretical Molecular Science Laboratory, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan)

    2014-02-28

    A perturbative extension to optimized coordinate vibrational self-consistent field (oc-VSCF) is proposed based on the quasi-degenerate perturbation theory (QDPT). A scheme to construct the degenerate space (P space) is developed, which incorporates degenerate configurations and alleviates the divergence of perturbative expansion due to localized coordinates in oc-VSCF (e.g., local O–H stretching modes of water). An efficient configuration selection scheme is also implemented, which screens out the Hamiltonian matrix element between the P space configuration (p) and the complementary Q space configuration (q) based on a difference in their quantum numbers (λ{sub pq} = ∑{sub s}|p{sub s} − q{sub s}|). It is demonstrated that the second-order vibrational QDPT based on optimized coordinates (oc-VQDPT2) smoothly converges with respect to the order of the mode coupling, and outperforms the conventional one based on normal coordinates. Furthermore, an improved, fast algorithm is developed for optimizing the coordinates. First, the minimization of the VSCF energy is conducted in a restricted parameter space, in which only a portion of pairs of coordinates is selectively transformed. A rational index is devised for this purpose, which identifies the important coordinate pairs to mix from others that may remain unchanged based on the magnitude of harmonic coupling induced by the transformation. Second, a cubic force field (CFF) is employed in place of a quartic force field, which bypasses intensive procedures that arise due to the presence of the fourth-order force constants. It is found that oc-VSCF based on CFF together with the pair selection scheme yields the coordinates similar in character to the conventional ones such that the final vibrational energy is affected very little while gaining an order of magnitude acceleration. The proposed method is applied to ethylene and trans-1,3-butadiene. An accurate, multi-resolution potential, which combines the MP2 and

  3. Stepwise optimization and global chaos of nonlinear parameters in exact calculations of few-particle systems

    International Nuclear Information System (INIS)

    Frolov, A.M.

    1986-01-01

    The problem of exact variational calculations of few-particle systems in the exponential basis of the relative coordinates using nonlinear parameters is studied. The techniques of stepwise optimization and global chaos of nonlinear parameters are used to calculate the S and P states of homonuclear muonic molecules with an error of no more than +0.001 eV. The global-chaos technique also has proved to be successful in the case of the nuclear systems 3 H and 3 He

  4. Parameter Identification with the Random Perturbation Particle Swarm Optimization Method and Sensitivity Analysis of an Advanced Pressurized Water Reactor Nuclear Power Plant Model for Power Systems

    Directory of Open Access Journals (Sweden)

    Li Wang

    2017-02-01

    Full Text Available The ability to obtain appropriate parameters for an advanced pressurized water reactor (PWR unit model is of great significance for power system analysis. The attributes of that ability include the following: nonlinear relationships, long transition time, intercoupled parameters and difficult obtainment from practical test, posed complexity and difficult parameter identification. In this paper, a model and a parameter identification method for the PWR primary loop system were investigated. A parameter identification process was proposed, using a particle swarm optimization (PSO algorithm that is based on random perturbation (RP-PSO. The identification process included model variable initialization based on the differential equations of each sub-module and program setting method, parameter obtainment through sub-module identification in the Matlab/Simulink Software (Math Works Inc., Natick, MA, USA as well as adaptation analysis for an integrated model. A lot of parameter identification work was carried out, the results of which verified the effectiveness of the method. It was found that the change of some parameters, like the fuel temperature and coolant temperature feedback coefficients, changed the model gain, of which the trajectory sensitivities were not zero. Thus, obtaining their appropriate values had significant effects on the simulation results. The trajectory sensitivities of some parameters in the core neutron dynamic module were interrelated, causing the parameters to be difficult to identify. The model parameter sensitivity could be different, which would be influenced by the model input conditions, reflecting the parameter identifiability difficulty degree for various input conditions.

  5. Event-Triggered Distributed Approximate Optimal State and Output Control of Affine Nonlinear Interconnected Systems.

    Science.gov (United States)

    Narayanan, Vignesh; Jagannathan, Sarangapani

    2017-06-08

    This paper presents an approximate optimal distributed control scheme for a known interconnected system composed of input affine nonlinear subsystems using event-triggered state and output feedback via a novel hybrid learning scheme. First, the cost function for the overall system is redefined as the sum of cost functions of individual subsystems. A distributed optimal control policy for the interconnected system is developed using the optimal value function of each subsystem. To generate the optimal control policy, forward-in-time, neural networks are employed to reconstruct the unknown optimal value function at each subsystem online. In order to retain the advantages of event-triggered feedback for an adaptive optimal controller, a novel hybrid learning scheme is proposed to reduce the convergence time for the learning algorithm. The development is based on the observation that, in the event-triggered feedback, the sampling instants are dynamic and results in variable interevent time. To relax the requirement of entire state measurements, an extended nonlinear observer is designed at each subsystem to recover the system internal states from the measurable feedback. Using a Lyapunov-based analysis, it is demonstrated that the system states and the observer errors remain locally uniformly ultimately bounded and the control policy converges to a neighborhood of the optimal policy. Simulation results are presented to demonstrate the performance of the developed controller.

  6. Adaptive critic designs for optimal control of uncertain nonlinear systems with unmatched interconnections.

    Science.gov (United States)

    Yang, Xiong; He, Haibo

    2018-05-26

    In this paper, we develop a novel optimal control strategy for a class of uncertain nonlinear systems with unmatched interconnections. To begin with, we present a stabilizing feedback controller for the interconnected nonlinear systems by modifying an array of optimal control laws of auxiliary subsystems. We also prove that this feedback controller ensures a specified cost function to achieve optimality. Then, under the framework of adaptive critic designs, we use critic networks to solve the Hamilton-Jacobi-Bellman equations associated with auxiliary subsystem optimal control laws. The critic network weights are tuned through the gradient descent method combined with an additional stabilizing term. By using the newly established weight tuning rules, we no longer need the initial admissible control condition. In addition, we demonstrate that all signals in the closed-loop auxiliary subsystems are stable in the sense of uniform ultimate boundedness by using classic Lyapunov techniques. Finally, we provide an interconnected nonlinear plant to validate the present control scheme. Copyright © 2018 Elsevier Ltd. All rights reserved.

  7. A non-linear optimal control problem in obtaining homogeneous concentration for semiconductor materials

    International Nuclear Information System (INIS)

    Huang, C.-H.; Li, J.-X.

    2006-01-01

    A non-linear optimal control algorithm is examined in this study for the diffusion process of semiconductor materials. The purpose of this algorithm is to estimate an optimal control function such that the homogeneity of the concentration can be controlled during the diffusion process and the diffusion-induced stresses for the semiconductor materials can thus be reduced. The validation of this optimal control analysis utilizing the conjugate gradient method of minimization is analysed by using numerical experiments. Three different diffusion processing times are given and the corresponding optimal control functions are to be determined. Results show that the diffusion time can be shortened significantly by applying the optimal control function at the boundary and the homogeneity of the concentration is also guaranteed. This control function can be obtained within a very short CPU time on a Pentium III 600 MHz PC

  8. Optimization of Thermal Object Nonlinear Control Systems by Energy Efficiency Criterion.

    Science.gov (United States)

    Velichkin, Vladimir A.; Zavyalov, Vladimir A.

    2018-03-01

    This article presents the results of thermal object functioning control analysis (heat exchanger, dryer, heat treatment chamber, etc.). The results were used to determine a mathematical model of the generalized thermal control object. The appropriate optimality criterion was chosen to make the control more energy-efficient. The mathematical programming task was formulated based on the chosen optimality criterion, control object mathematical model and technological constraints. The “maximum energy efficiency” criterion helped avoid solving a system of nonlinear differential equations and solve the formulated problem of mathematical programming in an analytical way. It should be noted that in the case under review the search for optimal control and optimal trajectory reduces to solving an algebraic system of equations. In addition, it is shown that the optimal trajectory does not depend on the dynamic characteristics of the control object.

  9. Nonlinear perturbations of differential operators with nontrivial kernel and applications to third order periodic boundary value problems

    International Nuclear Information System (INIS)

    Afuwape, A.U.; Omari, P.

    1987-11-01

    This paper deals with the solvability of the nonlinear operator equations in normed spaces Lx=EGx+f, where L is a linear map with possible nontrivial kernel. Applications are given to the existence of periodic solutions for the third order scalar differential equation x'''+ax''+bx'+cx+g(t,x)=p(t), under various conditions on the interaction of g(t,x)/x with spectral configurations of a, b and c. (author). 48 refs

  10. Simplex sliding mode control for nonlinear uncertain systems via chaos optimization

    International Nuclear Information System (INIS)

    Lu, Zhao; Shieh, Leang-San; Chen, Guanrong; Coleman, Norman P.

    2005-01-01

    As an emerging effective approach to nonlinear robust control, simplex sliding mode control demonstrates some attractive features not possessed by the conventional sliding mode control method, from both theoretical and practical points of view. However, no systematic approach is currently available for computing the simplex control vectors in nonlinear sliding mode control. In this paper, chaos-based optimization is exploited so as to develop a systematic approach to seeking the simplex control vectors; particularly, the flexibility of simplex control is enhanced by making the simplex control vectors dependent on the Euclidean norm of the sliding vector rather than being constant, which result in both reduction of the chattering and speedup of the convergence. Computer simulation on a nonlinear uncertain system is given to illustrate the effectiveness of the proposed control method

  11. State and parameter estimation in nonlinear systems as an optimal tracking problem

    International Nuclear Information System (INIS)

    Creveling, Daniel R.; Gill, Philip E.; Abarbanel, Henry D.I.

    2008-01-01

    In verifying and validating models of nonlinear processes it is important to incorporate information from observations in an efficient manner. Using the idea of synchronization of nonlinear dynamical systems, we present a framework for connecting a data signal with a model in a way that minimizes the required coupling yet allows the estimation of unknown parameters in the model. The need to evaluate unknown parameters in models of nonlinear physical, biophysical, and engineering systems occurs throughout the development of phenomenological or reduced models of dynamics. Our approach builds on existing work that uses synchronization as a tool for parameter estimation. We address some of the critical issues in that work and provide a practical framework for finding an accurate solution. In particular, we show the equivalence of this problem to that of tracking within an optimal control framework. This equivalence allows the application of powerful numerical methods that provide robust practical tools for model development and validation

  12. An optimal approach to active damping of nonlinear vibrations in composite plates using piezoelectric patches

    International Nuclear Information System (INIS)

    Saviz, M R

    2015-01-01

    In this paper a nonlinear approach to studying the vibration characteristic of laminated composite plate with surface-bonded piezoelectric layer/patch is formulated, based on the Green Lagrange type of strain–displacements relations, by incorporating higher-order terms arising from nonlinear relations of kinematics into mathematical formulations. The equations of motion are obtained through the energy method, based on Lagrange equations and by using higher-order shear deformation theories with von Karman–type nonlinearities, so that transverse shear strains vanish at the top and bottom surfaces of the plate. An isoparametric finite element model is provided to model the nonlinear dynamics of the smart plate with piezoelectric layer/ patch. Different boundary conditions are investigated. Optimal locations of piezoelectric patches are found using a genetic algorithm to maximize spatial controllability/observability and considering the effect of residual modes to reduce spillover effect. Active attenuation of vibration of laminated composite plate is achieved through an optimal control law with inequality constraint, which is related to the maximum and minimum values of allowable voltage in the piezoelectric elements. To keep the voltages of actuator pairs in an allowable limit, the Pontryagin’s minimum principle is implemented in a system with multi-inequality constraint of control inputs. The results are compared with similar ones, proving the accuracy of the model especially for the structures undergoing large deformations. The convergence is studied and nonlinear frequencies are obtained for different thickness ratios. The structural coupling between plate and piezoelectric actuators is analyzed. Some examples with new features are presented, indicating that the piezo-patches significantly improve the damping characteristics of the plate for suppressing the geometrically nonlinear transient vibrations. (paper)

  13. Effect of Perturbations in Coriolis and Centrifugal Forces on the Nonlinear Stability of Equilibrium Point in Robe's Restricted Circular Three-Body Problem

    Directory of Open Access Journals (Sweden)

    P. P. Hallan

    2008-01-01

    Full Text Available The effect of perturbations in Coriolis and cetrifugal forces on the nonlinear stability of the equilibrium point of the Robe's (1977 restricted circular three-body problem has been studied when the density parameter K is zero. By applying Kolmogorov-Arnold-Moser (KAM theory, it has been found that the equilibrium point is stable for all mass ratios μ in the range of linear stability 8/9+(2/3((43/25ϵ1−(10/3ϵ<μ<1, where ϵ and ϵ1 are, respectively, the perturbations in Coriolis and centrifugal forces, except for five mass ratios μ1=0.93711086−1.12983217ϵ+1.50202694ϵ1, μ2 = 0.9672922−0.5542091ϵ+ 1.2443968ϵ1, μ3=0.9459503−0.70458206ϵ+ 1.28436549ϵ1, μ4=0.9660792−0.30152273ϵ + 1.11684064ϵ1, μ5=0.893981−2.37971679ϵ + 1.22385421ϵ1, where the theory is not applicable.

  14. Nonlinear Time Series Prediction Using LS-SVM with Chaotic Mutation Evolutionary Programming for Parameter Optimization

    International Nuclear Information System (INIS)

    Xu Ruirui; Chen Tianlun; Gao Chengfeng

    2006-01-01

    Nonlinear time series prediction is studied by using an improved least squares support vector machine (LS-SVM) regression based on chaotic mutation evolutionary programming (CMEP) approach for parameter optimization. We analyze how the prediction error varies with different parameters (σ, γ) in LS-SVM. In order to select appropriate parameters for the prediction model, we employ CMEP algorithm. Finally, Nasdaq stock data are predicted by using this LS-SVM regression based on CMEP, and satisfactory results are obtained.

  15. Study on Rail Profile Optimization Based on the Nonlinear Relationship between Profile and Wear Rate

    Directory of Open Access Journals (Sweden)

    Jianxi Wang

    2017-01-01

    Full Text Available This paper proposes a rail profile optimization method that takes account of wear rate within design cycle so as to minimize rail wear at the curve in heavy haul railway and extend the service life of rail. Taking rail wear rate as the object function, the vertical coordinate of rail profile at range optimization as independent variable, and the geometric characteristics and grinding depth of rail profile as constraint conditions, the support vector machine regression theory was used to fit the nonlinear relationship between rail profile and its wear rate. Then, the profile optimization model was built. Based on the optimization principle of genetic algorithm, the profile optimization model was solved to achieve the optimal rail profile. A multibody dynamics model was used to check the dynamic performance of carriage running on optimal rail profile. The result showed that the average relative error of support vector machine regression model remained less than 10% after a number of training processes. The dynamic performance of carriage running on optimized rail profile met the requirements on safety index and stability. The wear rate of optimized profile was lower than that of standard profile by 5.8%; the allowable carrying gross weight increased by 12.7%.

  16. Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers

    Directory of Open Access Journals (Sweden)

    Marinca Vasile

    2017-10-01

    Full Text Available Dynamic response time is an important feature for determining the performance of magnetorheological (MR dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.

  17. Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers

    Science.gov (United States)

    Marinca, Vasile; Ene, Remus-Daniel; Bereteu, Liviu

    2017-10-01

    Dynamic response time is an important feature for determining the performance of magnetorheological (MR) dampers in practical civil engineering applications. The objective of this paper is to show how to use the Optimal Homotopy Asymptotic Method (OHAM) to give approximate analytical solutions of the nonlinear differential equation of a modified Bingham model with non-viscous exponential damping. Our procedure does not depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximate solutions. OHAM is very efficient in practice for ensuring very rapid convergence of the solution after only one iteration and with a small number of steps.

  18. The optimization of the nonlinear parameters in the transcorrelated method: the hydrogen molecule

    International Nuclear Information System (INIS)

    Huggett, J.P.; Armour, E.A.G.

    1976-01-01

    The nonlinear parameters in a transcorrelated calculation of the groundstate energy and wavefunction of the hydrogen molecule are optimized using the method of Boys and Handy (Proc. R. Soc. A.; 309:195 and 209, 310:43 and 63, 311:309 (1969)). The method gives quite accurate results in all cases and in some cases the results are highly accurate. This is the first time the method has been applied to the optimization of a term in the correlation function which depends linearly on the interelectronic distance. (author)

  19. Optimal Control of Nonlinear Hydraulic Networks in the Presence of Disturbance

    DEFF Research Database (Denmark)

    Tahavori, Maryamsadat; Leth, John-Josef; Kallesøe, Carsten

    2014-01-01

    Water leakage is an important component of water loss. Many methods have emerged from urban water supply systems for leakage control, but it still remains a challenge in many countries. Pressure management is an effective way to reduce the leakage in a system. It can also reduce the power...... consumption. To this end, an optimal control strategy is proposed in this paper. In the water supply system model, the hydraulic resistance of the valve is estimated by the real data from a water supply system and it is considered to be a disturbance. The method which is used to solve the nonlinear optimal...

  20. Developments in perturbation theory

    International Nuclear Information System (INIS)

    Greenspan, E.

    1976-01-01

    Included are sections dealing with perturbation expressions for reactivity, methods for the calculation of perturbed fluxes, integral transport theory formulations for reactivity, generalized perturbation theory, sensitivity and optimization studies, multigroup calculations of bilinear functionals, and solution of inhomogeneous Boltzmann equations with singular operators

  1. Exposures involving perturbations of the EM field have non-linear effects on radiation response and can alter the expression of radiation induced bystander effects

    Science.gov (United States)

    Mothersill, Carmel; Seymour, Colin

    2012-07-01

    Our recent data suggest there is a physical component to the bystander signal induced by radiation exposure and that alternative medicine techniques such as Reiki and acupuncture or exposures to weak EM fields alter the response of cells to direct irradiation and either altered bystander signal production or altered the response of cells receiving bystander signals. Our proposed mechanism to explain these findings is that perturbation of electromagnetic (EM) fields is central to the induction of low radiation dose responses especially non-targeted bystander effects. In this presentation we review the alternative medicine data and other data sets from our laboratory which test our hypothesis that perturbation of bio-fields will modulate radiation response in the low dose region. The other data sets include exposure to MRI, shielding using lead and or Faraday cages, the use of physical barriers to bystander signal transmission and the use of membrane channel blockers. The data taken together strongly suggest that EM field perturbation can modulate low dose response and that in fact the EM field rather than the targeted deposition of ionizing energy in the DNA may be the key determinant of dose response in a cell or organism The results also lead us to suspect that at least when chemical transmission is blocked, bystander signals can be transmitted by other means. Our recent experiments suggest light signals and volatiles are not likely. We conclude that alternative medicine and other techniques involving electromagnetic perturbations can modify the response of cells to low doses of ionizing radiation and can induce bystander effects similar to those seen in medium transfer experiments. In addition to the obvious implications for mechanistic studies of low dose effects, this could perhaps provide a novel target to exploit in space radiation protection and in optimizing therapeutic gain during radiotherapy.

  2. Method and Apparatus for Performance Optimization Through Physical Perturbation of Task Elements

    Science.gov (United States)

    Prinzel, Lawrence J., III (Inventor); Pope, Alan T. (Inventor); Palsson, Olafur S. (Inventor); Turner, Marsha J. (Inventor)

    2016-01-01

    The invention is an apparatus and method of biofeedback training for attaining a physiological state optimally consistent with the successful performance of a task, wherein the probability of successfully completing the task is made is inversely proportional to a physiological difference value, computed as the absolute value of the difference between at least one physiological signal optimally consistent with the successful performance of the task and at least one corresponding measured physiological signal of a trainee performing the task. The probability of successfully completing the task is made inversely proportional to the physiological difference value by making one or more measurable physical attributes of the environment in which the task is performed, and upon which completion of the task depends, vary in inverse proportion to the physiological difference value.

  3. An optimally weighted estimator of the linear power spectrum disentangling the growth of density perturbations across galaxy surveys

    International Nuclear Information System (INIS)

    Sorini, D.

    2017-01-01

    Measuring the clustering of galaxies from surveys allows us to estimate the power spectrum of matter density fluctuations, thus constraining cosmological models. This requires careful modelling of observational effects to avoid misinterpretation of data. In particular, signals coming from different distances encode information from different epochs. This is known as ''light-cone effect'' and is going to have a higher impact as upcoming galaxy surveys probe larger redshift ranges. Generalising the method by Feldman, Kaiser and Peacock (1994) [1], I define a minimum-variance estimator of the linear power spectrum at a fixed time, properly taking into account the light-cone effect. An analytic expression for the estimator is provided, and that is consistent with the findings of previous works in the literature. I test the method within the context of the Halofit model, assuming Planck 2014 cosmological parameters [2]. I show that the estimator presented recovers the fiducial linear power spectrum at present time within 5% accuracy up to k ∼ 0.80 h Mpc −1 and within 10% up to k ∼ 0.94 h Mpc −1 , well into the non-linear regime of the growth of density perturbations. As such, the method could be useful in the analysis of the data from future large-scale surveys, like Euclid.

  4. Weighted Optimization-Based Distributed Kalman Filter for Nonlinear Target Tracking in Collaborative Sensor Networks.

    Science.gov (United States)

    Chen, Jie; Li, Jiahong; Yang, Shuanghua; Deng, Fang

    2017-11-01

    The identification of the nonlinearity and coupling is crucial in nonlinear target tracking problem in collaborative sensor networks. According to the adaptive Kalman filtering (KF) method, the nonlinearity and coupling can be regarded as the model noise covariance, and estimated by minimizing the innovation or residual errors of the states. However, the method requires large time window of data to achieve reliable covariance measurement, making it impractical for nonlinear systems which are rapidly changing. To deal with the problem, a weighted optimization-based distributed KF algorithm (WODKF) is proposed in this paper. The algorithm enlarges the data size of each sensor by the received measurements and state estimates from its connected sensors instead of the time window. A new cost function is set as the weighted sum of the bias and oscillation of the state to estimate the "best" estimate of the model noise covariance. The bias and oscillation of the state of each sensor are estimated by polynomial fitting a time window of state estimates and measurements of the sensor and its neighbors weighted by the measurement noise covariance. The best estimate of the model noise covariance is computed by minimizing the weighted cost function using the exhaustive method. The sensor selection method is in addition to the algorithm to decrease the computation load of the filter and increase the scalability of the sensor network. The existence, suboptimality and stability analysis of the algorithm are given. The local probability data association method is used in the proposed algorithm for the multitarget tracking case. The algorithm is demonstrated in simulations on tracking examples for a random signal, one nonlinear target, and four nonlinear targets. Results show the feasibility and superiority of WODKF against other filtering algorithms for a large class of systems.

  5. Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

    KAUST Repository

    Gottlieb, Sigal

    2015-04-10

    High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.

  6. Multi-Body Ski Jumper Model with Nonlinear Dynamic Inversion Muscle Control for Trajectory Optimization

    Directory of Open Access Journals (Sweden)

    Patrick Piprek

    2018-02-01

    Full Text Available This paper presents an approach to model a ski jumper as a multi-body system for an optimal control application. The modeling is based on the constrained Newton-Euler-Equations. Within this paper the complete multi-body modeling methodology as well as the musculoskeletal modeling is considered. For the musculoskeletal modeling and its incorporation in the optimization model, we choose a nonlinear dynamic inversion control approach. This approach uses the muscle models as nonlinear reference models and links them to the ski jumper movement by a control law. This strategy yields a linearized input-output behavior, which makes the optimal control problem easier to solve. The resulting model of the ski jumper can then be used for trajectory optimization whose results are compared to literature jumps. Ultimately, this enables the jumper to get a very detailed feedback of the flight. To achieve the maximal jump length, exact positioning of his body with respect to the air can be displayed.

  7. Actor-critic-based optimal tracking for partially unknown nonlinear discrete-time systems.

    Science.gov (United States)

    Kiumarsi, Bahare; Lewis, Frank L

    2015-01-01

    This paper presents a partially model-free adaptive optimal control solution to the deterministic nonlinear discrete-time (DT) tracking control problem in the presence of input constraints. The tracking error dynamics and reference trajectory dynamics are first combined to form an augmented system. Then, a new discounted performance function based on the augmented system is presented for the optimal nonlinear tracking problem. In contrast to the standard solution, which finds the feedforward and feedback terms of the control input separately, the minimization of the proposed discounted performance function gives both feedback and feedforward parts of the control input simultaneously. This enables us to encode the input constraints into the optimization problem using a nonquadratic performance function. The DT tracking Bellman equation and tracking Hamilton-Jacobi-Bellman (HJB) are derived. An actor-critic-based reinforcement learning algorithm is used to learn the solution to the tracking HJB equation online without requiring knowledge of the system drift dynamics. That is, two neural networks (NNs), namely, actor NN and critic NN, are tuned online and simultaneously to generate the optimal bounded control policy. A simulation example is given to show the effectiveness of the proposed method.

  8. Robust Optimization Using Supremum of the Objective Function for Nonlinear Programming Problems

    International Nuclear Information System (INIS)

    Lee, Se Jung; Park, Gyung Jin

    2014-01-01

    In the robust optimization field, the robustness of the objective function emphasizes an insensitive design. In general, the robustness of the objective function can be achieved by reducing the change of the objective function with respect to the variation of the design variables and parameters. However, in conventional methods, when an insensitive design is emphasized, the performance of the objective function can be deteriorated. Besides, if the numbers of the design variables are increased, the numerical cost is quite high in robust optimization for nonlinear programming problems. In this research, the robustness index for the objective function and a process of robust optimization are proposed. Moreover, a method using the supremum of linearized functions is also proposed to reduce the computational cost. Mathematical examples are solved for the verification of the proposed method and the results are compared with those from the conventional methods. The proposed approach improves the performance of the objective function and its efficiency

  9. Controller Parameter Optimization for Nonlinear Systems Using Enhanced Bacteria Foraging Algorithm

    Directory of Open Access Journals (Sweden)

    V. Rajinikanth

    2012-01-01

    Full Text Available An enhanced bacteria foraging optimization (EBFO algorithm-based Proportional + integral + derivative (PID controller tuning is proposed for a class of nonlinear process models. The EBFO algorithm is a modified form of standard BFO algorithm. A multiobjective performance index is considered to guide the EBFO algorithm for discovering the best possible value of controller parameters. The efficiency of the proposed scheme has been validated through a comparative study with classical BFO, adaptive BFO, PSO, and GA based controller tuning methods proposed in the literature. The proposed algorithm is tested in real time on a nonlinear spherical tank system. The real-time results show that, EBFO tuned PID controller gives a smooth response for setpoint tracking performance.

  10. Nonlinear optimization of the modern synchrotron radiation storage ring based on frequency map analysis

    International Nuclear Information System (INIS)

    Tian Shunqiang; Liu Guimin; Hou Jie; Chen Guangling; Wan Chenglan; Li Haohu

    2009-01-01

    In this paper, we present a rule to improve the nonlinear solution with frequency map analysis (FMA), and without frequently revisiting the optimization algorithm. Two aspects of FMA are emphasized. The first one is the tune shift with amplitude, which can be used to improve the solution of harmonic sextupoles, and thus obtain a large dynamic aperture. The second one is the tune diffusion rate, which can be used to select a quiet tune. Application of these ideas is carried out in the storage ring of the Shanghai Synchrotron Radiation Facility (SSRF), and the detailed processes, as well as better solutions, are presented in this paper. Discussions about the nonlinear behaviors of off-momentum particles are also presented. (authors)

  11. Adaptive near-optimal neuro controller for continuous-time nonaffine nonlinear systems with constrained input.

    Science.gov (United States)

    Esfandiari, Kasra; Abdollahi, Farzaneh; Talebi, Heidar Ali

    2017-09-01

    In this paper, an identifier-critic structure is introduced to find an online near-optimal controller for continuous-time nonaffine nonlinear systems having saturated control signal. By employing two Neural Networks (NNs), the solution of Hamilton-Jacobi-Bellman (HJB) equation associated with the cost function is derived without requiring a priori knowledge about system dynamics. Weights of the identifier and critic NNs are tuned online and simultaneously such that unknown terms are approximated accurately and the control signal is kept between the saturation bounds. The convergence of NNs' weights, identification error, and system states is guaranteed using Lyapunov's direct method. Finally, simulation results are performed on two nonlinear systems to confirm the effectiveness of the proposed control strategy. Copyright © 2017 Elsevier Ltd. All rights reserved.

