The tanh-coth method combined with the Riccati equation for solving non-linear equation
Energy Technology Data Exchange (ETDEWEB)
Bekir, Ahmet [Dumlupinar University, Art-Science Faculty, Department of Mathematics, Kuetahya (Turkey)], E-mail: abekir@dumlupinar.edu.tr
2009-05-15
In this work, we established abundant travelling wave solutions for some non-linear evolution equations. This method was used to construct solitons and traveling wave solutions of non-linear evolution equations. The tanh-coth method combined with Riccati equation presents a wider applicability for handling non-linear wave equations.
A combined modification of Newton`s method for systems of nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Monteiro, M.T.; Fernandes, E.M.G.P. [Universidade do Minho, Braga (Portugal)
1996-12-31
To improve the performance of Newton`s method for the solution of systems of nonlinear equations a modification to the Newton iteration is implemented. The modified step is taken as a linear combination of Newton step and steepest descent directions. In the paper we describe how the coefficients of the combination can be generated to make effective use of the two component steps. Numerical results that show the usefulness of the combined modification are presented.
Hu, Zhan; Zheng, Gangtie
2016-08-01
A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.
On approximation of nonlinear boundary integral equations for the combined method
Energy Technology Data Exchange (ETDEWEB)
Gregus, M.; Khoromsky, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.
1989-09-22
The nonlinear boundary integral equations that arise in research of nonlinear magnetostatic problems are investigated in combined formulation on an unbounded domain. Approximations of the derived operator equations are studied based on the Galerkin method. The investigated boundary operators are strongly monotone, Lipschitz-continuous, potential and have a symmetrical Gateaux derivative. The error estimates of the Galerkin's approximation in Sobolev spaces of fractional powers are obtained using the above-mentioned properties of the operators, too. The problem has been studied on surfaces in two and three-dimensional spaces. We answer also some questions on convergence connected with the discretized systems of equations. 21 refs.
A nonlinear combination forecasting method based on the fuzzy inference system
Institute of Scientific and Technical Information of China (English)
董景荣; YANG; Jun; 等
2002-01-01
It has been shown in recent economic and statistical studies that combining forecasts may produce more accurate forecasts than individual ones,However,the literature on combining forecasts has almost exclusively focused on linear combining forecasts.In this paper,a new nonlinear combination forecasting method based on fuzzy inference system is present to overcome the difficulties and drawbacks in linear combination modeling of non-stationary time series.Furthermore,the optimization algorithm based on a hierarchical structure of learning automata is used to identify the parameters of the fuzzy system.Experiment results related to numerical examples demonstrate that the new technique has excellent identification performances and forecasting accuracy superior to other existing linear combining forecasts.
Combined indirect and direct method for adaptive fuzzy output feedback control of nonlinear system
Institute of Scientific and Technical Information of China (English)
Ding Quanxin; Chen Haitong; Jiang Changsheng; Chen Zongji
2007-01-01
A novel control method for a general class of nonlinear systems using fuzzy logic systems (FLSs) is presertted.Indirect and direct methods are combined to design the adaptive fuzzy output feedback controller and a high-gain observer is used to estimate the derivatives of the system output. The closed-loop system is proven to be semiglobally uniformly ultimately bounded. In addition, it is shown that if the approximation accuracy of the fuzzy logic system is high enough and the observer gain is chosen sufficiently large, an arbitrarily small tracking error can be achieved. Simulation results verify the effectiveness of the newly designed scheme and the theoretical discussion.
Islam, Md Shafiqul; Khan, Kamruzzaman; Akbar, M Ali; Mastroberardino, Antonio
2014-10-01
The purpose of this article is to present an analytical method, namely the improved F-expansion method combined with the Riccati equation, for finding exact solutions of nonlinear evolution equations. The present method is capable of calculating all branches of solutions simultaneously, even if multiple solutions are very close and thus difficult to distinguish with numerical techniques. To verify the computational efficiency, we consider the modified Benjamin-Bona-Mahony equation and the modified Korteweg-de Vries equation. Our results reveal that the method is a very effective and straightforward way of formulating the exact travelling wave solutions of nonlinear wave equations arising in mathematical physics and engineering.
Directory of Open Access Journals (Sweden)
Jurado-Piña, R.
2014-12-01
Full Text Available When designing a tension structure the shape is not known at the beginning of the process. Form-finding methods allow the designer to obtain an initial shape from given boundary conditions. Several form-finding methods for tension structures are already available in the technical literature; all of them posses certain limitations and drawbacks and no single method is optimal for all problems. The engineer may select the proper combination of methods best suited to the designer’s needs. In this paper it is proposed a combined method to achieve satisfactory equilibrium configurations for fabric tension structures. The force density method (FDM implemented with topological mapping (TM is used as a search engine for the preliminary design, and a procedure that employs nonlinear structural analysis is proposed for final refinement of the initial equilibrium configuration hence allowing the use of the same analysis tool for both refinement of the solution and analysis under loading.Al diseñar una estructura tensada la forma inicial es normalmente desconocida. Los métodos de búsqueda de forma permiten al ingeniero obtener una geometría inicial dadas unas condiciones de contorno. Existen diferentes métodos de búsqueda de formas de equilibrio, pero todos tienen limitaciones y no existe uno único óptimo para cualquier tipo de problema. El ingeniero debe elegir la combinación de métodos que mejor se adapte a sus necesidades. En este artículo se propone un método combinado para generar configuraciones de equilibrio satisfactorias en estructuras tensadas. Como motor de búsqueda para el diseño preliminar se emplea el método de las densidades de fuerza (FDM implementado con mallado en topología (TM, y se propone un procedimiento basado en análisis no lineal de estructuras para el refinamiento de la configuración inicial de equilibrio, permitiéndose así el empleo de las mismas herramientas tanto para el refinamiento de la solución inicial
Nourazar, S. S.; Nazari-Golshan, A.
2015-01-01
A hybrid of Fourier transform and new modified homotopy perturbation method based on the Adomian method is developed to solve linear and nonlinear partial differential equations. The Taylor series expansion is used to expand nonlinear term of partial differential equation and the Adomian polynomial incorporated into homotopy perturbation method combined with Fourier transform, is used to solve partial differential equations. Three case study problems, partial differential equations, are handled using homotopy perturbation method and Fourier transform modified homotopy perturbation method (FTMHPM). Results obtained are compared with exact solution. The comparison reveals that for same components of recursive sequences, errors associated with Fourier transform modified method are much less than the other and are valid for a large range of x-axis coordinates.
Liu, Yung-Tien; Fung, Rong-Fong; Wang, Chun-Chao
2007-02-01
In this research, the nonlinear, double-dynamic Taguchi method was used as design and analysis methods for a high-precision positioning device using the combined piezo-voice-coil motor (VCM) actuator. An experimental investigation into the effects of two input signals and three control factors were carried out to determine the optimum parametric configuration of the positioning device. The double-dynamic Taguchi method, which permits optimization of several control factors concurrently, is particularly suitable for optimizing the performance of a positioning device with multiple actuators. In this study, matrix experiments were conducted with L9(3(4)) orthogonal arrays (OAs). The two most critical processes for the optimization of positioning device are the identification of the nonlinear ideal function and the combination of the double-dynamic signal factors for the ideal function's response. The driving voltage of the VCM and the waveform amplitude of the PZT actuator are combined into a single quality characteristic to evaluate the positioning response. The application of the double-dynamic Taguchi method, with dynamic signal-to-noise ratio (SNR) and L9(3(4)) OAs, reduced the number of necessary experiments. The analysis of variance (ANOVA) was applied to set the optimum parameters based on the high-precision positioning process.
Combined algorithms in nonlinear problems of magnetostatics
Energy Technology Data Exchange (ETDEWEB)
Gregus, M.; Khoromsky, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.
1988-05-09
To solve boundary problems of magnetostatics in unbounded two- or three-dimensional regions, we construct combined algorithms based on a combination of the method of boundary integral equations with the grid methods. We study the question of substantiation of the combined method in nonlinear magnetostatic problems without the preliminary discretization of equations and give some results on the convergence of iterative processes that arise in nonlinear cases. We also discuss economical iterative processes and algorithms that solve boundary integral equations on certain surfaces. Finally, examples of numerical solutions of magnetostatic problems that arose when modelling the fields of electrophysical installations are given, too. 14 refs., 2 figs.
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.
Combined forecasts from linear and nonlinear time series models
N. Terui (Nobuhiko); H.K. van Dijk (Herman)
1999-01-01
textabstractCombined forecasts from a linear and a nonlinear model are investigated for time series with possibly nonlinear characteristics. The forecasts are combined by a constant coefficient regression method as well as a time varying method. The time varying method allows for a locally (non)line
Improved nonlinear prediction method
Adenan, Nur Hamiza; Md Noorani, Mohd Salmi
2014-06-01
The analysis and prediction of time series data have been addressed by researchers. Many techniques have been developed to be applied in various areas, such as weather forecasting, financial markets and hydrological phenomena involving data that are contaminated by noise. Therefore, various techniques to improve the method have been introduced to analyze and predict time series data. In respect of the importance of analysis and the accuracy of the prediction result, a study was undertaken to test the effectiveness of the improved nonlinear prediction method for data that contain noise. The improved nonlinear prediction method involves the formation of composite serial data based on the successive differences of the time series. Then, the phase space reconstruction was performed on the composite data (one-dimensional) to reconstruct a number of space dimensions. Finally the local linear approximation method was employed to make a prediction based on the phase space. This improved method was tested with data series Logistics that contain 0%, 5%, 10%, 20% and 30% of noise. The results show that by using the improved method, the predictions were found to be in close agreement with the observed ones. The correlation coefficient was close to one when the improved method was applied on data with up to 10% noise. Thus, an improvement to analyze data with noise without involving any noise reduction method was introduced to predict the time series data.
Ni, Li-Jun; Zhong, Lin; Zhang, Xin; Zhang, Li-Guo; Huang, Shi-Xinz
2014-10-01
correlative analysis between the discrimination accuracy rate and the content levels of the adulterants indicated that near infrared spectroscopy combined with non-linear pattern recognition methods can distinguish dextrin and starch in milks with higher concentration levels (> 0.15%), but do not work well on identifying the adulterants with lower concentrations such as melamine (365.5 to 1,096.5 mg kg(-1)), urea (524 to 1,572 mg · kg(-1)), ammonium nitrate (700 to 2,100 mg · kg(-1)). Therefore near Infrared Spectroscopy is not suitable for identifying the adulterants with concentrations are below 0.1%.
Chen, Jianxin; Zhuo, Shuangmu; Luo, Tianshu; Liu, Dingzhong; Zhao, Jingjun
2008-08-01
Collagen and elastin are the most important proteins of the connective tissues in higher vertebrates. In this paper, we present a combined nonlinear optical imaging technique of second-harmonic generation and two-photon excited fluorescence to simultaneously observe the collagen and elastic fiber of dermis in a freshly excised human skin and rabbit aorta using a two-channel synchronized detection method. The obtained two-channel overlay image in the backward direction can clearly distinguish the morphological structure and distribution of collagen and elastic fibers. Tissue spectrum further confirms the obtained structural information. These results suggest that the combined nonlinear optical imaging technique coupled with two-channel synchronized detection method can be an effective tool for detecting collage and elastic fibers without any invasive tissue procedure of slicing, embedding, fixation and staining when two structural proteins are simultaneously present in the biological tissue.
Institute of Scientific and Technical Information of China (English)
杨轶华; 吕显瑞; 刘庆怀
2006-01-01
In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP)for convex nonlinear programming problems. For any convex nonlinear programming,without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.
Gorban, A. N.; Karlin, I.V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
Nonlinear programming analysis and methods
Avriel, Mordecai
2012-01-01
This text provides an excellent bridge between principal theories and concepts and their practical implementation. Topics include convex programming, duality, generalized convexity, analysis of selected nonlinear programs, techniques for numerical solutions, and unconstrained optimization methods.
Nonlinear programming analysis and methods
Avriel, Mordecai
2003-01-01
Comprehensive and complete, this overview provides a single-volume treatment of key algorithms and theories. The author provides clear explanations of all theoretical aspects, with rigorous proof of most results. The two-part treatment begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs. The second part concerns techniques for numerical solutions and unconstrained optimization methods, and it presents commonly used algorithms for constrained nonlinear optimization problems. This g
μ Synthesis Method for Robust Control of Uncertain Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
μ synthesis method for robust control of uncertain nonlinear systems is propored, which is based on feedback linearization. First, nonlinear systems are linearized as controllable linear systems by I/O linearization,such that uncertain nonlinear systems are expressed as the linear fractional transformations (LFTs) on the generalized linearized plants and uncertainty.Then,linear robust controllers are obtained for the LFTs usingμsynthesis method based on H∞ optimization.Finally,the nonlinear robust controllers are constructed by combining the linear robust controllers and the nonlinear feedback.An example is given to illustrate the design.
Statistical methods in nonlinear dynamics
Indian Academy of Sciences (India)
K P N Murthy; R Harish; S V M Satyanarayana
2005-03-01
Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical methods employed in the study of deterministic and stochastic dynamical systems. These include power spectral analysis and aliasing, extreme value statistics and order statistics, recurrence time statistics, the characterization of intermittency in the Sinai disorder problem, random walk analysis of diffusion in the chaotic pendulum, and long-range correlations in stochastic sequences of symbols.
Beam Combining by Phase Transition Nonlinear Media
1990-02-01
use the Redlich Kwong equation of state for the media we consider. This equation of state can be written RT a p - -b -FT(p.-’ + b)p ; 2-I M (2-1) where...as ac 3 dg-A7 C VA/\\CIIJT (6) The Redlich - Kwong equation of state; i.e., _ RT T-1/2 v-P v(v+P) (7) can be used to compute aP/lT, where the relevant...practical the application of nonlinear phase conjugate techniques to the beam combining of multiple lasers with a coherence characteristic of a
Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances
Directory of Open Access Journals (Sweden)
Ali H. Nayfeh
1998-01-01
Full Text Available The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.
Nonlinear structural analysis using integrated force method
Indian Academy of Sciences (India)
N R B Krishnam Raju; J Nagabhushanam
2000-08-01
Though the use of the integrated force method for linear investigations is well-recognised, no efforts were made to extend this method to nonlinear structural analysis. This paper presents the attempts to use this method for analysing nonlinear structures. General formulation of nonlinear structural analysis is given. Typically highly nonlinear bench-mark problems are considered. The characteristic matrices of the elements used in these problems are developed and later these structures are analysed. The results of the analysis are compared with the results of the displacement method. It has been demonstrated that the integrated force method is equally viable and efficient as compared to the displacement method.
Nonlinear modal methods for crack localization
Sutin, Alexander; Ostrovsky, Lev; Lebedev, Andrey
2003-10-01
A nonlinear method for locating defects in solid materials is discussed that is relevant to nonlinear modal tomography based on the signal cross-modulation. The scheme is illustrated by a theoretical model in which a thin plate or bar with a single crack is excited by a strong low-frequency wave and a high-frequency probing wave (ultrasound). A crack is considered as a small contact-type defect which does not perturb the modal structure of sound in linear approximation but creates combinational-frequency components whose amplitudes depend on their closeness to a resonance and crack position. Using different crack models, including the hysteretic ones, the nonlinear part of its volume variations under the given stress and then the combinational wave components in the bar can be determined. Evidently, their amplitude depends strongly on the crack position with respect to the peaks or nodes of the corresponding linear signals which can be used for localization of the crack position. Exciting the sample by sweeping ultrasound frequencies through several resonances (modes) reduces the ambiguity in the localization. Some aspects of inverse problem solution are also discussed, and preliminary experimental results are presented.
Modified Homotopy Analysis Method for Nonlinear Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
D. Ziane
2017-05-01
Full Text Available In this paper, a combined form of natural transform with homotopy analysis method is proposed to solve nonlinear fractional partial differential equations. This method is called the fractional homotopy analysis natural transform method (FHANTM. The FHANTM can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. The results show that the FHANTM is an appropriate method for solving nonlinear fractional partial differentia equation.
Some geometrical iteration methods for nonlinear equations
Institute of Scientific and Technical Information of China (English)
LU Xing-jiang; QIAN Chun
2008-01-01
This paper describes geometrical essentials of some iteration methods (e.g. Newton iteration,secant line method,etc.) for solving nonlinear equations and advances some geomet-rical methods of iteration that are flexible and efficient.
Convergence of some asynchronous nonlinear multisplitting methods
Szyld, Daniel B.; Xu, Jian-Jun
2000-09-01
Frommer's nonlinear multisplitting methods for solving nonlinear systems of equations are extended to the asynchronous setting. Block methods are extended to include overlap as well. Several specific cases are discussed. Sufficient conditions to guarantee their local convergence are given. A numerical example is presented illustrating the performance of the new approach.
LIMITED MEMORY BFGS METHOD FOR NONLINEAR MONOTONE EQUATIONS
Institute of Scientific and Technical Information of China (English)
Weijun Zhou; Donghui Li
2007-01-01
In this paper, we propose an algorithm for solving nonlinear monotone equations by combining the limited memory BFGS method (L-BFGS) with a projection method. We show that the method is globally convergent if the equation involves a Lipschitz continuous monotone function. We also present some preliminary numerical results.
TAYLOR EXPANSION METHOD FOR NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
HE Yin-nian
2005-01-01
A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0-th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1-st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example,namely, the two-dimensional Navier-Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.