  12. [On the problems of the evolutionary optimization of life history. II. To justification of optimization criterion for nonlinear Leslie model].

    Science.gov (United States)

    Pasekov, V P

    2013-03-01

    The paper considers the problems in the adaptive evolution of life-history traits for individuals in the nonlinear Leslie model of age-structured population. The possibility to predict adaptation results as the values of organism's traits (properties) that provide for the maximum of a certain function of traits (optimization criterion) is studied. An ideal criterion of this type is Darwinian fitness as a characteristic of success of an individual's life history. Criticism of the optimization approach is associated with the fact that it does not take into account the changes in the environmental conditions (in a broad sense) caused by evolution, thereby leading to losses in the adequacy of the criterion. In addition, the justification for this criterion under stationary conditions is not usually rigorous. It has been suggested to overcome these objections in terms of the adaptive dynamics theory using the concept of invasive fitness. The reasons are given that favor the application of the average number of offspring for an individual, R(L), as an optimization criterion in the nonlinear Leslie model. According to the theory of quantitative genetics, the selection for fertility (that is, for a set of correlated quantitative traits determined by both multiple loci and the environment) leads to an increase in R(L). In terms of adaptive dynamics, the maximum R(L) corresponds to the evolutionary stability and, in certain cases, convergent stability of the values for traits. The search for evolutionarily stable values on the background of limited resources for reproduction is a problem of linear programming.

  13. An Optimal Homotopy Asymptotic Approach Applied to Nonlinear MHD Jeffery-Hamel Flow

    Directory of Open Access Journals (Sweden)

    Vasile Marinca

    2011-01-01

    Full Text Available A simple and effective procedure is employed to propose a new analytic approximate solution for nonlinear MHD Jeffery-Hamel flow. This technique called the Optimal Homotopy Asymptotic Method (OHAM does not depend upon any small/large parameters and provides us with a convenient way to control the convergence of the solution. The examples given in this paper lead to the conclusion that the accuracy of the obtained results is growing along with increasing the number of constants in the auxiliary function, which are determined using a computer technique. The results obtained through the proposed method are in very good agreement with the numerical results.

  14. Global stability, periodic solutions, and optimal control in a nonlinear differential delay model

    Directory of Open Access Journals (Sweden)

    Anatoli F. Ivanov

    2010-09-01

    Full Text Available A nonlinear differential equation with delay serving as a mathematical model of several applied problems is considered. Sufficient conditions for the global asymptotic stability and for the existence of periodic solutions are given. Two particular applications are treated in detail. The first one is a blood cell production model by Mackey, for which new periodicity criteria are derived. The second application is a modified economic model with delay due to Ramsey. An optimization problem for a maximal consumption is stated and solved for the latter.

  15. Comparison of Linear and Nonlinear Model Predictive Control for Optimization of Spray Dryer Operation

    DEFF Research Database (Denmark)

    Petersen, Lars Norbert; Poulsen, Niels Kjølstad; Niemann, Hans Henrik

    2015-01-01

    In this paper, we compare the performance of an economically optimizing Nonlinear Model Predictive Controller (E-NMPC) to a linear tracking Model Predictive Controller (MPC) for a spray drying plant. We find in this simulation study, that the economic performance of the two controllers are almost...... equal. We evaluate the economic performance with an industrially recorded disturbance scenario, where unmeasured disturbances and model mismatch are present. The state of the spray dryer, used in the E-NMPC and MPC, is estimated using Kalman Filters with noise covariances estimated by a maximum...

  16. Segmentation of deformable organs from medical images using particle swarm optimization and nonlinear shape priors

    Science.gov (United States)

    Afifi, Ahmed; Nakaguchi, Toshiya; Tsumura, Norimichi

    2010-03-01

    In many medical applications, the automatic segmentation of deformable organs from medical images is indispensable and its accuracy is of a special interest. However, the automatic segmentation of these organs is a challenging task according to its complex shape. Moreover, the medical images usually have noise, clutter, or occlusion and considering the image information only often leads to meager image segmentation. In this paper, we propose a fully automated technique for the segmentation of deformable organs from medical images. In this technique, the segmentation is performed by fitting a nonlinear shape model with pre-segmented images. The kernel principle component analysis (KPCA) is utilized to capture the complex organs deformation and to construct the nonlinear shape model. The presegmentation is carried out by labeling each pixel according to its high level texture features extracted using the overcomplete wavelet packet decomposition. Furthermore, to guarantee an accurate fitting between the nonlinear model and the pre-segmented images, the particle swarm optimization (PSO) algorithm is employed to adapt the model parameters for the novel images. In this paper, we demonstrate the competence of proposed technique by implementing it to the liver segmentation from computed tomography (CT) scans of different patients.

  17. Linear and nonlinear market correlations: Characterizing financial crises and portfolio optimization

    Science.gov (United States)

    Haluszczynski, Alexander; Laut, Ingo; Modest, Heike; Räth, Christoph

    2017-12-01

    Pearson correlation and mutual information-based complex networks of the day-to-day returns of U.S. S&P500 stocks between 1985 and 2015 have been constructed to investigate the mutual dependencies of the stocks and their nature. We show that both networks detect qualitative differences especially during (recent) turbulent market periods, thus indicating strongly fluctuating interconnections between the stocks of different companies in changing economic environments. A measure for the strength of nonlinear dependencies is derived using surrogate data and leads to interesting observations during periods of financial market crises. In contrast to the expectation that dependencies reduce mainly to linear correlations during crises, we show that (at least in the 2008 crisis) nonlinear effects are significantly increasing. It turns out that the concept of centrality within a network could potentially be used as some kind of an early warning indicator for abnormal market behavior as we demonstrate with the example of the 2008 subprime mortgage crisis. Finally, we apply a Markowitz mean variance portfolio optimization and integrate the measure of nonlinear dependencies to scale the investment exposure. This leads to significant outperformance as compared to a fully invested portfolio.

  18. Optimizing optical nonlinearities in GaInAs/AlInAs quantum cascade lasers

    Directory of Open Access Journals (Sweden)

    Gajić Aleksandra D.

    2014-01-01

    Full Text Available Regardless of the huge advances made in the design and fabrication of mid-infrared and terahertz quantum cascade lasers, success in accessing the ~3-4 mm region of the electromagnetic spectrum has remained limited. This fact has brought about the need to exploit resonant intersubband transitions as powerful nonlinear oscillators, consequently enabling the occurrence of large nonlinear optical susceptibilities as a means of reaching desired wavelengths. In this work, we present a computational model developed for the optimization of second-order optical nonlinearities in In0.53Ga0.47As/Al0.48In0.52As quantum cascade laser structures based on the implementation of the Genetic algorithm. The carrier transport and the power output of the structure were calculated by self-consistent solutions to the system of rate equations for carriers and photons. Both stimulated and simultaneous double-photon absorption processes occurring between the second harmonic generation-relevant levels are incorporated into rate equations and the material-dependent effective mass and band non-parabolicity are taken into account, as well. The developed method is quite general and can be applied to any higher order effect which requires the inclusion of the photon density equation. [Projekat Ministarstva nauke Republike Srbije, br. III 45010

  19. Economic Optimization of Spray Dryer Operation using Nonlinear Model Predictive Control

    DEFF Research Database (Denmark)

    Petersen, Lars Norbert; Poulsen, Niels Kjølstad; Niemann, Hans Henrik

    2014-01-01

    In this paper we investigate an economically optimizing Nonlinear Model Predictive Control (E-NMPC) for a spray drying process. By simulation we evaluate the economic potential of this E-NMPC compared to a conventional PID based control strategy. Spray drying is the preferred process to reduce...... the water content for many liquid foodstuffs and produces a free flowing powder. The main challenge in controlling the spray drying process is to meet the residual moisture specifications and avoid that the powder sticks to the chamber walls of the spray dryer. We present a model for a spray dryer that has...... been validated on experimental data from a pilot plant. We use this model for simulation as well as for prediction in the E-NMPC. The E-NMPC is designed with hard input constraints and soft output constraints. The open-loop optimal control problem in the E-NMPC is solved using the single...

  20. Robust Fault Detection for a Class of Uncertain Nonlinear Systems Based on Multiobjective Optimization

    Directory of Open Access Journals (Sweden)

    Bingyong Yan

    2015-01-01

    Full Text Available A robust fault detection scheme for a class of nonlinear systems with uncertainty is proposed. The proposed approach utilizes robust control theory and parameter optimization algorithm to design the gain matrix of fault tracking approximator (FTA for fault detection. The gain matrix of FTA is designed to minimize the effects of system uncertainty on residual signals while maximizing the effects of system faults on residual signals. The design of the gain matrix of FTA takes into account the robustness of residual signals to system uncertainty and sensitivity of residual signals to system faults simultaneously, which leads to a multiobjective optimization problem. Then, the detectability of system faults is rigorously analyzed by investigating the threshold of residual signals. Finally, simulation results are provided to show the validity and applicability of the proposed approach.

  1. Economic Optimization of Spray Dryer Operation using Nonlinear Model Predictive Control with State Estimation

    DEFF Research Database (Denmark)

    Petersen, Lars Norbert; Jørgensen, John Bagterp; Rawlings, James B.

    2015-01-01

    In this paper, we develop an economically optimizing Nonlinear Model Predictive Controller (E-NMPC) for a complete spray drying plant with multiple stages. In the E-NMPC the initial state is estimated by an extended Kalman Filter (EKF) with noise covariances estimated by an autocovariance least...... squares method (ALS). We present a model for the spray drying plant and use this model for simulation as well as for prediction in the E-NMPC. The open-loop optimal control problem in the E-NMPC is solved using the single-shooting method combined with a quasi-Newton Sequential Quadratic programming (SQP......) algorithm and the adjoint method for computation of gradients. We evaluate the economic performance when unmeasured disturbances are present. By simulation, we demonstrate that the E-NMPC improves the profit of spray drying by 17% compared to conventional PI control....

  2. Robust non-gradient C subroutines for non-linear optimization

    DEFF Research Database (Denmark)

    Brock, Pernille; Madsen, Kaj; Nielsen, Hans Bruun

    2004-01-01

    This report presents a package of robust and easy-to-use C subroutines for solving unconstrained and constrained non-linear optimization problems, where gradient information is not required. The intention is that the routines should use the currently best algorithms available. All routines have...... subroutines are obtained by changing 0 to 1. The present report is a new and updated version of a previous report NI-91-04 with the title Non-gradient c Subroutines for Non- Linear Optimization, [16]. Both the previous and the present report describe a collection of subroutines, which have been translated...... from Fortran to C. The reason for writing the present report is that some of the C subroutines have been replaced by more e ective and robust versions translated from the original Fortran subroutines to C by the Bandler Group, see [1]. Also the test examples have been modified to some extent...

  3. Landmark Optimization Using Local Curvature for Point-Based Nonlinear Rodent Brain Image Registration

    Directory of Open Access Journals (Sweden)

    Yutong Liu

    2012-01-01

    Full Text Available Purpose. To develop a technique to automate landmark selection for point-based interpolating transformations for nonlinear medical image registration. Materials and Methods. Interpolating transformations were calculated from homologous point landmarks on the source (image to be transformed and target (reference image. Point landmarks are placed at regular intervals on contours of anatomical features, and their positions are optimized along the contour surface by a function composed of curvature similarity and displacements of the homologous landmarks. The method was evaluated in two cases (=5 each. In one, MRI was registered to histological sections; in the second, geometric distortions in EPI MRI were corrected. Normalized mutual information and target registration error were calculated to compare the registration accuracy of the automatically and manually generated landmarks. Results. Statistical analyses demonstrated significant improvement (<0.05 in registration accuracy by landmark optimization in most data sets and trends towards improvement (<0.1 in others as compared to manual landmark selection.

  4. A real-frequency solver for the Anderson impurity model based on bath optimization and cluster perturbation theory

    Science.gov (United States)

    Zingl, Manuel; Nuss, Martin; Bauernfeind, Daniel; Aichhorn, Markus

    2018-05-01

    Recently solvers for the Anderson impurity model (AIM) working directly on the real-frequency axis have gained much interest. A simple and yet frequently used impurity solver is exact diagonalization (ED), which is based on a discretization of the AIM bath degrees of freedom. Usually, the bath parameters cannot be obtained directly on the real-frequency axis, but have to be determined by a fit procedure on the Matsubara axis. In this work we present an approach where the bath degrees of freedom are first discretized directly on the real-frequency axis using a large number of bath sites (≈ 50). Then, the bath is optimized by unitary transformations such that it separates into two parts that are weakly coupled. One part contains the impurity site and its interacting Green's functions can be determined with ED. The other (larger) part is a non-interacting system containing all the remaining bath sites. Finally, the Green's function of the full AIM is calculated via coupling these two parts with cluster perturbation theory.

  5. Thrust generation by a heaving flexible foil: Resonance, nonlinearities, and optimality

    Science.gov (United States)

    Paraz, Florine; Schouveiler, Lionel; Eloy, Christophe

    2016-01-01

    Flexibility of marine animal fins has been thought to enhance swimming performance. However, despite numerous experimental and numerical studies on flapping flexible foils, there is still no clear understanding of the effect of flexibility and flapping amplitude on thrust generation and swimming efficiency. Here, to address this question, we combine experiments on a model system and a weakly nonlinear analysis. Experiments consist in immersing a flexible rectangular plate in a uniform flow and forcing this plate into a heaving motion at its leading edge. A complementary theoretical model is developed assuming a two-dimensional inviscid problem. In this model, nonlinear effects are taken into account by considering a transverse resistive drag. Under these hypotheses, a modal decomposition of the system motion allows us to predict the plate response amplitude and the generated thrust, as a function of the forcing amplitude and frequency. We show that this model can correctly predict the experimental data on plate kinematic response and thrust generation, as well as other data found in the literature. We also discuss the question of efficiency in the context of bio-inspired propulsion. Using the proposed model, we show that the optimal propeller for a given thrust and a given swimming speed is achieved when the actuating frequency is tuned to a resonance of the system, and when the optimal forcing amplitude scales as the square root of the required thrust.

  6. Mathematical modeling of zika virus disease with nonlinear incidence and optimal control

    Science.gov (United States)

    Goswami, Naba Kumar; Srivastav, Akhil Kumar; Ghosh, Mini; Shanmukha, B.

    2018-04-01

    The Zika virus was first discovered in a rhesus monkey in the Zika Forest of Uganda in 1947, and it was isolated from humans in Nigeria in 1952. Zika virus disease is primarily a mosquito-borne disease, which is transmitted to human primarily through the bite of an infected Aedes species mosquito. However, there is documented evidence of sexual transmission of this disease too. In this paper, a nonlinear mathematical model for Zika virus by considering nonlinear incidence is formulated and analyzed. The equilibria and the basic reproduction number (R0) of the model are found. The stability of the different equilibria of the model is discussed in detail. When the basic reproduction number R0 1, we have endemic equilibrium which is locally stable under some restriction on parameters. Further this model is extended to optimal control model and is analyzed by using Pontryagin’s Maximum Principle. It has been observed that optimal control plays a significant role in reducing the number of zika infectives. Finally, numerical simulation is performed to illustrate the analytical findings.

  7. Nonlinear Optimization-Based Device-Free Localization with Outlier Link Rejection

    Directory of Open Access Journals (Sweden)

    Wendong Xiao

    2015-04-01

    Full Text Available Device-free localization (DFL is an emerging wireless technique for estimating the location of target that does not have any attached electronic device. It has found extensive use in Smart City applications such as healthcare at home and hospitals, location-based services at smart spaces, city emergency response and infrastructure security. In DFL, wireless devices are used as sensors that can sense the target by transmitting and receiving wireless signals collaboratively. Many DFL systems are implemented based on received signal strength (RSS measurements and the location of the target is estimated by detecting the changes of the RSS measurements of the wireless links. Due to the uncertainty of the wireless channel, certain links may be seriously polluted and result in erroneous detection. In this paper, we propose a novel nonlinear optimization approach with outlier link rejection (NOOLR for RSS-based DFL. It consists of three key strategies, including: (1 affected link identification by differential RSS detection; (2 outlier link rejection via geometrical positional relationship among links; (3 target location estimation by formulating and solving a nonlinear optimization problem. Experimental results demonstrate that NOOLR is robust to the fluctuation of the wireless signals with superior localization accuracy compared with the existing Radio Tomographic Imaging (RTI approach.

  8. Nonlinear Multiuser Receiver for Optimized Chaos-Based DS-CDMA Systems

    Directory of Open Access Journals (Sweden)

    S. Shaerbaf

    2011-09-01

    Full Text Available Chaos based communications have drawn increasing attention over the past years. Chaotic signals are derived from non-linear dynamic systems. They are aperiodic, broadband and deterministic signals that appear random in the time domain. Because of these properties, chaotic signals have been proposed to generate spreading sequences for wide-band secure communication recently. Like conventional DS-CDMA systems, chaos-based CDMA systems suffer from multi-user interference (MUI due to other users transmitting in the cell. In this paper, we propose a novel method based on radial basis function (RBF for both blind and non-blind multiuser detection in chaos-based DS-CDMA systems. We also propose a new method for optimizing generation of binary chaotic sequences using Genetic Algorithm. Simulation results show that our proposed nonlinear receiver with optimized chaotic sequences outperforms in comparison to other conventional detectors such as a single-user detector, decorrelating detector and minimum mean square error detector, particularly for under-loaded CDMA condition, which the number of active users is less than processing gain.

  9. An efficient identification approach for stable and unstable nonlinear systems using Colliding Bodies Optimization algorithm.

    Science.gov (United States)

    Pal, Partha S; Kar, R; Mandal, D; Ghoshal, S P

    2015-11-01

    This paper presents an efficient approach to identify different stable and practically useful Hammerstein models as well as unstable nonlinear process along with its stable closed loop counterpart with the help of an evolutionary algorithm as Colliding Bodies Optimization (CBO) optimization algorithm. The performance measures of the CBO based optimization approach such as precision, accuracy are justified with the minimum output mean square value (MSE) which signifies that the amount of bias and variance in the output domain are also the least. It is also observed that the optimization of output MSE in the presence of outliers has resulted in a very close estimation of the output parameters consistently, which also justifies the effective general applicability of the CBO algorithm towards the system identification problem and also establishes the practical usefulness of the applied approach. Optimum values of the MSEs, computational times and statistical information of the MSEs are all found to be the superior as compared with those of the other existing similar types of stochastic algorithms based approaches reported in different recent literature, which establish the robustness and efficiency of the applied CBO based identification scheme. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  10. Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics

    Science.gov (United States)

    Lv, Yongfeng; Na, Jing; Yang, Qinmin; Wu, Xing; Guo, Yu

    2016-01-01

    An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.

  11. Nonlinear Dynamic in an Ecological System with Impulsive Effect and Optimal Foraging

    Directory of Open Access Journals (Sweden)

    Min Zhao

    2014-01-01

    Full Text Available The population dynamics of a three-species ecological system with impulsive effect are investigated. Using the theories of impulsive equations and small-amplitude perturbation scales, the conditions for the system to be permanent when the number of predators released is less than some critical value can be obtained. Furthermore, because the predator in the system follows the predictions of optimal foraging theory, it follows that optimal foraging promotes species coexistence. In particular, the less beneficial prey can support the predator alone when the more beneficial prey goes extinct. Moreover, the influences of the impulsive effect and optimal foraging on inherent oscillations are studied using simulation, which reveals rich dynamic behaviors such as period-halving bifurcations, a chaotic band, a periodic window, and chaotic crises. In addition, the largest Lyapunov exponent and the power spectra of the strange attractor, which can help analyze the chaotic dynamic behavior of the model, are investigated. This information will be useful for studying the dynamic complexity of ecosystems.

  12. φq-field theory for portfolio optimization: “fat tails” and nonlinear correlations

    Science.gov (United States)

    Sornette, D.; Simonetti, P.; Andersen, J. V.

    2000-08-01

    Physics and finance are both fundamentally based on the theory of random walks (and their generalizations to higher dimensions) and on the collective behavior of large numbers of correlated variables. The archetype examplifying this situation in finance is the portfolio optimization problem in which one desires to diversify on a set of possibly dependent assets to optimize the return and minimize the risks. The standard mean-variance solution introduced by Markovitz and its subsequent developments is basically a mean-field Gaussian solution. It has severe limitations for practical applications due to the strongly non-Gaussian structure of distributions and the nonlinear dependence between assets. Here, we present in details a general analytical characterization of the distribution of returns for a portfolio constituted of assets whose returns are described by an arbitrary joint multivariate distribution. In this goal, we introduce a non-linear transformation that maps the returns onto Gaussian variables whose covariance matrix provides a new measure of dependence between the non-normal returns, generalizing the covariance matrix into a nonlinear covariance matrix. This nonlinear covariance matrix is chiseled to the specific fat tail structure of the underlying marginal distributions, thus ensuring stability and good conditioning. The portfolio distribution is then obtained as the solution of a mapping to a so-called φq field theory in particle physics, of which we offer an extensive treatment using Feynman diagrammatic techniques and large deviation theory, that we illustrate in details for multivariate Weibull distributions. The interaction (non-mean field) structure in this field theory is a direct consequence of the non-Gaussian nature of the distribution of asset price returns. We find that minimizing the portfolio variance (i.e. the relatively “small” risks) may often increase the large risks, as measured by higher normalized cumulants. Extensive

  13. Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and Pareto filters.

    Directory of Open Access Journals (Sweden)

    Carlos Pozo

    Full Text Available Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study

  14. Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and Pareto filters.

    Science.gov (United States)

    Pozo, Carlos; Guillén-Gosálbez, Gonzalo; Sorribas, Albert; Jiménez, Laureano

    2012-01-01

    Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the

  15. Fluctuations in Nonlinear Systems: A Short Review

    International Nuclear Information System (INIS)

    Rubia, F.J. de la; Buceta, J.; Cabrera, J.L.; Olarrea, J.; Parrondo, J.M.R.

    2003-01-01

    We review some results that illustrate the constructive role of noise in nonlinear systems. Several phenomena are briefly discussed: optimal localization of orbits in a system with limit cycle behavior and perturbed by colored noise; stochastic branch selection at secondary bifurcations; noise- induced order/disorder transitions and pattern formation in spatially extended systems. In all cases the presence of noise is crucial, and the results reinforce the modern view of the importance of noise in the evolution of nonlinear systems. (author)

  16. Linearly and nonlinearly optimized weighted essentially non-oscillatory methods for compressible turbulence

    Science.gov (United States)

    Taylor, Ellen Meredith

    Weighted essentially non-oscillatory (WENO) methods have been developed to simultaneously provide robust shock-capturing in compressible fluid flow and avoid excessive damping of fine-scale flow features such as turbulence. This is accomplished by constructing multiple candidate numerical stencils that adaptively combine so as to provide high order of accuracy and high bandwidth-resolving efficiency in continuous flow regions while averting instability-provoking interpolation across discontinuities. Under certain conditions in compressible turbulence, however, numerical dissipation remains unacceptably high even after optimization of the linear optimal stencil combination that dominates in smooth regions. The remaining nonlinear error arises from two primary sources: (i) the smoothness measurement that governs the application of adaptation away from the optimal stencil and (ii) the numerical properties of individual candidate stencils that govern numerical accuracy when adaptation engages. In this work, both of these sources are investigated, and corrective modifications to the WENO methodology are proposed and evaluated. Excessive nonlinear error due to the first source is alleviated through two separately considered procedures appended to the standard smoothness measurement technique that are designated the "relative smoothness limiter" and the "relative total variation limiter." In theory, appropriate values of their associated parameters should be insensitive to flow configuration, thereby sidestepping the prospect of costly parameter tuning; and this expectation of broad effectiveness is assessed in direct numerical simulations (DNS) of one-dimensional inviscid test problems, three-dimensional compressible isotropic turbulence of varying Reynolds and turbulent Mach numbers, and shock/isotropic-turbulence interaction (SITI). In the process, tools for efficiently comparing WENO adaptation behavior in smooth versus shock-containing regions are developed. The

  17. Perturbed nonlinear models from noncommutativity

    International Nuclear Information System (INIS)

    Cabrera-Carnero, I.; Correa-Borbonet, Luis Alejandro; Valadares, G.C.S.

    2007-01-01

    By means of the Ehrenfest's Theorem inside the context of a noncommutative Quantum Mechanics it is obtained the Newton's Second Law in noncommutative space. Considering discrete systems with infinite degrees of freedom whose dynamical evolutions are governed by the noncommutative Newton's Second Law we have constructed some alternative noncommutative generalizations of two-dimensional field theories. (author)

  18. Optimal Constant-Stress Accelerated Degradation Test Plans Using Nonlinear Generalized Wiener Process

    Directory of Open Access Journals (Sweden)

    Zhen Chen

    2016-01-01

    Full Text Available Accelerated degradation test (ADT has been widely used to assess highly reliable products’ lifetime. To conduct an ADT, an appropriate degradation model and test plan should be determined in advance. Although many historical studies have proposed quite a few models, there is still room for improvement. Hence we propose a Nonlinear Generalized Wiener Process (NGWP model with consideration of the effects of stress level, product-to-product variability, and measurement errors for a higher estimation accuracy and a wider range of use. Then under the constraints of sample size, test duration, and test cost, the plans of constant-stress ADT (CSADT with multiple stress levels based on the NGWP are designed by minimizing the asymptotic variance of the reliability estimation of the products under normal operation conditions. An optimization algorithm is developed to determine the optimal stress levels, the number of units allocated to each level, inspection frequency, and measurement times simultaneously. In addition, a comparison based on degradation data of LEDs is made to show better goodness-of-fit of the NGWP than that of other models. Finally, optimal two-level and three-level CSADT plans under various constraints and a detailed sensitivity analysis are demonstrated through examples in this paper.

  19. Distributed Optimal Consensus Control for Nonlinear Multiagent System With Unknown Dynamic.

    Science.gov (United States)

    Zhang, Jilie; Zhang, Huaguang; Feng, Tao

    2017-08-01

    This paper focuses on the distributed optimal cooperative control for continuous-time nonlinear multiagent systems (MASs) with completely unknown dynamics via adaptive dynamic programming (ADP) technology. By introducing predesigned extra compensators, the augmented neighborhood error systems are derived, which successfully circumvents the system knowledge requirement for ADP. It is revealed that the optimal consensus protocols actually work as the solutions of the MAS differential game. Policy iteration algorithm is adopted, and it is theoretically proved that the iterative value function sequence strictly converges to the solution of the coupled Hamilton-Jacobi-Bellman equation. Based on this point, a novel online iterative scheme is proposed, which runs based on the data sampled from the augmented system and the gradient of the value function. Neural networks are employed to implement the algorithm and the weights are updated, in the least-square sense, to the ideal value, which yields approximated optimal consensus protocols. Finally, a numerical example is given to illustrate the effectiveness of the proposed scheme.