ACCELERATION METHODS OF NONLINEAR ITERATION FOR NONLINEAR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
Guang-wei Yuan; Xu-deng Hang
2006-01-01
This paper discusses the accelerating iterative methods for solving the implicit scheme of nonlinear parabolic equations. Two new nonlinear iterative methods named by the implicit-explicit quasi-Newton (IEQN) method and the derivative free implicit-explicit quasi-Newton (DFIEQN) method are introduced, in which the resulting linear equations from the linearization can preserve the parabolic characteristics of the original partial differential equations. It is proved that the iterative sequence of the iteration method can converge to the solution of the implicit scheme quadratically. Moreover, compared with the Jacobian Free Newton-Krylov (JFNK) method, the DFIEQN method has some advantages, e.g., its implementation is easy, and it gives a linear algebraic system with an explicit coefficient matrix, so that the linear (inner) iteration is not restricted to the Krylov method. Computational results by the IEQN, DFIEQN, JFNK and Picard iteration meth-ods are presented in confirmation of the theory and comparison of the performance of these methods.
A granular computing method for nonlinear convection-diffusion equation
Directory of Open Access Journals (Sweden)
Tian Ya Lan
2016-01-01
Full Text Available This paper introduces a method of solving nonlinear convection-diffusion equation (NCDE, based on the combination of granular computing (GrC and characteristics finite element method (CFEM. The key idea of the proposed method (denoted as GrC-CFEM is to reconstruct the solution from coarse-grained layer to fine-grained layer. It first gets the nonlinear solution on the coarse-grained layer, and then the function (Taylor expansion is applied to linearize the NCDE on the fine-grained layer. Switch to the fine-grained layer, the linear solution is directly derived from the nonlinear solution. The full nonlinear problem is solved only on the coarse-grained layer. Numerical experiments show that the GrC-CFEM can accelerate the convergence and improve the computational efficiency without sacrificing the accuracy.
Control methods for localization of nonlinear waves
Porubov, Alexey; Andrievsky, Boris
2017-03-01
A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions. This article is part of the themed issue 'Horizons of cybernetical physics'.
LINEARIZATION AND CORRECTION METHOD FOR NONLINEAR PROBLEMS
Institute of Scientific and Technical Information of China (English)
何吉欢
2002-01-01
A new perturbation-like technique called linearization and correction method is proposed. Contrary to the traditional perturbation techniques, the present theory does not assume that the solution is expressed in the form of a power series of small parameter. To obtain an asymptotic solution of nonlinear system, the technique first searched for a solution for the linearized system, then a correction was added to the linearized solution. So the obtained results are uniformly valid for both weakly and strongly nonlinear equations.
Method for conducting nonlinear electrochemical impedance spectroscopy
Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.
2015-06-02
A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.
Method for conducting nonlinear electrochemical impedance spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.
2015-06-02
A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.
Advances in iterative methods for nonlinear equations
Busquier, Sonia
2016-01-01
This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations...
Analytic treatment of nonlinear evolution equations using ﬁrst integral method
Indian Academy of Sciences (India)
Ahmet Bekir; Ömer Ünsal
2012-07-01
In this paper, we show the applicability of the ﬁrst integral method to combined KdV-mKdV equation, Pochhammer–Chree equation and coupled nonlinear evolution equations. The power of this manageable method is conﬁrmed by applying it for three selected nonlinear evolution equations. This approach can also be applied to other nonlinear differential equations.
Entropy viscosity method for nonlinear conservation laws
Guermond, Jean-Luc
2011-05-01
A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.
Numerical methods for nonlinear partial differential equations
Bartels, Sören
2015-01-01
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Nonlinear Methods in Riemannian and Kählerian Geometry
Jost, Jürgen
1991-01-01
In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps ...
Adaptive control method for nonlinear time-delay processes
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Two complex properties,varying time-delay and block-oriented nonlinearity,are very common in chemical engineering processes and not easy to be controlled by routine control methods.Aimed at these two complex properties,a novel adaptive control algorithm the basis of nonlinear OFS(orthonormal functional series) model is proposed.First,the hybrid model which combines OFS and Volterra series is introduced.Then,a stable state feedback strategy is used to construct a nonlinear adaptive control algorithm that can guarantee the closed-loop stability and can track the set point curve without steady-state errors.Finally,control simulations and experiments on a nonlinear process with varying time-delay are presented.A number of experimental results validate the efficiency and superiority of this algorithm.
DEFF Research Database (Denmark)
Jensen, Jørgen Juncher
2015-01-01
For non-linear systems the estimation of fatigue damage under stochastic loadings can be rather time-consuming. Usually Monte Carlo simulation (MCS) is applied, but the coefficient-of-variation (COV) can be large if only a small set of simulations can be done due to otherwise excessive CPU time. ...... the COV. For a specific example dealing with stresses in a tendon in a tension leg platform the COV is thereby reduced by a factor of three....
Monotone method for nonlinear nonlocal hyperbolic problems
Directory of Open Access Journals (Sweden)
Azmy S. Ackleh
2003-02-01
Full Text Available We present recent results concerning the application of the monotone method for studying existence and uniqueness of solutions to general first-order nonlinear nonlocal hyperbolic problems. The limitations of comparison principles for such nonlocal problems are discussed. To overcome these limitations, we introduce new definitions for upper and lower solutions.
Review of Nonlinear Methods and Modelling
Borg, F G
2005-01-01
The first part of this Review describes a few of the main methods that have been employed in non-linear time series analysis with special reference to biological applications (biomechanics). The second part treats the physical basis of posturogram data (human balance) and EMG (electromyography, a measure of muscle activity).
Nonlinear system compound inverse control method
Institute of Scientific and Technical Information of China (English)
Yan ZHANG; Zengqiang CHEN; Peng YANG; Zhuzhi YUAN
2005-01-01
A compound neural network is utilized to identify the dynamic nonlinear system.This network is composed of two parts: one is a linear neural network,and the other is a recurrent neural network.Based on the inverse theory a compound inverse control method is proposed.The controller has also two parts:a linear controller and a nonlinear neural network controller.The stability condition of the closed-loop neural network-based compound inverse control system is demonstrated based on the Lyapunov theory.Simulation studies have shown that this scheme is simple and has good control accuracy and robustness.
Neural Network for Combining Linear and Non-Linear Modelling of Dynamic Systems
DEFF Research Database (Denmark)
Madsen, Per Printz
1994-01-01
The purpose of this paper is to develop a method to combine linear models with MLP networks. In other words to find a method to make a non-linear and multivariable model that performs at least as good as a linear model, when the training data lacks information.......The purpose of this paper is to develop a method to combine linear models with MLP networks. In other words to find a method to make a non-linear and multivariable model that performs at least as good as a linear model, when the training data lacks information....
Nonlinear modal method of crack localization
Ostrovsky, Lev; Sutin, Alexander; Lebedev, Andrey
2004-05-01
A simple scheme for crack localization is discussed that is relevant to nonlinear modal tomography based on the cross-modulation of two signals at different frequencies. The scheme is illustrated by a theoretical model, in which a thin plate or bar with a single crack is excited by a strong low-frequency wave and a high-frequency probing wave (ultrasound). The crack is assumed to be small relative to all wavelengths. Nonlinear scattering from the crack is studied using a general matrix approach as well as simplified models allowing one to find the nonlinear part of crack volume variations under the given stress and then the combinational wave components in the tested material. The nonlinear response strongly depends on the crack position with respect to the peaks or nodes of the corresponding interacting signals which can be used for determination of the crack position. Juxtaposing various resonant modes interacting at the crack it is possible to retrieve both crack location and orientation. Some aspects of inverse problem solutions are also discussed, and preliminary experimental results are presented.
Cheng, Xing; Miao, Changxing; Zhao, Lifeng
2016-09-01
We consider the Cauchy problem for the nonlinear Schrödinger equation with combined nonlinearities, one of which is defocusing mass-critical and the other is focusing energy-critical or energy-subcritical. The threshold is given by means of variational argument. We establish the profile decomposition in H1 (Rd) and then utilize the concentration-compactness method to show the global wellposedness and scattering versus blowup in H1 (Rd) below the threshold for radial data when d ≤ 4.
Nonlinear combined forecasting model based on fuzzy adaptive variable weight and its application
Institute of Scientific and Technical Information of China (English)
JIANG Ai-hua; MEI Chi; E Jia-qiang; SHI Zhang-ming
2010-01-01
In order to enhance forecasting precision of problems about nonlinear time series in a complex industry system,a new nonlinear fuzzy adaptive variable weight combined forecasting model was established by using conceptions of the relative error,the change tendency of the forecasted object,gray basic weight and adaptive control coefficient on the basis of the method of fuzzy variable weight.Based on Visual Basic 6.0 platform,a fuzzy adaptive variable weight combined forecasting and management system was developed.The application results reveal that the forecasting precisions from the new nonlinear combined forecasting model are higher than those of other single combined forecasting models and the combined forecasting and management system is very powerful tool for the required decision in complex industry system.
A method for generating highly nonlinear periodic waves in physical wave basins
DEFF Research Database (Denmark)
Zhang, Haiwen; Schäffer, Hemming A.; Bingham, Harry B.
2006-01-01
This abstract describes a new method for generating nonlinear waves of constant form in physical wave basins. The idea is to combine fully dispersive linear wavemaker theory with nonlinear shallow water wave generation theory; and use an exact nonlinear theory as the target. We refer to the metho...... as an ad-hoc unified wave generation theory, since there is no rigorous analysis behind the idea which is simply justified by the improved results obtained for the practical generation of steady nonlinear waves....
Multigrid Methods for Nonlinear Problems: An Overview
Energy Technology Data Exchange (ETDEWEB)
Henson, V E
2002-12-23
Since their early application to elliptic partial differential equations, multigrid methods have been applied successfully to a large and growing class of problems, from elasticity and computational fluid dynamics to geodetics and molecular structures. Classical multigrid begins with a two-grid process. First, iterative relaxation is applied, whose effect is to smooth the error. Then a coarse-grid correction is applied, in which the smooth error is determined on a coarser grid. This error is interpolated to the fine grid and used to correct the fine-grid approximation. Applying this method recursively to solve the coarse-grid problem leads to multigrid. The coarse-grid correction works because the residual equation is linear. But this is not the case for nonlinear problems, and different strategies must be employed. In this presentation we describe how to apply multigrid to nonlinear problems. There are two basic approaches. The first is to apply a linearization scheme, such as the Newton's method, and to employ multigrid for the solution of the Jacobian system in each iteration. The second is to apply multigrid directly to the nonlinear problem by employing the so-called Full Approximation Scheme (FAS). In FAS a nonlinear iteration is applied to smooth the error. The full equation is solved on the coarse grid, after which the coarse-grid error is extracted from the solution. This correction is then interpolated and applied to the fine grid approximation. We describe these methods in detail, and present numerical experiments that indicate the efficacy of them.
Latorre-Ossa, Heldmuth; Gennisson, Jean-Luc; De Brosses, Emilie; Tanter, Mickaël
2012-04-01
The study of new tissue mechanical properties such as shear nonlinearity could lead to better tissue characterization and clinical diagnosis. This work proposes a method combining static elastography and shear wave elastography to derive the nonlinear shear modulus by applying the acoustoelasticity theory in quasi-incompressible soft solids. Results demonstrate that by applying a moderate static stress at the surface of the investigated medium, and by following the quantitative evolution of its shear modulus, it is possible to accurately and quantitatively recover the local Landau (A) coefficient characterizing the shear nonlinearity of soft tissues.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Directory of Open Access Journals (Sweden)
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Propagating Class and Method Combination
DEFF Research Database (Denmark)
Ernst, Erik
1999-01-01
This paper presents a mixin based class and method combination mechanism with block structure propagation. Traditionally, mixins can be composed to form new classes, possibly merging the implementations of methods (as in CLOS). In our approach, a class or method combination operation may cause any...... number of implicit combinations. For example, it is possible to specify separate aspects of a family of classes, and then combine several aspects into a full-fledged class family. The combination expressions would explicitly combine whole-family aspects, and by propagation implicitly combine the aspects...... for each member of the class family, and again by propagation implicitly compose each method from its aspects. As opposed to CLOS, this is type-checked statically; and as opposed to other systems for advanced class combination/ merging/weaving, it is integrated directly in the language, ensuring a clear...
Nonlinear ordinary differential equations analytical approximation and numerical methods
Hermann, Martin
2016-01-01
The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...
A NUMERICAL METHOD FOR NONLINEAR WATER WAVES
Institute of Scientific and Technical Information of China (English)
ZHAO Xi-zeng; SUN Zhao-chen; LIANG Shu-xiu; HU Chang-hong
2009-01-01
This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral (HOS) method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform (FFT) algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.
Linear combination of forecasts with numerical adjustment via MINIMAX non-linear programming
Directory of Open Access Journals (Sweden)
Jairo Marlon Corrêa
2016-03-01
Full Text Available This paper proposes a linear combination of forecasts obtained from three forecasting methods (namely, ARIMA, Exponential Smoothing and Artificial Neural Networks whose adaptive weights are determined via a multi-objective non-linear programming problem, which seeks to minimize, simultaneously, the statistics: MAE, MAPE and MSE. The results achieved by the proposed combination are compared with the traditional approach of linear combinations of forecasts, where the optimum adaptive weights are determined only by minimizing the MSE; with the combination method by arithmetic mean; and with individual methods
Slope stability analysis using limit equilibrium method in nonlinear criterion.
Lin, Hang; Zhong, Wenwen; Xiong, Wei; Tang, Wenyu
2014-01-01
In slope stability analysis, the limit equilibrium method is usually used to calculate the safety factor of slope based on Mohr-Coulomb criterion. However, Mohr-Coulomb criterion is restricted to the description of rock mass. To overcome its shortcomings, this paper combined Hoek-Brown criterion and limit equilibrium method and proposed an equation for calculating the safety factor of slope with limit equilibrium method in Hoek-Brown criterion through equivalent cohesive strength and the friction angle. Moreover, this paper investigates the impact of Hoek-Brown parameters on the safety factor of slope, which reveals that there is linear relation between equivalent cohesive strength and weakening factor D. However, there are nonlinear relations between equivalent cohesive strength and Geological Strength Index (GSI), the uniaxial compressive strength of intact rock σ ci , and the parameter of intact rock m i . There is nonlinear relation between the friction angle and all Hoek-Brown parameters. With the increase of D, the safety factor of slope F decreases linearly; with the increase of GSI, F increases nonlinearly; when σ ci is relatively small, the relation between F and σ ci is nonlinear, but when σ ci is relatively large, the relation is linear; with the increase of m i , F decreases first and then increases.
Nonlinear calculating method of pile settlement
Institute of Scientific and Technical Information of China (English)
贺炜; 王桂尧; 王泓华
2008-01-01
To study calculating method of settlement on top of extra-long large-diameter pile, the relevant research results were summarized. The hyperbola model, a nonlinear load transfer function, was introduced to establish the basic differential equation with load transfer method. Assumed that the displacement of pile shaft was the high order power series of buried depth, through merging the same orthometric items and arranging the relevant coefficients, the solution which could take the nonlinear pile-soil interaction and stratum properties of soil into account was solved by power series. On the basis of the solution, by determining the load transfer depth with criterion of settlement on pile tip, the method by making boundary conditions compatible was advised to solve the load-settlement curve of pile. The relevant flow chart and mathematic expressions of boundary conditions were also listed. Lastly, the load transfer methods based on both two-broken-line model and hyperbola model were applied to analyzing a real project. The related coefficients of fitting curves by hyperbola were not less than 0.96, which shows that the hyperbola model is truthfulness, and is propitious to avoid personal error. The calculating value of load-settlement curve agrees well with the measured one, which indicates that it can be applied in engineering practice and making the theory that limits the design bearing capacity by settlement on pile top comes true.
Fatigue Life Prediction of Metallic Materials Based on the Combined Nonlinear Ultrasonic Parameter
Zhang, Yuhua; Li, Xinxin; Wu, Zhenyong; Huang, Zhenfeng; Mao, Hanling
2017-07-01
The fatigue life prediction of metallic materials is always a tough problem that needs to be solved in the mechanical engineering field because it is very important for the secure service of mechanical components. In this paper, a combined nonlinear ultrasonic parameter based on the collinear wave mixing technique is applied for fatigue life prediction of a metallic material. Sweep experiments are first conducted to explore the influence of driving frequency on the interaction of two driving signals and the fatigue damage of specimens, and the amplitudes of sidebands at the difference frequency and sum frequency are tracked when the driving frequency changes. Then, collinear wave mixing tests are carried out on a pair of cylindrically notched specimens with different fatigue damage to explore the relationship between the fatigue damage and the relative nonlinear parameters. The experimental results show when the fatigue degree is below 65% the relative nonlinear parameter increases quickly, and the growth rate is approximately 130%. If the fatigue degree is above 65%, the increase in the relative nonlinear parameter is slow, which has a close relationship with the microstructure evolution of specimens. A combined nonlinear ultrasonic parameter is proposed to highlight the relationship of the relative nonlinear parameter and fatigue degree of specimens; the fatigue life prediction model is built based on the relationship, and the prediction error is below 3%, which is below the prediction error based on the relative nonlinear parameters at the difference and sum frequencies. Therefore, the combined nonlinear ultrasonic parameter using the collinear wave mixing method can effectively estimate the fatigue degree of specimens, which provides a fast and convenient method for fatigue life prediction.
Fatigue Life Prediction of Metallic Materials Based on the Combined Nonlinear Ultrasonic Parameter
Zhang, Yuhua; Li, Xinxin; Wu, Zhenyong; Huang, Zhenfeng; Mao, Hanling
2017-08-01
The fatigue life prediction of metallic materials is always a tough problem that needs to be solved in the mechanical engineering field because it is very important for the secure service of mechanical components. In this paper, a combined nonlinear ultrasonic parameter based on the collinear wave mixing technique is applied for fatigue life prediction of a metallic material. Sweep experiments are first conducted to explore the influence of driving frequency on the interaction of two driving signals and the fatigue damage of specimens, and the amplitudes of sidebands at the difference frequency and sum frequency are tracked when the driving frequency changes. Then, collinear wave mixing tests are carried out on a pair of cylindrically notched specimens with different fatigue damage to explore the relationship between the fatigue damage and the relative nonlinear parameters. The experimental results show when the fatigue degree is below 65% the relative nonlinear parameter increases quickly, and the growth rate is approximately 130%. If the fatigue degree is above 65%, the increase in the relative nonlinear parameter is slow, which has a close relationship with the microstructure evolution of specimens. A combined nonlinear ultrasonic parameter is proposed to highlight the relationship of the relative nonlinear parameter and fatigue degree of specimens; the fatigue life prediction model is built based on the relationship, and the prediction error is below 3%, which is below the prediction error based on the relative nonlinear parameters at the difference and sum frequencies. Therefore, the combined nonlinear ultrasonic parameter using the collinear wave mixing method can effectively estimate the fatigue degree of specimens, which provides a fast and convenient method for fatigue life prediction.
NONLINEAR DYNAMICS RESPONSE OF CASING PIPE UNDER COMBINED WAVE-CURRENT
Institute of Scientific and Technical Information of China (English)
TANG You-gang; GU Jia-yang; ZUO Jian-li; MIN Jian-qin
2005-01-01
The vortex-induced nonlinear vibration of casing pipes in the deep water was studied considering the loads of current and combined wave-current. The vortex-induced vibration equation of a casing pipe was set up considering the beam mode and Morison's nonlinear fluid loads as well as the vortex-excited loads. The approach of calculating vortex-excited nonlinear vibration by Galerkin's method was proposed. The natural vibration frequencies and modes were obtained, and the response including primary resonance induced by current and the composite resonance under combined wave-current for the 170 m long casing pipe in the 160 m depth of water were investigated. The results show that the dynamics response of casing pipe obviously increases, and the complicated response behaviors of casing pipe are described under combined wave-current.
Reproducing wavelet kernel method in nonlinear system identification
Institute of Scientific and Technical Information of China (English)
WEN Xiang-jun; XU Xiao-ming; CAI Yun-ze
2008-01-01
By combining the wavelet decomposition with kernel method, a practical approach of universal multi-scale wavelet kernels constructed in reproducing kernel Hilbert space (RKHS) is discussed, and an identifica-tion scheme using wavelet support vector machines ( WSVM ) estimator is proposed for nonlinear dynamic sys-tems. The good approximating properties of wavelet kernel function enhance the generalization ability of the pro-posed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.
Identification methods for nonlinear stochastic systems.
Fullana, Jose-Maria; Rossi, Maurice
2002-03-01
Model identifications based on orbit tracking methods are here extended to stochastic differential equations. In the present approach, deterministic and statistical features are introduced via the time evolution of ensemble averages and variances. The aforementioned quantities are shown to follow deterministic equations, which are explicitly written within a linear as well as a weakly nonlinear approximation. Based on such equations and the observed time series, a cost function is defined. Its minimization by simulated annealing or backpropagation algorithms then yields a set of best-fit parameters. This procedure is successfully applied for various sampling time intervals, on a stochastic Lorenz system.
Optimal Variational Method for Truly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Vasile Marinca
2013-01-01
Full Text Available The Optimal Variational Method (OVM is introduced and applied for calculating approximate periodic solutions of “truly nonlinear oscillators”. The main advantage of this procedure consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. This approach does not depend upon any small or large parameters. A very good agreement was found between approximate and numerical solution, which proves that OVM is very efficient and accurate.
NONLINEAR DATA RECONCILIATION METHOD BASED ON KERNEL PRINCIPAL COMPONENT ANALYSIS
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
In the industrial process situation, principal component analysis (PCA) is a general method in data reconciliation.However, PCA sometime is unfeasible to nonlinear feature analysis and limited in application to nonlinear industrial process.Kernel PCA (KPCA) is extension of PCA and can be used for nonlinear feature analysis.A nonlinear data reconciliation method based on KPCA is proposed.The basic idea of this method is that firstly original data are mapped to high dimensional feature space by nonlinear function, and PCA is implemented in the feature space.Then nonlinear feature analysis is implemented and data are reconstructed by using the kernel.The data reconciliation method based on KPCA is applied to ternary distillation column.Simulation results show that this method can filter the noise in measurements of nonlinear process and reconciliated data can represent the true information of nonlinear process.
Successful combination of the stochastic linearization and Monte Carlo methods
Elishakoff, I.; Colombi, P.
1993-01-01
A combination of a stochastic linearization and Monte Carlo techniques is presented for the first time in literature. A system with separable nonlinear damping and nonlinear restoring force is considered. The proposed combination of the energy-wise linearization with the Monte Carlo method yields an error under 5 percent, which corresponds to the error reduction associated with the conventional stochastic linearization by a factor of 4.6.
A simplified NARMAX method using nonlinear input-output data
Institute of Scientific and Technical Information of China (English)
Jie CHEN; Sheng FENG
2007-01-01
A system identification method for nonlinear systems with unknown structure is presented using short input-output data. The method simplifies the original NARMAX method. It introduces more general model structures for nonlinear systems. The group method of data handling (GMDH) method is employed to obtain the model terms and parameters. Effectiveness of the proposed method is illustrated by a typical nonlinear system with unknown structure and deficient input-output data.
Adaptive explicit Magnus numerical method for nonlinear dynamical systems
Institute of Scientific and Technical Information of China (English)
LI Wen-cheng; DENG Zi-chen
2008-01-01
Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group,an efficient numerical method is proposed for nonlinear dynamical systems.To improve computational efficiency,the integration step size can be adaptively controlled.Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system,the van der Pol system with strong stiffness,and the nonlinear Hamiltonian pendulum system.
Directory of Open Access Journals (Sweden)
Baiyu Liu
2014-01-01
Full Text Available We consider a class of coupled nonlinear Schrödinger systems with potential terms and combined power-type nonlinearities. We establish the existence of ground states, by using a variational method. As an application, some symmetry results for ground states of Schrödinger systems with harmonic potential terms are obtained.
Wideband quin-stable energy harvesting via combined nonlinearity
Directory of Open Access Journals (Sweden)
Chen Wang
2017-04-01
Full Text Available In this work, we propose a wideband quintuple-well potential piezoelectric-based vibration energy harvester using a combined nonlinearity: the magnetic nonlinearity induced by magnetic force and the piecewise-linearity produced by mechanical impact. With extra stable states compared to other multi-stable harvesters, the quin-stable harvester can distribute its potential energy more uniformly, which provides shallower potential wells and results in lower excitation threshold for interwell motion. The mathematical model of this quin-stable harvester is derived and its equivalent piecewise-nonlinear restoring force is measured in the experiment and identified as piecewise polynomials. Numerical simulations and experimental verifications are performed in different levels of sinusoid excitation ranging from 1 to 25 Hz. The results demonstrate that, with lower potential barriers compared with tri-stable counterpart, the quin-stable arrangement can escape potential wells more easily for doing high-energy interwell motion over a wider band of frequencies. Moreover, by utilizing the mechanical stoppers, this harvester can produce significant output voltage under small tip deflections, which results in a high power density and is especially suitable for a compact MEMS approach.
Wideband nonlinear time reversal seismo-acoustic method for landmine detection.
Sutin, Alexander; Libbey, Brad; Fillinger, Laurent; Sarvazyan, Armen
2009-04-01
Acoustic and seismic waves provide a method to localize compliant mines by vibrating the top plate and a thin soil layer above the mine. This vibration is mostly linear, but also includes a small nonlinear deviation. The main goal of this paper is to introduce a method of processing that uses phase-inversion to observe nonlinear effects in a wide frequency band. The method extracts a nonlinear part of surface velocity from two similar broadcast signals of opposite sign by summing and cancelling the linear components and leaving the nonlinear components. This phase-inversion method is combined with time reversal focusing to provide increased seismic vibration and enhance the nonlinear effect. The experiments used six loudspeakers in a wood box placed over sand in which inert landmines were buried. The nonlinear surface velocity of the sand with a mine compared to the sand without a mine was greater as compared to a linear technique.
Scalable nonlinear iterative methods for partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Cai, X-C
2000-10-29
We conducted a six-month investigation of the design, analysis, and software implementation of a class of singularity-insensitive, scalable, parallel nonlinear iterative methods for the numerical solution of nonlinear partial differential equations. The solutions of nonlinear PDEs are often nonsmooth and have local singularities, such as sharp fronts. Traditional nonlinear iterative methods, such as Newton-like methods, are capable of reducing the global smooth nonlinearities at a nearly quadratic convergence rate but may become very slow once the local singularities appear somewhere in the computational domain. Even with global strategies such as line search or trust region the methods often stagnate at local minima of {parallel}F{parallel}, especially for problems with unbalanced nonlinearities, because the methods do not have built-in machinery to deal with the unbalanced nonlinearities. To find the same solution u* of F(u) = 0, we solve, instead, an equivalent nonlinearly preconditioned system G(F(u*)) = 0 whose nonlinearities are more balanced. In this project, we proposed and studied a nonlinear additive Schwarz based parallel nonlinear preconditioner and showed numerically that the new method converges well even for some difficult problems, such as high Reynolds number flows, when a traditional inexact Newton method fails.
Variational iteration method for solving non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Hemeda, A.A. [Department of Mathematics, Faculty of Science, University of Tanta, Tanta (Egypt)], E-mail: aahemeda@yahoo.com
2009-02-15
In this paper, we shall use the variational iteration method to solve some problems of non-linear partial differential equations (PDEs) such as the combined KdV-MKdV equation and Camassa-Holm equation. The variational iteration method is superior than the other non-linear methods, such as the perturbation methods where this method does not depend on small parameters, such that it can fined wide application in non-linear problems without linearization or small perturbation. In this method, the problems are initially approximated with possible unknowns, then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
SIMULATION OF THE COMBINED METHOD
Directory of Open Access Journals (Sweden)
Ilya Levin
2011-10-01
Full Text Available DDoS attacks have become one of the most dangerous issues in the Internet today. Because of theseattacks, legitimate users can not access the resources they need. In [1] authors proposeda combined method for tracing and blocking the sources of DDoS-attacks. The essence of the method isthat each router marks the network packet that passes through it using a random hash function from theset. At the receiving side this information is stored and used to filter unwanted traffic and traceback thesource of distributed attack. This article describes the simulation and its results of the combined method.
Comparative study of homotopy continuation methods for nonlinear algebraic equations
Nor, Hafizudin Mohamad; Ismail, Ahmad Izani Md.; Majid, Ahmad Abd.
2014-07-01
We compare some recent homotopy continuation methods to see which method has greater applicability and greater accuracy. We test the methods on systems of nonlinear algebraic equations. The results obtained indicate the superior accuracy of Newton Homotopy Continuation Method (NHCM).
An hp symplectic pseudospectral method for nonlinear optimal control
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.
Nonlinear generalization of Den Hartog's equal-peak method
Habib, G.; Detroux, T.; Viguié, R.; Kerschen, G.
2015-02-01
This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog's equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments.
Vibrations of Nonlinear Systems. The Method of Integral Equations,
Many diverse applied methods of investigating oscillations of nonlinear systems often in different mathematical formulations and outwardly not...parameter classical methods and the methods of investigating nonlinear systems of automatic control based on the so-called filter hypothesis, and to
Variational Iteration Method for the Magnetohydrodynamic Flow over a Nonlinear Stretching Sheet
Directory of Open Access Journals (Sweden)
Lan Xu
2013-01-01
Full Text Available The variational iteration method (VIM is applied to solve the boundary layer problem of magnetohydrodynamic flow over a nonlinear stretching sheet. The combination of the VIM and the Padé approximants is shown to be a powerful method for solving two-point boundary value problems consisting of systems of nonlinear differential equations. And the comparison of the obtained results with other available results shows that the method is very effective and convenient for solving boundary layer problems.
Nonlinear Ultrasonic Characterization Using the Noncollinear Method
Croxford, A. J.; Drinkwater, B. W.; Wilcox, P. D.
2011-06-01
The measurement of material non-linearity using ultrasound is an attractive concept, offering the potential to detect fatigue damage earlier than is possible with conventional techniques. Despite this advantage and much work in the field the currently developed approaches are primarily limited to the lab environment. This is due to the difficulty in separating the material nonlinearity from that generated by equipment. This paper reports on an approach that eliminates this problem. When two shear waves interact a third wave is generated due to the material nonlinearity. This paper shows how this interaction can be used to measure material properties in damaged specimens. It goes on to show that this approach can be used to make measurements of material non-linearity both across a specimen.
A Hybrid of DL and WYL Nonlinear Conjugate Gradient Methods
Directory of Open Access Journals (Sweden)
Shengwei Yao
2014-01-01
Full Text Available The conjugate gradient method is an efficient method for solving large-scale nonlinear optimization problems. In this paper, we propose a nonlinear conjugate gradient method which can be considered as a hybrid of DL and WYL conjugate gradient methods. The given method possesses the sufficient descent condition under the Wolfe-Powell line search and is globally convergent for general functions. Our numerical results show that the proposed method is very robust and efficient for the test problems.
Hybrid discretization method for time-delay nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zheng [Xi' an Jiaotong University, Xi' an (China); Zhang, Yuanliang; Kil Chong, To [Chonbuk National University, Jeonju (Korea, Republic of); Kostyukova, Olga [3Institute of Mathematics National Academy of Science of Belarus, Minsk (Belarus)
2010-03-15
A hybrid discretization scheme that combines the virtues of the Taylor series and Matrix exponential integration methods is proposed. In the algorithm, each sampling time interval is divided into two subintervals to be considered according to the time delay and sampling period. The algorithm is not too expensive computationally and lends itself to be easily inserted into large simulation packages. The mathematical structure of the new discretization scheme is explored and described in detail. The performance of the proposed discretization procedure is evaluated by employing case studies. Various input signals, sampling rates, and time-delay values are considered to test the proposed method. The results demonstrate that the proposed discretization scheme is better than previous Taylor series method for nonlinear time-delay systems, especially when a large sampling period is inevitable
Auxiliary equation method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Sirendaoreji,; Jiong, Sun
2003-03-31
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation.
Combining biomarkers linearly and nonlinearly for classification using the area under the ROC curve.
Fong, Youyi; Yin, Shuxin; Huang, Ying
2016-09-20
In biomedical studies, it is often of interest to classify/predict a subject's disease status based on a variety of biomarker measurements. A commonly used classification criterion is based on area under the receiver operating characteristic curve (AUC). Many methods have been proposed to optimize approximated empirical AUC criteria, but there are two limitations to the existing methods. First, most methods are only designed to find the best linear combination of biomarkers, which may not perform well when there is strong nonlinearity in the data. Second, many existing linear combination methods use gradient-based algorithms to find the best marker combination, which often result in suboptimal local solutions. In this paper, we address these two problems by proposing a new kernel-based AUC optimization method called ramp AUC (RAUC). This method approximates the empirical AUC loss function with a ramp function and finds the best combination by a difference of convex functions algorithm. We show that as a linear combination method, RAUC leads to a consistent and asymptotically normal estimator of the linear marker combination when the data are generated from a semiparametric generalized linear model, just as the smoothed AUC method. Through simulation studies and real data examples, we demonstrate that RAUC outperforms smooth AUC in finding the best linear marker combinations, and can successfully capture nonlinear pattern in the data to achieve better classification performance. We illustrate our method with a dataset from a recent HIV vaccine trial. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
NONLINEAR GALERKIN METHOD FOR THE EXTERIOR NONSTATIONARY NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
何银年; 李开泰
2002-01-01
A new algorithm combining nonlinear Galerkin method and coupling method of finite element and boundary element is introduced to solve the exterior nonstationary Navier-Stokes equations. The regularity of the coupling variational formulation and the convergence of the approximate solution corresponding to the algorithm are proved. If the fine mesh h is choosed as coarse mesh H-sgure, the nonlinear Galerkin method, nonlinearity is only treated on the coarse grid and linearity is treated on the fine grid. Hence, the new algorithm can save a large amount of computational time.
Nonlinear fault diagnosis method based on kernel principal component analysis
Institute of Scientific and Technical Information of China (English)
Yan Weiwu; Zhang Chunkai; Shao Huihe
2005-01-01
To ensure the system run under working order, detection and diagnosis of faults play an important role in industrial process. This paper proposed a nonlinear fault diagnosis method based on kernel principal component analysis (KPCA). In proposed method, using essential information of nonlinear system extracted by KPCA, we constructed KPCA model of nonlinear system under normal working condition. Then new data were projected onto the KPCA model. When new data are incompatible with the KPCA model, it can be concluded that the nonlinear system isout of normal working condition. Proposed method was applied to fault diagnosison rolling bearings. Simulation results show proposed method provides an effective method for fault detection and diagnosis of nonlinear system.