  20. Ensemble perturbation smoother for optimizing tidal boundary conditions by assimilation of High-Frequency radar surface currents – application to the German Bight

    Directory of Open Access Journals (Sweden)

    A. Barth

    2010-02-01

    Full Text Available High-Frequency (HF radars measure the ocean surface currents at various spatial and temporal scales. These include tidal currents, wind-driven circulation, density-driven circulation and Stokes drift. Sequential assimilation methods updating the model state have been proven successful to correct the density-driven currents by assimilation of observations such as sea surface height, sea surface temperature and in-situ profiles. However, the situation is different for tides in coastal models since these are not generated within the domain, but are rather propagated inside the domain through the boundary conditions. For improving the modeled tidal variability it is therefore not sufficient to update the model state via data assimilation without updating the boundary conditions. The optimization of boundary conditions to match observations inside the domain is traditionally achieved through variational assimilation methods. In this work we present an ensemble smoother to improve the tidal boundary values so that the model represents more closely the observed currents. To create an ensemble of dynamically realistic boundary conditions, a cost function is formulated which is directly related to the probability of each boundary condition perturbation. This cost function ensures that the boundary condition perturbations are spatially smooth and that the structure of the perturbations satisfies approximately the harmonic linearized shallow water equations. Based on those perturbations an ensemble simulation is carried out using the full three-dimensional General Estuarine Ocean Model (GETM. Optimized boundary values are obtained by assimilating all observations using the covariances of the ensemble simulation.

  1. Chaotic behaviour in the non-linear optimal control of unilaterally contacting building systems during earthquakes

    CERN Document Server

    Liolios, A

    2003-01-01

    The paper presents a new numerical approach for a non-linear optimal control problem arising in earthquake civil engineering. This problem concerns the elastoplastic softening-fracturing unilateral contact between neighbouring buildings during earthquakes when Coulomb friction is taken into account under second-order instabilizing effects. So, the earthquake response of the adjacent structures can appear instabilities and chaotic behaviour. The problem formulation presented here leads to a set of equations and inequalities, which is equivalent to a dynamic hemivariational inequality in the way introduced by Panagiotopoulos [Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993]. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the Wilson-theta method. The generally non-convex constitutive contact laws are piecewise linearized, and in each time-step a non-c...

  2. Efficient high-precision matrix algebra on parallel architectures for nonlinear combinatorial optimization

    KAUST Repository

    Gunnels, John; Lee, Jon; Margulies, Susan

    2010-01-01

    We provide a first demonstration of the idea that matrix-based algorithms for nonlinear combinatorial optimization problems can be efficiently implemented. Such algorithms were mainly conceived by theoretical computer scientists for proving efficiency. We are able to demonstrate the practicality of our approach by developing an implementation on a massively parallel architecture, and exploiting scalable and efficient parallel implementations of algorithms for ultra high-precision linear algebra. Additionally, we have delineated and implemented the necessary algorithmic and coding changes required in order to address problems several orders of magnitude larger, dealing with the limits of scalability from memory footprint, computational efficiency, reliability, and interconnect perspectives. © Springer and Mathematical Programming Society 2010.

  3. Efficient high-precision matrix algebra on parallel architectures for nonlinear combinatorial optimization

    KAUST Repository

    Gunnels, John

    2010-06-01

    We provide a first demonstration of the idea that matrix-based algorithms for nonlinear combinatorial optimization problems can be efficiently implemented. Such algorithms were mainly conceived by theoretical computer scientists for proving efficiency. We are able to demonstrate the practicality of our approach by developing an implementation on a massively parallel architecture, and exploiting scalable and efficient parallel implementations of algorithms for ultra high-precision linear algebra. Additionally, we have delineated and implemented the necessary algorithmic and coding changes required in order to address problems several orders of magnitude larger, dealing with the limits of scalability from memory footprint, computational efficiency, reliability, and interconnect perspectives. © Springer and Mathematical Programming Society 2010.

  4. Dynamics and optimal control of a non-linear epidemic model with relapse and cure

    Science.gov (United States)

    Lahrouz, A.; El Mahjour, H.; Settati, A.; Bernoussi, A.

    2018-04-01

    In this work, we introduce the basic reproduction number R0 for a general epidemic model with graded cure, relapse and nonlinear incidence rate in a non-constant population size. We established that the disease free-equilibrium state Ef is globally asymptotically exponentially stable if R0 1, we proved that the system model has at least one endemic state Ee. Then, by means of an appropriate Lyapunov function, we showed that Ee is unique and globally asymptotically stable under some acceptable biological conditions. On the other hand, we use two types of control to reduce the number of infectious individuals. The optimality system is formulated and solved numerically using a Gauss-Seidel-like implicit finite-difference method.

  5. Nonlinear optimization method of ship floating condition calculation in wave based on vector

    Science.gov (United States)

    Ding, Ning; Yu, Jian-xing

    2014-08-01

    Ship floating condition in regular waves is calculated. New equations controlling any ship's floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship's displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.

  6. Optimized parallel convolutions for non-linear fluid models of tokamak ηi turbulence

    International Nuclear Information System (INIS)

    Milovich, J.L.; Tomaschke, G.; Kerbel, G.D.

    1993-01-01

    Non-linear computational fluid models of plasma turbulence based on spectral methods typically spend a large fraction of the total computing time evaluating convolutions. Usually these convolutions arise from an explicit or semi implicit treatment of the convective non-linearities in the problem. Often the principal convective velocity is perpendicular to magnetic field lines allowing a reduction of the convolution to two dimensions in an appropriate geometry, but beyond this, different models vary widely in the particulars of which mode amplitudes are selectively evolved to get the most efficient representation of the turbulence. As the number of modes in the problem, N, increases, the amount of computation required for this part of the evolution algorithm then scales as N 2 /timestep for a direct or analytic method and N ln N/timestep for a pseudospectral method. The constants of proportionality depend on the particulars of mode selection and determine the size problem for which the method will perform equally. For large enough N, the pseudospectral method performance is always superior, though some problems do not require correspondingly high resolution. Further, the Courant condition for numerical stability requires that the timestep size must decrease proportionately as N increases, thus accentuating the need to have fast methods for larger N problems. The authors have developed a package for the Cray system which performs these convolutions for a rather arbitrary mode selection scheme using either method. The package is highly optimized using a combination of macro and microtasking techniques, as well as vectorization and in some cases assembly coded routines. Parts of the package have also been developed and optimized for the CM200 and CM5 system. Performance comparisons with respect to problem size, parallelization, selection schemes and architecture are presented

  7. Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models.

    Science.gov (United States)

    Pozo, Carlos; Marín-Sanguino, Alberto; Alves, Rui; Guillén-Gosálbez, Gonzalo; Jiménez, Laureano; Sorribas, Albert

    2011-08-25

    Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA) models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC) models that extend the power-law formalism to deal with saturation and cooperativity. Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

  8. Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models

    Directory of Open Access Journals (Sweden)

    Sorribas Albert

    2011-08-01

    Full Text Available Abstract Background Design of newly engineered microbial strains for biotechnological purposes would greatly benefit from the development of realistic mathematical models for the processes to be optimized. Such models can then be analyzed and, with the development and application of appropriate optimization techniques, one could identify the modifications that need to be made to the organism in order to achieve the desired biotechnological goal. As appropriate models to perform such an analysis are necessarily non-linear and typically non-convex, finding their global optimum is a challenging task. Canonical modeling techniques, such as Generalized Mass Action (GMA models based on the power-law formalism, offer a possible solution to this problem because they have a mathematical structure that enables the development of specific algorithms for global optimization. Results Based on the GMA canonical representation, we have developed in previous works a highly efficient optimization algorithm and a set of related strategies for understanding the evolution of adaptive responses in cellular metabolism. Here, we explore the possibility of recasting kinetic non-linear models into an equivalent GMA model, so that global optimization on the recast GMA model can be performed. With this technique, optimization is greatly facilitated and the results are transposable to the original non-linear problem. This procedure is straightforward for a particular class of non-linear models known as Saturable and Cooperative (SC models that extend the power-law formalism to deal with saturation and cooperativity. Conclusions Our results show that recasting non-linear kinetic models into GMA models is indeed an appropriate strategy that helps overcoming some of the numerical difficulties that arise during the global optimization task.

  9. An optimized Nash nonlinear grey Bernoulli model based on particle swarm optimization and its application in prediction for the incidence of Hepatitis B in Xinjiang, China.

    Science.gov (United States)

    Zhang, Liping; Zheng, Yanling; Wang, Kai; Zhang, Xueliang; Zheng, Yujian

    2014-06-01

    In this paper, by using a particle swarm optimization algorithm to solve the optimal parameter estimation problem, an improved Nash nonlinear grey Bernoulli model termed PSO-NNGBM(1,1) is proposed. To test the forecasting performance, the optimized model is applied for forecasting the incidence of hepatitis B in Xinjiang, China. Four models, traditional GM(1,1), grey Verhulst model (GVM), original nonlinear grey Bernoulli model (NGBM(1,1)) and Holt-Winters exponential smoothing method, are also established for comparison with the proposed model under the criteria of mean absolute percentage error and root mean square percent error. The prediction results show that the optimized NNGBM(1,1) model is more accurate and performs better than the traditional GM(1,1), GVM, NGBM(1,1) and Holt-Winters exponential smoothing method. Copyright © 2014. Published by Elsevier Ltd.

  10. PID Controller Design of Nonlinear System using a New Modified Particle Swarm Optimization with Time-Varying Constriction Coefficient

    Directory of Open Access Journals (Sweden)

    Alrijadjis .

    2014-12-01

    Full Text Available The proportional integral derivative (PID controllers have been widely used in most process control systems for a long time. However, it is a very important problem how to choose PID parameters, because these parameters give a great influence on the control performance. Especially, it is difficult to tune these parameters for nonlinear systems. In this paper, a new modified particle swarm optimization (PSO is presented to search for optimal PID parameters for such system. The proposed algorithm is to modify constriction coefficient which is nonlinearly decreased time-varying for improving the final accuracy and the convergence speed of PSO. To validate the control performance of the proposed method, a typical nonlinear system control, a continuous stirred tank reactor (CSTR process, is illustrated. The results testify that a new modified PSO algorithm can perform well in the nonlinear PID control system design in term of lesser overshoot, rise-time, settling-time, IAE and ISE. Keywords: PID controller, Particle Swarm Optimization (PSO,constriction factor, nonlinear system.

  11. Decoupled ARX and RBF Neural Network Modeling Using PCA and GA Optimization for Nonlinear Distributed Parameter Systems.

    Science.gov (United States)

    Zhang, Ridong; Tao, Jili; Lu, Renquan; Jin, Qibing

    2018-02-01

    Modeling of distributed parameter systems is difficult because of their nonlinearity and infinite-dimensional characteristics. Based on principal component analysis (PCA), a hybrid modeling strategy that consists of a decoupled linear autoregressive exogenous (ARX) model and a nonlinear radial basis function (RBF) neural network model are proposed. The spatial-temporal output is first divided into a few dominant spatial basis functions and finite-dimensional temporal series by PCA. Then, a decoupled ARX model is designed to model the linear dynamics of the dominant modes of the time series. The nonlinear residual part is subsequently parameterized by RBFs, where genetic algorithm is utilized to optimize their hidden layer structure and the parameters. Finally, the nonlinear spatial-temporal dynamic system is obtained after the time/space reconstruction. Simulation results of a catalytic rod and a heat conduction equation demonstrate the effectiveness of the proposed strategy compared to several other methods.

  12. Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.

    Science.gov (United States)

    Wei, Qinglai; Liu, Derong; Lin, Hanquan

    2016-03-01

    In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.

  13. Calibration of Mine Ventilation Network Models Using the Non-Linear Optimization Algorithm

    Directory of Open Access Journals (Sweden)

    Guang Xu

    2017-12-01

    Full Text Available Effective ventilation planning is vital to underground mining. To ensure stable operation of the ventilation system and to avoid airflow disorder, mine ventilation network (MVN models have been widely used in simulating and optimizing the mine ventilation system. However, one of the challenges for MVN model simulation is that the simulated airflow distribution results do not match the measured data. To solve this problem, a simple and effective calibration method is proposed based on the non-linear optimization algorithm. The calibrated model not only makes simulated airflow distribution results in accordance with the on-site measured data, but also controls the errors of other parameters within a minimum range. The proposed method was then applied to calibrate an MVN model in a real case, which is built based on ventilation survey results and Ventsim software. Finally, airflow simulation experiments are carried out respectively using data before and after calibration, whose results were compared and analyzed. This showed that the simulated airflows in the calibrated model agreed much better to the ventilation survey data, which verifies the effectiveness of calibrating method.

  14. Near-optimal alternative generation using modified hit-and-run sampling for non-linear, non-convex problems

    Science.gov (United States)

    Rosenberg, D. E.; Alafifi, A.

    2016-12-01

    Water resources systems analysis often focuses on finding optimal solutions. Yet an optimal solution is optimal only for the modelled issues and managers often seek near-optimal alternatives that address un-modelled objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as the region comprising the original problem constraints plus a new constraint that allowed performance within a specified tolerance of the optimal objective function value. MGA identified a few maximally-different alternatives from the near-optimal region. Subsequent work applied Markov Chain Monte Carlo (MCMC) sampling to generate a larger number of alternatives that span the near-optimal region of linear problems or select portions for non-linear problems. We extend the MCMC Hit-And-Run method to generate alternatives that span the full extent of the near-optimal region for non-linear, non-convex problems. First, start at a feasible hit point within the near-optimal region, then run a random distance in a random direction to a new hit point. Next, repeat until generating the desired number of alternatives. The key step at each iterate is to run a random distance along the line in the specified direction to a new hit point. If linear equity constraints exist, we construct an orthogonal basis and use a null space transformation to confine hits and runs to a lower-dimensional space. Linear inequity constraints define the convex bounds on the line that runs through the current hit point in the specified direction. We then use slice sampling to identify a new hit point along the line within bounds defined by the non-linear inequity constraints. This technique is computationally efficient compared to prior near-optimal alternative generation techniques such MGA, MCMC Metropolis-Hastings, evolutionary, or firefly algorithms because search at each iteration is confined to the hit line, the algorithm can move in one

  15. A nonlinear optimal control approach to stabilization of a macroeconomic development model

    Science.gov (United States)

    Rigatos, G.; Siano, P.; Ghosh, T.; Sarno, D.

    2017-11-01

    A nonlinear optimal (H-infinity) control approach is proposed for the problem of stabilization of the dynamics of a macroeconomic development model that is known as the Grossman-Helpman model of endogenous product cycles. The dynamics of the macroeconomic development model is divided in two parts. The first one describes economic activities in a developed country and the second part describes variation of economic activities in a country under development which tries to modify its production so as to serve the needs of the developed country. The article shows that through control of the macroeconomic model of the developed country, one can finally control the dynamics of the economy in the country under development. The control method through which this is achieved is the nonlinear H-infinity control. The macroeconomic model for the country under development undergoes approximate linearization round a temporary operating point. This is defined at each time instant by the present value of the system's state vector and the last value of the control input vector that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. For the linearized model an H-infinity feedback controller is computed. The controller's gain is calculated by solving an algebraic Riccati equation at each iteration of the control method. The asymptotic stability of the control approach is proven through Lyapunov analysis. This assures that the state variables of the macroeconomic model of the country under development will finally converge to the designated reference values.

  16. Optimization of nonlinear, non-Gaussian Bayesian filtering for diagnosis and prognosis of monotonic degradation processes

    Science.gov (United States)

    Corbetta, Matteo; Sbarufatti, Claudio; Giglio, Marco; Todd, Michael D.

    2018-05-01

    The present work critically analyzes the probabilistic definition of dynamic state-space models subject to Bayesian filters used for monitoring and predicting monotonic degradation processes. The study focuses on the selection of the random process, often called process noise, which is a key perturbation source in the evolution equation of particle filtering. Despite the large number of applications of particle filtering predicting structural degradation, the adequacy of the picked process noise has not been investigated. This paper reviews existing process noise models that are typically embedded in particle filters dedicated to monitoring and predicting structural damage caused by fatigue, which is monotonic in nature. The analysis emphasizes that existing formulations of the process noise can jeopardize the performance of the filter in terms of state estimation and remaining life prediction (i.e., damage prognosis). This paper subsequently proposes an optimal and unbiased process noise model and a list of requirements that the stochastic model must satisfy to guarantee high prognostic performance. These requirements are useful for future and further implementations of particle filtering for monotonic system dynamics. The validity of the new process noise formulation is assessed against experimental fatigue crack growth data from a full-scale aeronautical structure using dedicated performance metrics.

  17. Memetic Algorithms to Solve a Global Nonlinear Optimization Problem. A Review

    Directory of Open Access Journals (Sweden)

    M. K. Sakharov

    2015-01-01

    Full Text Available In recent decades, evolutionary algorithms have proven themselves as the powerful optimization techniques of search engine. Their popularity is due to the fact that they are easy to implement and can be used in all areas, since they are based on the idea of universal evolution. For example, in the problems of a large number of local optima, the traditional optimization methods, usually, fail in finding the global optimum. To solve such problems using a variety of stochastic methods, in particular, the so-called population-based algorithms, which are a kind of evolutionary methods. The main disadvantage of this class of methods is their slow convergence to the exact solution in the neighborhood of the global optimum, as these methods incapable to use the local information about the landscape of the function. This often limits their use in largescale real-world problems where the computation time is a critical factor.One of the promising directions in the field of modern evolutionary computation are memetic algorithms, which can be regarded as a combination of population search of the global optimum and local procedures for verifying solutions, which gives a synergistic effect. In the context of memetic algorithms, the meme is an implementation of the local optimization method to refine solution in the search.The concept of memetic algorithms provides ample opportunities for the development of various modifications of these algorithms, which can vary the frequency of the local search, the conditions of its end, and so on. The practically significant memetic algorithm modifications involve the simultaneous use of different memes. Such algorithms are called multi-memetic.The paper gives statement of the global problem of nonlinear unconstrained optimization, describes the most promising areas of AI modifications, including hybridization and metaoptimization. The main content of the work is the classification and review of existing varieties of

  18. Adaptive Constrained Optimal Control Design for Data-Based Nonlinear Discrete-Time Systems With Critic-Only Structure.

    Science.gov (United States)

    Luo, Biao; Liu, Derong; Wu, Huai-Ning

    2018-06-01

    Reinforcement learning has proved to be a powerful tool to solve optimal control problems over the past few years. However, the data-based constrained optimal control problem of nonaffine nonlinear discrete-time systems has rarely been studied yet. To solve this problem, an adaptive optimal control approach is developed by using the value iteration-based Q-learning (VIQL) with the critic-only structure. Most of the existing constrained control methods require the use of a certain performance index and only suit for linear or affine nonlinear systems, which is unreasonable in practice. To overcome this problem, the system transformation is first introduced with the general performance index. Then, the constrained optimal control problem is converted to an unconstrained optimal control problem. By introducing the action-state value function, i.e., Q-function, the VIQL algorithm is proposed to learn the optimal Q-function of the data-based unconstrained optimal control problem. The convergence results of the VIQL algorithm are established with an easy-to-realize initial condition . To implement the VIQL algorithm, the critic-only structure is developed, where only one neural network is required to approximate the Q-function. The converged Q-function obtained from the critic-only VIQL method is employed to design the adaptive constrained optimal controller based on the gradient descent scheme. Finally, the effectiveness of the developed adaptive control method is tested on three examples with computer simulation.

  19. A non-linear branch and cut method for solving discrete minimum compliance problems to global optimality

    DEFF Research Database (Denmark)

    Stolpe, Mathias; Bendsøe, Martin P.

    2007-01-01

    This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed...... finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities...

  20. A non-linear branch and cut method for solving discrete minimum compliance problems to global optimality

    DEFF Research Database (Denmark)

    Stolpe, Mathias; Bendsøe, Martin P.

    2007-01-01

    This paper present some initial results pertaining to a search for globally optimal solutions to a challenging benchmark example proposed by Zhou and Rozvany. This means that we are dealing with global optimization of the classical single load minimum compliance topology design problem with a fixed...... finite element discretization and with discrete design variables. Global optimality is achieved by the implementation of some specially constructed convergent nonlinear branch and cut methods, based on the use of natural relaxations and by applying strengthening constraints (linear valid inequalities......) and cuts....

  1. Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller-Plesset perturbation theory

    Science.gov (United States)

    Bozkaya, Uǧur; Turney, Justin M.; Yamaguchi, Yukio; Schaefer, Henry F.; Sherrill, C. David

    2011-09-01

    Using a Lagrangian-based approach, we present a more elegant derivation of the equations necessary for the variational optimization of the molecular orbitals (MOs) for the coupled-cluster doubles (CCD) method and second-order Møller-Plesset perturbation theory (MP2). These orbital-optimized theories are referred to as OO-CCD and OO-MP2 (or simply "OD" and "OMP2" for short), respectively. We also present an improved algorithm for orbital optimization in these methods. Explicit equations for response density matrices, the MO gradient, and the MO Hessian are reported both in spin-orbital and closed-shell spin-adapted forms. The Newton-Raphson algorithm is used for the optimization procedure using the MO gradient and Hessian. Further, orbital stability analyses are also carried out at correlated levels. The OD and OMP2 approaches are compared with the standard MP2, CCD, CCSD, and CCSD(T) methods. All these methods are applied to H2O, three diatomics, and the O_4^+ molecule. Results demonstrate that the CCSD and OD methods give nearly identical results for H2O and diatomics; however, in symmetry-breaking problems as exemplified by O_4^+, the OD method provides better results for vibrational frequencies. The OD method has further advantages over CCSD: its analytic gradients are easier to compute since there is no need to solve the coupled-perturbed equations for the orbital response, the computation of one-electron properties are easier because there is no response contribution to the particle density matrices, the variational optimized orbitals can be readily extended to allow inactive orbitals, it avoids spurious second-order poles in its response function, and its transition dipole moments are gauge invariant. The OMP2 has these same advantages over canonical MP2, making it promising for excited state properties via linear response theory. The quadratically convergent orbital-optimization procedure converges quickly for OMP2, and provides molecular properties that

  2. Stack emission monitoring using non-dispersive infrared spectroscopy with an optimized nonlinear absorption cross interference correction algorithm

    Directory of Open Access Journals (Sweden)

    Y. W. Sun

    2013-08-01

    Full Text Available In this paper, we present an optimized analysis algorithm for non-dispersive infrared (NDIR to in situ monitor stack emissions. The proposed algorithm simultaneously compensates for nonlinear absorption and cross interference among different gases. We present a mathematical derivation for the measurement error caused by variations in interference coefficients when nonlinear absorption occurs. The proposed algorithm is derived from a classical one and uses interference functions to quantify cross interference. The interference functions vary proportionally with the nonlinear absorption. Thus, interference coefficients among different gases can be modeled by the interference functions whether gases are characterized by linear or nonlinear absorption. In this study, the simultaneous analysis of two components (CO2 and CO serves as an example for the validation of the proposed algorithm. The interference functions in this case can be obtained by least-squares fitting with third-order polynomials. Experiments show that the results of cross interference correction are improved significantly by utilizing the fitted interference functions when nonlinear absorptions occur. The dynamic measurement ranges of CO2 and CO are improved by about a factor of 1.8 and 3.5, respectively. A commercial analyzer with high accuracy was used to validate the CO and CO2 measurements derived from the NDIR analyzer prototype in which the new algorithm was embedded. The comparison of the two analyzers show that the prototype works well both within the linear and nonlinear ranges.

  3. Step-by-step optimization and global chaos of nonlinear parameters in exact calculations of few-particle systems

    International Nuclear Information System (INIS)

    Frolov, A.M.

    1986-01-01

    Exact variational calculations are treated for few-particle systems in the exponential basis of relative coordinates using nonlinear parameters. The methods of step-by-step optimization and global chaos of nonlinear parameters are applied to calculate the S and P states of ppμ, ddμ, ttμ homonuclear mesomolecules within the error ≤±0.001 eV. The global chaos method turned out to be well applicable to nuclear 3 H and 3 He systems

  4. Step-by-step optimization and global chaos of nonlinear parameters in exact calculations of few-particle systems

    Energy Technology Data Exchange (ETDEWEB)

    Frolov, A M

    1986-09-01

    Exact variational calculations are treated for few-particle systems in the exponential basis of relative coordinates using nonlinear parameters. The methods of step-by-step optimization and global chaos of nonlinear parameters are applied to calculate the S and P states of pp..mu.., dd..mu.., tt..mu.. homonuclear mesomolecules within the error less than or equal to+-0.001 eV. The global chaos method turned out to be well applicable to nuclear /sup 3/H and /sup 3/He systems.

  5. Energy harvesting with stacked dielectric elastomer transducers: Nonlinear theory, optimization, and linearized scaling law

    Science.gov (United States)

    Tutcuoglu, A.; Majidi, C.

    2014-12-01

    Using principles of damped harmonic oscillation with continuous media, we examine electrostatic energy harvesting with a "soft-matter" array of dielectric elastomer (DE) transducers. The array is composed of infinitely thin and deformable electrodes separated by layers of insulating elastomer. During vibration, it deforms longitudinally, resulting in a change in the capacitance and electrical enthalpy of the charged electrodes. Depending on the phase of electrostatic loading, the DE array can function as either an actuator that amplifies small vibrations or a generator that converts these external excitations into electrical power. Both cases are addressed with a comprehensive theory that accounts for the influence of viscoelasticity, dielectric breakdown, and electromechanical coupling induced by Maxwell stress. In the case of a linearized Kelvin-Voigt model of the dielectric, we obtain a closed-form estimate for the electrical power output and a scaling law for DE generator design. For the complete nonlinear model, we obtain the optimal electrostatic voltage input for maximum electrical power output.

  6. Biomechanical optimization of implant diameter and length for immediate loading: a nonlinear finite element analysis.

    Science.gov (United States)

    Kong, Liang; Gu, Zexu; Li, Tao; Wu, Junjie; Hu, Kaijin; Liu, Yanpu; Zhou, Hongzhi; Liu, Baolin

    2009-01-01

    A nonlinear finite element method was applied to examine the effects of implant diameter and length on the maximum von Mises stresses in the jaw, and to evaluate the maximum displacement of the implant-abutment complex in immediate-loading models. The implant diameter (D) ranged from 3.0 to 5.0 mm and implant length (L) ranged from 6.0 to 16.0 mm. The results showed that the maximum von Mises stress in cortical bone was decreased by 65.8% under a buccolingual load with an increase in D. In cancellous bone, it was decreased by 71.5% under an axial load with an increase in L. The maximum displacement in the implant-abutment complex decreased by 64.8% under a buccolingual load with an increase in D. The implant was found to be more sensitive to L than to D under axial loads, while D played a more important role in enhancing its stability under buccolingual loads. When D exceeded 4.0 mm and L exceeded 11.0 mm, both minimum stress and displacement were obtained. Therefore, these dimensions were the optimal biomechanical selections for immediate-loading implants in type B/2 bone.

  7. The nurse scheduling problem: a goal programming and nonlinear optimization approaches

    Science.gov (United States)

    Hakim, L.; Bakhtiar, T.; Jaharuddin

    2017-01-01

    Nurses scheduling is an activity of allocating nurses to conduct a set of tasks at certain room at a hospital or health centre within a certain period. One of obstacles in the nurse scheduling is the lack of resources in order to fulfil the needs of the hospital. Nurse scheduling which is undertaken manually will be at risk of not fulfilling some nursing rules set by the hospital. Therefore, this study aimed to perform scheduling models that satisfy all the specific rules set by the management of Bogor State Hospital. We have developed three models to overcome the scheduling needs. Model 1 is designed to schedule nurses who are solely assigned to a certain inpatient unit and Model 2 is constructed to manage nurses who are assigned to an inpatient room as well as at Polyclinic room as conjunct nurses. As the assignment of nurses on each shift is uneven, then we propose Model 3 to minimize the variance of the workload in order to achieve equitable assignment on every shift. The first two models are formulated in goal programming framework, while the last model is in nonlinear optimization form.