Elhaj, Fatin A; Salim, Naomie; Harris, Arief R; Swee, Tan Tian; Ahmed, Taqwa
2016-04-01
Arrhythmia is a cardiac condition caused by abnormal electrical activity of the heart, and an electrocardiogram (ECG) is the non-invasive method used to detect arrhythmias or heart abnormalities. Due to the presence of noise, the non-stationary nature of the ECG signal (i.e. the changing morphology of the ECG signal with respect to time) and the irregularity of the heartbeat, physicians face difficulties in the diagnosis of arrhythmias. The computer-aided analysis of ECG results assists physicians to detect cardiovascular diseases. The development of many existing arrhythmia systems has depended on the findings from linear experiments on ECG data which achieve high performance on noise-free data. However, nonlinear experiments characterize the ECG signal more effectively sense, extract hidden information in the ECG signal, and achieve good performance under noisy conditions. This paper investigates the representation ability of linear and nonlinear features and proposes a combination of such features in order to improve the classification of ECG data. In this study, five types of beat classes of arrhythmia as recommended by the Association for Advancement of Medical Instrumentation are analyzed: non-ectopic beats (N), supra-ventricular ectopic beats (S), ventricular ectopic beats (V), fusion beats (F) and unclassifiable and paced beats (U). The characterization ability of nonlinear features such as high order statistics and cumulants and nonlinear feature reduction methods such as independent component analysis are combined with linear features, namely, the principal component analysis of discrete wavelet transform coefficients. The features are tested for their ability to differentiate different classes of data using different classifiers, namely, the support vector machine and neural network methods with tenfold cross-validation. Our proposed method is able to classify the N, S, V, F and U arrhythmia classes with high accuracy (98.91%) using a combined support
Institute of Scientific and Technical Information of China (English)
QIN Xinqiang; MA Yichen; GONG Chunqiong
2004-01-01
A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.
A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators
Smith, Ralph C.
1998-01-01
This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.
Energy Method to Obtain Approximate Solutions of Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available We introduce a nonlinearization procedure that replaces the system potential energy by an equivalent representation form that is used to derive analytical solutions of strongly nonlinear conservative oscillators. We illustrate the applicability of this method by finding the approximate solutions of two strongly nonlinear oscillators and show that this procedure provides solutions that follow well the numerical integration solutions of the corresponding equations of motion.
Dynamic decoupling nonlinear control method for aircraft gust alleviation
Lv, Yang; Wan, Xiaopeng; Li, Aijun
2008-10-01
A dynamic decoupling nonlinear control method for MIMO system is presented in this paper. The dynamic inversion method is used to decouple the multivariable system. The nonlinear control method is used to overcome the poor decoupling effect when the system model is inaccurate. The nonlinear control method has correcting function and is expressed in analytic form, it is easy to adjust the parameters of the controller and optimize the design of the control system. The method is used to design vertical transition mode of active control aircraft for gust alleviation. Simulation results show that the designed vertical transition mode improves the gust alleviation effect about 34% comparing with the normal aircraft.
Diagnosis of multiple sclerosis from EEG signals using nonlinear methods.
Torabi, Ali; Daliri, Mohammad Reza; Sabzposhan, Seyyed Hojjat
2017-09-08
EEG signals have essential and important information about the brain and neural diseases. The main purpose of this study is classifying two groups of healthy volunteers and Multiple Sclerosis (MS) patients using nonlinear features of EEG signals while performing cognitive tasks. EEG signals were recorded when users were doing two different attentional tasks. One of the tasks was based on detecting a desired change in color luminance and the other task was based on detecting a desired change in direction of motion. EEG signals were analyzed in two ways: EEG signals analysis without rhythms decomposition and EEG sub-bands analysis. After recording and preprocessing, time delay embedding method was used for state space reconstruction; embedding parameters were determined for original signals and their sub-bands. Afterwards nonlinear methods were used in feature extraction phase. To reduce the feature dimension, scalar feature selections were done by using T-test and Bhattacharyya criteria. Then, the data were classified using linear support vector machines (SVM) and k-nearest neighbor (KNN) method. The best combination of the criteria and classifiers was determined for each task by comparing performances. For both tasks, the best results were achieved by using T-test criterion and SVM classifier. For the direction-based and the color-luminance-based tasks, maximum classification performances were 93.08 and 79.79% respectively which were reached by using optimal set of features. Our results show that the nonlinear dynamic features of EEG signals seem to be useful and effective in MS diseases diagnosis.
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
Numerical Methods for Nonlinear PDEs in Finance
DEFF Research Database (Denmark)
Mashayekhi, Sima
Nonlinear Black-Scholes equations arise from considering parameters such as feedback and illiquid markets eects or large investor preferences, volatile portfolio and nontrivial transaction costs into option pricing models to have more accurate option price. Here some nite dierence schemes have been...
Numerical Methods for Nonlinear PDEs in Finance
DEFF Research Database (Denmark)
Mashayekhi, Sima
Nonlinear Black-Scholes equations arise from considering parameters such as feedback and illiquid markets eects or large investor preferences, volatile portfolio and nontrivial transaction costs into option pricing models to have more accurate option price. Here some nite dierence schemes have be...
Iterative regularization methods for nonlinear ill-posed problems
Scherzer, Otmar; Kaltenbacher, Barbara
2008-01-01
Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
Reproducing Kernel Particle Method for Non-Linear Fracture Analysis
Institute of Scientific and Technical Information of China (English)
Cao Zhongqing; Zhou Benkuan; Chen Dapeng
2006-01-01
To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method (RKPM). Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.
Online Fault Diagnosis Method Based on Nonlinear Spectral Analysis
Institute of Scientific and Technical Information of China (English)
WEI Rui-xuan; WU Li-xun; WANG Yong-chang; HAN Chong-zhao
2005-01-01
The fault diagnosis based on nonlinear spectral analysis is a new technique for the nonlinear fault diagnosis, but its online application could be limited because of the enormous compution requirements for the estimation of general frequency response functions. Based on the fully decoupled Volterra identification algorithm, a new online fault diagnosis method based on nonlinear spectral analysis is presented, which can availably reduce the online compution requirements of general frequency response functions. The composition and working principle of the method are described, the test experiments have been done for damping spring of a vehicle suspension system by utilizing the new method, and the results indicate that the method is efficient.
Hyperbolic function method for solving nonlinear differential-different equations
Institute of Scientific and Technical Information of China (English)
Zhu Jia-Min
2005-01-01
An algorithm is devised to obtained exact travelling wave solutions of differential-different equations by means of hyperbolic function. For illustration, we apply the method to solve the discrete nonlinear (2+1)-dimensional Toda lattice equation and the discretized nonlinear mKdV lattice equation, and successfully constructed some explicit and exact travelling wave solutions.
Directory of Open Access Journals (Sweden)
J. Prakash
2016-03-01
Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.
GHM method for obtaining rationalsolutions of nonlinear differential equations.
Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo
2015-01-01
In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.
On filter-successive linearization methods for nonlinear semidefinite programming
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially effcient.
On filter-successive linearization methods for nonlinear semidefinite programming
Institute of Scientific and Technical Information of China (English)
LI ChengJin; SUN WenYui
2009-01-01
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially efficient.
Directory of Open Access Journals (Sweden)
E. M. E. Zayed
2014-01-01
Full Text Available We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
Directory of Open Access Journals (Sweden)
Wang Pidong
2016-01-01
Full Text Available Blind source separation is a hot topic in signal processing. Most existing works focus on dealing with linear combined signals, while in practice we always encounter with nonlinear mixed signals. To address the problem of nonlinear source separation, in this paper we propose a novel algorithm using radial basis function neutral network, optimized by multi-universe parallel quantum genetic algorithm. Experiments show the efficiency of the proposed method.
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
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.
A Numerical Embedding Method for Solving the Nonlinear Optimization Problem
Institute of Scientific and Technical Information of China (English)
田保锋; 戴云仙; 孟泽红; 张建军
2003-01-01
A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the basic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Based on the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove its convergence carefully. Numerical experiments show that the algorithm is effective.
Exact solutions of some nonlinear partial differential equations using functional variable method
Indian Academy of Sciences (India)
A Nazarzadeh; M Eslami; M Mirzazadeh
2013-08-01
The functional variable method is a powerful solution method for obtaining exact solutions of some nonlinear partial differential equations. In this paper, the functional variable method is used to establish exact solutions of the generalized forms of Klein–Gordon equation, the (2 + 1)-dimensional Camassa–Holm Kadomtsev–Petviashvili equation and the higher-order nonlinear Schrödinger equation. By using this useful method, we found some exact solutions of the above-mentioned equations. The obtained solutions include solitary wave solutions, periodic wave solutions and combined formal solutions. It is shown that the proposed method is effective and general.
A Hybrid Method for Nonlinear Least Squares Problems
Institute of Scientific and Technical Information of China (English)
Zhongyi Liu; Linping Sun
2007-01-01
A negative curvature method is applied to nonlinear least squares problems with indefinite Hessian approximation matrices. With the special structure of the method,a new switch is proposed to form a hybrid method. Numerical experiments show that this method is feasible and effective for zero-residual,small-residual and large-residual problems.
Directory of Open Access Journals (Sweden)
S. S. Motsa
2014-01-01
Full Text Available This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs. The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Motsa, S S; Magagula, V M; Sibanda, P
2014-01-01
This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation. The results are compared with known exact analytical solutions from literature to confirm accuracy, convergence, and effectiveness of the method. There is congruence between the numerical results and the exact solutions to a high order of accuracy. Tables were generated to present the order of accuracy of the method; convergence graphs to verify convergence of the method and error graphs are presented to show the excellent agreement between the results from this study and the known results from literature.
Combination of nonlinear ultrasonics and guided wave tomography for imaging the micro-defects.
Li, Weibin; Cho, Younho
2016-02-01
The use of guided wave tomography has become an attractive alternative to convert ultrasonic wave raw data to visualized results for quantitative signal interpretation. For more accurate life prediction and efficient management strategies for critical structural components, there is a demand of imaging micro-damages in early stage. However, there is rarely investigation on guided wave tomographic imaging of micro-defects. One of the reasons for this might be that it becomes challenging to monitor tiny signal difference coefficient in a reliable manner for wave propagation in the specimens with micro-damages. Nonlinear acoustic signal whose frequency differs from that of the input signal can be found in the specimens with micro-damages. Therefore, the combination of guided wave tomography and nonlinear acoustic response induced by micro-damages could be a feasibility study for imaging micro-damages. In this paper, the nonlinear Rayleigh surface wave tomographic method is investigated to locate and size micro-corrosive defect region in an isotropic solid media. The variations of acoustic nonlinear responses of ultrasonic waves in the specimens with and without defects are used in guided wave tomographic algorithm to construct the images. The comparisons between images obtained by experimental signals and real defect region induced by hydrogen corrosion are presented in this paper. Results show that the images of defect regions with different shape, size and location are successfully obtained by this novel technique, while there is no visualized result constructed by conventional linear ultrasonic tomographic one. The present approach shows a potential for inspecting, locating and imaging micro-defects by nonlinear Rayleigh surface wave tomography. Copyright © 2015 Elsevier B.V. All rights reserved.
Nonlinear Dimensionality Reduction Methods in Climate Data Analysis
Ross, Ian
2008-01-01
Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be appropriate for the analysis of data arising from nonlinear processes occurring in the climate system. Numerous techniques for nonlinear dimensionality reduction have been developed recently that may provide a potentially useful tool for the identification of low-dimensional manifolds in climate data sets arising from nonlinear dynamics. In this thesis I apply three such techniques to the study of El Nino/Southern Oscillation variability in tropical Pacific sea surface temperatures and thermocline depth, comparing observational data with simulations from coupled atmosphere-ocean general circulation models from the CMIP3 multi-model ensemble. The three methods used here are a nonlinear principal component analysis (NLPCA) approach based on neural networks, the Isomap isometric mappin...
NOLB: Nonlinear Rigid Block Normal Mode Analysis Method
Hoffmann, Alexandre; Grudinin, Sergei
2017-01-01
International audience; We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velo...
Gorelick, S.M.; Voss, C.I.; Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H.
1984-01-01
A simulation-management methodology is demonstrated for the rehabilitation of aquifers that have been subjected to chemical contamination. Finite element groundwater flow and contaminant transport simulation are combined with nonlinear optimization. The model is capable of determining well locations plus pumping and injection rates for groundwater quality control. Examples demonstrate linear or nonlinear objective functions subject to linear and nonlinear simulation and water management constraints. -from Authors
Probabilistic methods for discrete nonlinear Schr\\"odinger equations
Chatterjee, Sourav
2010-01-01
Using techniques from probability theory, we show that the thermodynamics of the focusing cubic discrete nonlinear Schrodinger equation (NLS) are exactly solvable in dimensions three and higher. A number of explicit formulas are derived. The probabilistic results, combined with dynamical information, prove the existence and typicality of solutions to the discrete NLS with highly stable localized modes that are sometimes called discrete breathers.
A simple harmonic balance method for solving strongly nonlinear oscillators
Directory of Open Access Journals (Sweden)
Md. Abdur Razzak
2016-10-01
Full Text Available In this paper, a simple harmonic balance method (HBM is proposed to obtain higher-order approximate periodic solutions of strongly nonlinear oscillator systems having a rational and an irrational force. With the proposed procedure, the approximate frequencies and the corresponding periodic solutions can be easily determined. It gives high accuracy for both small and large amplitudes of oscillations and better result than those obtained by other existing results. The main advantage of the present method is that its simplicity and the second-order approximate solutions almost coincide with the corresponding numerical solutions (considered to be exact. The method is illustrated by examples. The present method is very effective and convenient method for solving strongly nonlinear oscillator systems arising in nonlinear science and engineering.
CONVERGENCE OF NONLINEAR CONJUGATE GRADIENT METHODS
Institute of Scientific and Technical Information of China (English)
Yu-hong Dai
2001-01-01
This paper proves that a simplified Armijo-type line search can ensure the global con vergences of the Fletcher-Reeves method and the Polak-Ribiére-Polyak method for un constrained optimization. Although it seems not possible to verify that the PRP method using the generalized Armijo line search converges globally for generally problems, it can be shown that in this case the PRP method always solves uniformly convex problems.
Improved HPC method for nonlinear wave tank
DEFF Research Database (Denmark)
Zhu, Wenbo; Greco, Marilena; Shao, Yanlin
2017-01-01
The recently developed Harmonic Polynomial Cell (HPC) method has been proved to be a promising choice for solving potential-flow Boundary Value Problem (BVP). In this paper, a flux method is proposed to consistently deal with the Neumann boundary condition of the original HPC method and enhance...
Energy Technology Data Exchange (ETDEWEB)
Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere, E-mail: kyandoghere.kyamakya@uni-klu.ac.a, E-mail: jean.chedjou@uni-klu.ac.a [Transportation Informatics Group, Institute of Smart Systems Technologies, University of Klagenfurt (Austria)
2010-10-15
It is well known that a machine vision-based analysis of a dynamic scene, for example in the context of advanced driver assistance systems (ADAS), does require real-time processing capabilities. Therefore, the system used must be capable of performing both robust and ultrafast analyses. Machine vision in ADAS must fulfil the above requirements when dealing with a dynamically changing visual context (i.e. driving in darkness or in a foggy environment, etc). Among the various challenges related to the analysis of a dynamic scene, this paper focuses on contrast enhancement, which is a well-known basic operation to improve the visual quality of an image (dynamic or static) suffering from poor illumination. The key objective is to develop a systematic and fundamental concept for image contrast enhancement that should be robust despite a dynamic environment and that should fulfil the real-time constraints by ensuring an ultrafast analysis. It is demonstrated that the new approach developed in this paper is capable of fulfilling the expected requirements. The proposed approach combines the good features of the 'coupled oscillators'-based signal processing paradigm with the good features of the 'cellular neural network (CNN)'-based one. The first paradigm in this combination is the 'master system' and consists of a set of coupled nonlinear ordinary differential equations (ODEs) that are (a) the so-called 'van der Pol oscillator' and (b) the so-called 'Duffing oscillator'. It is then implemented or realized on top of a 'slave system' platform consisting of a CNN-processors platform. An offline bifurcation analysis is used to find out, a priori, the windows of parameter settings in which the coupled oscillator system exhibits the best and most appropriate behaviours of interest for an optimal resulting image processing quality. In the frame of the extensive bifurcation analysis carried out, analytical formulae have
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.
Baranwal, Vipul K; Pandey, Ram K; Singh, Om P
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
Extended Trial Equation Method for Nonlinear Partial Differential Equations
Gepreel, Khaled A.; Nofal, Taher A.
2015-04-01
The main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber-Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.
The optical nonlinearity of gold nanoparticles prepared by bioreduction method
Balbuena Ortega, A.; Arroyo Carrasco, M. L.; Gayou, V. L.; Orduña Díaz, A.; Delgado Macuil, R.; Rojas López, Marlon
2013-11-01
Nonlinear optical and electronic properties of nanosized metal particles have drawn considerable attention because of their strong and size-dependent plasmon resonance absorption. In a metal nanoparticle system such as gold dispersed in a transparent matrix, an absorption peak due to surface plasmon resonance is usually observed in the visible spectral region. Metal nanoparticles are of special interest as nonlinear materials for optical switching and computing because of their relatively large third-order nonlinearity (χ3) and ultrafast response time. The purpose of this study was to analyze the nonlinear optical properties of biosynthesized gold nanoparticles. The samples were prepared by biosynthesis method using yeast extract as reducing agent and the nonlinear optical properties of the nanoparticles were investigated using a single beam Z-scan technique with a beam power of 20 mW and operated at wavelength of 514 nm. The reaction between metal ions and yeast extracts were monitored by UV-visible spectra of Au nanoparticles in aqueous solution with different pH (3-6). The surface plasmon peak position was shifted from 528 nm to 573 nm, according to of pH variation 4 to 6. The average particle size was calculated by the absorption peak position using the Fernig method, from 42 to 103 nm. The z-scan curves showed a negative nonlocal nonlinear refractive index with a magnitude dependent on the nanoparticle size.