  8. Chaotic behaviour in the non-linear optimal control of unilaterally contacting building systems during earthquakes

    International Nuclear Information System (INIS)

    Liolios, A.A.; Boglou, A.K.

    2003-01-01

    The paper presents a new numerical approach for a non-linear optimal control problem arising in earthquake civil engineering. This problem concerns the elastoplastic softening-fracturing unilateral contact between neighbouring buildings during earthquakes when Coulomb friction is taken into account under second-order instabilizing effects. So, the earthquake response of the adjacent structures can appear instabilities and chaotic behaviour. The problem formulation presented here leads to a set of equations and inequalities, which is equivalent to a dynamic hemivariational inequality in the way introduced by Panagiotopoulos [Hemivariational Inequalities. Applications in Mechanics and Engineering, Springer-Verlag, Berlin, 1993]. The numerical procedure is based on an incremental problem formulation and on a double discretization, in space by the finite element method and in time by the Wilson-θ method. The generally non-convex constitutive contact laws are piecewise linearized, and in each time-step a non-convex linear complementarity problem is solved with a reduced number of unknowns

  9. Optimal the tilt angles for photovoltaic modules using PSO method with nonlinear time-varying evolution

    International Nuclear Information System (INIS)

    Chang, Ying-Pin

    2010-01-01

    A particle-swarm optimization method with nonlinear time-varying evolution (PSO-NTVE) is employed in determining the tilt angle of photovoltaic (PV) modules in Taiwan. The objective is to maximize the output electrical energy of the modules. In this study, seven Taiwanese cities were selected for analysis. First, the sun's position at any time and location was predicted by the mathematical procedure of Julian dating, and then the solar irradiation was obtained at each site under a clear sky. By combining the temperature effect, the PSO-NTVE method is adopted to calculate the optimal tilt angles for fixed south-facing PV modules. In this method, the parameters are determined by using matrix experiments with an orthogonal array, in which a minimal number of experiments have an effect that approximates the full factorial experiments. Statistical error analysis was performed to compare the results between the four PSO methods and experimental results. Hengchun city in which the minimum total error value of 6.12% the reasons for the weather more stability and less building shade. A comparison of the measurement results in electrical energy between the four PSO methods and the PV modules set a six tilt angles. Obviously four types of PSO methods simulation of electrical energy value from 231.12 kWh/m 2 for Taipei to 233.81 kWh/m 2 for Hengchun greater than the measurement values from 224.71 kWh/m 2 for Taichung to 228.47 kWh/m 2 for Hengchun by PV module which is due to instability caused by climate change. Finally, the results show that the annual optimal angle for the Taipei area is 18.16 o ; for Taichung, 17.3 o ; for Tainan, 16.15 o ; for Kaosiung, 15.79 o ; for Hengchung, 15.17 o ; for Hualian, 17.16 o ; and for Taitung, 15.94 o . It is evident that the authorized Industrial Technology Research Institute (ITRI) recommends that tilt angle of 23.5 o was not an appropriate use of Taiwan's seven cities. PV modules with the installation of the tilt angle should be

  10. PREFACE: International Conference on 'Quantum Control, Exact or Perturbative, Linear or Nonlinear' to celebrate 50 years of the scientific career of Professor Bogdan Mielnik (Mielnik50)

    Science.gov (United States)

    Bretón, N.; Fernández, D.; Kielanowski, P.

    2015-06-01

    The International Conference on 'Quantum Control, Exact or Perturbative, Linear or Nonlinear', took place in Mexico City on 22-24 October 2014. It was held with the aim of celebrating the first fifty years of scientific career of Bogdan Mielnik, an outstanding scientist whose professional trajectory spans over Poland and Mexico and who is currently Professor Emeritus in the Physics Department of Centro de Investigación y de Estudios Avanzados del IPN (Cinvestav) in Mexico. Bogdan Mielnik was born on May 6th, 1936 in Warsaw, Poland. He studied elementary and high school until 1953. In the autumn of 1953 he started the studies in the Faculty of Mathematics and Physics at the University of Warsaw, and at the end of 1957 he did his master work under the direction of Professor Jerzy Plebański. In 1962 he was invited to the newly opened Research Center of IPN (Cinvestav), in Mexico, as an assistant and PhD student of Jerzy Plebański. On October 22nd, 1964, he submitted to Cinvestav his PhD Thesis entitled ''Analytic functions of the displacement operator'', marking the offcial beginning of his scientific career. It is worth mentioning that Bogdan Mielnik is the first PhD graduate of the Physics Department of Cinvestav, so with this Conference our Department was also celebrating an important date on its calendar. A more detailed information can be found in the website http://www.fis.cinvestav.mx/mielnik50/. It was our great pleasure to see that many collaborators and former students of Bogdan Mielnik attended this Conference. The articles collected in this volume are the written contributions of the majority of talks presented at the conference. They have been organized according to the research subjects that Bogdan Mielnik has been involved in. Thus, the articles of JG Hirsch, L Hughston, G Morales-Luna, O Rosas-Ortiz and G Torres-Vega deal with Fundamental Problems in Quantum Mechanics. On the other hand, the papers by F Delgado, H Hernández-Coronado, G Herrera

  11. Optimal signal constellation design for ultra-high-speed optical transport in the presence of nonlinear phase noise.

    Science.gov (United States)

    Liu, Tao; Djordjevic, Ivan B

    2014-12-29

    In this paper, we first describe an optimal signal constellation design algorithm suitable for the coherent optical channels dominated by the linear phase noise. Then, we modify this algorithm to be suitable for the nonlinear phase noise dominated channels. In optimization procedure, the proposed algorithm uses the cumulative log-likelihood function instead of the Euclidian distance. Further, an LDPC coded modulation scheme is proposed to be used in combination with signal constellations obtained by proposed algorithm. Monte Carlo simulations indicate that the LDPC-coded modulation schemes employing the new constellation sets, obtained by our new signal constellation design algorithm, outperform corresponding QAM constellations significantly in terms of transmission distance and have better nonlinearity tolerance.

  12. Multiplex protein pattern unmixing using a non-linear variable-weighted support vector machine as optimized by a particle swarm optimization algorithm.

    Science.gov (United States)

    Yang, Qin; Zou, Hong-Yan; Zhang, Yan; Tang, Li-Juan; Shen, Guo-Li; Jiang, Jian-Hui; Yu, Ru-Qin

    2016-01-15

    Most of the proteins locate more than one organelle in a cell. Unmixing the localization patterns of proteins is critical for understanding the protein functions and other vital cellular processes. Herein, non-linear machine learning technique is proposed for the first time upon protein pattern unmixing. Variable-weighted support vector machine (VW-SVM) is a demonstrated robust modeling technique with flexible and rational variable selection. As optimized by a global stochastic optimization technique, particle swarm optimization (PSO) algorithm, it makes VW-SVM to be an adaptive parameter-free method for automated unmixing of protein subcellular patterns. Results obtained by pattern unmixing of a set of fluorescence microscope images of cells indicate VW-SVM as optimized by PSO is able to extract useful pattern features by optimally rescaling each variable for non-linear SVM modeling, consequently leading to improved performances in multiplex protein pattern unmixing compared with conventional SVM and other exiting pattern unmixing methods. Copyright © 2015 Elsevier B.V. All rights reserved.

  13. Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems.

    Science.gov (United States)

    Miró, Anton; Pozo, Carlos; Guillén-Gosálbez, Gonzalo; Egea, Jose A; Jiménez, Laureano

    2012-05-10

    The estimation of parameter values for mathematical models of biological systems is an optimization problem that is particularly challenging due to the nonlinearities involved. One major difficulty is the existence of multiple minima in which standard optimization methods may fall during the search. Deterministic global optimization methods overcome this limitation, ensuring convergence to the global optimum within a desired tolerance. Global optimization techniques are usually classified into stochastic and deterministic. The former typically lead to lower CPU times but offer no guarantee of convergence to the global minimum in a finite number of iterations. In contrast, deterministic methods provide solutions of a given quality (i.e., optimality gap), but tend to lead to large computational burdens. This work presents a deterministic outer approximation-based algorithm for the global optimization of dynamic problems arising in the parameter estimation of models of biological systems. Our approach, which offers a theoretical guarantee of convergence to global minimum, is based on reformulating the set of ordinary differential equations into an equivalent set of algebraic equations through the use of orthogonal collocation methods, giving rise to a nonconvex nonlinear programming (NLP) problem. This nonconvex NLP is decomposed into two hierarchical levels: a master mixed-integer linear programming problem (MILP) that provides a rigorous lower bound on the optimal solution, and a reduced-space slave NLP that yields an upper bound. The algorithm iterates between these two levels until a termination criterion is satisfied. The capabilities of our approach were tested in two benchmark problems, in which the performance of our algorithm was compared with that of the commercial global optimization package BARON. The proposed strategy produced near optimal solutions (i.e., within a desired tolerance) in a fraction of the CPU time required by BARON.

  14. Design optimization of single mixed refrigerant natural gas liquefaction process using the particle swarm paradigm with nonlinear constraints

    International Nuclear Information System (INIS)

    Khan, Mohd Shariq; Lee, Moonyong

    2013-01-01

    The particle swarm paradigm is employed to optimize single mixed refrigerant natural gas liquefaction process. Liquefaction design involves multivariable problem solving and non-optimal execution of these variables can waste energy and contribute to process irreversibilities. Design optimization requires these variables to be optimized simultaneously; minimizing the compression energy requirement is selected as the optimization objective. Liquefaction is modeled using Honeywell UniSim Design ™ and the resulting rigorous model is connected with the particle swarm paradigm coded in MATLAB. Design constraints are folded into the objective function using the penalty function method. Optimization successfully improved efficiency by reducing the compression energy requirement by ca. 10% compared with the base case. -- Highlights: ► The particle swarm paradigm (PSP) is employed for design optimization of SMR NG liquefaction process. ► Rigorous SMR process model based on UniSim is connected with PSP coded in MATLAB. ► Stochastic features of PSP give more confidence in the optimality of complex nonlinear problems. ► Optimization with PSP notably improves energy efficiency of the SMR process.

  15. Optimization of Nonlinear Figure-of-Merits of Integrated Power MOSFETs in Partial SOI Process

    DEFF Research Database (Denmark)

    Fan, Lin; Jørgensen, Ivan Harald Holger; Knott, Arnold

    2016-01-01

    State-of-the-art power semiconductor industry uses figure-of-merits (FOMs) for technology-to-technology and/or device-to-device comparisons. However, the existing FOMs are fundamentally nonlinear due to the nonlinearities of the parameters such as the gate charge and the output charge versus...

  16. Adaptive Optimizing Nonlinear Control Design for an Over-actuated Aircraft Model

    NARCIS (Netherlands)

    Van Oort, E.R.; Sonneveldt, L.; Chu, Q.P.; Mulder, J.A.

    2011-01-01

    In this paper nonlinear adaptive flight control laws based on the backstepping approach are proposed which are applicable to over-actuated nonlinear systems. Instead of solving the control allocation exactly, update laws for the desired control effector signals are defined such that they converge to

  17. A Quasi-Dynamic Optimal Control Strategy for Non-Linear Multivariable Processes Based upon Non-Quadratic Objective Functions

    Directory of Open Access Journals (Sweden)

    Jens G. Balchen

    1984-10-01

    Full Text Available The problem of systematic derivation of a quasi-dynamic optimal control strategy for a non-linear dynamic process based upon a non-quadratic objective function is investigated. The wellknown LQG-control algorithm does not lead to an optimal solution when the process disturbances have non-zero mean. The relationships between the proposed control algorithm and LQG-control are presented. The problem of how to constrain process variables by means of 'penalty' - terms in the objective function is dealt with separately.

  18. Variable Structure Disturbance Rejection Control for Nonlinear Uncertain Systems with State and Control Delays via Optimal Sliding Mode Surface Approach

    Directory of Open Access Journals (Sweden)

    Jing Lei

    2013-01-01

    Full Text Available The paper considers the problem of variable structure control for nonlinear systems with uncertainty and time delays under persistent disturbance by using the optimal sliding mode surface approach. Through functional transformation, the original time-delay system is transformed into a delay-free one. The approximating sequence method is applied to solve the nonlinear optimal sliding mode surface problem which is reduced to a linear two-point boundary value problem of approximating sequences. The optimal sliding mode surface is obtained from the convergent solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. Then, the variable structure disturbance rejection control is presented by adopting an exponential trending law, where the state and control memory terms are designed to compensate the state and control delays, a feedforward control term is designed to reject the disturbance, and an adjoint compensator is designed to compensate the effects generated by the nonlinearity and the uncertainty. Furthermore, an observer is constructed to make the feedforward term physically realizable, and thus the dynamical observer-based dynamical variable structure disturbance rejection control law is produced. Finally, simulations are demonstrated to verify the effectiveness of the presented controller and the simplicity of the proposed approach.

  19. Experimental study of the semi-active control of a nonlinear two-span bridge using stochastic optimal polynomial control

    Science.gov (United States)

    El-Khoury, O.; Kim, C.; Shafieezadeh, A.; Hur, J. E.; Heo, G. H.

    2015-06-01

    This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion.

  20. Experimental study of the semi-active control of a nonlinear two-span bridge using stochastic optimal polynomial control

    International Nuclear Information System (INIS)

    El-Khoury, O; Shafieezadeh, A; Hur, J E; Kim, C; Heo, G H

    2015-01-01

    This study performs a series of numerical simulations and shake-table experiments to design and assess the performance of a nonlinear clipped feedback control algorithm based on optimal polynomial control (OPC) to mitigate the response of a two-span bridge equipped with a magnetorheological (MR) damper. As an extended conventional linear quadratic regulator, OPC provides more flexibility in the control design and further enhances system performance. The challenges encountered in this case are (1) the linearization of the nonlinear behavior of various components and (2) the selection of the weighting matrices in the objective function of OPC. The first challenge is addressed by using stochastic linearization which replaces the nonlinear portion of the system behavior with an equivalent linear time-invariant model considering the stochasticity in the excitation. Furthermore, a genetic algorithm is employed to find optimal weighting matrices for the control design. The input current to the MR damper installed between adjacent spans is determined using a clipped stochastic optimal polynomial control algorithm. The performance of the controlled system is assessed through a set of shake-table experiments for far-field and near-field ground motions. The proposed method showed considerable improvements over passive cases especially for the far-field ground motion. (paper)

  1. A Novel Scheme for Optimal Control of a Nonlinear Delay Differential Equations Model to Determine Effective and Optimal Administrating Chemotherapy Agents in Breast Cancer.

    Science.gov (United States)

    Ramezanpour, H R; Setayeshi, S; Akbari, M E

    2011-01-01

    Determining the optimal and effective scheme for administrating the chemotherapy agents in breast cancer is the main goal of this scientific research. The most important issue here is the amount of drug or radiation administrated in chemotherapy and radiotherapy for increasing patient's survival. This is because in these cases, the therapy not only kills the tumor cells, but also kills some of the healthy tissues and causes serious damages. In this paper we investigate optimal drug scheduling effect for breast cancer model which consist of nonlinear ordinary differential time-delay equations. In this paper, a mathematical model of breast cancer tumors is discussed and then optimal control theory is applied to find out the optimal drug adjustment as an input control of system. Finally we use Sensitivity Approach (SA) to solve the optimal control problem. The goal of this paper is to determine optimal and effective scheme for administering the chemotherapy agent, so that the tumor is eradicated, while the immune systems remains above a suitable level. Simulation results confirm the effectiveness of our proposed procedure. In this paper a new scheme is proposed to design a therapy protocol for chemotherapy in Breast Cancer. In contrast to traditional pulse drug delivery, a continuous process is offered and optimized, according to the optimal control theory for time-delay systems.

  2. Performance of a Nonlinear Real-Time Optimal Control System for HEVs/PHEVs during Car Following

    Directory of Open Access Journals (Sweden)

    Kaijiang Yu

    2014-01-01

    Full Text Available This paper presents a real-time optimal control approach for the energy management problem of hybrid electric vehicles (HEVs and plug-in hybrid electric vehicles (PHEVs with slope information during car following. The new features of this study are as follows. First, the proposed method can optimize the engine operating points and the driving profile simultaneously. Second, the proposed method gives the freedom of vehicle spacing between the preceding vehicle and the host vehicle. Third, using the HEV/PHEV property, the desired battery state of charge is designed according to the road slopes for better recuperation of free braking energy. Fourth, all of the vehicle operating modes engine charge, electric vehicle, motor assist and electric continuously variable transmission, and regenerative braking, can be realized using the proposed real-time optimal control approach. Computer simulation results are shown among the nonlinear real-time optimal control approach and the ADVISOR rule-based approach. The conclusion is that the nonlinear real-time optimal control approach is effective for the energy management problem of the HEV/PHEV system during car following.

  3. A mixed-integer nonlinear programming approach to the optimal design of heat network in a polygeneration energy system

    International Nuclear Information System (INIS)

    Zhang, Jianyun; Liu, Pei; Zhou, Zhe; Ma, Linwei; Li, Zheng; Ni, Weidou

    2014-01-01

    Highlights: • Integration of heat streams with HRSG in a polygeneration system is studied. • A mixed-integer nonlinear programming model is proposed to optimize heat network. • Operating parameters and heat network configuration are optimized simultaneously. • The optimized heat network highly depends on the HRSG type and model specification. - Abstract: A large number of heat flows at various temperature and pressure levels exist in a polygeneration plant which co-produces electricity and chemical products. Integration of these external heat flows in a heat recovery steam generator (HRSG) has great potential to further enhance energy efficiency of such a plant; however, it is a challenging problem arising from the large design space of heat exchanger network. In this paper, a mixed-integer nonlinear programming model is developed for the design optimization of a HRSG with consideration of all alternative matches between the HRSG and external heat flows. This model is applied to four polygeneration cases with different HRSG types, and results indicate that the optimized heat network mainly depends on the HRSG type and the model specification

  4. Optimal Performance of a Nonlinear Gantry Crane System via Priority-based Fitness Scheme in Binary PSO Algorithm

    International Nuclear Information System (INIS)

    Jaafar, Hazriq Izzuan; Ali, Nursabillilah Mohd; Selamat, Nur Asmiza; Kassim, Anuar Mohamed; Mohamed, Z; Abidin, Amar Faiz Zainal; Jamian, J J

    2013-01-01

    This paper presents development of an optimal PID and PD controllers for controlling the nonlinear gantry crane system. The proposed Binary Particle Swarm Optimization (BPSO) algorithm that uses Priority-based Fitness Scheme is adopted in obtaining five optimal controller gains. The optimal gains are tested on a control structure that combines PID and PD controllers to examine system responses including trolley displacement and payload oscillation. The dynamic model of gantry crane system is derived using Lagrange equation. Simulation is conducted within Matlab environment to verify the performance of system in terms of settling time (Ts), steady state error (SSE) and overshoot (OS). This proposed technique demonstrates that implementation of Priority-based Fitness Scheme in BPSO is effective and able to move the trolley as fast as possible to the various desired position

  5. An Optimized Elasto-Plastic Subgrade Reaction For Modeling The Response Of A Nonlinear Foundation For A Structural Analysis

    Directory of Open Access Journals (Sweden)

    Ray Richard Paul

    2015-09-01

    Full Text Available Geotechnical and structural engineers are faced with a difficult task when their designs interact with each other. For complex projects, this is more the norm than the exception. In order to help bridge that gap, a method for modeling the behavior of a foundation using a simple elasto-plastic subgrade reaction was developed. The method uses an optimization technique to position 4-6 springs along a pile foundation to produce similar load deflection characteristics that were modeled by more sophisticated geotechnical finite element software. The methodology uses an Excel spreadsheet for accepting user input and delivering an optimized subgrade spring stiffness, yield, and position along the pile. In this way, the behavior developed from the geotechnical software can be transferred to the structural analysis software. The optimization is achieved through the solver add-in within Excel. Additionally, a beam on a nonlinear elastic foundation model is used to compute deflections of the optimized subgrade reaction configuration.

  6. Policy Iteration for $H_\\infty $ Optimal Control of Polynomial Nonlinear Systems via Sum of Squares Programming.

    Science.gov (United States)

    Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao

    2018-02-01

    Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest -gain and the associated optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.

  7. Analysis and design of robust decentralized controllers for nonlinear systems

    Energy Technology Data Exchange (ETDEWEB)

    Schoenwald, D.A.

    1993-07-01

    Decentralized control strategies for nonlinear systems are achieved via feedback linearization techniques. New results on optimization and parameter robustness of non-linear systems are also developed. In addition, parametric uncertainty in large-scale systems is handled by sensitivity analysis and optimal control methods in a completely decentralized framework. This idea is applied to alleviate uncertainty in friction parameters for the gimbal joints on Space Station Freedom. As an example of decentralized nonlinear control, singular perturbation methods and distributed vibration damping are merged into a control strategy for a two-link flexible manipulator.

  8. Nonlinear switching dynamics in a photonic-crystal nanocavity

    International Nuclear Information System (INIS)

    Yu, Yi; Palushani, Evarist; Heuck, Mikkel; Vukovic, Dragana; Peucheret, Christophe; Yvind, Kresten; Mork, Jesper

    2014-01-01

    We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching contrast.

  9. Nonlinear switching dynamics in a photonic-crystal nanocavity

    DEFF Research Database (Denmark)

    Yu, Yi; Palushani, Evarist; Heuck, Mikkel

    2014-01-01

    We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When...... of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching...... the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms...

  10. Perturbed asymptotically linear problems

    OpenAIRE

    Bartolo, R.; Candela, A. M.; Salvatore, A.

    2012-01-01

    The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which is just continuous. Also in the case when the problem has not a variational structure, suitable procedures and estimates allow us to prove that the number of distinct crtitical levels of the functional associated to the unperturbed problem is "stable" unde...

  11. Detecting unstable periodic orbits of nonlinear mappings by a novel quantum-behaved particle swarm optimization non-Lyapunov way

    International Nuclear Information System (INIS)

    Gao Fei; Gao Hongrui; Li Zhuoqiu; Tong Hengqing; Lee, Ju-Jang

    2009-01-01

    It is well known that set of unstable periodic orbits (UPOs) can be thought of as the skeleton for the dynamics. However, detecting UPOs of nonlinear map is one of the most challenging problems of nonlinear science in both numerical computations and experimental measures. In this paper, a new method is proposed to detect the UPOs in a non-Lyapunov way. Firstly three special techniques are added to quantum-behaved particle swarm optimization (QPSO), a novel mbest particle, contracting the searching space self-adaptively and boundaries restriction (NCB), then the new method NCB-QPSO is proposed. It can maintain an effective search mechanism with fine equilibrium between exploitation and exploration. Secondly, the problems of detecting the UPOs are converted into a non-negative functions' minimization through a proper translation in a non-Lyapunov way. Thirdly the simulations to 6 benchmark optimization problems and different high order UPOs of 5 classic nonlinear maps are done by the proposed method. And the results show that NCB-QPSO is a successful method in detecting the UPOs, and it has the advantages of fast convergence, high precision and robustness.

  12. Nonlinear H∞ Optimal Control Scheme for an Underwater Vehicle with Regional Function Formulation

    Directory of Open Access Journals (Sweden)

    Zool H. Ismail

    2013-01-01

    Full Text Available A conventional region control technique cannot meet the demands for an accurate tracking performance in view of its inability to accommodate highly nonlinear system dynamics, imprecise hydrodynamic coefficients, and external disturbances. In this paper, a robust technique is presented for an Autonomous Underwater Vehicle (AUV with region tracking function. Within this control scheme, nonlinear H∞ and region based control schemes are used. A Lyapunov-like function is presented for stability analysis of the proposed control law. Numerical simulations are presented to demonstrate the performance of the proposed tracking control of the AUV. It is shown that the proposed control law is robust against parameter uncertainties, external disturbances, and nonlinearities and it leads to uniform ultimate boundedness of the region tracking error.

  13. Maximized gust loads for a nonlinear airplane using matched filter theory and constrained optimization

    Science.gov (United States)

    Scott, Robert C.; Perry, Boyd, III; Pototzky, Anthony S.

    1991-01-01

    This paper describes and illustrates two matched-filter-theory based schemes for obtaining maximized and time-correlated gust-loads for a nonlinear airplane. The first scheme is computationally fast because it uses a simple one-dimensional search procedure to obtain its answers. The second scheme is computationally slow because it uses a more complex multidimensional search procedure to obtain its answers, but it consistently provides slightly higher maximum loads than the first scheme. Both schemes are illustrated with numerical examples involving a nonlinear control system.

  14. Non-Linear Multi-Physics Analysis and Multi-Objective Optimization in Electroheating Applications

    Czech Academy of Sciences Publication Activity Database

    di Barba, P.; Doležel, Ivo; Mognaschi, M. E.; Savini, A.; Karban, P.

    2014-01-01

    Roč. 50, č. 2 (2014), s. 7016604-7016604 ISSN 0018-9464 Institutional support: RVO:61388998 Keywords : coupled multi-physics problems * finite element method * non-linear equations Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 1.386, year: 2014

  15. Enhanced nonlinearity interval mapping scheme for high-performance simulation-optimization of watershed-scale BMP placement

    Science.gov (United States)

    Zou, Rui; Riverson, John; Liu, Yong; Murphy, Ryan; Sim, Youn

    2015-03-01

    Integrated continuous simulation-optimization models can be effective predictors of a process-based responses for cost-benefit optimization of best management practices (BMPs) selection and placement. However, practical application of simulation-optimization model is computationally prohibitive for large-scale systems. This study proposes an enhanced Nonlinearity Interval Mapping Scheme (NIMS) to solve large-scale watershed simulation-optimization problems several orders of magnitude faster than other commonly used algorithms. An efficient interval response coefficient (IRC) derivation method was incorporated into the NIMS framework to overcome a computational bottleneck. The proposed algorithm was evaluated using a case study watershed in the Los Angeles County Flood Control District. Using a continuous simulation watershed/stream-transport model, Loading Simulation Program in C++ (LSPC), three nested in-stream compliance points (CP)—each with multiple Total Maximum Daily Loads (TMDL) targets—were selected to derive optimal treatment levels for each of the 28 subwatersheds, so that the TMDL targets at all the CP were met with the lowest possible BMP implementation cost. Genetic Algorithm (GA) and NIMS were both applied and compared. The results showed that the NIMS took 11 iterations (about 11 min) to complete with the resulting optimal solution having a total cost of 67.2 million, while each of the multiple GA executions took 21-38 days to reach near optimal solutions. The best solution obtained among all the GA executions compared had a minimized cost of 67.7 million—marginally higher, but approximately equal to that of the NIMS solution. The results highlight the utility for decision making in large-scale watershed simulation-optimization formulations.

  16. Optimal Tuning of Decentralized PI Controller of Nonlinear Multivariable Process Using Archival Based Multiobjective Particle Swarm Optimization

    Directory of Open Access Journals (Sweden)

    R. Kotteeswaran

    2014-01-01

    Full Text Available A Multiobjective Particle Swarm Optimization (MOPSO algorithm is proposed to fine-tune the baseline PI controller parameters of Alstom gasifier. The existing baseline PI controller is not able to meet the performance requirements of Alstom gasifier for sinusoidal pressure disturbance at 0% load. This is considered the major drawback of controller design. A best optimal solution for Alstom gasifier is obtained from a set of nondominated solutions using MOPSO algorithm. Performance of gasifier is investigated at all load conditions. The controller with optimized controller parameters meets all the performance requirements at 0%, 50%, and 100% load conditions. The investigations are also extended for variations in coal quality, which shows an improved stability of the gasifier over a wide range of coal quality variations.

  17. OPTIMAL CONTROL OF A NONLINEAR COUPLED ELECTROMAGNETIC INDUCTION HEATING SYSTEM WITH POINTWISE STATE CONSTRAINTS

    Directory of Open Access Journals (Sweden)

    Irwin Yousept

    2010-07-01

    Full Text Available An optimal control problem arising in the context of 3D electromagnetic induction heating is investigated. The state equation is given by a quasilinear stationary heat equation coupled with a semilinear time harmonic eddy current equation. The temperature-dependent electrical conductivity and the presence of pointwise inequality state-constraints represent the main challenge of the paper. In the first part of the paper, the existence and regularity of the state are addressed. The second part of the paper deals with the analysis of the corresponding linearized equation. Some suffcient conditions are presented which guarantee thesolvability of the linearized system. The final part of the paper is concerned with the optimal control. The aim of the optimization is to find the optimal voltage such that a desired temperature can be achieved optimally. The corresponding first-order necessary optimality condition is presented.

  18. Mixed-integer nonlinear approach for the optimal scheduling of a head-dependent hydro chain

    Energy Technology Data Exchange (ETDEWEB)

    Catalao, J.P.S.; Pousinho, H.M.I. [Department of Electromechanical Engineering, University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilha (Portugal); Mendes, V.M.F. [Department of Electrical Engineering and Automation, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Emidio Navarro, 1950-062 Lisbon (Portugal)

    2010-08-15

    This paper is on the problem of short-term hydro scheduling (STHS), particularly concerning a head-dependent hydro chain. We propose a novel mixed-integer nonlinear programming (MINLP) approach, considering hydroelectric power generation as a nonlinear function of water discharge and of the head. As a new contribution to earlier studies, we model the on-off behavior of the hydro plants using integer variables, in order to avoid water discharges at forbidden areas. Thus, an enhanced STHS is provided due to the more realistic modeling presented in this paper. Our approach has been applied successfully to solve a test case based on one of the Portuguese cascaded hydro systems with a negligible computational time requirement. (author)

  19. Interior-Point Method for Non-Linear Non-Convex Optimization

    Czech Academy of Sciences Publication Activity Database

    Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan

    2004-01-01

    Roč. 11, č. 5-6 (2004), s. 431-453 ISSN 1070-5325 R&D Projects: GA AV ČR IAA1030103 Institutional research plan: CEZ:AV0Z1030915 Keywords : non-linear programming * interior point methods * indefinite systems * indefinite preconditioners * preconditioned conjugate gradient method * merit functions * algorithms * computational experiments Subject RIV: BA - General Mathematics Impact factor: 0.727, year: 2004

  20. Non-linear optimization of track layouts in loop-sorting-systems

    DEFF Research Database (Denmark)

    Sørensen, Søren Emil; Hansen, Michael R.; Ebbesen, Morten K.

    2013-01-01

    Optimization used for enhancing geometric structures iswell known. Applying obstacles to the shape optimization problemis on the other hand not very common. It requires a fast contact search algorithmand an exact continuous formulation to solve the problem robustly. This paper focuses on combining...

  1. Optimal Control of Evolution Mixed Variational Inclusions

    Energy Technology Data Exchange (ETDEWEB)

    Alduncin, Gonzalo, E-mail: alduncin@geofisica.unam.mx [Universidad Nacional Autónoma de México, Departamento de Recursos Naturales, Instituto de Geofísica (Mexico)

    2013-12-15

    Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory.

  2. Optimal Control of Evolution Mixed Variational Inclusions

    International Nuclear Information System (INIS)

    Alduncin, Gonzalo

    2013-01-01

    Optimal control problems of primal and dual evolution mixed variational inclusions, in reflexive Banach spaces, are studied. The solvability analysis of the mixed state systems is established via duality principles. The optimality analysis is performed in terms of perturbation conjugate duality methods, and proximation penalty-duality algorithms to mixed optimality conditions are further presented. Applications to nonlinear diffusion constrained problems as well as quasistatic elastoviscoplastic bilateral contact problems exemplify the theory

  3. Optimal Decision-Making in Fuzzy Economic Order Quantity (EOQ Model under Restricted Space: A Non-Linear Programming Approach

    Directory of Open Access Journals (Sweden)

    M. Pattnaik

    2013-08-01

    Full Text Available In this paper the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model under restricted space. Since various types of uncertainties and imprecision are inherent in real inventory problems they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment how to interpret optimal solutions arise. This paper allows the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price and the setup cost varies with the quantity produced/Purchased. This paper considers the modification of objective function and storage area in the presence of imprecisely estimated parameters. The model is developed for the problem by employing different modeling approaches over an infinite planning horizon. It incorporates all concepts of a fuzzy arithmetic approach, the quantity ordered and the demand per unit compares both fuzzy non linear and other models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated through an example problem and ugh MATLAB (R2009a version software, the two and three dimensional diagrams are represented to the application. Sensitivity analysis of the optimal solution is also studied with respect to changes in different parameter values and to draw managerial insights of the decision problem.

  4. Traffic Perturbation

    CERN Multimedia

    C. Colloca TS/FM

    2004-01-01

    TS/FM group informs you that, for the progress of the works at the Prévessin site entrance, some perturbation of the traffic may occur during the week between the 14th and 18th of June for a short duration. Access will be assured at any time. For more information, please contact 160239. C. Colloca TS/FM

  5. An integer optimization algorithm for robust identification of non-linear gene regulatory networks

    Directory of Open Access Journals (Sweden)

    Chemmangattuvalappil Nishanth

    2012-09-01

    Full Text Available Abstract Background Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. Results We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters

  6. Optimal Operation of Industrial Batch Crystallizers : A Nonlinear Model-based Control Approach

    NARCIS (Netherlands)

    Mesbah, A.

    2010-01-01

    Batch crystallization is extensively employed in the chemical, pharmaceutical, and food industries to separate and purify high value-added chemical substances. Despite their widespread application, optimal operation of batch crystallizers is particularly challenging. The difficulties primarily

  7. Optimal Layout Design using the Element Connectivity Parameterization Method: Application to Three Dimensional Geometrical Nonlinear Structures

    DEFF Research Database (Denmark)

    Yoon, Gil Ho; Joung, Young Soo; Kim, Yoon Young

    2005-01-01

    The topology design optimization of “three-dimensional geometrically-nonlinear” continuum structures is still a difficult problem not only because of its problem size but also the occurrence of unstable continuum finite elements during the design optimization. To overcome this difficulty, the ele......) stiffness matrix of continuum finite elements. Therefore, any finite element code, including commercial codes, can be readily used for the ECP implementation. The key ideas and characteristics of these methods will be presented in this paper....

  8. Optimizing BAO measurements with non-linear transformations of the Lyman-α forest

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Xinkang; Font-Ribera, Andreu; Seljak, Uroš, E-mail: xinkang.wang@berkeley.edu, E-mail: afont@lbl.gov, E-mail: useljak@berkeley.edu [Department of Physics, University of California, South Hall Rd, Berkeley (United States)

    2015-04-01

    We explore the effect of applying a non-linear transformation to the Lyman-α forest transmitted flux F=e{sup −τ} and the ability of analytic models to predict the resulting clustering amplitude. Both the large-scale bias of the transformed field (signal) and the amplitude of small scale fluctuations (noise) can be arbitrarily modified, but we were unable to find a transformation that increases significantly the signal-to-noise ratio on large scales using Taylor expansion up to the third order. In particular, however, we achieve a 33% improvement in signal to noise for Gaussianized field in transverse direction. On the other hand, we explore an analytic model for the large-scale biasing of the Lyα forest, and present an extension of this model to describe the biasing of the transformed fields. Using hydrodynamic simulations we show that the model works best to describe the biasing with respect to velocity gradients, but is less successful in predicting the biasing with respect to large-scale density fluctuations, especially for very nonlinear transformations.

  9. Comparison of Traditional Design Nonlinear Programming Optimization and Stochastic Methods for Structural Design

    Science.gov (United States)

    Patnaik, Surya N.; Pai, Shantaram S.; Coroneos, Rula M.

    2010-01-01

    Structural design generated by traditional method, optimization method and the stochastic design concept are compared. In the traditional method, the constraints are manipulated to obtain the design and weight is back calculated. In design optimization, the weight of a structure becomes the merit function with constraints imposed on failure modes and an optimization algorithm is used to generate the solution. Stochastic design concept accounts for uncertainties in loads, material properties, and other parameters and solution is obtained by solving a design optimization problem for a specified reliability. Acceptable solutions were produced by all the three methods. The variation in the weight calculated by the methods was modest. Some variation was noticed in designs calculated by the methods. The variation may be attributed to structural indeterminacy. It is prudent to develop design by all three methods prior to its fabrication. The traditional design method can be improved when the simplified sensitivities of the behavior constraint is used. Such sensitivity can reduce design calculations and may have a potential to unify the traditional and optimization methods. Weight versus reliabilitytraced out an inverted-S-shaped graph. The center of the graph corresponded to mean valued design. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Weight can be reduced to a small value for a most failure-prone design. Probabilistic modeling of load and material properties remained a challenge.

  10. A single network adaptive critic (SNAC) architecture for optimal control synthesis for a class of nonlinear systems.

    Science.gov (United States)

    Padhi, Radhakant; Unnikrishnan, Nishant; Wang, Xiaohua; Balakrishnan, S N

    2006-12-01

    Even though dynamic programming offers an optimal control solution in a state feedback form, the method is overwhelmed by computational and storage requirements. Approximate dynamic programming implemented with an Adaptive Critic (AC) neural network structure has evolved as a powerful alternative technique that obviates the need for excessive computations and storage requirements in solving optimal control problems. In this paper, an improvement to the AC architecture, called the "Single Network Adaptive Critic (SNAC)" is presented. This approach is applicable to a wide class of nonlinear systems where the optimal control (stationary) equation can be explicitly expressed in terms of the state and costate variables. The selection of this terminology is guided by the fact that it eliminates the use of one neural network (namely the action network) that is part of a typical dual network AC setup. As a consequence, the SNAC architecture offers three potential advantages: a simpler architecture, lesser computational load and elimination of the approximation error associated with the eliminated network. In order to demonstrate these benefits and the control synthesis technique using SNAC, two problems have been solved with the AC and SNAC approaches and their computational performances are compared. One of these problems is a real-life Micro-Electro-Mechanical-system (MEMS) problem, which demonstrates that the SNAC technique is applicable to complex engineering systems.

  11. Computational Modelling and Optimal Control of Ebola Virus Disease with non-Linear Incidence Rate

    Science.gov (United States)

    Takaidza, I.; Makinde, O. D.; Okosun, O. K.

    2017-03-01

    The 2014 Ebola outbreak in West Africa has exposed the need to connect modellers and those with relevant data as pivotal to better understanding of how the disease spreads and quantifying the effects of possible interventions. In this paper, we model and analyse the Ebola virus disease with non-linear incidence rate. The epidemic model created is used to describe how the Ebola virus could potentially evolve in a population. We perform an uncertainty analysis of the basic reproductive number R 0 to quantify its sensitivity to other disease-related parameters. We also analyse the sensitivity of the final epidemic size to the time control interventions (education, vaccination, quarantine and safe handling) and provide the cost effective combination of the interventions.

  12. Performance analysis and optimization of radiating fins with a step change in thickness and variable thermal conductivity by homotopy perturbation method

    Science.gov (United States)

    Arslanturk, Cihat

    2011-02-01

    Although tapered fins transfer more rate of heat per unit volume, they are not found in every practical application because of the difficulty in manufacturing and fabrications. Therefore, there is a scope to modify the geometry of a constant thickness fin in view of the less difficulty in manufacturing and fabrication as well as betterment of heat transfer rate per unit volume of the fin material. For the better utilization of fin material, it is proposed a modified geometry of new fin with a step change in thickness (SF) in the literature. In the present paper, the homotopy perturbation method has been used to evaluate the temperature distribution within the straight radiating fins with a step change in thickness and variable thermal conductivity. The temperature profile has an abrupt change in the temperature gradient where the step change in thickness occurs and thermal conductivity parameter describing the variation of thermal conductivity has an important role on the temperature profile and the heat transfer rate. The optimum geometry which maximizes the heat transfer rate for a given fin volume has been found. The derived condition of optimality gives an open choice to the designer.

  13. Role of statistical linearization in the solution of nonlinear stochastic equations

    International Nuclear Information System (INIS)

    Budgor, A.B.

    1977-01-01

    The solution of a generalized Langevin equation is referred to as a stochastic process. If the external forcing function is Gaussian white noise, the forward Kolmogarov equation yields the transition probability density function. Nonlinear problems must be handled by approximation procedures e.g., perturbation theories, eigenfunction expansions, and nonlinear optimization procedures. After some comments on the first two of these, attention is directed to the third, and the method of statistical linearization is used to demonstrate a relation to the former two. Nonlinear stochastic systems exhibiting sustained or forced oscillations and the centered nonlinear Schroedinger equation in the presence of Gaussian white noise excitation are considered as examples. 5 figures, 2 tables

  14. Comparison of two perturbation methods to estimate the land surface modeling uncertainty

    Science.gov (United States)

    Su, H.; Houser, P.; Tian, Y.; Kumar, S.; Geiger, J.; Belvedere, D.

    2007-12-01

    In land surface modeling, it is almost impossible to simulate the land surface processes without any error because the earth system is highly complex and the physics of the land processes has not yet been understood sufficiently. In most cases, people want to know not only the model output but also the uncertainty in the modeling, to estimate how reliable the modeling is. Ensemble perturbation is an effective way to estimate the uncertainty in land surface modeling, since land surface models are highly nonlinear which makes the analytical approach not applicable in this estimation. The ideal perturbation noise is zero mean Gaussian distribution, however, this requirement can't be satisfied if the perturbed variables in land surface model have physical boundaries because part of the perturbation noises has to be removed to feed the land surface models properly. Two different perturbation methods are employed in our study to investigate their impact on quantifying land surface modeling uncertainty base on the Land Information System (LIS) framework developed by NASA/GSFC land team. One perturbation method is the built-in algorithm named "STATIC" in LIS version 5; the other is a new perturbation algorithm which was recently developed to minimize the overall bias in the perturbation by incorporating additional information from the whole time series for the perturbed variable. The statistical properties of the perturbation noise generated by the two different algorithms are investigated thoroughly by using a large ensemble size on a NASA supercomputer and then the corresponding uncertainty estimates based on the two perturbation methods are compared. Their further impacts on data assimilation are also discussed. Finally, an optimal perturbation method is suggested.

  15. Flexible aluminum tubes and a least square multi-objective non-linear optimization scheme

    International Nuclear Information System (INIS)

    Endelt, Benny; Nielsen, Karl Brian; Olsen, Soeren

    2004-01-01

    The automotive industry currently uses rubber hoses as the media carrier between e.g. the radiator and the engine, and the basic idea is to replace the rubber hoses with flexible aluminum tubes.A good quality is defined through several quality measurements, i.e. in the current case the key objective is to produce a flexible convolution through optimization of the tool geometry, but the process should also be stable, and the process stability is evaluated through Forming Limit Diagrams. Typically the defined objectives are conflicting, i.e. the optimized configuration represents therefore a trade-off between the individual objectives, in this case flexibility versus process stability.The optimization problem is solved through iteratively minimizing the object function. A second-order least square scheme is used for the approximation of the quadratic model, and the change in the design parameters is evaluated through the trust region scheme and box constraints are introduced within the trust region framework. Furthermore, the object function is minimized by applying the non-monotone scheme, and the trust region subproblem is solved by applying the Cholesky factorization scheme.An optimal bell shaped geometry is identified and the design is verified experimentally

  16. Combatting nonlinear phase noise in coherent optical systems with an optimized decision processor based on machine learning

    Science.gov (United States)

    Wang, Danshi; Zhang, Min; Cai, Zhongle; Cui, Yue; Li, Ze; Han, Huanhuan; Fu, Meixia; Luo, Bin

    2016-06-01

    An effective machine learning algorithm, the support vector machine (SVM), is presented in the context of a coherent optical transmission system. As a classifier, the SVM can create nonlinear decision boundaries to mitigate the distortions caused by nonlinear phase noise (NLPN). Without any prior information or heuristic assumptions, the SVM can learn and capture the link properties from only a few training data. Compared with the maximum likelihood estimation (MLE) algorithm, a lower bit-error rate (BER) is achieved by the SVM for a given launch power; moreover, the launch power dynamic range (LPDR) is increased by 3.3 dBm for 8 phase-shift keying (8 PSK), 1.2 dBm for QPSK, and 0.3 dBm for BPSK. The maximum transmission distance corresponding to a BER of 1 ×10-3 is increased by 480 km for the case of 8 PSK. The larger launch power range and longer transmission distance improve the tolerance to amplitude and phase noise, which demonstrates the feasibility of the SVM in digital signal processing for M-PSK formats. Meanwhile, in order to apply the SVM method to 16 quadratic amplitude modulation (16 QAM) detection, we propose a parameter optimization scheme. By utilizing a cross-validation and grid-search techniques, the optimal parameters of SVM can be selected, thus leading to the LPDR improvement by 2.8 dBm. Additionally, we demonstrate that the SVM is also effective in combating the laser phase noise combined with the inphase and quadrature (I/Q) modulator imperfections, but the improvement is insignificant for the linear noise and separate I/Q imbalance. The computational complexity of SVM is also discussed. The relatively low complexity makes it possible for SVM to implement the real-time processing.

  17. Second-order generalized perturbation theory for source-driven systems

    International Nuclear Information System (INIS)

    Greenspan, E.; Gilai, D.; Oblow, E.M.

    1978-01-01

    A second-order generalized perturbation theory (GPT) for the effect of multiple system variations on a general flux functional in source-driven systems is derived. The derivation is based on a functional Taylor series in which second-order derivatives are retained. The resulting formulation accounts for the nonlinear effect of a given variation accurate to third order in the flux and adjoint perturbations. It also accounts for the effect of interaction between any number of variations. The new formulation is compared with exact perturbation theory as well as with perturbation theory for altered systems. The usefulnes of the second-order GPT formulation is illustrated by applying it to optimization problems. Its applicability to areas of cross-section sensitivity analysis and system design and evaluation is also discussed

  18. Optimal nonlinear information processing capacity in delay-based reservoir computers

    Science.gov (United States)

    Grigoryeva, Lyudmila; Henriques, Julie; Larger, Laurent; Ortega, Juan-Pablo

    2015-09-01

    Reservoir computing is a recently introduced brain-inspired machine learning paradigm capable of excellent performances in the processing of empirical data. We focus in a particular kind of time-delay based reservoir computers that have been physically implemented using optical and electronic systems and have shown unprecedented data processing rates. Reservoir computing is well-known for the ease of the associated training scheme but also for the problematic sensitivity of its performance to architecture parameters. This article addresses the reservoir design problem, which remains the biggest challenge in the applicability of this information processing scheme. More specifically, we use the information available regarding the optimal reservoir working regimes to construct a functional link between the reservoir parameters and its performance. This function is used to explore various properties of the device and to choose the optimal reservoir architecture, thus replacing the tedious and time consuming parameter scannings used so far in the literature.

  19. An Optimal Biparametric Multipoint Family and Its Self-Acceleration with Memory for Solving Nonlinear Equations

    Directory of Open Access Journals (Sweden)

    Quan Zheng

    2015-12-01

    Full Text Available In this paper, a family of Steffensen-type methods of optimal order of convergence with two parameters is constructed by direct Newtonian interpolation. It satisfies the conjecture proposed by Kung and Traub (J. Assoc. Comput. Math. 1974, 21, 634–651 that an iterative method based on m evaluations per iteration without memory would arrive at the optimal convergence of order 2m-1 . Furthermore, the family of Steffensen-type methods of super convergence is suggested by using arithmetic expressions for the parameters with memory but no additional new evaluation of the function. Their error equations, asymptotic convergence constants and convergence orders are obtained. Finally, they are compared with related root-finding methods in the numerical examples.

  20. Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems

    Science.gov (United States)

    Tobasco, Ian; Goluskin, David; Doering, Charles R.

    2018-02-01

    For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper bounds on time averages can be proved a priori using auxiliary functions, the optimal choice of which is a convex optimization problem. We prove that the problems of finding maximal trajectories and minimal auxiliary functions are strongly dual. Thus, auxiliary functions provide arbitrarily sharp upper bounds on time averages. Moreover, any nearly minimal auxiliary function provides phase space volumes in which all nearly maximal trajectories are guaranteed to lie. For polynomial equations, auxiliary functions can be constructed by semidefinite programming, which we illustrate using the Lorenz system.

  1. Breaking Computational Barriers: Real-time Analysis and Optimization with Large-scale Nonlinear Models via Model Reduction

    Energy Technology Data Exchange (ETDEWEB)

    Carlberg, Kevin Thomas [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Quantitative Modeling and Analysis; Drohmann, Martin [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Quantitative Modeling and Analysis; Tuminaro, Raymond S. [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Computational Mathematics; Boggs, Paul T. [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Quantitative Modeling and Analysis; Ray, Jaideep [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Quantitative Modeling and Analysis; van Bloemen Waanders, Bart Gustaaf [Sandia National Lab. (SNL-CA), Livermore, CA (United States). Optimization and Uncertainty Estimation

    2014-10-01

    -model errors. This enables ROMs to be rigorously incorporated in uncertainty-quantification settings, as the error model can be treated as a source of epistemic uncertainty. This work was completed as part of a Truman Fellowship appointment. We note that much additional work was performed as part of the Fellowship. One salient project is the development of the Trilinos-based model-reduction software module Razor , which is currently bundled with the Albany PDE code and currently allows nonlinear reduced-order models to be constructed for any application supported in Albany. Other important projects include the following: 1. ROMES-equipped ROMs for Bayesian inference: K. Carlberg, M. Drohmann, F. Lu (Lawrence Berkeley National Laboratory), M. Morzfeld (Lawrence Berkeley National Laboratory). 2. ROM-enabled Krylov-subspace recycling: K. Carlberg, V. Forstall (University of Maryland), P. Tsuji, R. Tuminaro. 3. A pseudo balanced POD method using only dual snapshots: K. Carlberg, M. Sarovar. 4. An analysis of discrete v. continuous optimality in nonlinear model reduction: K. Carlberg, M. Barone, H. Antil (George Mason University). Journal articles for these projects are in progress at the time of this writing.

  2. Twisting perturbed parafermions

    Directory of Open Access Journals (Sweden)

    A.V. Belitsky

    2017-07-01

    Full Text Available The near-collinear expansion of scattering amplitudes in maximally supersymmetric Yang–Mills theory at strong coupling is governed by the dynamics of stings propagating on the five sphere. The pentagon transitions in the operator product expansion which systematize the series get reformulated in terms of matrix elements of branch-point twist operators in the two-dimensional O(6 nonlinear sigma model. The facts that the latter is an asymptotically free field theory and that there exists no local realization of twist fields prevents one from explicit calculation of their scaling dimensions and operator product expansion coefficients. This complication is bypassed making use of the equivalence of the sigma model to the infinite-level limit of WZNW models perturbed by current–current interactions, such that one can use conformal symmetry and conformal perturbation theory for systematic calculations. Presently, to set up the formalism, we consider the O(3 sigma model which is reformulated as perturbed parafermions.

  3. Evaluating optimal CNR as a preset criteria for nonlinear moidal blending of dual energy CT data

    Science.gov (United States)

    Holmes, D. R., III; Apel, A.; Fletcher, J. G.; Guimaraes, L. S.; Eusemann, C. E.; Robb, R. A.

    2009-02-01

    Nonlinear blending of dual-energy CT data is available on current scanners. Selection of the blending parameters can be time-consuming and challenging. The purpose of this study was to determine if the Contrast-To-Noise Ratio (CNR) may be used ti automatic select of blending parameters. A Bovine liver was built with six syringes filled with varying concentrations of CT contrast yielding six 140kV HU levels (15, 47, 64, 79, 116, and 145). The phantom was scanned using 95 mAs @ 140kV and 404mAs @ 80 kV. The 80 and 140 kV datasets were blended using a modified sigmoid (moidal) function which requires two parameters - level and width. Every combination of moidal level and width was applied to the data, and the CNR was calculated as (mean(syringe ROI) - mean(liver ROI)) / STD(water). The maximum CNR was determined for each of the 6 HU levels. Pairs of blended images were presented in a blind manner to observers. Nine comparisons for each of the 6 HU settings were made by a staff radiologist, a resident, and a physicist. For each comparison, the observer selected the more "visually appealing" image. Outcomes from the study were compared using the Fisher Sign Test statistic. Analysis by observer showed a statistical (penergy CT data may provide consistency across radiologists and facilitate the clinical review process.

  4. Nonlinear dynamics in Nuclotron

    International Nuclear Information System (INIS)

    Dinev, D.

    1997-01-01

    The paper represents an extensive study of the nonlinear beam dynamics in the Nuclotron. Chromatic effects, including the dependence of the betatron tunes on the amplitude, and chromatic perturbations have been investigated taking into account the measured field imperfections. Beam distortion, smear, dynamic aperture and nonlinear acceptance have been calculated for different particle energies and betatron tunes

  5. Neural-Fuzzy Digital Strategy of Continuous-Time Nonlinear Systems Using Adaptive Prediction and Random-Local-Optimization Design

    Directory of Open Access Journals (Sweden)

    Zhi-Ren Tsai

    2013-01-01

    Full Text Available A tracking problem, time-delay, uncertainty and stability analysis of a predictive control system are considered. The predictive control design is based on the input and output of neural plant model (NPM, and a recursive fuzzy predictive tracker has scaling factors which limit the value zone of measured data and cause the tuned parameters to converge to obtain a robust control performance. To improve the further control performance, the proposed random-local-optimization design (RLO for a model/controller uses offline initialization to obtain a near global optimal model/controller. Other issues are the considerations of modeling error, input-delay, sampling distortion, cost, greater flexibility, and highly reliable digital products of the model-based controller for the continuous-time (CT nonlinear system. They are solved by a recommended two-stage control design with the first-stage (offline RLO and second-stage (online adaptive steps. A theorizing method is then put forward to replace the sensitivity calculation, which reduces the calculation of Jacobin matrices of the back-propagation (BP method. Finally, the feedforward input of reference signals helps the digital fuzzy controller improve the control performance, and the technique works to control the CT systems precisely.

  6. Bio-inspired varying subspace based computational framework for a class of nonlinear constrained optimal trajectory planning problems.

    Science.gov (United States)

    Xu, Y; Li, N

    2014-09-01

    Biological species have produced many simple but efficient rules in their complex and critical survival activities such as hunting and mating. A common feature observed in several biological motion strategies is that the predator only moves along paths in a carefully selected or iteratively refined subspace (or manifold), which might be able to explain why these motion strategies are effective. In this paper, a unified linear algebraic formulation representing such a predator-prey relationship is developed to simplify the construction and refinement process of the subspace (or manifold). Specifically, the following three motion strategies are studied and modified: motion camouflage, constant absolute target direction and local pursuit. The framework constructed based on this varying subspace concept could significantly reduce the computational cost in solving a class of nonlinear constrained optimal trajectory planning problems, particularly for the case with severe constraints. Two non-trivial examples, a ground robot and a hypersonic aircraft trajectory optimization problem, are used to show the capabilities of the algorithms in this new computational framework.