THE MORTAR ELEMENT METHOD FOR A NONLINEAR BIHARMONIC EQUATION
Institute of Scientific and Technical Information of China (English)
Zhong-ci Shi; Xue-jun Xu
2005-01-01
The mortar element method is a new domain decomposition method(DDM) with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H1-norm estimates are obtained under a reasonable elliptic regularity assumption.
Direct Perturbation Method for Derivative Nonlinear Schrodinger Equation
Institute of Scientific and Technical Information of China (English)
CHENG Xue-Ping; LIN Ji; HAN Ping
2008-01-01
We extend Lou's direct perturbation method for solving the nonlinear SchrSdinger equation to the case of the derivative nonlinear Schrodinger equation (DNLSE). By applying this method, different types of perturbation solutions axe obtained. Based on these approximate solutions, the analytical forms of soliton parameters, such as the velocity, the width and the initial position, are carried out and the effects of perturbation on solitons are analyzed at the same time. A numerical simulation of perturbed DNLSE finally verifies the results of the perturbation method.
New Efficient Fourth Order Method for Solving Nonlinear Equations
Directory of Open Access Journals (Sweden)
Farooq Ahmad
2013-12-01
Full Text Available In a paper [Appl. Math. Comput., 188 (2 (2007 1587--1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a quintic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method having convergence of fourth order, is efficient.
Nonlinear model predictive control using parameter varying BP-ARX combination model
Yang, J.-F.; Xiao, L.-F.; Qian, J.-X.; Li, H.
2012-03-01
A novel back-propagation AutoRegressive with eXternal input (BP-ARX) combination model is constructed for model predictive control (MPC) of MIMO nonlinear systems, whose steady-state relation between inputs and outputs can be obtained. The BP neural network represents the steady-state relation, and the ARX model represents the linear dynamic relation between inputs and outputs of the nonlinear systems. The BP-ARX model is a global model and is identified offline, while the parameters of the ARX model are rescaled online according to BP neural network and operating data. Sequential quadratic programming is employed to solve the quadratic objective function online, and a shift coefficient is defined to constrain the effect time of the recursive least-squares algorithm. Thus, a parameter varying nonlinear MPC (PVNMPC) algorithm that responds quickly to large changes in system set-points and shows good dynamic performance when system outputs approach set-points is proposed. Simulation results in a multivariable stirred tank and a multivariable pH neutralisation process illustrate the applicability of the proposed method and comparisons of the control effect between PVNMPC and multivariable recursive generalised predictive controller are also performed.
Chaos Control in Nonlinear Systems Using the Generalized Backstopping Method
Directory of Open Access Journals (Sweden)
A. R. Sahab
2008-01-01
Full Text Available One of the most important nonlinear systems for checking the abilities of control methods is chaos. In this study chaos in Lorenz system was used for checking abilities of new control method. This new method to control nonlinear systems was called Generalized Backstepping method because of its similarity to Backstepping but its abilities to control more systems than Backstepping. This new method was applied to Lorenz system in three ways: 1.Stabilized states of equations. 2. Track step response. 3. Track sinusoidal response. In every way, simulations proved abilities of method. Comparing this new method with Backstepping showed that in this method, states stabilize at zero in shorter time than Backstepping and input control is more limited. So new method not only is used in more systems but also has better response.
APPLICATION OF MODIFIED CONVERSION METHOD TO A NONLINEAR DYNAMICAL SYSTEM
Directory of Open Access Journals (Sweden)
G.I. Melnikov
2015-01-01
Full Text Available The paper deals with a mathematical model of dynamical system with single degree of freedom, presented in the form of ordinary differential equations with nonlinear parts in the form of polynomials with constant and periodic coefficients. A modified method for the study of self-oscillations of nonlinear mechanical systems is presented. A refined method of transformation and integration of the equation, based on Poincare-Dulac normalization method has been developed. Refinement of the method lies in consideration of higher order nonlinear terms by Chebyshev economization technique that improves the accuracy of the calculations. Approximation of the higher order remainder terms by homogeneous forms of lower orders is performed; in the present case, it is done by cubic forms. An application of the modified method for the Van-der-Pol equation is considered as an example; the expressions for the amplitude and the phase of the oscillations are obtained in an analytical form. The comparison of the solution of the Van-der-Pol equation obtained by the developed method and the exact solution is performed. The error of the solution obtained by the modified method equals to 1%, which shows applicability of the developed method for analysis of self-oscillations of nonlinear dynamic systems with constant and periodic parameters.
An averaging method for nonlinear laminar Ekman layers
DEFF Research Database (Denmark)
Andersen, Anders Peter; Lautrup, B.; Bohr, T.
2003-01-01
We study steady laminar Ekman boundary layers in rotating systems using,an averaging method similar to the technique of von Karman and Pohlhausen. The method allows us to explore nonlinear corrections to the standard Ekman theory even at large Rossby numbers. We consider both the standard self...
Tensor methods for large sparse systems of nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science
1996-12-31
This paper introduces censor methods for solving, large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium- sized dense problems. They base each iteration on a quadratic model of the nonlinear equations. where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown censor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue that must be considered is how to make efficient use of sparsity in forming and solving the censor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method. in terms of iterations, function evaluations. and execution time.
A Spectral Element Method for Nonlinear and Dispersive Water Waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bigoni, Daniele; Eskilsson, Claes
The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...... methods is of key interest. We present a high-order general-purpose three-dimensional numerical model solving fully nonlinear and dispersive potential flow equations with a free surface.......The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...
Analysis of Nonlinear Dynamics by Square Matrix Method
Energy Technology Data Exchange (ETDEWEB)
Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II
2016-07-25
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.
Akbarzade, M.; Langari, J.
2011-02-01
In this paper a new approach combining the features of the homotopy concept with variational approach is proposed to find accurate analytical solutions for nonlinear oscillators with and without a fractional power restoring force. Since the first-order approximation leads to very accurate results, comparisons with other results are presented to show the effectiveness of this method. The validity of the method is independent of whether or not there exist small or large parameters in the considered nonlinear equations; the obtained results prove the validity and efficiency of the method, which can be easily extended to other strongly nonlinear problems. At the end we compare our procedure with the optimal homotopy perturbation method.
Nonlinear Direct Robust Adaptive Control Using Lyapunov Method
Directory of Open Access Journals (Sweden)
Chunbo Xiu
2013-07-01
Full Text Available The problem of robust adaptive stabilization of a class of multi-input nonlinear systems with arbitrary unknown parameters and unknown structure of bounded variation have been considered. By employing the direct adaptive and control Lyapunov function method, a robust adaptive controller is designed to complete the globally adaptive stability of the system states. By employing our result, a kind of nonlinear system is analyzed, the concrete form of the control law is given and the meaningful quadratic control Lyapunov function for the system is constructed. Simulation of parallel manipulator is provided to illustrate the effectiveness of the proposed method.
Convergence analysis of combinations of different methods
Energy Technology Data Exchange (ETDEWEB)
Kang, Y. [Clarkson Univ., Potsdam, NY (United States)
1994-12-31
This paper provides a convergence analysis for combinations of different numerical methods for solving systems of differential equations. The author proves that combinations of two convergent linear multistep methods or Runge-Kutta methods produce a new convergent method of which the order is equal to the smaller order of the two original methods.
Recursive prediction error methods for online estimation in nonlinear state-space models
Directory of Open Access Journals (Sweden)
Dag Ljungquist
1994-04-01
Full Text Available Several recursive algorithms for online, combined state and parameter estimation in nonlinear state-space models are discussed in this paper. Well-known algorithms such as the extended Kalman filter and alternative formulations of the recursive prediction error method are included, as well as a new method based on a line-search strategy. A comparison of the algorithms illustrates that they are very similar although the differences can be important for the online tracking capabilities and robustness. Simulation experiments on a simple nonlinear process show that the performance under certain conditions can be improved by including a line-search strategy.
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
An Analytical Approximation Method for Strongly Nonlinear Oscillators
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Wang Shimin
2012-01-01
Full Text Available An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of the spring varies with the vibration amplitude for nonstationary oscillations. The varied stiffness is constructed by means of the first and second averaged derivatives of the restoring force with respect to the displacement. Then, this stiffness gives the amplitude frequency and the phase frequency characteristics of the oscillator. Various examples show that this method can be applied extensively to oscillators with nonlinear restoring force, and that the solving process is extremely simple.
C-L METHOD AND ITS APPLICATION TO ENGINEERING NONLINEAR DYNAMICAL PROBLEMS
Institute of Scientific and Technical Information of China (English)
陈予恕; 丁千
2001-01-01
The C-L method was generalized from Liapunov-Schmidt reduction method,combined with theory of singularities, for study of non-autonomous dynamical systems to obtain the typical bifurcating response curves in the system parameter spaces. This method has been used , as an example, to analyze the engineering nonlinear dynamical problems by obtaining the bifurcation programs and response curves which are useful in developing tech niques of control to subharmonic instability of large rotating machinery.
Institute of Scientific and Technical Information of China (English)
FU Jing-Li; FU Hao
2008-01-01
We deai with the generalization of the field method to weakly non-linear mechanico-electricai coupling systems.The field co-ordinates and field momenta approaches are combined with the method of multiple time scales in order to obtain the amplitudes and phase of oscillations in the frst approximation. An example in mechanico-electrical coupling systems is given to illustrate this method.
Linear Algebraic Method for Non-Linear Map Analysis
Energy Technology Data Exchange (ETDEWEB)
Yu,L.; Nash, B.
2009-05-04
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
Application of homotopy analysis method for solving nonlinear Cauchy problem
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V.G. Gupta
2012-11-01
Full Text Available In this paper, by means of the homotopy analysis method (HAM, the solutions of some nonlinear Cauchy problem of parabolic-hyperbolic type are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter \\hbar that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.
Forecasting RMB Exchange Rate Based on a Nonlinear Combination Model of ARFIMA, SVM, and BPNN
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Chi Xie
2015-01-01
Full Text Available There are various models to predict financial time series like the RMB exchange rate. In this paper, considering the complex characteristics of RMB exchange rate, we build a nonlinear combination model of the autoregressive fractionally integrated moving average (ARFIMA model, the support vector machine (SVM model, and the back-propagation neural network (BPNN model to forecast the RMB exchange rate. The basic idea of the nonlinear combination model (NCM is to make the prediction more effective by combining different models’ advantages, and the weight of the combination model is determined by a nonlinear weighted mechanism. The RMB exchange rate against US dollar (RMB/USD and the RMB exchange rate against Euro (RMB/EUR are used as the empirical examples to evaluate the performance of NCM. The results show that the prediction performance of the nonlinear combination model is better than the single models and the linear combination models, and the nonlinear combination model is suitable for the prediction of the special time series, such as the RMB exchange rate.
An Agent Interaction Based Method for Nonlinear Process Plan Scheduling
Institute of Scientific and Technical Information of China (English)
GAO Qinglu; WU Bo; GUO Guang
2006-01-01
This article puts forward a scheduling method for nonlinear process plan shop floor. Task allocation and load balance are realized by bidding mechanism. Though the agent interaction process, the execution of tasks is determined and the coherence of manufacturing decision is verified. The employment of heuristic index can help to optimize the system performance.
Applications of non-linear methods in astronomy
Martens, P.C.H.
1984-01-01
In this review I discuss catastrophes, bifurcations and strange attractors in a non-mathematical manner by giving very simple examples that st ill contain the essence of the phenomenon. The salientresults of the applications of these non-linear methods in astrophysics are reviewed and include such d
Time-varying Combinations of Predictive Densities using Nonlinear Filtering
M. Billio (Monica); R. Casarin (Roberto); F. Ravazzolo (Francesco); H.K. van Dijk (Herman)
2012-01-01
textabstractWe propose a Bayesian combination approach for multivariate predictive densities which relies upon a distributional state space representation of the combination weights. Several specifications of multivariate time-varying weights are introduced with a particular focus on weight dynamics
Method for Measuring Small Nonlinearities of Electric Characteristics
DEFF Research Database (Denmark)
Guldbrandsen, Tom; Meyer, Niels I; Schjær-Jacobsen, Jørgen
1965-01-01
A method is described for measuring very small deviations from linearity in electric characteristics. The measurement is based on the harmonics generated by the nonlinear element when subjected to a sine wave signal. A special bridge circuit is used to balance out the undesired harmonics...... of the signal generator together with the first harmonic frequency. The set-up measures the small-signal value and the first and second derivative with respect to voltage. The detailed circuits are given for measuring nonlinearities in Ohmic and capacitive components. In the Ohmic case, a sensitivity...
Various Newton-type iterative methods for solving nonlinear equations
Directory of Open Access Journals (Sweden)
Manoj Kumar
2013-10-01
Full Text Available The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods.
Stanko, Z.; Boyce, S. E.; Yeh, W. W. G.
2015-12-01
Model reduction techniques using proper orthogonal decomposition (POD) have been very effective in applications to confined groundwater flow models. These techniques consist of performing a projection of the solution of the full model onto a reduced basis. POD combined with the snapshot approach has been successfully applied to highly discretized linear models. In many cases, the reduced model is orders of magnitude smaller than the full model and runs 1,000 times faster. For nonlinear models, such as the unconfined groundwater flow, direct application of POD requires additional calls to the full model to generate additional snapshots. This is time consuming and increases the dimension of the reduced model. The discrete empirical interpolation method (DEIM) is a technique that avoids the additional full model calls and captures the dynamics of the nonlinear term while reducing the dimensions. Here, POD and DEIM are combined to reduce both the nonlinear unconfined groundwater flow and solute transport equations. To prove the concept, simple one-dimensional models are created for MODFLOW and MT3DMS separately. The dual approach is then tested on a density-dependent flow and transport simulation using the LMT package developed for MODFLOW. For each iteration of the nonlinear flow solver and the transport solver, the respective reduced models are solved instead. Numerical experiments show that significant reduction is obtainable before errors become too large. This method is well suited for a coastal aquifer seawater intrusion scenario, where nonlinearities only exist in small subregions of the model domain. A fine discretization can be utilized and POD will effectively eliminate unnecessary parameterization by projecting the full model system matrix onto a subspace with fewer column dimensions. DEIM can then reduce the row dimension of the original system by using only those state variable nodes with the most influence. This combined approach allows for full
Method of Conjugate Radii for Solving Linear and Nonlinear Systems
Nachtsheim, Philip R.
1999-01-01
This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.
Relaxation and decomposition methods for mixed integer nonlinear programming
Nowak, Ivo; Bank, RE
2005-01-01
This book presents a comprehensive description of efficient methods for solving nonconvex mixed integer nonlinear programs, including several numerical and theoretical results, which are presented here for the first time. It contains many illustrations and an up-to-date bibliography. Because on the emphasis on practical methods, as well as the introduction into the basic theory, the book is accessible to a wide audience. It can be used both as a research and as a graduate text.
A Filter Method for Nonlinear Semidefinite Programming with Global Convergence
Institute of Scientific and Technical Information of China (English)
Zhi Bin ZHU; Hua Li ZHU
2014-01-01
In this study, a new filter algorithm is presented for solving the nonlinear semidefinite programming. This algorithm is inspired by the classical sequential quadratic programming method. Unlike the traditional filter methods, the suffi cient descent is ensured by changing the step size instead of the trust region radius. Under some suitable conditions, the global convergence is obtained. In the end, some numerical experiments are given to show that the algorithm is eff ective.
A numerical-perturbation method for the nonlinear analysis of structural vibrations
Nayfeh, A. H.; Mook, D. T.; Lobitz, D. W.
1974-01-01
A numerical-perturbation method is proposed for the determination of the nonlinear forced response of structural elements. Purely analytical techniques are capable of determining the response of structural elements having simple geometries and simple variations in thickness and properties, but they are not applicable to elements with complicated structure and boundaries. Numerical techniques are effective in determining the linear response of complicated structures, but they are not optimal for determining the nonlinear response of even simple elements when modal interactions take place due to the complicated nature of the response. Therefore, the optimum is a combined numerical and perturbation technique. The present technique is applied to beams with varying cross sections.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Sheng [Department of Mathematics, Bohai University, Jinzhou 121000 (China)]. E-mail: zhshaeng@yahoo.com.cn; Xia, Tiecheng [Department of Mathematics, Bohai University, Jinzhou 121000 (China); Department of Mathematics, Shanghai University, Shanghai 200444 (China)
2007-04-09
In this Letter, a generalized new auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the combined KdV-mKdV equation and the (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equations to illustrate the validity and advantages of the method. As a result, many new and more general exact solutions are obtained.
Robust Optimal Design of a Nonlinear Dynamic Vibration Absorber Combining Sensitivity Analysis
Directory of Open Access Journals (Sweden)
R.A. Borges
2010-01-01
Full Text Available Dynamic vibration absorbers are discrete devices developed in the beginning of the last century used to attenuate the vibrations of different engineering structures. They have been used in several engineering applications, such as ships, power lines, aeronautic structures, civil engineering constructions subjected to seismic induced excitations, compressor systems, etc. However, in the context of nonlinear dynamics, few works have been proposed regarding the robust optimal design of nonlinear dynamic vibration absorbers. In this paper, a robust optimization strategy combined with sensitivity analysis of systems incorporating nonlinear dynamic vibration absorbers is proposed. Although sensitivity analysis is a well known numerical technique, the main contribution intended for this study is its extension to nonlinear systems. Due to the numerical procedure used to solve the nonlinear equations, the sensitivities addressed herein are computed from the first-order finite-difference approximations. With the aim of increasing the efficiency of the nonlinear dynamic absorber into a frequency band of interest, and to augment the robustness of the optimal design, a robust optimization strategy combined with the previous sensitivities is addressed. After presenting the underlying theoretical foundations, the proposed robust design methodology is performed for a two degree-of-freedom system incorporating a nonlinear dynamic vibration absorber. Based on the obtained results, the usefulness of the proposed methodology is highlighted.
A New Nonlinear Compound Forecasting Method Based on ANN
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper the compound-forecasting method is discussed. The compound-forecasting method is one of the hotspots in the current predication. Firstly, the compound-forecasting method is introduced and various existing compound-forecasting methods arediscussed. Secondly, the Artificial Neural Network (ANN) is brought in compound-prediction research and a nonlinear compound-prediction model based on ANN is presented. Finally, inorder to avoid irregular weight, a new method is presented which uses principal component analyses to increase the availability of compound-forecasting information. Higherforecasting precision is achieved in practice.
Perturbation and harmonic balance methods for nonlinear panel flutter.
Kuo, C.-C.; Morino, L.; Dugundji, J.
1972-01-01
A systematic way of applying both perturbation methods and harmonic balance methods to nonlinear panel flutter problems is developed here. Results obtained by both these methods for two-dimensional simply supported and three-dimensional clamped-clamped plates with six modes agree well with those obtained by the straightforward direct integration method, yet require less computer time and provide better insight into the solutions. Effects of viscoelastic structural damping on the flutter stability boundary are generally found to be destabilizing and the postflutter behavior becomes more explosive. The methods developed here may be of interest in related vibration problems.
Multi-level damage detection with nonlinear ultrasonic methods
Matlack, Kathryn H.; Kim, Jin-Yeon; Jacobs, Laurence J.; Qu, Jianmin
2013-01-01
The nonlinear ultrasonic method of second harmonic generation is used to detect multiple levels of damage on a single specimen. There is a breadth of research in the literature that measures the second harmonic and the resulting nonlinear parameter to monitor increasing amounts of uniform damage, but for this method to be applicable as an in situ technique, it must be able to scan an area of a structure with varying amounts of damage over a region. To investigate this, an aluminum alloy sample is shot-peened to two intensity levels along its length, to produce different sections of cold work and residual stress as a function of spatial location. Previous research has shown that the residual stress and cold work introduced in a material from shot peening causes an increase in the nonlinear parameter. Rayleigh waves are generated in the sample and the first and second harmonic amplitudes are measured at increasing propagation distances that encompass an undamaged section and two sections, each with different levels of shot peening. Results show that the nonlinear parameter increases as the Rayleigh wedge sensor is scanned over the shot peening sections.
Motulsky, Harvey J; Brown, Ronald E
2006-03-09
Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely) one or more outlier in only about 1-3% of experiments. When analyzing data contaminated with one or several outliers, the ROUT method performs well at outlier identification, with an average False Discovery Rate less than 1%. Our method, which combines a new method of robust nonlinear regression with a new method of outlier identification, identifies outliers from nonlinear curve fits with reasonable power and few false positives.
Directory of Open Access Journals (Sweden)
Motulsky Harvey J
2006-03-01
Full Text Available Abstract Background Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. Results We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely one or more outlier in only about 1–3% of experiments. When analyzing data contaminated with one or several outliers, the ROUT method performs well at outlier identification, with an average False Discovery Rate less than 1%. Conclusion Our method, which combines a new method of robust nonlinear regression with a new method of outlier identification, identifies outliers from nonlinear curve fits with reasonable power and few false positives.
Shuttle entry guidance revisited using nonlinear geometric methods
Mease, Kenneth D.; Kremer, Jean-Paul
1994-11-01
The entry guidance law for the space shuttle orbiter is revisited using nonlinear geometric methods. The shuttle guidance concept is to track a reference drag trajectory that has been designed to lead a specified range and velocity. It is shown that the approach taken in the original derivation of the shuttle entry guidance has much in common with the more recently developed feedback linearization method of differential geometric control. Using the feedback linearization method, however, an alternative, potentially superior, guidance law was formulated. Comparing the two guidance laws based performance domains in state space, taking into account the nonlinear dynamics, the alternative guidance law achieves the desired performance over larger domains in state space; the stability domain of the laws are similar. With larger operating domain for the shuttle or some other entry vehicle, the alternative guidance law should be considered.
Analysis of Nonlinear Missile Guidance Systems Through Linear Adjoint Method
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Khaled Gamal Eltohamy
2015-12-01
Full Text Available In this paper, a linear simulation algorithm, the adjoint method, is modified and employed as an efficient tool for analyzing the contributions of system parameters to the miss - distance of a nonlinear time-varying missile guidance system model. As an example for the application of the linear adjoint method, the effect of missile flight time on the miss - distance is studied. Since the missile model is highly nonlinear and a time-varying linearized model is required to apply the adjoint method, a new technique that utilizes the time-reversed linearized coefficients of the missile as a replacement for the time-varying describing functions is applied and proven to be successful. It is found that, when compared with Monte Carlo generated results, simulation results of this linear adjoint technique provide acceptable accuracy and can be produced with much less effort.
Bayesian Methods for Nonlinear System Identification of Civil Structures
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Conte Joel P.
2015-01-01
Full Text Available This paper presents a new framework for the identification of mechanics-based nonlinear finite element (FE models of civil structures using Bayesian methods. In this approach, recursive Bayesian estimation methods are utilized to update an advanced nonlinear FE model of the structure using the input-output dynamic data recorded during an earthquake event. Capable of capturing the complex damage mechanisms and failure modes of the structural system, the updated nonlinear FE model can be used to evaluate the state of health of the structure after a damage-inducing event. To update the unknown time-invariant parameters of the FE model, three alternative stochastic filtering methods are used: the extended Kalman filter (EKF, the unscented Kalman filter (UKF, and the iterated extended Kalman filter (IEKF. For those estimation methods that require the computation of structural FE response sensitivities with respect to the unknown modeling parameters (EKF and IEKF, the accurate and computationally efficient direct differentiation method (DDM is used. A three-dimensional five-story two-by-one bay reinforced concrete (RC frame is used to illustrate the performance of the framework and compare the performance of the different filters in terms of convergence, accuracy, and robustness. Excellent estimation results are obtained with the UKF, EKF, and IEKF. Because of the analytical linearization used in the EKF and IEKF, abrupt and large jumps in the estimates of the modeling parameters are observed when using these filters. The UKF slightly outperforms the EKF and IEKF.
Institute of Scientific and Technical Information of China (English)
崔霞
2002-01-01
Alternating direction finite element (ADFE) scheme for d-dimensional nonlinear system of parabolic integro-differential equations is studied. By using a local approximation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized; by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using finite element method, high accuracy for space variant is kept; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coefficients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence properties for both FE and ADFE schemes are rigorously demonstrated, and optimal H1 and L2norm space estimates and O((△t)2) estimate for time variant are obtained.
Multi-crack imaging using nonclassical nonlinear acoustic method
Zhang, Lue; Zhang, Ying; Liu, Xiao-Zhou; Gong, Xiu-Fen
2014-10-01
Solid materials with cracks exhibit the nonclassical nonlinear acoustical behavior. The micro-defects in solid materials can be detected by nonlinear elastic wave spectroscopy (NEWS) method with a time-reversal (TR) mirror. While defects lie in viscoelastic solid material with different distances from one another, the nonlinear and hysteretic stress—strain relation is established with Preisach—Mayergoyz (PM) model in crack zone. Pulse inversion (PI) and TR methods are used in numerical simulation and defect locations can be determined from images obtained by the maximum value. Since false-positive defects might appear and degrade the imaging when the defects are located quite closely, the maximum value imaging with a time window is introduced to analyze how defects affect each other and how the fake one occurs. Furthermore, NEWS-TR-NEWS method is put forward to improve NEWS-TR scheme, with another forward propagation (NEWS) added to the existing phases (NEWS and TR). In the added phase, scanner locations are determined by locations of all defects imaged in previous phases, so that whether an imaged defect is real can be deduced. NEWS-TR-NEWS method is proved to be effective to distinguish real defects from the false-positive ones. Moreover, it is also helpful to detect the crack that is weaker than others during imaging procedure.
Institute of Scientific and Technical Information of China (English)
顾成奎; 王正欧; 孙雅明
2003-01-01
A new method for identifying nonlinear time-varying systems with unknown structure is presented. The method extends the application area of basis sequence identification. The essential idea is to utilize the learning and nonlinear approximating ability of neural networks to model the non-linearity of the system, characterize time-varying dynamics of the system by the time-varying parametric vector of the network, then the parametric vector of the network is approximated by a weighted sum of known basis sequences. Because of black-box modeling ability of neural networks, the presented method can identify nonlinear time-varying systems with unknown structure. In order to improve the real-time capability of the algorithm, the neural network is trained by a simple fast learning algorithm based on local least squares presented by the authors. The effectiveness and the performance of the method are demonstrated by some simulation results.
Condition Monitoring of Turbines Using Nonlinear Mapping Method
Institute of Scientific and Technical Information of China (English)
Liao Guang-lan; Shi Tie-lin; Jiang Nan
2004-01-01
Aiming at the non-linear nature of the signals generated from turbines, curvilinear component analysis (CCA), a novel nonlinear projection method that favors local topology conservation is presented for turbines conditions monitoring. This is accomplished in two steps. Time domain features are extracted from raw vibration signals, and then they are projected into a two-dimensional output space by using CCA method and form regions indicative of specific conditions, which helps classify and identify turbine states visually. Therefore, the variation of turbine conditions can be observed clearly with the trajectory of image points for the feature data in the two-dimensional space, and the occurrence and development of failures can be monitored in time.
Application of the homotopy perturbation method to the nonlinear pendulum
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Hernandez, A; Belendez, T; Neipp, C; Marquez, A [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-01-15
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as high as 130{sup 0}. Another important point is that this method provides an analytical expression for the angular displacement as a function of time as the sum of an infinite number of harmonics; although for practical purposes it is sufficient to consider only a finite number of harmonics. We believe that the present study may be a suitable and fruitful exercise for teaching and better understanding perturbation techniques in advanced undergraduate courses on classical mechanics.
Lavrentiev regularization method for nonlinear ill-posed problems
Kinh, N V
2002-01-01
In this paper we shall be concerned with Lavientiev regularization method to reconstruct solutions x sub 0 of non ill-posed problems F(x)=y sub o , where instead of y sub 0 noisy data y subdelta is an element of X with absolut(y subdelta-y sub 0) X is an accretive nonlinear operator from a real reflexive Banach space X into itself. In this regularization method solutions x subalpha supdelta are obtained by solving the singularly perturbed nonlinear operator equation F(x)+alpha(x-x*)=y subdelta with some initial guess x*. Assuming certain conditions concerning the operator F and the smoothness of the element x*-x sub 0 we derive stability estimates which show that the accuracy of the regularized solutions is order optimal provided that the regularization parameter alpha has been chosen properly.
Adomian decomposition method for nonlinear Sturm-Liouville problems
Directory of Open Access Journals (Sweden)
Sennur Somali
2007-09-01
Full Text Available In this paper the Adomian decomposition method is applied to the nonlinear Sturm-Liouville problem-y" + y(tp=λy(t, y(t > 0, t ∈ I = (0, 1, y(0 = y(1 = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.
Institute of Scientific and Technical Information of China (English)
郭抗抗; 曹树谦
2014-01-01
A modified Lindstedt-Poincaré (LP) method for obtaining the resonance periodic solutions of nonlinear non-autonomous vibration systems is proposed in this paper. In the modified method, nonlinear non-autonomous equa-tions are converted into a group of linear ordinary differential equations by introducing a set of simple transformations. An approximate resonance solution for the original equation can then be obtained. The periodic solutions of primary, super-harmonic, sub-harmonic, zero-frequency and combination resonances can be solved effectively using the modi-fied method. Some examples, such as damped cubic nonlinear systems under single and double frequency excitation, and damped quadratic nonlinear systems under double frequency excitation, are given to illustrate its convenience and effectiveness. Using the modified LP method, the first-order approximate solutions for each equation are obtained. By comparison, the modified method proposed in this paper produces the same results as the method of multiple scales.
Homotopy deform method for reproducing kernel space for nonlinear boundary value problems
Indian Academy of Sciences (India)
MIN-QIANG XU; YING-ZHEN LIN
2016-10-01
In this paper, the combination of homotopy deform method (HDM) and simplified reproducing kernel method (SRKM) is introduced for solving the boundary value problems (BVPs) of nonlinear differential equations. The solution methodology is based on Adomian decomposition and reproducing kernel method (RKM). By the HDM, the nonlinear equations can be converted into a series of linear BVPs. After that, the simplified reproducing kernel method, which not only facilitates the reproducing kernel but also avoids the time-consuming Schmidt orthogonalization process, is proposed to solve linear equations. Some numerical test problems including ordinary differential equations and partial differential equations are analysed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that our algorithm is considerably accurate and effective as expected.
Sharma, Dinkar; Singh, Prince; Chauhan, Shubha
2016-01-01
In this paper, a combined form of the Laplace transform method with the homotopy perturbation method (HPTM) is applied to solve nonlinear systems of partial differential equations viz. the system of third order KdV Equations and the systems of coupled Burgers' equations in one- and two- dimensions. The nonlinear terms can be easily handled by the use of He's polynomials. The results shows that the HPTM is very efficient, simple and avoids the round-off errors. Four test examples are considered to illustrate the present scheme. Further the results are compared with Homotopy perturbation method (HPM) which shows that this method is a suitable method for solving systems of partial differential equations.
The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions
Directory of Open Access Journals (Sweden)
Shoukry Ibrahim Atia El-Ganaini
2013-01-01
Full Text Available The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1-dimensional hyperbolic nonlinear Schrodinger (HNLS equation, the generalized nonlinear Schrodinger (GNLS equation with a source, and the higher-order nonlinear Schrodinger equation in nonlinear optical fibers. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner.
Sequential Combination Methods forData Clustering Analysis
Institute of Scientific and Technical Information of China (English)
钱 涛; Ching Y.Suen; 唐远炎
2002-01-01
This paper proposes the use of more than one clustering method to improve clustering performance. Clustering is an optimization procedure based on a specific clustering criterion. Clustering combination can be regardedasatechnique that constructs and processes multiple clusteringcriteria.Sincetheglobalandlocalclusteringcriteriaarecomplementary rather than competitive, combining these two types of clustering criteria may enhance theclustering performance. In our past work, a multi-objective programming based simultaneous clustering combination algorithmhasbeenproposed, which incorporates multiple criteria into an objective function by a weighting method, and solves this problem with constrained nonlinear optimization programming. But this algorithm has high computationalcomplexity.Hereasequential combination approach is investigated, which first uses the global criterion based clustering to produce an initial result, then uses the local criterion based information to improve the initial result with aprobabilisticrelaxation algorithm or linear additive model.Compared with the simultaneous combination method, sequential combination haslow computational complexity. Results on some simulated data and standard test data arereported.Itappearsthatclustering performance improvement can be achieved at low cost through sequential combination.
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2012-01-01
Full Text Available We modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, the discrete nonlinear Klein-Gordon equation, and the quintic discrete nonlinear Schrodinger equation. Some new types of the Jacobi elliptic solutions are obtained for some nonlinear differential difference equations in mathematical physics. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.
Institute of Scientific and Technical Information of China (English)
GAO Jie
2009-01-01
In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC Ⅱ. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations.
A mixed finite element method for nonlinear diffusion equations
Burger, Martin
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
A Stabilised Nodal Spectral Element Method for Fully Nonlinear Water Waves
Engsig-Karup, Allan Peter; Bigoni, Daniele
2015-01-01
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al (1998) \\cite{CaiEtAl1998}, although the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global $L^2$ projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively removes any aliasing driven instabilities while retaining the high-order accuracy of the numerical...
Zha, Yikun; Wei, Jingsong; Gan, Fuxi
2013-04-01
With the continuous development of the field of information technology, there has been a demand for recording mark size of optical data storage, optical imaging resolving power, and characteristic linewidth of photolithography to reach nanoscale. However, it is very difficult to realize the goal due to the optical diffraction limit restrictions. Much interest has focused on the study of optical far-field super-resolution spot by using pupil filters. However, common concerns have continued to plague super-resolving pupil filters based on either scalar diffraction theory or vector diffraction theory. These concerns include the fact that the side lobe becomes non-negligible when the central lobe is squeezed to a certain extent. Moreover, it is difficult to reduce the super-resolving spot to nanoscale. In this work, we proposed a novel method to combine the super-resolving pupil filters with nonlinear saturable absorption thin films to reduce the central spot size to nanoscale, lower the intensity ratio of side lobe to central lobe, and elongate the depth of focus or tunable tolerance distance between the super-resolving spot and sample. The simulated results indicate that by using the three-zone annular binary phase filter as the super-resolving pupil filter and Sb2Te3 as the nonlinear saturable absorption thin films, the central spot size can be reduced to nanoscale, the side lobe intensity is squeezed to about 10% of the central lobe intensity, and the tunable tolerance distance between the super-resolving spot and the sample is about two times that of the depth of focus of the diffraction limited spot at the incident laser wavelength of 405 nm and the numerical aperture of focusing lens of 0.95. The combination of the super-resolving pupil filters with the nonlinear saturable absorption thin films is very useful for nano-optical data storage, maskless nanolithography, and nano-optical imaging. It is also easy to use in actual applications because of the operation
Mapping deformation method and its application to nonlinear equations
Institute of Scientific and Technical Information of China (English)
李画眉
2002-01-01
An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinearpartial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraicmapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein-Gordon equation. This isapplied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained,including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions.