  7. Bio-inspired varying subspace based computational framework for a class of nonlinear constrained optimal trajectory planning problems

    International Nuclear Information System (INIS)

    Xu, Y; Li, N

    2014-01-01

    Biological species have produced many simple but efficient rules in their complex and critical survival activities such as hunting and mating. A common feature observed in several biological motion strategies is that the predator only moves along paths in a carefully selected or iteratively refined subspace (or manifold), which might be able to explain why these motion strategies are effective. In this paper, a unified linear algebraic formulation representing such a predator–prey relationship is developed to simplify the construction and refinement process of the subspace (or manifold). Specifically, the following three motion strategies are studied and modified: motion camouflage, constant absolute target direction and local pursuit. The framework constructed based on this varying subspace concept could significantly reduce the computational cost in solving a class of nonlinear constrained optimal trajectory planning problems, particularly for the case with severe constraints. Two non-trivial examples, a ground robot and a hypersonic aircraft trajectory optimization problem, are used to show the capabilities of the algorithms in this new computational framework. (paper)

  8. Nonlinear Modeling and Coordinate Optimization of a Semi-Active Energy Regenerative Suspension with an Electro-Hydraulic Actuator

    Directory of Open Access Journals (Sweden)

    Farong Kou

    2018-01-01

    Full Text Available In order to coordinate the damping performance and energy regenerative performance of energy regenerative suspension, this paper proposes a structure of a vehicle semi-active energy regenerative suspension with an electro-hydraulic actuator (EHA. In light of the proposed concept, a specific energy regenerative scheme is designed and a mechanical properties test is carried out. Based on the test results, the parameter identification for the system model is conducted using a recursive least squares algorithm. On the basis of the system principle, the nonlinear model of the semi-active energy regenerative suspension with an EHA is built. Meanwhile, linear-quadratic-Gaussian control strategy of the system is designed. Then, the influence of the main parameters of the EHA on the damping performance and energy regenerative performance of the suspension is analyzed. Finally, the main parameters of the EHA are optimized via the genetic algorithm. The test results show that when a sinusoidal is input at the frequency of 2 Hz and the amplitude of 30 mm, the spring mass acceleration root meam square value of the optimized EHA semi-active energy regenerative suspension is reduced by 22.23% and the energy regenerative power RMS value is increased by 40.51%, which means that while meeting the requirements of vehicle ride comfort and driving safety, the energy regenerative performance is improved significantly.

  9. Nonlinear bioheat transfer models and multi-objective numerical optimization of the cryosurgery operations

    Energy Technology Data Exchange (ETDEWEB)

    Kudryashov, Nikolay A.; Shilnikov, Kirill E. [National Research Nuclear University MEPhI, Department of Applied Mathematics, Moscow (Russian Federation)

    2016-06-08

    Numerical computation of the three dimensional problem of the freezing interface propagation during the cryosurgery coupled with the multi-objective optimization methods is used in order to improve the efficiency and safety of the cryosurgery operations performing. Prostate cancer treatment and cutaneous cryosurgery are considered. The heat transfer in soft tissue during the thermal exposure to low temperature is described by the Pennes bioheat model and is coupled with an enthalpy method for blurred phase change computations. The finite volume method combined with the control volume approximation of the heat fluxes is applied for the cryosurgery numerical modeling on the tumor tissue of a quite arbitrary shape. The flux relaxation approach is used for the stability improvement of the explicit finite difference schemes. The method of the additional heating elements mounting is studied as an approach to control the cellular necrosis front propagation. Whereas the undestucted tumor tissue and destucted healthy tissue volumes are considered as objective functions, the locations of additional heating elements in cutaneous cryosurgery and cryotips in prostate cancer cryotreatment are considered as objective variables in multi-objective problem. The quasi-gradient method is proposed for the searching of the Pareto front segments as the multi-objective optimization problem solutions.

  10. Investigation of nonlinear 2D bottom transportation dynamics in coastal zone on optimal curvilinear boundary adaptive grids

    Directory of Open Access Journals (Sweden)

    Sukhinov Alexander

    2017-01-01

    Full Text Available One of the practically important tasks of hydrophysics for sea coastal systems is the problem of modeling and forecasting bottom sediment transportation. A number of problems connected to ship safety traffic, water medium condition near the coastal line etc. depends on forecasting bottom deposit transportation under natural and technogenic influences. Coastal systems are characterized by a complicated form of coastline - the presence of long, narrow and curvilinear peninsulas and bays. Water currents and waves near the beach are strongly depend on complicated coastal line and in turn, exert on the bottom sediment transportation near the shore. The use of rectangular grids in the construction of discrete models leads to significant errors in both the specification of boundary conditions and in the modeling of hydrophysical processes in the coastal zone. In this paper, we consider the construction of a finite-element approximation of the initial-boundary value problem for the spatially two-dimensional linearized equation of sediment transportation using optimal boundary-adaptive grid. First, the linearization of a spatially two-dimensional nonlinear parabolic equation on the time grid is performed-when the coefficients of the equation that are nonlinearly dependent on the bottom relief function are set on the previous time layer, and the corresponding initial conditions are used on the first time layer. The algorithm for constructing the grid is based on the procedure for minimizing the generalized Dirichlet functional. On the constructed grid, finite element approximation using bilinear basis functions is performed, which completes the construction of a discrete model for the given problem. The using of curvilinear boundary adaptive grids leads to decreasing of total grid number in 5-20 times and respectively the total modeling time and/or it allows to improve modeling accuracy.

  11. Nonlinear Transient Growth and Boundary Layer Transition

    Science.gov (United States)

    Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

    2016-01-01

    Parabolized stability equations (PSE) are used in a variational approach to study the optimal, non-modal disturbance growth in a Mach 3 at plate boundary layer and a Mach 6 circular cone boundary layer. As noted in previous works, the optimal initial disturbances correspond to steady counter-rotating streamwise vortices, which subsequently lead to the formation of streamwise-elongated structures, i.e., streaks, via a lift-up effect. The nonlinear evolution of the linearly optimal stationary perturbations is computed using the nonlinear plane-marching PSE for stationary perturbations. A fully implicit marching technique is used to facilitate the computation of nonlinear streaks with large amplitudes. To assess the effect of the finite-amplitude streaks on transition, the linear form of plane- marching PSE is used to investigate the instability of the boundary layer flow modified by spanwise periodic streaks. The onset of bypass transition is estimated by using an N- factor criterion based on the amplification of the streak instabilities. Results show that, for both flow configurations of interest, streaks of sufficiently large amplitude can lead to significantly earlier onset of transition than that in an unperturbed boundary layer without any streaks.

  12. A nonlinear approach of elastic reflection waveform inversion

    KAUST Repository

    Guo, Qiang

    2016-09-06

    Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.

  13. A nonlinear approach of elastic reflection waveform inversion

    KAUST Repository

    Guo, Qiang; Alkhalifah, Tariq Ali

    2016-01-01

    Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.

  14. First order normalization in the perturbed restricted three–body ...

    African Journals Online (AJOL)

    This paper performs the first order normalization that will be employed in the study of the nonlinear stability of triangular points of the perturbed restricted three – body problem with variable mass. The problem is perturbed in the sense that small perturbations are given in the coriolis and centrifugal forces. It is with variable ...

  15. Data-Driven Zero-Sum Neuro-Optimal Control for a Class of Continuous-Time Unknown Nonlinear Systems With Disturbance Using ADP.

    Science.gov (United States)

    Wei, Qinglai; Song, Ruizhuo; Yan, Pengfei

    2016-02-01

    This paper is concerned with a new data-driven zero-sum neuro-optimal control problem for continuous-time unknown nonlinear systems with disturbance. According to the input-output data of the nonlinear system, an effective recurrent neural network is introduced to reconstruct the dynamics of the nonlinear system. Considering the system disturbance as a control input, a two-player zero-sum optimal control problem is established. Adaptive dynamic programming (ADP) is developed to obtain the optimal control under the worst case of the disturbance. Three single-layer neural networks, including one critic and two action networks, are employed to approximate the performance index function, the optimal control law, and the disturbance, respectively, for facilitating the implementation of the ADP method. Convergence properties of the ADP method are developed to show that the system state will converge to a finite neighborhood of the equilibrium. The weight matrices of the critic and the two action networks are also convergent to finite neighborhoods of their optimal ones. Finally, the simulation results will show the effectiveness of the developed data-driven ADP methods.

  16. Nonlinear system identification for prostate cancer and optimality of intermittent androgen suppression therapy.

    Science.gov (United States)

    Suzuki, Taiji; Aihara, Kazuyuki

    2013-09-01

    These days prostate cancer is one of the most common types of malignant neoplasm in men. Androgen ablation therapy (hormone therapy) has been shown to be effective for advanced prostate cancer. However, continuous hormone therapy often causes recurrence. This results from the progression of androgen-dependent cancer cells to androgen-independent cancer cells during the continuous hormone therapy. One possible method to prevent the progression to the androgen-independent state is intermittent androgen suppression (IAS) therapy, which ceases dosing intermittently. In this paper, we propose two methods to estimate the dynamics of prostate cancer, and investigate the IAS therapy from the viewpoint of optimality. The two methods that we propose for dynamics estimation are a variational Bayesian method for a piecewise affine (PWA) system and a Gaussian process regression method. We apply the proposed methods to real clinical data and compare their predictive performances. Then, using the estimated dynamics of prostate cancer, we observe how prostate cancer behaves for various dosing schedules. It can be seen that the conventional IAS therapy is a way of imposing high cost for dosing while keeping the prostate cancer in a safe state. We would like to dedicate this paper to the memory of Professor Luigi M. Ricciardi. Copyright © 2013 The Authors. Published by Elsevier Inc. All rights reserved.

  17. Supersingular quantum perturbations

    International Nuclear Information System (INIS)

    Detwiler, L.C.; Klauder, J.R.

    1975-01-01

    A perturbation potential is called supersingular whenever generally every matrix element of the perturbation in the unperturbed eigenstates is infinite. It follows that supersingular perturbations do not have conventional perturbation expansions, say for energy eigenvalues. By invoking variational arguments, we determine the asymptotic behavior of the energy eigenvalues for asymptotically small values of the coupling constant of the supersingular perturbation

  18. Nonlinear drift tearing mode

    International Nuclear Information System (INIS)

    Zelenyj, L.M.; Kuznetsova, M.M.

    1989-01-01

    Nonlinear study of magnetic perturbation development under single-mode conditions in collision-free plasma in configurations with the magnetic field shear is investigated. Results are obtained with regard of transverse component of electrical field and its effect on ion dynamics within wide range of ion Larmor radius value and values of magnetic field shear. Increments of nonlinear drift tearing mode are obtained and it is shown that excitation drastic conditions of even linearly stable modes are possible. Mechanism of instability nonlinear stabilization is considered and the value of magnetic island at the saturation threshold is estimeted. Energy of nonlinear drift tearing mode is discussed

  19. Bounded Perturbation Regularization for Linear Least Squares Estimation

    KAUST Repository

    Ballal, Tarig

    2017-10-18

    This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded norm is allowed into the linear transformation matrix to improve the singular-value structure. Following this, the problem is formulated as a min-max optimization problem. Next, the min-max problem is converted to an equivalent minimization problem to estimate the unknown vector quantity. The solution of the minimization problem is shown to converge to that of the ℓ2 -regularized least squares problem, with the unknown regularizer related to the norm bound of the introduced perturbation through a nonlinear constraint. A procedure is proposed that combines the constraint equation with the mean squared error (MSE) criterion to develop an approximately optimal regularization parameter selection algorithm. Both direct and indirect applications of the proposed method are considered. Comparisons with different Tikhonov regularization parameter selection methods, as well as with other relevant methods, are carried out. Numerical results demonstrate that the proposed method provides significant improvement over state-of-the-art methods.

  20. expansion method and travelling wave solutions for the perturbed ...

    Indian Academy of Sciences (India)

    Abstract. In this paper, we construct the travelling wave solutions to the perturbed nonlinear. Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (G /G)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with. Kerr law nonlinearity with arbitrary ...

  1. Linear and Nonlinear Dynamics of Heart Rate Variability are Correlated with Purpose in Life and Degree of Optimism in Anxiety Disorder Patients.

    Science.gov (United States)

    Oh, Jihoon; Chae, Jeong-Ho

    2018-04-01

    Although heart rate variability (HRV) may be a crucial marker of mental health, how it is related to positive psychological factors (i.e. attitude to life and positive thinking) is largely unknown. Here we investigated the correlation of HRV linear and nonlinear dynamics with psychological scales that measured degree of optimism and happiness in patients with anxiety disorders. Results showed that low- to high-frequency HRV ratio (LF/HF) was increased and the HRV HF parameter was decreased in subjects who were more optimistic and who felt happier in daily living. Nonlinear analysis also showed that HRV dispersion and regulation were significantly correlated with the subjects' optimism and purpose in life. Our findings showed that HRV properties might be related to degree of optimistic perspectives on life and suggests that HRV markers of autonomic nervous system function could reflect positive human mind states.

  2. PetClaw: Parallelization and Performance Optimization of a Python-Based Nonlinear Wave Propagation Solver Using PETSc

    KAUST Repository

    Alghamdi, Amal Mohammed

    2012-04-01

    Clawpack, a conservation laws package implemented in Fortran, and its Python-based version, PyClaw, are existing tools providing nonlinear wave propagation solvers that use state of the art finite volume methods. Simulations using those tools can have extensive computational requirements to provide accurate results. Therefore, a number of tools, such as BearClaw and MPIClaw, have been developed based on Clawpack to achieve significant speedup by exploiting parallel architectures. However, none of them has been shown to scale on a large number of cores. Furthermore, these tools, implemented in Fortran, achieve parallelization by inserting parallelization logic and MPI standard routines throughout the serial code in a non modular manner. Our contribution in this thesis research is three-fold. First, we demonstrate an advantageous use case of Python in implementing easy-to-use modular extensible scalable scientific software tools by developing an implementation of a parallelization framework, PetClaw, for PyClaw using the well-known Portable Extensible Toolkit for Scientific Computation, PETSc, through its Python wrapper petsc4py. Second, we demonstrate the possibility of getting acceptable Python code performance when compared to Fortran performance after introducing a number of serial optimizations to the Python code including integrating Clawpack Fortran kernels into PyClaw for low-level computationally intensive parts of the code. As a result of those optimizations, the Python overhead in PetClaw for a shallow water application is only 12 percent when compared to the corresponding Fortran Clawpack application. Third, we provide a demonstration of PetClaw scalability on up to the entirety of Shaheen; a 16-rack Blue Gene/P IBM supercomputer that comprises 65,536 cores and located at King Abdullah University of Science and Technology (KAUST). The PetClaw solver achieved above 0.98 weak scaling efficiency for an Euler application on the whole machine excluding the

  3. Improved binary dragonfly optimization algorithm and wavelet packet based non-linear features for infant cry classification.

    Science.gov (United States)

    Hariharan, M; Sindhu, R; Vijean, Vikneswaran; Yazid, Haniza; Nadarajaw, Thiyagar; Yaacob, Sazali; Polat, Kemal

    2018-03-01

    Infant cry signal carries several levels of information about the reason for crying (hunger, pain, sleepiness and discomfort) or the pathological status (asphyxia, deaf, jaundice, premature condition and autism, etc.) of an infant and therefore suited for early diagnosis. In this work, combination of wavelet packet based features and Improved Binary Dragonfly Optimization based feature selection method was proposed to classify the different types of infant cry signals. Cry signals from 2 different databases were utilized. First database contains 507 cry samples of normal (N), 340 cry samples of asphyxia (A), 879 cry samples of deaf (D), 350 cry samples of hungry (H) and 192 cry samples of pain (P). Second database contains 513 cry samples of jaundice (J), 531 samples of premature (Prem) and 45 samples of normal (N). Wavelet packet transform based energy and non-linear entropies (496 features), Linear Predictive Coding (LPC) based cepstral features (56 features), Mel-frequency Cepstral Coefficients (MFCCs) were extracted (16 features). The combined feature set consists of 568 features. To overcome the curse of dimensionality issue, improved binary dragonfly optimization algorithm (IBDFO) was proposed to select the most salient attributes or features. Finally, Extreme Learning Machine (ELM) kernel classifier was used to classify the different types of infant cry signals using all the features and highly informative features as well. Several experiments of two-class and multi-class classification of cry signals were conducted. In binary or two-class experiments, maximum accuracy of 90.18% for H Vs P, 100% for A Vs N, 100% for D Vs N and 97.61% J Vs Prem was achieved using the features selected (only 204 features out of 568) by IBDFO. For the classification of multiple cry signals (multi-class problem), the selected features could differentiate between three classes (N, A & D) with the accuracy of 100% and seven classes with the accuracy of 97.62%. The experimental

  4. Investigation and optimization of transverse non-linear beam dynamics in the high-energy storage ring HESR

    Energy Technology Data Exchange (ETDEWEB)

    Welsch, Dominic Markus

    2010-03-10

    The High-Energy Storage Ring (HESR) is part of the upcoming Facility for Antiproton and Ion Research (FAIR) which is planned as a major extension to the present facility of the Helmholtzzentrum fuer Schwerionenforschung (GSI) in Darmstadt. The HESR will provide antiprotons in the momentum range from 1.5 to 15 GeV/c for the internal target experiment PANDA. The demanding requirements of PANDA in terms of beam quality and luminosity together with a limited production rate of antiprotons call for a long beam life time and a minimum of beam loss. Therefore, an effective closed orbit correction and a sufficiently large dynamic aperture of the HESR are crucial. With this thesis I present my work on both of these topics. The expected misalignments of beam guiding magnets have been estimated and used to simulate the closed orbit in the HESR. A closed orbit correction scheme has been developed for different ion optical settings of the HESR and numerical simulations have been performed to validate the scheme. The proposed closed orbit correction method which uses the orbit response matrix has been benchmarked at the Cooler Synchrotron COSY of the Forschungszentrum Juelich. A chromaticity correction scheme for the HESR consisting of sextupole magnets has been developed to reduce tune spread and thus to minimize the emittance growth caused by betatron resonances. The chromaticity correction scheme has been optimized through dynamic aperture calculations. The estimated field errors of the HESR dipole and quadrupole magnets have been included in the non-linear beam dynamics studies. Investigations concerning their optimization have been carried out. The ion optical settings of the HESR have been improved using dynamic aperture calculations and the technique of frequency map analysis. The related diffusion coefficient was also used to predict long-term stability based on short-term particle tracking. With a reasonable reduction of the quadrupole magnets field errors and a

  5. Cylindrical dust acoustic waves with transverse perturbation

    International Nuclear Information System (INIS)

    Xue Jukui

    2003-01-01

    The nonlinear dust acoustic waves in dusty plasmas with the combined effects of bounded cylindrical geometry and the transverse perturbation are studied. Using the perturbation method, a cylindrical Kadomtsev-Petviashvili (CKP) equation that describes the dust acoustic waves is deduced for the first time. A particular solution of this CKP equation is also obtained. It is shown that the dust acoustic solitary waves can exist in the CKP equation

  6. Nonlinear pre-coding apparatus of multi-antenna system, has pre-coding unit that extents original constellation points of modulated symbols to several constellation points by using limited perturbation vector

    DEFF Research Database (Denmark)

    2008-01-01

    A Coding/Modulating units (200-1-200-N) outputs modulated symbols by modulating coding bit streams based on certain modulation scheme. The limited perturbation vector is calculated by using distribution of perturbation vectors. The original constellation points of modulated symbols are extended t...

  7. 一类含非线性扰动的区间变时滞系统鲁棒稳定性判据%Robust Stability Criteria for Systems with Interval Time-varying Delay and Nonlinear Perturbations

    Institute of Scientific and Technical Information of China (English)

    惠俊军; 张合新; 周鑫; 孟飞; 张金生

    2014-01-01

    Interval time delay is an important delay type in practical systems. In such sys-tems, the delay may vary in a range for which the lower bound is not restricted to being zero. In this paper, we consider the robust stability for a class of linear systems with interval time-varying delay and nonlinear perturbations. Based on the delay decomposition approach, both the lower and upper bounds of the interval time-varying delay are proposed. By applying a new Lyapunov-Krasovskii (L-K) functional, and free-weighing matrix approach, a less conservative delay-dependent stability criteria are obtained, which are established in the forms of linear matrix inequalities (LMIs). The main advantage of the method is that more information of the interval delay is employed, and hence yields less conservative. Finally, numerical examples indicate the effectiveness and superiority of the proposed method.%区间时滞是在实际应用当中一类重要的时滞类型。在这类系统当中,时滞往往处于一个变化的区间之内,而时滞的下界不一定为零。本文讨论一类含非线性扰动的区间变时滞系统的稳定性问题。基于时滞分解法,把时滞下界分成两个相等的子区间,通过构造包含时滞区间下界和上界新Lyapunov-Krasovskii (L-K)泛函,结合改进的自由权矩阵技术,建立了线性矩阵不等式(LMI)形式的时滞相关稳定性判据。该方法充分利用了系统的时滞信息,因而具有更低的保守性。数值算例说明了该方法的有效性和优越性。

  8. Perturbed solutions of fixed boundary MHD equilibria

    International Nuclear Information System (INIS)

    Portone, A.

    2004-01-01

    In this study, the fixed boundary plasma MHD equilibrium problem is solved by the finite element method; then, by perturbing the flux at the plasma boundary nodes, linear formulae are derived linking the variation of several plasma parameters of interest to the variation of the currents flowing in the external circuits. On the basis of these formulae it is shown how it is possible to efficiently solve two central problems in plasma engineering, namely (1) the optimization of the currents in a given set of coils necessary to maintain a specified equilibrium configuration and (2) the derivation of a linear dynamic model describing the plasma axisymmetric displacement (n = 0 mode) about a given magnetic configuration. A case study-based on the ITER reference equilibrium magnetic configuration at burn-is analysed both in terms of equilibrium currents optimality as well as axisymmetric stability features. The results obtained by these formulae are also compared with the predictions of a non-linear free boundary code and of a linear, dynamic model. As shown, the formulae derived here are in good agreement with such predictions, confirming the validity of the present approach. (author)

  9. Analysis, control and optimal operations in hybrid power systems advanced techniques and applications for linear and nonlinear systems

    CERN Document Server

    Bizon, Nicu; Mahdavi Tabatabaei, Naser

    2014-01-01

    This book explains and analyzes the dynamic performance of linear and nonlinear systems, particularly for Power Systems including Hybrid Power Sources. Offers a detailed description of system stability using state space energy conservation principle, and more.

  10. Non-linear modeling of 1H NMR metabonomic data using kernel-based orthogonal projections to latent structures optimized by simulated annealing

    International Nuclear Information System (INIS)

    Fonville, Judith M.; Bylesjoe, Max; Coen, Muireann; Nicholson, Jeremy K.; Holmes, Elaine; Lindon, John C.; Rantalainen, Mattias

    2011-01-01

    Highlights: → Non-linear modeling of metabonomic data using K-OPLS. → automated optimization of the kernel parameter by simulated annealing. → K-OPLS provides improved prediction performance for exemplar spectral data sets. → software implementation available for R and Matlab under GPL v2 license. - Abstract: Linear multivariate projection methods are frequently applied for predictive modeling of spectroscopic data in metabonomic studies. The OPLS method is a commonly used computational procedure for characterizing spectral metabonomic data, largely due to its favorable model interpretation properties providing separate descriptions of predictive variation and response-orthogonal structured noise. However, when the relationship between descriptor variables and the response is non-linear, conventional linear models will perform sub-optimally. In this study we have evaluated to what extent a non-linear model, kernel-based orthogonal projections to latent structures (K-OPLS), can provide enhanced predictive performance compared to the linear OPLS model. Just like its linear counterpart, K-OPLS provides separate model components for predictive variation and response-orthogonal structured noise. The improved model interpretation by this separate modeling is a property unique to K-OPLS in comparison to other kernel-based models. Simulated annealing (SA) was used for effective and automated optimization of the kernel-function parameter in K-OPLS (SA-K-OPLS). Our results reveal that the non-linear K-OPLS model provides improved prediction performance in three separate metabonomic data sets compared to the linear OPLS model. We also demonstrate how response-orthogonal K-OPLS components provide valuable biological interpretation of model and data. The metabonomic data sets were acquired using proton Nuclear Magnetic Resonance (NMR) spectroscopy, and include a study of the liver toxin galactosamine, a study of the nephrotoxin mercuric chloride and a study of

  11. A Nonlinear Programming and Artificial Neural Network Approach for Optimizing the Performance of a Job Dispatching Rule in a Wafer Fabrication Factory

    Directory of Open Access Journals (Sweden)

    Toly Chen

    2012-01-01

    Full Text Available A nonlinear programming and artificial neural network approach is presented in this study to optimize the performance of a job dispatching rule in a wafer fabrication factory. The proposed methodology fuses two existing rules and constructs a nonlinear programming model to choose the best values of parameters in the two rules by dynamically maximizing the standard deviation of the slack, which has been shown to benefit scheduling performance by several studies. In addition, a more effective approach is also applied to estimate the remaining cycle time of a job, which is empirically shown to be conducive to the scheduling performance. The efficacy of the proposed methodology was validated with a simulated case; evidence was found to support its effectiveness. We also suggested several directions in which it can be exploited in the future.

  12. How to link pyrene to its host lipid to minimize the extent of membrane perturbations and to optimize pyrene dimer formation

    DEFF Research Database (Denmark)

    Franova, M. D.; Repakova, J.; Holopainen, J. M.

    2014-01-01

    We study how lipid probes based on pyrene-labeling could be designed to minimize perturbations in lipid bilayers, and how the same design principles could be exploited to develop probes which gauge lipid dynamics primarily within a single lipid monolayer or between them. To this end, we use......, simulations suggest that formation of dimers is a slow process, where the rate is limited by both lateral diffusion and the dimerization process once the two probes are neighbors to one another. Typical lifetimes of pyrene dimers turn out be of the order of nanoseconds. The results are expected to pave...

  13. Singularly perturbed Burger-Huxley equation: Analytical solution ...

    African Journals Online (AJOL)

    user

    solutions of singularly perturbed nonlinear differential equations. ... for solving generalized Burgers-Huxley equation but this equation is not singularly ...... Solitary waves solutions of the generalized Burger Huxley equations, Journal of.

  14. An approach of optimal sensitivity applied in the tertiary loop of the automatic generation control

    Energy Technology Data Exchange (ETDEWEB)

    Belati, Edmarcio A. [CIMATEC - SENAI, Salvador, BA (Brazil); Alves, Dilson A. [Electrical Engineering Department, FEIS, UNESP - Sao Paulo State University (Brazil); da Costa, Geraldo R.M. [Electrical Engineering Department, EESC, USP - Sao Paulo University (Brazil)

    2008-09-15

    This paper proposes an approach of optimal sensitivity applied in the tertiary loop of the automatic generation control. The approach is based on the theorem of non-linear perturbation. From an optimal operation point obtained by an optimal power flow a new optimal operation point is directly determined after a perturbation, i.e., without the necessity of an iterative process. This new optimal operation point satisfies the constraints of the problem for small perturbation in the loads. The participation factors and the voltage set point of the automatic voltage regulators (AVR) of the generators are determined by the technique of optimal sensitivity, considering the effects of the active power losses minimization and the network constraints. The participation factors and voltage set point of the generators are supplied directly to a computational program of dynamic simulation of the automatic generation control, named by power sensitivity mode. Test results are presented to show the good performance of this approach. (author)

  15. Redshift-space distortions from vector perturbations

    Science.gov (United States)

    Bonvin, Camille; Durrer, Ruth; Khosravi, Nima; Kunz, Martin; Sawicki, Ignacy

    2018-02-01

    We compute a general expression for the contribution of vector perturbations to the redshift space distortion of galaxy surveys. We show that they contribute to the same multipoles of the correlation function as scalar perturbations and should thus in principle be taken into account in data analysis. We derive constraints for next-generation surveys on the amplitude of two sources of vector perturbations, namely non-linear clustering and topological defects. While topological defects leave a very small imprint on redshift space distortions, we show that the multipoles of the correlation function are sensitive to vorticity induced by non-linear clustering. Therefore future redshift surveys such as DESI or the SKA should be capable of measuring such vector modes, especially with the hexadecapole which appears to be the most sensitive to the presence of vorticity.