The simplex method for nonlinear sliding mode control
Directory of Open Access Journals (Sweden)
Bartolini G.
1998-01-01
Full Text Available General nonlinear control systems described by ordinary differential equations with a prescribed sliding manifold are considered. A method of designing a feedback control law such that the state variable fulfills the sliding condition in finite time is based on the construction of a suitable simplex of vectors in the tangent space of the manifold. The convergence of the method is proved under an obtuse angle condition and a way to build the required simplex is indicated. An example of engineering interest is presented.
Method of guiding functions in problems of nonlinear analysis
Obukhovskii, Valeri; Van Loi, Nguyen; Kornev, Sergei
2013-01-01
This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for “pure” mathematicians, but also for students and researchers working in applied mathematics, the engineering sciences and physics.
High-Order Energy Balance Method to Nonlinear Oscillators
Seher Durmaz; Metin Orhan Kaya
2012-01-01
Energy balance method (EBM) is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated fo...
High-Order Energy Balance Method to Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Seher Durmaz
2012-01-01
Full Text Available Energy balance method (EBM is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator.
The energy balance to nonlinear oscillations via Jacobi collocation method
Directory of Open Access Journals (Sweden)
M.K. Yazdi
2015-06-01
Full Text Available This study develops the energy balance based on Jacobi collocation method for accurate prediction of conservative nonlinear oscillator models with a single collocation point. The node points are taken as the roots of Jacobi orthogonal polynomials. Several examples are included to demonstrate the applicability and accuracy of the proposed algorithm, and some comparisons are made with the existing results. The method is suitable and the approximate frequencies are valid for small as well as large amplitudes of oscillation. Excellent agreement with exact ones is presented for the first order approximation.
Institute of Scientific and Technical Information of China (English)
SUN LiYing; WANG YuZhen
2009-01-01
This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonlan function method.Firstly,based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback,two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation,and a sufficient condition for two closed-loop systems to be impulse-free is given.The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique,based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems.Secondly,the case of more than two nonlinear descriptor systems is investigated,and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization,respectively.Finally,an illustrative example is studied by using the results proposed in this paper,and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.
A new method for nonlinear optimization - experimental results
Energy Technology Data Exchange (ETDEWEB)
Loskovska, S.; Percinkova, B.
1994-12-31
In this paper an application of a new method for nonlinear optimization problems suggested and presented by B. Percinkova is performed. The method is originally developed and applicated on nonlinear systems. Basis of the method is following: A system of n-nonlinear equations gives as F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) = 0; 1 = 1, 2, ..., n and solution domain x{sub pi} {<=} x{sub i} {<=} x{sub ki} i = 1, 2, ..., n is modified by introducing a new variable z. The new system is given by: F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) = z; i = 1, 2, ..., n. The system defines a curve in (n + 1) dimensional space. System`s point X = (x{sub i}, x{sub 2}, x{sub 3}, ..., x{sub n}, z) that, the solution of the system is obtained using an interative procedure moving along the curve until the point with z = 0 is reached. In order to applicate method on optimization problems, a basic optimization model given with (min, max)F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) with the following optimization space: F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) ({<=}{>=})0 : i = 1, 2, ..., n is transformed into a system equivalent to system (2) by (dF/dx{sub i}) = z; i - 1, 2, ..., n. The main purpose of this work is to make relevant evaluation of the method by standard test problems.
Pulse wave attenuation measurement by linear and nonlinear methods in nonlinearly elastic tubes.
Bertram, C D; Pythoud, F; Stergiopulos, N; Meister, J J
1999-04-01
Reasons for the continuing difficulty in making definitive measurements of pulse wave attenuation in elastic tubes and arteries in the presence of reflections are sought. The measurement techniques available were re-examined in elastic tubes mimicking the arterial compliance nonlinearity, under conditions of strong reflection. The pulse was of physiological shape, and two different pulse amplitudes in the physiological range were used. Measurements of pressure, flow-rate and diameter pulsation allowed the deployment of four of the classical linear methods of analysis. In addition, a method of separating the forward- and backward-travelling waves that does not require linearising assumptions was used, and the attenuation in the forward and reverse directions was calculated from the resulting waveforms. Overall, the results obtained here suggest that a fully satisfactory way of measuring arterial attenuation has yet to be devised. The classical linear methods all provided comparable attenuation estimates in terms of average value and degree of scatter across frequency. Increased scatter was generally found at the higher pulse amplitude. When the forward waveforms from the separation were similarly compared in terms of frequency components, the average value at energetic harmonics was similar to both the value indicated by the linear methods and the values predicted from linear theory on the basis of estimated viscous and viscoelastic parameter data. The backward waveforms indicated a physically unreasonable result, attributed as the expression for this technique of the same difficulties that normally manifest in scatter. Data in the literature suggesting that one of the classical methods, the three-point, systematically over-estimates attenuation were not supported, but it was confirmed that this method becomes prone to negative attenuation estimates at low harmonics as pulse amplitude increases. Although the goal of definitive attenuation measurement remains elusive
Directory of Open Access Journals (Sweden)
Sumit Gupta
2015-09-01
Full Text Available The aim of this paper was to present a user friendly numerical algorithm based on homotopy perturbation transform method for solving various linear and nonlinear convection-diffusion problems arising in physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. The homotopy perturbation transform method is a combined form of the homotopy perturbation method and Laplace transform method. The nonlinear terms can be easily obtained by the use of He’s polynomials. The technique presents an accurate methodology to solve many types of partial differential equations The approximate solutions obtained by proposed scheme in a wide range of the problem’s domain were compared with those results obtained from the actual solutions. The comparison shows a precise agreement between the results.
Directory of Open Access Journals (Sweden)
Ji Juan-Juan
2017-01-01
Full Text Available A table lookup method for solving nonlinear fractional partial differential equations (fPDEs is proposed in this paper. Looking up the corresponding tables, we can quickly obtain the exact analytical solutions of fPDEs by using this method. To illustrate the validity of the method, we apply it to construct the exact analytical solutions of four nonlinear fPDEs, namely, the time fractional simplified MCH equation, the space-time fractional combined KdV-mKdV equation, the (2+1-dimensional time fractional Zoomeron equation, and the space-time fractional ZKBBM equation. As a result, many new types of exact analytical solutions are obtained including triangular periodic solution, hyperbolic function solution, singular solution, multiple solitary wave solution, and Jacobi elliptic function solution.
STUDY ON PREDICTION METHODS FOR DYNAMIC SYSTEMS OF NONLINEAR CHAOTIC TIME SERIES
Institute of Scientific and Technical Information of China (English)
马军海; 陈予恕; 辛宝贵
2004-01-01
The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions.By combining neural networks and wavelet theories,the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given.Based on wavelet networks,a new method for parameter identification was suggested,which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series.Through pre-treatment and comparison of results before and after the treatment,several useful conclusions are reached:High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper presents a method on non-linear correction of broadband LFMCW signal utilizing its relativenonlinear error. The deriving procedure and the results simulated by a computer and tested by a practical system arealso introduced. The method has two obvious advantages compared with the previous methods: (1) Correction has norelation with delay time td and sweep bandwidth B; (2) The inherent non-linear error of VCO has no influence on thecorrection and its last results.
Prediction of biodegradation kinetics using a nonlinear group contribution method
Energy Technology Data Exchange (ETDEWEB)
Tabak, H.H. (Environmental Protection Agency, Cincinnati, OH (United States)); Govind, R. (Univ. of Cincinnati, OH (United States))
1993-02-01
The fate of organic chemicals in the environment depends on their susceptibility to biodegradation. Hence, development of regulations concerning their manufacture and use requires information on the extent and rate of biodegradation. Recent studies have attempted to correlate the kinetics of biodegradation with the molecular structure of the compound. This has led to the development of structure-biodegradation relationships (SBRs) using the group contribution approach. Each defined group present in the chemical structure of the compound is assigned a unique numerical contribution toward the calculation of the biodegradation kinetic constants. In this paper, a nonlinear group contribution method has been developed using neural networks; it is trained using literature data on the first-order biodegradation kinetic rate constant for a number of priority pollutants. The trained neural network is then used to predict the biodegradation kinetic constant for a new list of compounds, and results have been compared with the experimental values and the predictions obtained from a linear group contribution method. It has been shown that the nonlinear group contribution method using neural networks is able to provide a superior fit to the training set data and test data set and produce a lower prediction error than the previous linear method.
Mei, Chuh; Shen, Mo-How
1987-01-01
Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.
Estimation methods for nonlinear state-space models in ecology
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Berg, Casper Willestofte; Thygesen, Uffe Høgsbro
2011-01-01
The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta...... logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden...... Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance...
Similar Constructive Method for Solving a nonlinearly Spherical Percolation Model
Directory of Open Access Journals (Sweden)
WANG Yong
2013-01-01
Full Text Available In the view of nonlinear spherical percolation problem of dual porosity reservoir, a mathematical model considering three types of outer boundary conditions: closed, constant pressure, infinity was established in this paper. The mathematical model was linearized by substitution of variable and became a boundary value problem of ordinary differential equation in Laplace space by Laplace transformation. It was verified that such boundary value problem with one type of outer boundary had a similar structure of solution. And a new method: Similar Constructive Method was obtained for solving such boundary value problem. By this method, solutions with similar structure in other two outer boundary conditions were obtained. The Similar Constructive Method raises efficiency of solving such percolation model.
A nonlinear analytic function expansion nodal method for transient calculations
Energy Technology Data Exchange (ETDEWEB)
Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1998-12-31
The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)
CAD—Oriented Noise Analysis Method of Nonlinear Microwave Chircuits
Institute of Scientific and Technical Information of China (English)
WANGJun; TANGGaodi; CHENHuilian
2003-01-01
A general method is introduced which is capable of making accurate,quantitative predictions about the noise of different type of nonlinear microwave circuits.This new approach also elucidates several design criteria for making it suitable to CAD-oriented analysis via identifying the mechanisms by which intrinsic device noise and external noise sources contribute to the total equivalent noise.In particular,it explains the details of how noise spectrum at the interesting port is obtained.And the theory also naturally leads to additional important design insights.In the illustrative experiments,excellent agreement among theory,simulations,and measurements is observed.
Method of the Logistic Function for Finding Analytical Solutions of Nonlinear Differential Equations
Kudryashov, N. A.
2015-01-01
The method of the logistic function is presented for finding exact solutions of nonlinear differential equations. The application of the method is illustrated by using the nonlinear ordinary differential equation of the fourth order. Analytical solutions obtained by this method are presented. These solutions are expressed via exponential functions.logistic function, nonlinear wave, nonlinear ordinary differential equation, Painlev´e test, exact solution
A modal method for ﬁnite amplitude, nonlinear sloshing
Indian Academy of Sciences (India)
P N Shankar; R Kidambi
2002-10-01
A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefﬁcients in the expansions of the interface and the potential. The effects of capillarity are included in the formulation. The simplicity, generality and power of the method are exhibited not only by recovering the earlier results obtained, for example, by Penney and Price [1], Tadjbakhsh and Keller [2] and Faltinsen et al [3], but also by obtaining new and interesting results of the effects of capillarity and shallow depth, which would be difﬁcult to obtain otherwise. For example, it is found that for the initial interface proﬁle considered here, parasitic capillary waves, borne by the higher number wave modes, are generated for moderate capillarity but disappear for larger values of the parameter. The method can be extended to other simple geometries.
Combination of measurements and the BLUE method
Lista, Luca
2016-01-01
The most accurate method to combine measurement from different experiments is to build a combined likelihood function and use it to perform the desired inference. This is not always possible for various reasons, hence approximate methods are often convenient. Among those, the best linear unbiased estimator (BLUE) is the most popular, allowing to take into account individual uncertainties and their correlations. The method is unbiased by construction if the true uncertainties and their correlations are known, but it may exhibit a bias if uncertainty estimates are used in place of the true ones, in particular if those estimated uncertainties depend on measured values. In those cases, an iterative application of the BLUE method may reduce the bias of the combined measurement.
Fast nonlinear regression method for CT brain perfusion analysis.
Bennink, Edwin; Oosterbroek, Jaap; Kudo, Kohsuke; Viergever, Max A; Velthuis, Birgitta K; de Jong, Hugo W A M
2016-04-01
Although computed tomography (CT) perfusion (CTP) imaging enables rapid diagnosis and prognosis of ischemic stroke, current CTP analysis methods have several shortcomings. We propose a fast nonlinear regression method with a box-shaped model (boxNLR) that has important advantages over the current state-of-the-art method, block-circulant singular value decomposition (bSVD). These advantages include improved robustness to attenuation curve truncation, extensibility, and unified estimation of perfusion parameters. The method is compared with bSVD and with a commercial SVD-based method. The three methods were quantitatively evaluated by means of a digital perfusion phantom, described by Kudo et al. and qualitatively with the aid of 50 clinical CTP scans. All three methods yielded high Pearson correlation coefficients ([Formula: see text]) with the ground truth in the phantom. The boxNLR perfusion maps of the clinical scans showed higher correlation with bSVD than the perfusion maps from the commercial method. Furthermore, it was shown that boxNLR estimates are robust to noise, truncation, and tracer delay. The proposed method provides a fast and reliable way of estimating perfusion parameters from CTP scans. This suggests it could be a viable alternative to current commercial and academic methods.
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
Ultrasound Tomography in Circular Measurement Configuration using Nonlinear Reconstruction Method
Directory of Open Access Journals (Sweden)
Tran Quang-Huy
2015-12-01
Full Text Available Ultrasound tomography offers the potential for detecting of very small tumors whose sizes are smaller than the wavelength of the incident pressure wave without ionizing radiation. Based on inverse scattering technique, this imaging modality uses some material properties such as sound contrast and attenuation in order to detect small objects. One of the most commonly used methods in ultrasound tomography is the Distorted Born Iterative Method (DBIM. The compressed sensing technique was applied in the DBIM as a promising approach for the image reconstruction quality improvement. Nevertheless, the random measurement configuration of transducers in this method is very difficult to set up in practice. Therefore, in this paper, we take advantages of simpler sparse uniform measurement configuration set-up of transducers and high-quality image reconstruction of 1 non-linear regularization in sparse scattering domain. The simulation results demonstrate the high performance of the proposed approach in terms of tremendously reduced total runtime and normalized error.
Optimization of nonlinear structural resonance using the incremental harmonic balance method
DEFF Research Database (Denmark)
Dou, Suguang; Jensen, Jakob Søndergaard
2015-01-01
We present an optimization procedure for tailoring the nonlinear structural resonant response with time-harmonic loads. A nonlinear finite element method is used for modeling beam structures with a geometric nonlinearity and the incremental harmonic balance method is applied for accurate nonlinea...
NOLB : Non-linear rigid block normal mode analysis method.
Hoffmann, Alexandre; Grudinin, Sergei
2017-04-05
We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velocities. The key observation of our method is that the angular velocity of a rigid block can be interpreted as the result of an implicit force, such that the motion of the rigid block can be considered as a pure rotation about a certain center. We demonstrate the motions produced with the NOLB method on three different molecular systems and show that some of the lowest frequency normal modes correspond to the biologically relevant motions. For example, NOLB detects the spiral sliding motion of the TALE protein, which is capable of rapid diffusion along its target DNA. Overall, our method produces better structures compared to the standard approach, especially at large deformation amplitudes, as we demonstrate by visual inspection, energy and topology analyses, and also by the MolProbity service validation. Finally, our method is scalable and can be applied to very large molecular systems, such as ribosomes. Standalone executables of the NOLB normal mode analysis method are available at https://team.inria.fr/nano-d/software/nolb-normal-modes. A graphical user interfaces created for the SAMSON software platform will be made available at https: //www.samson-connect.net.
Combination prediction method of chaotic time series
Institute of Scientific and Technical Information of China (English)
ZHAO DongHua; RUAN Jiong; CAI ZhiJie
2007-01-01
In the present paper, we propose an approach of combination prediction of chaotic time series. The method is based on the adding-weight one-rank local-region method of chaotic time series. The method allows us to define an interval containing a future value with a given probability, which is obtained by studying the prediction error distribution. Its effectiveness is shown with data generated by Logistic map.
Pan, Shoukui; Okano, Y.; Tsunekawa, S.; Fukuda, T.
1993-03-01
The Kyropoulus method was used to grow nonlinear optical organic crystals ABP (4-aminobenzophenone). The crystals were characterized by nonlinear optical measurements and had a large effect of frequency doubling.
A preconditioned inexact newton method for nonlinear sparse electromagnetic imaging
Desmal, Abdulla
2015-03-01
A nonlinear inversion scheme for the electromagnetic microwave imaging of domains with sparse content is proposed. Scattering equations are constructed using a contrast-source (CS) formulation. The proposed method uses an inexact Newton (IN) scheme to tackle the nonlinearity of these equations. At every IN iteration, a system of equations, which involves the Frechet derivative (FD) matrix of the CS operator, is solved for the IN step. A sparsity constraint is enforced on the solution via thresholded Landweber iterations, and the convergence is significantly increased using a preconditioner that levels the FD matrix\\'s singular values associated with contrast and equivalent currents. To increase the accuracy, the weight of the regularization\\'s penalty term is reduced during the IN iterations consistently with the scheme\\'s quadratic convergence. At the end of each IN iteration, an additional thresholding, which removes small \\'ripples\\' that are produced by the IN step, is applied to maintain the solution\\'s sparsity. Numerical results demonstrate the applicability of the proposed method in recovering sparse and discontinuous dielectric profiles with high contrast values.
Finite Volume Evolution Galerkin Methods for Nonlinear Hyperbolic Systems
Lukáčová-Medvid'ová, M.; Saibertová, J.; Warnecke, G.