  16. Comparison of linear and nonlinear programming approaches for "worst case dose" and "minmax" robust optimization of intensity-modulated proton therapy dose distributions.

    Science.gov (United States)

    Zaghian, Maryam; Cao, Wenhua; Liu, Wei; Kardar, Laleh; Randeniya, Sharmalee; Mohan, Radhe; Lim, Gino

    2017-03-01

    Robust optimization of intensity-modulated proton therapy (IMPT) takes uncertainties into account during spot weight optimization and leads to dose distributions that are resilient to uncertainties. Previous studies demonstrated benefits of linear programming (LP) for IMPT in terms of delivery efficiency by considerably reducing the number of spots required for the same quality of plans. However, a reduction in the number of spots may lead to loss of robustness. The purpose of this study was to evaluate and compare the performance in terms of plan quality and robustness of two robust optimization approaches using LP and nonlinear programming (NLP) models. The so-called "worst case dose" and "minmax" robust optimization approaches and conventional planning target volume (PTV)-based optimization approach were applied to designing IMPT plans for five patients: two with prostate cancer, one with skull-based cancer, and two with head and neck cancer. For each approach, both LP and NLP models were used. Thus, for each case, six sets of IMPT plans were generated and assessed: LP-PTV-based, NLP-PTV-based, LP-worst case dose, NLP-worst case dose, LP-minmax, and NLP-minmax. The four robust optimization methods behaved differently from patient to patient, and no method emerged as superior to the others in terms of nominal plan quality and robustness against uncertainties. The plans generated using LP-based robust optimization were more robust regarding patient setup and range uncertainties than were those generated using NLP-based robust optimization for the prostate cancer patients. However, the robustness of plans generated using NLP-based methods was superior for the skull-based and head and neck cancer patients. Overall, LP-based methods were suitable for the less challenging cancer cases in which all uncertainty scenarios were able to satisfy tight dose constraints, while NLP performed better in more difficult cases in which most uncertainty scenarios were hard to meet

  17. A purely nonlinear route to transition approaching the edge of chaos in a boundary layer

    International Nuclear Information System (INIS)

    Cherubini, S; De Palma, P; Robinet, J-Ch; Bottaro, A

    2012-01-01

    The understanding of transition in shear flows has recently progressed along new paradigms based on the central role of coherent flow structures and their nonlinear interactions. We follow such paradigms to identify, by means of a nonlinear optimization of the energy growth at short time, the initial perturbation which most easily induces transition in a boundary layer. Moreover, a bisection procedure has been used to identify localized flow structures living on the edge of chaos, found to be populated by hairpin vortices and streaks. Such an edge structure appears to act as a relative attractor for the trajectory of the laminar base state perturbed by the initial finite-amplitude disturbances, mediating the route to turbulence of the flow, via the triggering of a regeneration cycle of Λ and hairpin structures at different space and time scales. These findings introduce a new, purely nonlinear scenario of transition in a boundary-layer flow. (paper)

  18. Solitary wave solution to a singularly perturbed generalized Gardner ...

    Indian Academy of Sciences (India)

    2017-03-24

    Mar 24, 2017 ... Abstract. This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the ...

  19. A nonlinear support vector machine model with hard penalty function based on glowworm swarm optimization for forecasting daily global solar radiation

    International Nuclear Information System (INIS)

    Jiang, He; Dong, Yao

    2016-01-01

    Highlights: • Eclat data mining algorithm is used to determine the possible predictors. • Support vector machine is converted into a ridge regularization problem. • Hard penalty selects the number of radial basis functions to simply the structure. • Glowworm swarm optimization is utilized to determine the optimal parameters. - Abstract: For a portion of the power which is generated by grid connected photovoltaic installations, an effective solar irradiation forecasting approach must be crucial to ensure the quality and the security of power grid. This paper develops and investigates a novel model to forecast 30 daily global solar radiation at four given locations of the United States. Eclat data mining algorithm is first presented to discover association rules between solar radiation and several meteorological factors laying a theoretical foundation for these correlative factors as input vectors. An effective and innovative intelligent optimization model based on nonlinear support vector machine and hard penalty function is proposed to forecast solar radiation by converting support vector machine into a regularization problem with ridge penalty, adding a hard penalty function to select the number of radial basis functions, and using glowworm swarm optimization algorithm to determine the optimal parameters of the model. In order to illustrate our validity of the proposed method, the datasets at four sites of the United States are split to into training data and test data, separately. The experiment results reveal that the proposed model delivers the best forecasting performances comparing with other competitors.

  20. Nonlinear Approaches in Engineering Applications

    CERN Document Server

    Jazar, Reza

    2012-01-01

    Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...

  1. Nonlinear dynamics aspects of particle accelerators

    International Nuclear Information System (INIS)

    Araki, H.; Ehlers, J.; Hepp, K.; Kippenhahn, R.; Weidenmuller, A.; Zittartz, J.

    1986-01-01

    This book contains 18 selections. Some of the titles are: Integrable and Nonintegrable Hamiltonian Systems; Nonlinear Dynamics Aspects of Modern Storage Rings; Nonlinear Beam-Beam Resonances; Synchro-Betatron Resonances; Review of Beam-Beam Simulations; and Perturbation Method in Nonlinear Dynamics

  2. Beyond perturbation introduction to the homotopy analysis method

    CERN Document Server

    Liao, Shijun

    2003-01-01

    Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity.This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra''s population model, Von Kármán swirling viscous flow, and nonlinear progressive waves in deep water.Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be ...

  3. Comparative Study of Evolutionary Multi-objective Optimization Algorithms for a Non-linear Greenhouse Climate Control Problem

    DEFF Research Database (Denmark)

    Ghoreishi, Newsha; Sørensen, Jan Corfixen; Jørgensen, Bo Nørregaard

    2015-01-01

    Non-trivial real world decision-making processes usually involve multiple parties having potentially conflicting interests over a set of issues. State-of-the-art multi-objective evolutionary algorithms (MOEA) are well known to solve this class of complex real-world problems. In this paper, we...... compare the performance of state-of-the-art multi-objective evolutionary algorithms to solve a non-linear multi-objective multi-issue optimisation problem found in Greenhouse climate control. The chosen algorithms in the study includes NSGAII, eNSGAII, eMOEA, PAES, PESAII and SPEAII. The performance...... of all aforementioned algorithms is assessed and compared using performance indicators to evaluate proximity, diversity and consistency. Our insights to this comparative study enhanced our understanding of MOEAs performance in order to solve a non-linear complex climate control problem. The empirical...

  4. A Novel Method to Magnetic Flux Linkage Optimization of Direct-Driven Surface-Mounted Permanent Magnet Synchronous Generator Based on Nonlinear Dynamic Analysis

    Directory of Open Access Journals (Sweden)

    Qian Xie

    2016-07-01

    Full Text Available This paper pays attention to magnetic flux linkage optimization of a direct-driven surface-mounted permanent magnet synchronous generator (D-SPMSG. A new compact representation of the D-SPMSG nonlinear dynamic differential equations to reduce system parameters is established. Furthermore, the nonlinear dynamic characteristics of new D-SPMSG equations in the process of varying magnetic flux linkage are considered, which are illustrated by Lyapunov exponent spectrums, phase orbits, Poincaré maps, time waveforms and bifurcation diagrams, and the magnetic flux linkage stable region of D-SPMSG is acquired concurrently. Based on the above modeling and analyses, a novel method of magnetic flux linkage optimization is presented. In addition, a 2 MW D-SPMSG 2D/3D model is designed by ANSYS software according to the practical design requirements. Finally, five cases of D-SPMSG models with different magnetic flux linkages are simulated by using the finite element analysis (FEA method. The nephograms of magnetic flux density are agreement with theoretical analysis, which both confirm the correctness and effectiveness of the proposed approach.

  5. Singularly perturbed Burger-Huxley equation: Analytical solution ...

    African Journals Online (AJOL)

    The work presented considers the initial boundary value problem for nonlinear singularly perturbed time dependent Burger- Huxley equation. The equation contains two terms with nonlinearities, the cubic term and the advection term. Generally, the severe difficulties of two types encounter in solving this problem. The first ...

  6. On some perturbation techniques for quasi-linear parabolic equations

    Directory of Open Access Journals (Sweden)

    Igor Malyshev

    1990-01-01

    Full Text Available We study a nonhomogeneous quasi-linear parabolic equation and introduce a method that allows us to find the solution of a nonlinear boundary value problem in “explicit” form. This task is accomplished by perturbing the original equation with a source function, which is then found as a solution of some nonlinear operator equation.

  7. Asymptotic behavior of dynamical and control systems under perturbation and discretization

    CERN Document Server

    Grüne, Lars

    2002-01-01

    This book provides an approach to the study of perturbation and discretization effects on the long-time behavior of dynamical and control systems. It analyzes the impact of time and space discretizations on asymptotically stable attracting sets, attractors, asumptotically controllable sets and their respective domains of attractions and reachable sets. Combining robust stability concepts from nonlinear control theory, techniques from optimal control and differential games and methods from nonsmooth analysis, both qualitative and quantitative results are obtained and new algorithms are developed, analyzed and illustrated by examples.

  8. Output synchronization of chaotic systems under nonvanishing perturbations

    Energy Technology Data Exchange (ETDEWEB)

    Lopez-Mancilla, Didier [Departamento de Ciencias Exactas y Tecnologicas, Centro Universitario de los Lagos, Universidad de Guadalajara (CULagos-UdeG), Enrique Diaz de Leon s/n, 47460 Lagos de Moreno, Jal. (Mexico)], E-mail: didier@uabc.mx; Cruz-Hernandez, Cesar [Electronics and Telecommunications Department, Scientific Research and Advanced Studies of Ensenada (CICESE), Km. 107, Carretera Tijuana-Ensenada, 22860 Ensenada, B.C. (Mexico)], E-mail: ccruz@cicese.mx

    2008-08-15

    In this paper, an analysis for chaos synchronization under nonvanishing perturbations is presented. In particular, we use model-matching approach from nonlinear control theory for output synchronization of identical and nonidentical chaotic systems under nonvanishing perturbations in a master-slave configuration. We show that the proposed approach is indeed suitable to synchronize a class of perturbed slaves with a chaotic master system; that is the synchronization error trajectories remain bounded if the perturbations satisfy some conditions. In order to illustrate this robustness synchronization property, we present two cases of study: (i) for identical systems, a pair of coupled Roessler systems, the first like a master and the other like a perturbed slave, and (ii) for nonidentical systems, a Chua's circuit driving a Roessler/slave system with a perturbed control law, in both cases a quantitative analysis on the perturbation is included.

  9. Output synchronization of chaotic systems under nonvanishing perturbations

    International Nuclear Information System (INIS)

    Lopez-Mancilla, Didier; Cruz-Hernandez, Cesar

    2008-01-01

    In this paper, an analysis for chaos synchronization under nonvanishing perturbations is presented. In particular, we use model-matching approach from nonlinear control theory for output synchronization of identical and nonidentical chaotic systems under nonvanishing perturbations in a master-slave configuration. We show that the proposed approach is indeed suitable to synchronize a class of perturbed slaves with a chaotic master system; that is the synchronization error trajectories remain bounded if the perturbations satisfy some conditions. In order to illustrate this robustness synchronization property, we present two cases of study: (i) for identical systems, a pair of coupled Roessler systems, the first like a master and the other like a perturbed slave, and (ii) for nonidentical systems, a Chua's circuit driving a Roessler/slave system with a perturbed control law, in both cases a quantitative analysis on the perturbation is included

  10. Mode coupling of Schwarzschild perturbations: Ringdown frequencies

    International Nuclear Information System (INIS)

    Pazos, Enrique; Brizuela, David; Martin-Garcia, Jose M.; Tiglio, Manuel

    2010-01-01

    Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity (l=2, m=±2) perturbations and odd-parity (l=2, m=0) ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that--in contrast to previous predictions in the literature--the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observed behavior. This would indicate, in particular, that when modeling or searching for ringdown gravitational waves, appropriately including the standard quasinormal modes already takes into account nonlinear effects.

  11. ℋ- adaptive observer design and parameter identification for a class of nonlinear fractional-order systems

    KAUST Repository

    Ndoye, Ibrahima; Voos, Holger; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed

    2014-01-01

    In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown

  12. Optimizing optical pre-dispersion using transmit DSP for mitigation of Kerr nonlinearities in dispersion managed cables

    Science.gov (United States)

    Hopkins, James; Gaudette, Jamie; Mehta, Priyanth

    2013-10-01

    With the advent of digital signal processing (DSP) in optical transmitters and receivers, the ability to finely tune the ratio of pre and post dispersion compensation can be exploited to best mitigate the nonlinear penalties caused by the Kerr effect. A portion of the nonlinear penalty in optical communication channels has been explained by an increase in peak to average power ratio (PAPR) inherent in highly dispersed signals. The standard approach for minimizing these impairments applies 50% pre dispersion compensation and 50% post dispersion compensation, thereby decreasing average PAPR along the length of the cable, as compared with either 100% pre or post dispersion compensation. In this paper we demonstrate that simply considering the net accumulated dispersion, and applying 50/50 pre/post dispersion is not necessarily the best way to minimize PAPR and subsequent Kerr nonlinearities. Instead, we consider the cumulative dispersion along the entire length of the cable, and, taking into account this additional information, derive an analytic formula for the minimization of PAPR. Alignment with simulation and experimental measurements is presented using a commercially available 100Gb/s dual-polarization binary phase-shift-keying (DP-BPSK) coherent modem, with transmitter and receiver DSP. Measurements are provided from two different 5000km dispersion managed Submarine test-beds, as well as a 3800km terrestrial test-bed with a mixture of SMF-28 and TWRS optical fiber. This method is shown to deviate significantly from the conventional 50/50 method described above, in dispersion managed communications systems, and more closely aligns with results obtained from simulation and data collected from laboratory test-beds.

  13. Gain optimization in fiber optical parametric amplifiers by combining standard and high-SBS threshold highly nonlinear fibers

    DEFF Research Database (Denmark)

    Da Ros, Francesco; Rottwitt, Karsten; Peucheret, Christophe

    2012-01-01

    Combining Al-doped and Ge-doped HNLFs as gain media in FOPAs is proposed and optimized, resulting in efficient SBS mitigation while circumventing the additional loss of the high SBS threshold Al-doped fiber.......Combining Al-doped and Ge-doped HNLFs as gain media in FOPAs is proposed and optimized, resulting in efficient SBS mitigation while circumventing the additional loss of the high SBS threshold Al-doped fiber....

  14. A parallel competitive Particle Swarm Optimization for non-linear first arrival traveltime tomography and uncertainty quantification

    Science.gov (United States)

    Luu, Keurfon; Noble, Mark; Gesret, Alexandrine; Belayouni, Nidhal; Roux, Pierre-François

    2018-04-01

    Seismic traveltime tomography is an optimization problem that requires large computational efforts. Therefore, linearized techniques are commonly used for their low computational cost. These local optimization methods are likely to get trapped in a local minimum as they critically depend on the initial model. On the other hand, global optimization methods based on MCMC are insensitive to the initial model but turn out to be computationally expensive. Particle Swarm Optimization (PSO) is a rather new global optimization approach with few tuning parameters that has shown excellent convergence rates and is straightforwardly parallelizable, allowing a good distribution of the workload. However, while it can traverse several local minima of the evaluated misfit function, classical implementation of PSO can get trapped in local minima at later iterations as particles inertia dim. We propose a Competitive PSO (CPSO) to help particles to escape from local minima with a simple implementation that improves swarm's diversity. The model space can be sampled by running the optimizer multiple times and by keeping all the models explored by the swarms in the different runs. A traveltime tomography algorithm based on CPSO is successfully applied on a real 3D data set in the context of induced seismicity.

  15. A non-linear optimal Discontinuous Petrov-Galerkin method for stabilising the solution of the transport equation

    International Nuclear Information System (INIS)

    Merton, S. R.; Smedley-Stevenson, R. P.; Pain, C. C.; Buchan, A. G.; Eaton, M. D.

    2009-01-01

    This paper describes a new Non-Linear Discontinuous Petrov-Galerkin (NDPG) method and application to the one-speed Boltzmann Transport Equation (BTE) for space-time problems. The purpose of the method is to remove unwanted oscillations in the transport solution which occur in the vicinity of sharp flux gradients, while improving computational efficiency and numerical accuracy. This is achieved by applying artificial dissipation in the solution gradient direction, internal to an element using a novel finite element (FE) Riemann approach. The amount of dissipation added acts internal to each element. This is done using a gradient-informed scaling of the advection velocities in the stabilisation term. This makes the method in its most general form non-linear. The method is designed to be independent of angular expansion framework. This is demonstrated for the both discrete ordinates (S N ) and spherical harmonics (P N ) descriptions of the angular variable. Results show the scheme performs consistently well in demanding time dependent and multi-dimensional radiation transport problems. (authors)

  16. On the singular perturbations for fractional differential equation.

    Science.gov (United States)

    Atangana, Abdon

    2014-01-01

    The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  17. On the Singular Perturbations for Fractional Differential Equation

    Directory of Open Access Journals (Sweden)

    Abdon Atangana

    2014-01-01

    Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  18. Non-linear thermal optimization and design improvement of a new internal light concrete multi-holed brick walls by FEM

    International Nuclear Information System (INIS)

    Coz Diaz, J.J. del; Garcia Nieto, P.J.; Suarez Sierra, J.L.; Penuelas Sanchez, I.

    2008-01-01

    The aim of this work was carried out the optimization and numerical study by the finite element method of internal hollow bricks walls in order to determine the best candidate brick from the thermal point of view. With respect to the energy saving for housing and industrial structures, there is also a great interest in light building materials with good physical and thermal behaviors, which fulfills all thermal requirements of the new CTE Spanish rule. The conduction, convection and radiation phenomena are taking into account in this study for six different types of bricks varying the material conductivity obtained from five experimental tests. Mathematically, the non-linearity is due to the radiation boundary condition inside the inner recesses of the bricks. Optimization of the walls is carried out from the finite element analysis of the new hollow brick geometries by means of the average mass overall thermal efficiency and the equivalent thermal conductivity. Based on the previous thermal analysis and the optimization procedure described in this paper, the best candidate was chosen and then a full 1.22 x 0.23 x 1.05 m wall made of these bricks was simulated for fifteen different compositions. The main variables influencing the thermal conductivity of these walls are illustrated for different concrete and mortar properties and the temperature distribution is shown for some typical configurations. Finally, in order to select the appropriate wall satisfying the CTE requirements, detailed instructions are given and conclusions of this work are exposed

  19. Non-linear thermal optimization and design improvement of a new internal light concrete multi-holed brick walls by FEM

    Energy Technology Data Exchange (ETDEWEB)

    Del Coz Diaz, J.J.; Suarez Sierra, J.L.; Penuelas Sanchez, I. [Edificio Departamental Viesques, No. 7-33204 Gijon, Asturias (Spain); Garcia Nieto, P.J. [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain)

    2008-06-15

    The aim of this work was carried out the optimization and numerical study by the finite element method of internal hollow bricks walls in order to determine the best candidate brick from the thermal point of view. With respect to the energy saving for housing and industrial structures, there is also a great interest in light building materials with good physical and thermal behaviors, which fulfills all thermal requirements of the new CTE Spanish rule. The conduction, convection and radiation phenomena are taking into account in this study for six different types of bricks varying the material conductivity obtained from five experimental tests. Mathematically, the non-linearity is due to the radiation boundary condition inside the inner recesses of the bricks. Optimization of the walls is carried out from the finite element analysis of the new hollow brick geometries by means of the average mass overall thermal efficiency and the equivalent thermal conductivity. Based on the previous thermal analysis and the optimization procedure described in this paper, the best candidate was chosen and then a full 1.22 x 0.23 x 1.05 m wall made of these bricks was simulated for fifteen different compositions. The main variables influencing the thermal conductivity of these walls are illustrated for different concrete and mortar properties and the temperature distribution is shown for some typical configurations. Finally, in order to select the appropriate wall satisfying the CTE requirements, detailed instructions are given and conclusions of this work are exposed. (author)

  20. Non-linear thermal optimization and design improvement of a new internal light concrete multi-holed brick walls by FEM

    Energy Technology Data Exchange (ETDEWEB)

    Coz Diaz, J.J. del [Edificio Departamental Viesques, No. 7-33204 Gijon, Asturias (Spain)], E-mail: juanjo@constru.uniovi.es; Garcia Nieto, P.J. [Departamento de Matematicas, Facultad de Ciencias, C/Calvo Sotelo s/n, 33007 Oviedo, Asturias (Spain); Suarez Sierra, J.L.; Penuelas Sanchez, I. [Edificio Departamental Viesques, No. 7-33204 Gijon, Asturias (Spain)

    2008-06-15

    The aim of this work was carried out the optimization and numerical study by the finite element method of internal hollow bricks walls in order to determine the best candidate brick from the thermal point of view. With respect to the energy saving for housing and industrial structures, there is also a great interest in light building materials with good physical and thermal behaviors, which fulfills all thermal requirements of the new CTE Spanish rule. The conduction, convection and radiation phenomena are taking into account in this study for six different types of bricks varying the material conductivity obtained from five experimental tests. Mathematically, the non-linearity is due to the radiation boundary condition inside the inner recesses of the bricks. Optimization of the walls is carried out from the finite element analysis of the new hollow brick geometries by means of the average mass overall thermal efficiency and the equivalent thermal conductivity. Based on the previous thermal analysis and the optimization procedure described in this paper, the best candidate was chosen and then a full 1.22 x 0.23 x 1.05 m wall made of these bricks was simulated for fifteen different compositions. The main variables influencing the thermal conductivity of these walls are illustrated for different concrete and mortar properties and the temperature distribution is shown for some typical configurations. Finally, in order to select the appropriate wall satisfying the CTE requirements, detailed instructions are given and conclusions of this work are exposed.

  1. MORE: mixed optimization for reverse engineering--an application to modeling biological networks response via sparse systems of nonlinear differential equations.

    Science.gov (United States)

    Sambo, Francesco; de Oca, Marco A Montes; Di Camillo, Barbara; Toffolo, Gianna; Stützle, Thomas

    2012-01-01

    Reverse engineering is the problem of inferring the structure of a network of interactions between biological variables from a set of observations. In this paper, we propose an optimization algorithm, called MORE, for the reverse engineering of biological networks from time series data. The model inferred by MORE is a sparse system of nonlinear differential equations, complex enough to realistically describe the dynamics of a biological system. MORE tackles separately the discrete component of the problem, the determination of the biological network topology, and the continuous component of the problem, the strength of the interactions. This approach allows us both to enforce system sparsity, by globally constraining the number of edges, and to integrate a priori information about the structure of the underlying interaction network. Experimental results on simulated and real-world networks show that the mixed discrete/continuous optimization approach of MORE significantly outperforms standard continuous optimization and that MORE is competitive with the state of the art in terms of accuracy of the inferred networks.

  2. Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems

    Science.gov (United States)

    Campoamor-Stursberg, Rutwig

    2017-03-01

    Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.

  3. Application of a perturbation method for realistic dynamic simulation of industrial robots

    NARCIS (Netherlands)

    Waiboer, R.R.; Aarts, Ronald G.K.M.; Jonker, Jan B.

    2005-01-01

    This paper presents the application of a perturbation method for the closed-loop dynamic simulation of a rigid-link manipulator with joint friction. In this method the perturbed motion of the manipulator is modelled as a first-order perturbation of the nominal manipulator motion. A non-linear finite

  4. Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems

    International Nuclear Information System (INIS)

    Campoamor-Stursberg, Rutwig

    2017-01-01

    Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.

  5. Symmetry-preserving perturbations of the Bateman Lagrangian and dissipative systems

    Energy Technology Data Exchange (ETDEWEB)

    Campoamor-Stursberg, Rutwig, E-mail: rutwig@ucm.es [Faculted de Ciencias Matematicas Universidad Complutense, Instituto de Matemática Interdisciplinar and Departamento Geometría y Topología (Spain)

    2017-03-15

    Perturbations of the classical Bateman Lagrangian preserving a certain subalgebra of Noether symmetries are studied, and conservative perturbations are characterized by the Lie algebra sl(2, ℝ) ⊕ so(2). Non-conservative albeit integrable perturbations are determined by the simple Lie algebra sl(2,ℝ), showing further the relation of the corresponding non-linear systems with the notion of generalized Ermakov systems.

  6. Multi-step ahead nonlinear identification of Lorenz's chaotic system using radial basis neural network with learning by clustering and particle swarm optimization

    International Nuclear Information System (INIS)

    Guerra, Fabio A.; Coelho, Leandro dos S.

    2008-01-01

    An important problem in engineering is the identification of nonlinear systems, among them radial basis function neural networks (RBF-NN) using Gaussian activation functions models, which have received particular attention due to their potential to approximate nonlinear behavior. Several design methods have been proposed for choosing the centers and spread of Gaussian functions and training the RBF-NN. The selection of RBF-NN parameters such as centers, spreads, and weights can be understood as a system identification problem. This paper presents a hybrid training approach based on clustering methods (k-means and c-means) to tune the centers of Gaussian functions used in the hidden layer of RBF-NNs. This design also uses particle swarm optimization (PSO) for centers (local clustering search method) and spread tuning, and the Penrose-Moore pseudoinverse for the adjustment of RBF-NN weight outputs. Simulations involving this RBF-NN design to identify Lorenz's chaotic system indicate that the performance of the proposed method is superior to that of the conventional RBF-NN trained for k-means and the Penrose-Moore pseudoinverse for multi-step ahead forecasting

  7. Nonlinear undulator tapering in conventional SASE regime at baseline electron beam parameters as a way to optimize the radiation characteristics of the European XFEL

    Energy Technology Data Exchange (ETDEWEB)

    Serkez, Svitozar; Kocharyan, Vitali; Saldin, Evgeni; Zagorodnov, Igor [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Geloni, Gianluca [European XFEL GmbH, Hamburg (Germany)

    2013-09-15

    We demonstrate that the output radiation characteristics of the European XFEL sources at nominal operation point can be easily made significantly better than what is currently reported in the TDRs of scientific instruments and X-ray optics. In fact, the output SASE characteristics of the baseline European XFEL have been previously optimized assuming uniform undulators at a nominal operating point of 5 kA peak current, without considering the potential of undulator tapering in the SASE regime. In order to illustrate this point, we analyze the case of an electron bunch with nominal parameters. Based on start-to-end simulations, we demonstrate that nonlinear undulator tapering allows one to achieve up to a tenfold increase in peak power and photon spectral density in the conventional SASE regime, without modification to the baseline design. The FEL code Genesis has been extensively used for these studies. In order to increase our confidence in simulation results, we cross-checked outcomes by reproducing simulations in the deep nonlinear SASE regime with tapered undulator using the code ALICE.

  8. Optimized geometry, vibration (IR and Raman spectra and nonlinear optical activity of p-nitroanilinium perchlorate molecule: A theoretical study

    Directory of Open Access Journals (Sweden)

    Tamer Ömer

    2016-03-01

    Full Text Available The molecular modeling of p-nitroanilinium perchlorate molecule was carried out by using B3LYP and HSEH1PBE levels of density functional theory (DFT. The IR and Raman spectra were simulated and the assignments of vibrational modes were performed on the basis of relative contribution of various internal co-ordinates. NBO analysis was performed to demonstrate charge transfer, conjugative interactions and the formation of intramolecular hydrogen bonding interactions within PNAPC. Obtained large dipole moment values showed that PNAPC is a highly polarizable complex, and the charge transfer occurs within PNAPC. Hydrogen bonding and charge transfer interactions were also displayed by small HOMO-LUMO gap and molecular electrostatic potential (MEP surface. The strong evidences that the material can be used as an efficient nonlinear optical (NLO material of PNAPC were demonstrated by considerable polarizability and hyperpolarizability values obtained at DFT levels.

  9. Constrained non-linear optimization in 3D reflexion tomography; Problemes d'optimisation non-lineaire avec contraintes en tomographie de reflexion 3D

    Energy Technology Data Exchange (ETDEWEB)

    Delbos, F.

    2004-11-01

    Reflexion tomography allows the determination of a subsurface velocity model from the travel times of seismic waves. The introduction of a priori information in this inverse problem can lead to the resolution of a constrained non-linear least-squares problem. The goal of the thesis is to improve the resolution techniques of this optimization problem, whose main difficulties are its ill-conditioning, its large scale and an expensive cost function in terms of CPU time. Thanks to a detailed study of the problem and to numerous numerical experiments, we justify the use of a sequential quadratic programming method, in which the tangential quadratic programs are solved by an original augmented Lagrangian method. We show the global linear convergence of the latter. The efficiency and robustness of the approach are demonstrated on several synthetic examples and on two real data cases. (author)

  10. Constrained non-linear optimization in 3D reflexion tomography; Problemes d'optimisation non-lineaire avec contraintes en tomographie de reflexion 3D

    Energy Technology Data Exchange (ETDEWEB)

    Delbos, F

    2004-11-01

    Reflexion tomography allows the determination of a subsurface velocity model from the travel times of seismic waves. The introduction of a priori information in this inverse problem can lead to the resolution of a constrained non-linear least-squares problem. The goal of the thesis is to improve the resolution techniques of this optimization problem, whose main difficulties are its ill-conditioning, its large scale and an expensive cost function in terms of CPU time. Thanks to a detailed study of the problem and to numerous numerical experiments, we justify the use of a sequential quadratic programming method, in which the tangential quadratic programs are solved by an original augmented Lagrangian method. We show the global linear convergence of the latter. The efficiency and robustness of the approach are demonstrated on several synthetic examples and on two real data cases. (author)

  11. Contribution of higher order terms in the reductive perturbation theory, 2

    International Nuclear Information System (INIS)

    Ichikawa, Y.H.; Mitsuhashi, Teruo; Konno, Kimiaki.

    1977-01-01

    Contribution of higher order terms in the reductive perturbation theory has been investigated for nonlinear propagation of strongly dispersive ion plasma wave. The basic set of fluid equation is reduced to a coupled set of the nonlinear Schroedinger equation for the first order perturbed potential and a linear inhomogeneous equation for the second order perturbed potential. A steady state solution of the coupled set of equations has been solved analytically in the asymptotic limit of small wave number. (auth.)

  12. Numerical Methods for the Optimization of Nonlinear Residual-Based Sungrid-Scale Models Using the Variational Germano Identity

    NARCIS (Netherlands)

    Maher, G.D.; Hulshoff, S.J.

    2014-01-01

    The Variational Germano Identity [1, 2] is used to optimize the coefficients of residual-based subgrid-scale models that arise from the application of a Variational Multiscale Method [3, 4]. It is demonstrated that numerical iterative methods can be used to solve the Germano relations to obtain

  13. Optimal and robust control of a class of nonlinear systems using dynamically re-optimised single network adaptive critic design

    Science.gov (United States)

    Tiwari, Shivendra N.; Padhi, Radhakant

    2018-01-01

    Following the philosophy of adaptive optimal control, a neural network-based state feedback optimal control synthesis approach is presented in this paper. First, accounting for a nominal system model, a single network adaptive critic (SNAC) based multi-layered neural network (called as NN1) is synthesised offline. However, another linear-in-weight neural network (called as NN2) is trained online and augmented to NN1 in such a manner that their combined output represent the desired optimal costate for the actual plant. To do this, the nominal model needs to be updated online to adapt to the actual plant, which is done by synthesising yet another linear-in-weight neural network (called as NN3) online. Training of NN3 is done by utilising the error information between the nominal and actual states and carrying out the necessary Lyapunov stability analysis using a Sobolev norm based Lyapunov function. This helps in training NN2 successfully to capture the required optimal relationship. The overall architecture is named as 'Dynamically Re-optimised single network adaptive critic (DR-SNAC)'. Numerical results for two motivating illustrative problems are presented, including comparison studies with closed form solution for one problem, which clearly demonstrate the effectiveness and benefit of the proposed approach.

  14. Optimal planning of co-firing alternative fuels with coal in a power plant by grey nonlinear mixed integer programming model

    Energy Technology Data Exchange (ETDEWEB)

    Koa, A.S.; Chang, N.B. [University of Central Florida, Orlando, FL (United States). Dept. for Civil & Environmental Engineering

    2008-07-15

    Energy supply and use is of fundamental importance to society. Although the interactions between energy and environment were originally local in character, they have now widened to cover regional and global issues, such as acid rain and the greenhouse effect. It is for this reason that there is a need for covering the direct and indirect economic and environmental impacts of energy acquisition, transport, production and use. In this paper, particular attention is directed to ways of resolving conflict between economic and environmental goals by encouraging a power plant to consider co-firing biomass and refuse-derived fuel (RDF) with coal simultaneously. It aims at reducing the emission level of sulfur dioxide (SO{sub 2}) in an uncertain environment, using the power plant in Michigan City, Indiana as an example. To assess the uncertainty by a comparative way both deterministic and grey nonlinear mixed integer programming (MIP) models were developed to minimize the net operating cost with respect to possible fuel combinations. It aims at generating the optimal portfolio of alternative fuels while maintaining the same electricity generation simultaneously. To case the solution procedure stepwise relaxation algorithm was developed for solving the grey nonlinear MIP model. Breakeven alternative fuel value can be identified in the post-optimization stage for decision-making. Research findings show that the inclusion of RDF does not exhibit comparative advantage in terms of the net cost, albeit relatively lower air pollution impact. Yet it can be sustained by a charge system, subsidy program, or emission credit as the price of coal increases over time.

  15. Optimal planning of co-firing alternative fuels with coal in a power plant by grey nonlinear mixed integer programming model.

    Science.gov (United States)

    Ko, Andi Setiady; Chang, Ni-Bin

    2008-07-01

    Energy supply and use is of fundamental importance to society. Although the interactions between energy and environment were originally local in character, they have now widened to cover regional and global issues, such as acid rain and the greenhouse effect. It is for this reason that there is a need for covering the direct and indirect economic and environmental impacts of energy acquisition, transport, production and use. In this paper, particular attention is directed to ways of resolving conflict between economic and environmental goals by encouraging a power plant to consider co-firing biomass and refuse-derived fuel (RDF) with coal simultaneously. It aims at reducing the emission level of sulfur dioxide (SO(2)) in an uncertain environment, using the power plant in Michigan City, Indiana as an example. To assess the uncertainty by a comparative way both deterministic and grey nonlinear mixed integer programming (MIP) models were developed to minimize the net operating cost with respect to possible fuel combinations. It aims at generating the optimal portfolio of alternative fuels while maintaining the same electricity generation simultaneously. To ease the solution procedure stepwise relaxation algorithm was developed for solving the grey nonlinear MIP model. Breakeven alternative fuel value can be identified in the post-optimization stage for decision-making. Research findings show that the inclusion of RDF does not exhibit comparative advantage in terms of the net cost, albeit relatively lower air pollution impact. Yet it can be sustained by a charge system, subsidy program, or emission credit as the price of coal increases over time.

  16. Coupled nonlinear oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Chandra, J; Scott, A C

    1983-01-01

    Topics discussed include transitions in weakly coupled nonlinear oscillators, singularly perturbed delay-differential equations, and chaos in simple laser systems. Papers are presented on truncated Navier-Stokes equations in a two-dimensional torus, on frequency locking in Josephson point contacts, and on soliton excitations in Josephson tunnel junctions. Attention is also given to the nonlinear coupling of radiation pulses to absorbing anharmonic molecular media, to aspects of interrupted coarse-graining in stimulated excitation, and to a statistical analysis of long-term dynamic irregularity in an exactly soluble quantum mechanical model.

  17. Infrared problems in field perturbation theory

    International Nuclear Information System (INIS)

    David, Francois.

    1982-12-01

    The work presented mainly covers questions related to the presence of ''infrared'' divergences in perturbation expansions of the Green functions of certain massless field theories. It is important to determine the mathematical status of perturbation expansions in field theory in order to define the region in which they are valid. Renormalization and the symmetry of a theory are important factors in infrared problems. The main object of this thesis resides in the mathematical techniques employed: integral representations of the Feynman amplitudes; methods for desingularization, regularization and dimensional renormalization. Nonlinear two dimensional space-time sigma models describing Goldstone's low energy boson dynamics associated with a breaking of continuous symmetry are studied. Random surface models are then investigated followed by infrared divergences in super-renormalizable theories. Finally, nonperturbation effects in massless theories are studied by expanding the two-dimensional nonlinear sigma model in 1/N [fr

  18. Status of perturbative QCD

    International Nuclear Information System (INIS)

    Collins, J.C.

    1985-01-01

    Progress in quantum chromodynamics in the past year is reviewed in these specific areas: proof of factorization for hadron-hadron collisions, fast calculation of higher order graphs, perturbative Monte Carlo calculations for hadron-hadron scattering, applicability of perturbative methods to heavy quark production, and understanding of the small-x problem. 22 refs

  19. Stochastic effects on the nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Flessas, G P; Leach, P G L; Yannacopoulos, A N

    2004-01-01

    The aim of this article is to provide a brief review of recent advances in the field of stochastic effects on the nonlinear Schroedinger equation. The article reviews rigorous and perturbative results. (review article)

  20. Finite field-dependent symmetries in perturbative quantum gravity

    International Nuclear Information System (INIS)

    Upadhyay, Sudhaker

    2014-01-01

    In this paper we discuss the absolutely anticommuting nilpotent symmetries for perturbative quantum gravity in general curved spacetime in linear and non-linear gauges. Further, we analyze the finite field-dependent BRST (FFBRST) transformation for perturbative quantum gravity in general curved spacetime. The FFBRST transformation changes the gauge-fixing and ghost parts of the perturbative quantum gravity within functional integration. However, the operation of such symmetry transformation on the generating functional of perturbative quantum gravity does not affect the theory on physical ground. The FFBRST transformation with appropriate choices of finite BRST parameter connects non-linear Curci–Ferrari and Landau gauges of perturbative quantum gravity. The validity of the results is also established at quantum level using Batalin–Vilkovisky (BV) formulation. -- Highlights: •The perturbative quantum gravity is treated as gauge theory. •BRST and anti-BRST transformations are developed in linear and non-linear gauges. •BRST transformation is generalized by making it finite and field dependent. •Connection between linear and non-linear gauges is established. •Using BV formulation the results are established at quantum level also

  1. A comparative analysis of particle swarm optimization and differential evolution algorithms for parameter estimation in nonlinear dynamic systems

    International Nuclear Information System (INIS)

    Banerjee, Amit; Abu-Mahfouz, Issam

    2014-01-01

    The use of evolutionary algorithms has been popular in recent years for solving the inverse problem of identifying system parameters given the chaotic response of a dynamical system. The inverse problem is reformulated as a minimization problem and population-based optimizers such as evolutionary algorithms have been shown to be efficient solvers of the minimization problem. However, to the best of our knowledge, there has been no published work that evaluates the efficacy of using the two most popular evolutionary techniques – particle swarm optimization and differential evolution algorithm, on a wide range of parameter estimation problems. In this paper, the two methods along with their variants (for a total of seven algorithms) are applied to fifteen different parameter estimation problems of varying degrees of complexity. Estimation results are analyzed using nonparametric statistical methods to identify if an algorithm is statistically superior to others over the class of problems analyzed. Results based on parameter estimation quality suggest that there are significant differences between the algorithms with the newer, more sophisticated algorithms performing better than their canonical versions. More importantly, significant differences were also found among variants of the particle swarm optimizer and the best performing differential evolution algorithm

  2. Perturbative and constructive renormalization

    International Nuclear Information System (INIS)

    Veiga, P.A. Faria da

    2000-01-01

    These notes are a survey of the material treated in a series of lectures delivered at the X Summer School Jorge Andre Swieca. They are concerned with renormalization in Quantum Field Theories. At the level of perturbation series, we review classical results as Feynman graphs, ultraviolet and infrared divergences of Feynman integrals. Weinberg's theorem and Hepp's theorem, the renormalization group and the Callan-Symanzik equation, the large order behavior and the divergence of most perturbation series. Out of the perturbative regime, as an example of a constructive method, we review Borel summability and point out how it is possible to circumvent the perturbation diseases. These lectures are a preparation for the joint course given by professor V. Rivasseau at the same school, where more sophisticated non-perturbative analytical methods based on rigorous renormalization group techniques are presented, aiming at furthering our understanding about the subject and bringing field theoretical models to a satisfactory mathematical level. (author)

  3. A model for fuel shuffling and burnable absorbers optimization in low leakage PWRs

    International Nuclear Information System (INIS)

    Zavaljevski, N.

    1990-01-01

    A nonlinear model for the simultaneous optimization of fuel shuffling and burnable absorbers in PWRs is formulated using the depletion perturbation theory. The sensitivity coefficients are defined in a new way, using a macroscopic burnup model coupled with the explicit burnable absorbers depletion equation. Since first-order perturbation theory is limited to small changes in burnable absorber concentration, the associated control variable is continuous, with a constraint on maximal increment. Fuel shuffling is described by Boolean variables. Thus a special case of a mixed-integer quadratic programming problem is obtained, since the interaction of fuel and absorber optimization is considered. (author)

  4. Distributed cooperative H∞ optimal tracking control of MIMO nonlinear multi-agent systems in strict-feedback form via adaptive dynamic programming

    Science.gov (United States)

    Luy, N. T.

    2018-04-01

    The design of distributed cooperative H∞ optimal controllers for multi-agent systems is a major challenge when the agents' models are uncertain multi-input and multi-output nonlinear systems in strict-feedback form in the presence of external disturbances. In this paper, first, the distributed cooperative H∞ optimal tracking problem is transformed into controlling the cooperative tracking error dynamics in affine form. Second, control schemes and online algorithms are proposed via adaptive dynamic programming (ADP) and the theory of zero-sum differential graphical games. The schemes use only one neural network (NN) for each agent instead of three from ADP to reduce computational complexity as well as avoid choosing initial NN weights for stabilising controllers. It is shown that despite not using knowledge of cooperative internal dynamics, the proposed algorithms not only approximate values to Nash equilibrium but also guarantee all signals, such as the NN weight approximation errors and the cooperative tracking errors in the closed-loop system, to be uniformly ultimately bounded. Finally, the effectiveness of the proposed method is shown by simulation results of an application to wheeled mobile multi-robot systems.

  5. On nonlinear periodic drift waves

    International Nuclear Information System (INIS)

    Kauschke, U.; Schlueter, H.

    1990-09-01

    Nonlinear periodic drift waves are investigated on the basis of a simple perturbation scheme for both the amplitude and inverse frequency. The coefficients for the generation of the forced harmonics are derived, a nonlinear dispersion relation is suggested and a criterion for the onset of the modulational instability is obtained. The results are compared with the ones obtained with the help of a standard KBM-treatment. Moreover cnoidal drift waves are suggested and compared to an experimental observation. (orig.)

  6. Unidirectional reflection and invisibility in nonlinear media with an incoherent nonlinearity

    Science.gov (United States)

    Mostafazadeh, Ali; Oflaz, Neslihan

    2017-11-01

    We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirectional invisibility of these potentials. If the strength of the Kerr nonlinearity is so weak that the first-order perturbation theory is reliable, the presence of nonlinearity does not affect the unidirectional reflectionlessness and transmission reciprocity of the potential. We show that the expected violation of the latter is a second order perturbative effect.

  7. On modelling adiabatic N-soliton interactions and perturbations. Effects of external potentials

    International Nuclear Information System (INIS)

    Gerdjikov, V.; Baizakov, B.

    2005-01-01

    We analyze several perturbed versions of the complex Toda chain (CTC) in an attempt to describe the adiabatic N-soliton train interactions of the perturbed nonlinear Schrodinger equation (NLS). Particular types of perturbations, including quadratic and periodic external potentials are treated by both analytical and numerical means. We show that the perturbed CTC model provides a good description for the N-soliton interactions in the presence of a weak external potential. (authors)

  8. Perturbative approach to continuum generation in a fiber Bragg grating.

    Science.gov (United States)

    Westbrook, P S; Nicholson, J W

    2006-08-21

    We derive a perturbative solution to the nonlinear Schrödinger equation to include the effect of a fiber Bragg grating whose bandgap is much smaller than the pulse bandwidth. The grating generates a slow dispersive wave which may be computed from an integral over the unperturbed solution if nonlinear interaction between the grating and unperturbed waves is negligible. Our approach allows rapid estimation of large grating continuum enhancement peaks from a single nonlinear simulation of the waveguide without grating. We apply our method to uniform and sampled gratings, finding good agreement with full nonlinear simulations, and qualitatively reproducing experimental results.

  9. Simulated Annealing-based Optimal Proportional-Integral-Derivative (PID) Controller Design: A Case Study on Nonlinear Quadcopter Dynamics

    Science.gov (United States)

    Nemirsky, Kristofer Kevin

    In this thesis, the history and evolution of rotor aircraft with simulated annealing-based PID application were reviewed and quadcopter dynamics are presented. The dynamics of a quadcopter were then modeled, analyzed, and linearized. A cascaded loop architecture with PID controllers was used to stabilize the plant dynamics, which was improved upon through the application of simulated annealing (SA). A Simulink model was developed to test the controllers and verify the functionality of the proposed control system design. In addition, the data that the Simulink model provided were compared with flight data to present the validity of derived dynamics as a proper mathematical model representing the true dynamics of the quadcopter system. Then, the SA-based global optimization procedure was applied to obtain optimized PID parameters. It was observed that the tuned gains through the SA algorithm produced a better performing PID controller than the original manually tuned one. Next, we investigated the uncertain dynamics of the quadcopter setup. After adding uncertainty to the gyroscopic effects associated with pitch-and-roll rate dynamics, the controllers were shown to be robust against the added uncertainty. A discussion follows to summarize SA-based algorithm PID controller design and performance outcomes. Lastly, future work on SA application on multi-input-multi-output (MIMO) systems is briefly discussed.

  10. Perturbative QCD and jets

    International Nuclear Information System (INIS)

    Mueller, A.H.

    1986-03-01

    A brief review of some of the recent progress in perturbative QCD is given (heavy quark production, small-x physics, minijets and related topics, classical simulations in high energy reactions, coherence and the string effect)

  11. Generalized chiral perturbation theory

    International Nuclear Information System (INIS)

    Knecht, M.; Stern, J.

    1994-01-01

    The Generalized Chiral Perturbation Theory enlarges the framework of the standard χPT (Chiral Perturbation Theory), relaxing certain assumptions which do not necessarily follow from QCD or from experiment, and which are crucial for the usual formulation of the low energy expansion. In this way, experimental tests of the foundations of the standard χPT become possible. Emphasis is put on physical aspects rather than on formal developments of GχPT. (author). 31 refs

  12. Model-Based Control of a Nonlinear Aircraft Engine Simulation using an Optimal Tuner Kalman Filter Approach

    Science.gov (United States)

    Connolly, Joseph W.; Csank, Jeffrey Thomas; Chicatelli, Amy; Kilver, Jacob

    2013-01-01

    This paper covers the development of a model-based engine control (MBEC) methodology featuring a self tuning on-board model applied to an aircraft turbofan engine simulation. Here, the Commercial Modular Aero-Propulsion System Simulation 40,000 (CMAPSS40k) serves as the MBEC application engine. CMAPSS40k is capable of modeling realistic engine performance, allowing for a verification of the MBEC over a wide range of operating points. The on-board model is a piece-wise linear model derived from CMAPSS40k and updated using an optimal tuner Kalman Filter (OTKF) estimation routine, which enables the on-board model to self-tune to account for engine performance variations. The focus here is on developing a methodology for MBEC with direct control of estimated parameters of interest such as thrust and stall margins. Investigations using the MBEC to provide a stall margin limit for the controller protection logic are presented that could provide benefits over a simple acceleration schedule that is currently used in traditional engine control architectures.

  13. Photonic Crystal Nanocavity Devices for Nonlinear Signal Processing

    DEFF Research Database (Denmark)

    Yu, Yi

    , membranization of InP/InGaAs structure and wet etching. Experimental investigation of the switching dynamics of InP photonic crystal nanocavity structures are carried out using short-pulse homodyne pump-probe techniques, both in the linear and nonlinear region where the cavity is perturbed by a relatively small......This thesis deals with the investigation of InP material based photonic crystal cavity membrane structures, both experimentally and theoretically. The work emphasizes on the understanding of the physics underlying the structures’ nonlinear properties and their applications for all-optical signal...... processing. Based on the previous fabrication recipe developed in our III-V platform, several processing techniques are developed and optimized for the fabrication of InP photonic crystal membrane structures. Several key issues are identified to ensure a good device quality such as air hole size control...

  14. Lavrentiev regularization method for nonlinear ill-posed problems

    International Nuclear Information System (INIS)

    Kinh, Nguyen Van

    2002-10-01

    In this paper we shall be concerned with Lavientiev regularization method to reconstruct solutions x 0 of non ill-posed problems F(x)=y o , where instead of y 0 noisy data y δ is an element of X with absolut(y δ -y 0 ) ≤ δ are given and F:X→X is an accretive nonlinear operator from a real reflexive Banach space X into itself. In this regularization method solutions x α δ are obtained by solving the singularly perturbed nonlinear operator equation F(x)+α(x-x*)=y δ with some initial guess x*. Assuming certain conditions concerning the operator F and the smoothness of the element x*-x 0 we derive stability estimates which show that the accuracy of the regularized solutions is order optimal provided that the regularization parameter α has been chosen properly. (author)

  15. Acoustic-gravity nonlinear structures

    Directory of Open Access Journals (Sweden)

    D. Jovanović

    2002-01-01

    Full Text Available A catalogue of nonlinear vortex structures associated with acoustic-gravity perturbations in the Earth's atmosphere is presented. Besides the previously known Kelvin-Stewart cat's eyes, dipolar and tripolar structures, new solutions having the form of a row of counter-rotating vortices, and several weakly two-dimensional vortex chains are given. The existence conditions for these nonlinear structures are discussed with respect to the presence of inhomogeneities of the shear flows. The mode-coupling mechanism for the nonlinear generation of shear flows in the presence of linearly unstable acoustic-gravity waves, possibly also leading to intermittency and chaos, is presented.

  16. Nonlinear modulation of ionization waves

    International Nuclear Information System (INIS)

    Bekki, Naoaki

    1981-01-01

    In order to investigate the nonlinear characteristics of ionization waves (moving-striations) in the positive column of glow discharge, a nonlinear modulation of ionization waves in the region of the Pupp critical current is analysed by means of the reductive perturbation method. The modulation of ionization waves is described by a nonlinear Schroedinger type equation. The coefficients of the equation are evaluated using the data of the low pressure Argon-discharge, and the simple solutions (plane wave and envelope soliton type solutions) are presented. Under a certain condition an envelope soliton is propagated through the positive column. (author)

  17. Study of the hoop fracture behaviour of nuclear fuel cladding from ring compression tests by means of non-linear optimization techniques

    Energy Technology Data Exchange (ETDEWEB)

    Gómez, F.J., E-mail: javier.gomez@amsimulation.com [Advanced Material Simulation, AMS, Bilbao (Spain); Martin Rengel, M.A., E-mail: mamartin.rengel@upm.es [E.T.S.I. Caminos, Canales y Puertos, Universidad Politécnica de Madrid, C/Professor Aranguren SN, E-28040 Madrid (Spain); Ruiz-Hervias, J.; Puerta, M.A. [E.T.S.I. Caminos, Canales y Puertos, Universidad Politécnica de Madrid, C/Professor Aranguren SN, E-28040 Madrid (Spain)

    2017-06-15

    In this work, the hoop fracture toughness of ZIRLO{sup ®} fuel cladding is calculated as a function of three parameters: hydrogen concentration, temperature and displacement rate. To this end, pre-hydrided samples with nominal hydrogen concentrations of 0 (as-received), 150, 250, 500, 1200 and 2000 ppm were prepared. Hydrogen was precipitated as zirconium hydrides in the shape of platelets oriented along the hoop direction. Ring Compression Tests (RCTs) were conducted at three temperatures (20, 135 and 300 °C) and two displacement rates (0.5 and 100 mm/min). A new method has been proposed in this paper which allows the determination of fracture toughness from ring compression tests. The proposed method combines the experimental results, the cohesive crack model, finite elements simulations, numerical calculations and non-linear optimization techniques. The parameters of the cohesive crack model were calculated by minimizing the difference between the experimental data and the numerical results. An almost perfect fitting of the experimental results is achieved by this method. In addition, an estimation of the error in the calculated fracture toughness is also provided.

  18. Accurate Open-Shell Noncovalent Interaction Energies from the Orbital-Optimized Møller-Plesset Perturbation Theory: Achieving CCSD Quality at the MP2 Level by Orbital Optimization.

    Science.gov (United States)

    Soydaş, Emine; Bozkaya, Uğur

    2013-11-12

    The accurate description of noncovalent interactions is one of the most challenging problems in modern computational chemistry, especially those for open-shell systems. In this study, an investigation of open-shell noncovalent interactions with the orbital-optimized MP2 and MP3 (OMP2 and OMP3) is presented. For the considered test set of 23 complexes, mean absolute errors in noncovalent interaction energies (with respect to CCSD(T) at complete basis set limits) are 0.68 (MP2), 0.37 (OMP2), 0.59 (MP3), 0.23 (OMP3), and 0.38 (CCSD) kcal mol(-1) . Hence, with a greatly reduced computational cost, one may achieve CCSD quality at the MP2 level by orbital optimization [scaling formally as O(N(6)) for CCSD compared to O(N(5)) for OMP2, where N is the number of basis functions]. Further, one may obtain a considerably better performance than CCSD using the OMP3 method, which has also a lower cost than CCSD.

  19. Nonlinear Multiantenna Detection Methods

    Directory of Open Access Journals (Sweden)

    Chen Sheng

    2004-01-01

    Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.

  20. Perturbative anyon gas

    International Nuclear Information System (INIS)

    Dasnieres de Veigy, A.; Ouvry, S.; Paris-6 Univ., 75

    1992-06-01

    The problem of the statistical mechanics of an anyon gas is addressed. A perturbative analysis in the anyonic coupling constant α is reviewed, and the thermodynamical potential is computed at first and second order. An adequate second quantized formalism (field theory at finite temperature) is proposed. At first order in perturbation theory, the results are strikingly simple: only the second virial coefficient close to bosonic statistics is corrected. At second order, however, the complexity of the anyon model appears. One can compute exactly the perturbative correction to each cluster coefficient. However, and contrary to first order, a closed expression for the equation of state seems out of reach. As an illustration, the perturbative expressions of a 3 , a 4 , a 5 and a 6 are given at second order. Finally, using the same formalism, the equation of state of an anyon gas in a constant magnetic field is analyzed at first order in perturbation theory. (K.A.) 16 refs.; 3 figs.; 7 tabs