2002-12-01
We present new truly multidimensional schemes of higher order within the frame- work of finite volume evolution Galerkin (FVEG) methods for systems of nonlinear hyperbolic conservation laws. These methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of the multidimensional hyperbolic system, such that all of the infinitely many directions of wave propagation are taken into account. Following our previous results for the wave equation system, we derive approximate evolution operators for the linearized Euler equations. The integrals along the Mach cone and along the cell interfaces are evaluated exactly, as well as by means of numerical quadratures. The influence of these numerical quadratures will be discussed. Second-order resolution is obtained using a conservative piecewise bilinear recovery and the midpoint rule approximation for time integration. We prove error estimates for the finite volume evolution Galerkin scheme for linear systems with constant coefficients. Several numerical experiments for the nonlinear. Euler equations, which confirm the accuracy and good multidimensional behavior of the FVEG schemes, are presented as well.
Efficient computation method for two-dimensional nonlinear waves
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The theory and simulation of fully-nonlinear waves in a truncated two-dimensional wave tank in time domain are presented. A piston-type wave-maker is used to generate gravity waves into the tank field in finite water depth. A damping zone is added in front of the wave-maker which makes it become one kind of absorbing wave-maker and ensures the prescribed Neumann condition. The efficiency of nmerical tank is further enhanced by installation of a sponge layer beach (SLB) in front of downtank to absorb longer weak waves that leak through the entire wave train front. Assume potential flow, the space- periodic irrotational surface waves can be represented by mixed Euler- Lagrange particles. Solving the integral equation at each time step for new normal velocities, the instantaneous free surface is integrated following time history by use of fourth-order Runge- Kutta method. The double node technique is used to deal with geometric discontinuity at the wave- body intersections. Several precise smoothing methods have been introduced to treat surface point with high curvature. No saw-tooth like instability is observed during the total simulation.The advantage of proposed wave tank has been verified by comparing with linear theoretical solution and other nonlinear results, excellent agreement in the whole range of frequencies of interest has been obtained.
Institute of Scientific and Technical Information of China (English)
Fan Yuxin; Xia Jian
2014-01-01
A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute tran-sient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute infla-tion is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES) method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hil-ber–Hughes–Taylor (HHT) time integration method is employed. For the fluid dynamic simula-tions, the Roe and HLLC (Harten–Lax–van Leer contact) scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS) approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.
Directory of Open Access Journals (Sweden)
Fan Yuxin
2014-12-01
Full Text Available A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute transient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute inflation is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hilber–Hughes–Taylor (HHT time integration method is employed. For the fluid dynamic simulations, the Roe and HLLC (Harten–Lax–van Leer contact scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.
Conditions on Structural Controllability of Nonlinear Systems: Polynomial Method
Directory of Open Access Journals (Sweden)
Qiang Ma
2011-03-01
Full Text Available In this paper the structural controllability of a class of a nonlinear system is investigated. The transfer function (matrix of nonlinear systems is obtained by putting the nonlinear system model on non-commutative ring. Conditions of structural controllability of nonlinear systems are presented according to the criterion of linear systems structural controllability in frequency domain. An example is used to testify the presented conditions finally.
Simple noise-reduction method based on nonlinear forecasting
Tan, James P. L.
2017-03-01
Nonparametric detrending or noise reduction methods are often employed to separate trends from noisy time series when no satisfactory models exist to fit the data. However, conventional noise reduction methods depend on subjective choices of smoothing parameters. Here we present a simple multivariate noise reduction method based on available nonlinear forecasting techniques. These are in turn based on state-space reconstruction for which a strong theoretical justification exists for their use in nonparametric forecasting. The noise reduction method presented here is conceptually similar to Schreiber's noise reduction method using state-space reconstruction. However, we show that Schreiber's method has a minor flaw that can be overcome with forecasting. Furthermore, our method contains a simple but nontrivial extension to multivariate time series. We apply the method to multivariate time series generated from the Van der Pol oscillator, the Lorenz equations, the Hindmarsh-Rose model of neuronal spiking activity, and to two other univariate real-world data sets. It is demonstrated that noise reduction heuristics can be objectively optimized with in-sample forecasting errors that correlate well with actual noise reduction errors.
Nonlinear diffusion methods based on robust statistics for noise removal
Institute of Scientific and Technical Information of China (English)
JIA Di-ye; HUANG Feng-gang; SU Han
2007-01-01
A novel smoothness term of Bayesian regularization framework based on M-estimation of robust statistics is proposed, and from this term a class of fourth-order nonlinear diffusion methods is proposed. These methods attempt to approximate an observed image with a piecewise linear image, which looks more natural than piecewise constant image used to approximate an observed image by P-M[1] model. It is known that M-estimators and W-estimators are essentially equivalent and solve the same minimization problem. Then, we propose PL bilateral filter from equivalent W-estimator. This new model is designed for piecewise linear image filtering,which is more effective than normal bilateral filter.
Institute of Scientific and Technical Information of China (English)
LIM; C.W.
2010-01-01
Nonlinear combination parametric resonance is investigated for an axially accelerating viscoelastic string.The governing equation of in-planar motion of the string is established by introducing a coordinate transform in the Eulerian equation of a string with moving boundaries.The string under investigation is constituted by the standard linear solid model in which the material,not partial,time derivative was used.The governing equation leads to the Mote model for transverse vibration by omitting the longitudinal component and higher order terms.The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string.The two models are respectively analyzed via the method of multiple scales for principal parametric resonance.The amplitudes and the existence conditions of steady-state response and its stability can be numerically determined.Numerical calculations demonstrate the effects of the string material parameters,the initial tension,and the axial speed fluctuation amplitude.The outcomes of the two models are qualitatively and quantitatively compared.
Comparison of accounting methods for business combinations
Directory of Open Access Journals (Sweden)
Jaroslav Sedláček
2012-01-01
Full Text Available The revised accounting rules applicable to business combinations in force on July1st 2009, are the result of several years efforts the convergence of U.S. and International Committee of the Financial Accounting Standards. Following the harmonization of global accounting procedures are revised and implemented also Czech accounting regulations. In our research we wanted to see how changes can affect the strategy and timing of business combinations. Comparative analysis is mainly focused on the differences between U.S. and international accounting policies and Czech accounting regulations. Key areas of analysis and synthesis are the identification of business combination, accounting methods for business combinations and goodwill recognition. The result is to assess the impact of the identified differences in the reported financial position and profit or loss of company.
A new method for parameter estimation in nonlinear dynamical equations
Wang, Liu; He, Wen-Ping; Liao, Le-Jian; Wan, Shi-Quan; He, Tao
2015-01-01
Parameter estimation is an important scientific problem in various fields such as chaos control, chaos synchronization and other mathematical models. In this paper, a new method for parameter estimation in nonlinear dynamical equations is proposed based on evolutionary modelling (EM). This will be achieved by utilizing the following characteristics of EM which includes self-organizing, adaptive and self-learning features which are inspired by biological natural selection, and mutation and genetic inheritance. The performance of the new method is demonstrated by using various numerical tests on the classic chaos model—Lorenz equation (Lorenz 1963). The results indicate that the new method can be used for fast and effective parameter estimation irrespective of whether partial parameters or all parameters are unknown in the Lorenz equation. Moreover, the new method has a good convergence rate. Noises are inevitable in observational data. The influence of observational noises on the performance of the presented method has been investigated. The results indicate that the strong noises, such as signal noise ratio (SNR) of 10 dB, have a larger influence on parameter estimation than the relatively weak noises. However, it is found that the precision of the parameter estimation remains acceptable for the relatively weak noises, e.g. SNR is 20 or 30 dB. It indicates that the presented method also has some anti-noise performance.
Raffa, Robert B; Stagliano, Gregory W; Tallarida, Ronald J
2007-02-05
Elucidation of interactions between drugs used in polydrug abuse is especially important. However, the necessary experimental conditions for precise quantitative analysis are difficult to establish. Because withdrawal effects of cocaine and the cannabinoid receptor agonist WIN 55212-2 are easily quantified in planarians, demonstration of synergistic effects (P<0.01) of certain ratios of this combination was possible. This synergy, here analyzed with the latest (nonlinear) isobolographic methodology, is now quantitatively established for the first time.
Raffa, Robert B.; Stagliano, Gregory W.; Tallarida, Ronald J.
2006-01-01
Elucidation of interactions between drugs used in polydrug abuse is especially important. However, the necessary experimental conditions for precise quantitative analysis are difficult to establish. Because withdrawal effects of cocaine and the cannabinoid receptor agonist WIN 55212-2 are easily quantified in planarians, demonstration of synergistic effects (P < 0.01) of certain ratios of this combination was possible. This synergy, here analyzed with the latest (nonlinear) isobolographic met...
Three-Step Predictor-Corrector of Exponential Fitting Method for Nonlinear Schr(o)dinger Equations
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the threestep explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schr(o)dinger equation and the nonlinear Schr(o)dinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.
Zhang, Yitao; Muta, Osamu; Akaiwa, Yoshihiko
The adaptive predistorter and the negative feedback system are known as methods to compensate for the nonlinear distortion of a power amplifier. Although the feedback method is a simple technique, its instability impedes the capability of high-feedback gain to achieve a high-compensation effect. On the other hand, the predistorter requires a long time for convergence of the adaptive predistorters. In this paper, we propose a nonlinear distortion compensation method for a narrow-band signal. In this method, an adaptive predistorter and negative feedback are combined. In addition, to shorten the convergence time to minimize nonlinear distortion, a variable step-size (VS) method is also applied to the algorithm to determine the parameters of the adaptive predistorter. Using computer simulations, we show that the proposed scheme achieves both five times faster convergence speed than that of the predistorter and three times higher permissible delay time in the feedback amplifier than that of a negative feedback only amplifier.
Soft sensor modeling based on variable partition ensemble method for nonlinear batch processes
Wang, Li; Chen, Xiangguang; Yang, Kai; Jin, Huaiping
2017-01-01
Batch processes are always characterized by nonlinear and system uncertain properties, therefore, the conventional single model may be ill-suited. A local learning strategy soft sensor based on variable partition ensemble method is developed for the quality prediction of nonlinear and non-Gaussian batch processes. A set of input variable sets are obtained by bootstrapping and PMI criterion. Then, multiple local GPR models are developed based on each local input variable set. When a new test data is coming, the posterior probability of each best performance local model is estimated based on Bayesian inference and used to combine these local GPR models to get the final prediction result. The proposed soft sensor is demonstrated by applying to an industrial fed-batch chlortetracycline fermentation process.
Elsawy, Mahmoud M R
2016-01-01
Two distinct models are developed to investigate the transverse magnetic stationary solutions propagating in one-dimensional anisotropic nonlinear plasmonic structures made from a nonlinear metamaterial core of Kerr-type embedded between two semi-infinite metal claddings. The first model is semi-analytical, in which we assumed that the anisotropic nonlinearity depends only on the transverse component of the electric field and that the nonlinear refractive index modification is small compared to the linear one. This method allows us to derive analytically the field profiles and the nonlinear dispersion relations in terms of the Jacobi elliptical functions. The second model is fully numerical, it is based on the finite-element method in which all the components of the electric field are considered in the Kerr-type nonlinearity with no presumptions on the nonlinear refractive index change. Our finite-element based model is valid beyond weak nonlinearity regime and generalize the well-known single-component fixed...
Method and system for non-linear motion estimation
Lu, Ligang (Inventor)
2011-01-01
A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.
Some results of a nodal method for nonlinear space-time reactor dynamics
Energy Technology Data Exchange (ETDEWEB)
Le, T.T. (Westinghouse Savannah River Co., Aiken, SC (United States)); Grossman, L.M. (California Univ., Berkeley, CA (United States). Dept. of Nuclear Engineering)
1991-01-01
There are many reports about nodal methods for static and dynamic problems, but not many for the nonlinear feedback cases. In this paper, a class of nodal methods called mathematical nodal method'' (MNM) is studied with the temperature feedback problems. The spatially complex domain of the problem is represented as a collection of geometrically simple subdomains of the size of fuel assemblies called nodes. Over each node, the time dependent coefficients of the neutron flux, precursor concentrations, fuel and coolant temperatures are the surface and volume weighted average (moment) values of the unknown solutions; the space dependent basis functions are a combination of Legendre polynomials. If the material parameters are a linear function of fuel and coolant temperatures, the coupled equations can be put in a dimensionless form and a system of time dependent ordinary differential equations containing nonlinear feedback terms is obtained. These nonlinear feedback terms are updated at each time step during the time iteration process. Results of some benchmark problems are included in this report.
Some results of a nodal method for nonlinear space-time reactor dynamics
Energy Technology Data Exchange (ETDEWEB)
Le, T.T. [Westinghouse Savannah River Co., Aiken, SC (United States); Grossman, L.M. [California Univ., Berkeley, CA (United States). Dept. of Nuclear Engineering
1991-12-31
There are many reports about nodal methods for static and dynamic problems, but not many for the nonlinear feedback cases. In this paper, a class of nodal methods called ``mathematical nodal method`` (MNM) is studied with the temperature feedback problems. The spatially complex domain of the problem is represented as a collection of geometrically simple subdomains of the size of fuel assemblies called nodes. Over each node, the time dependent coefficients of the neutron flux, precursor concentrations, fuel and coolant temperatures are the surface and volume weighted average (moment) values of the unknown solutions; the space dependent basis functions are a combination of Legendre polynomials. If the material parameters are a linear function of fuel and coolant temperatures, the coupled equations can be put in a dimensionless form and a system of time dependent ordinary differential equations containing nonlinear feedback terms is obtained. These nonlinear feedback terms are updated at each time step during the time iteration process. Results of some benchmark problems are included in this report.
Applications of Automation Methods for Nonlinear Fracture Test Analysis
Allen, Phillip A.; Wells, Douglas N.
2013-01-01
Using automated and standardized computer tools to calculate the pertinent test result values has several advantages such as: 1. allowing high-fidelity solutions to complex nonlinear phenomena that would be impractical to express in written equation form, 2. eliminating errors associated with the interpretation and programing of analysis procedures from the text of test standards, 3. lessening the need for expertise in the areas of solid mechanics, fracture mechanics, numerical methods, and/or finite element modeling, to achieve sound results, 4. and providing one computer tool and/or one set of solutions for all users for a more "standardized" answer. In summary, this approach allows a non-expert with rudimentary training to get the best practical solution based on the latest understanding with minimum difficulty.Other existing ASTM standards that cover complicated phenomena use standard computer programs: 1. ASTM C1340/C1340M-10- Standard Practice for Estimation of Heat Gain or Loss Through Ceilings Under Attics Containing Radiant Barriers by Use of a Computer Program 2. ASTM F 2815 - Standard Practice for Chemical Permeation through Protective Clothing Materials: Testing Data Analysis by Use of a Computer Program 3. ASTM E2807 - Standard Specification for 3D Imaging Data Exchange, Version 1.0 The verification, validation, and round-robin processes required of a computer tool closely parallel the methods that are used to ensure the solution validity for equations included in test standard. The use of automated analysis tools allows the creation and practical implementation of advanced fracture mechanics test standards that capture the physics of a nonlinear fracture mechanics problem without adding undue burden or expense to the user. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.
Dynamic properties of the cubic nonlinear Schr(o)dinger equation by symplectic method
Institute of Scientific and Technical Information of China (English)
Liu Xue-Shen; Wei Jia-Yu; Ding Pei-Zhu
2005-01-01
The dynamic properties of a cubic nonlinear Schrodinger equation are investigated numerically by using the symplectic method with different space approximations. The behaviours of the cubic nonlinear Schrodinger equation are discussed with different cubic nonlinear parameters in the harmonically modulated initial condition. We show that the conserved quantities will be preserved for long-time computation but the system will exhibit different dynamic behaviours in space difference approximation for the strong cubic nonlinearity.
A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR GEOMETRICALLY NONLINEAR PROBLEMS
Institute of Scientific and Technical Information of China (English)
Xiong Yuanbo; Long Shuyao; Hu De'an; Li Guangyao
2005-01-01
Nonlinear formulations of the meshless local Petrov-Galerkin (MLPG) method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation are imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.
A Non-smooth Nonlinear Conjugate Gradient Method for Interactive Contact Force Problems
DEFF Research Database (Denmark)
Silcowitz, Morten; Niebe, Sarah Maria; Erleben, Kenny
2010-01-01
of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze...
DEFF Research Database (Denmark)
Kragh, Knud Abildgaard; Thomsen, Jon Juel; Tcherniak, Dmitri
2010-01-01
exists. The present study suggests a framework for the detection of structural nonlinearities. Two methods for detection are compared, the homogeneity method and a Hilbert transform based method. Based on these two methods, a nonlinearity index is suggested. Through simulations and laboratory experiments...
Energy Technology Data Exchange (ETDEWEB)
Zhao Xiqiang [Department of Mathematics, Ocean University of China, Qingdao Shandong 266071 (China)] e-mail: zhaodss@yahoo.com.cn; Wang Limin [Shandong University of Technology, Zibo Shandong 255049 (China); Sun Weijun [Shandong University of Technology, Zibo Shandong 255049 (China)
2006-04-01
In this letter, a new method, called the repeated homogeneous balance method, is proposed for seeking the traveling wave solutions of nonlinear partial differential equations. The Burgers-KdV equation is chosen to illustrate our method. It has been confirmed that more traveling wave solutions of nonlinear partial differential equations can be effectively obtained by using the repeated homogeneous balance method.
Sunbuloglu, Emin; Bozdag, Ergun; Toprak, Tuncer; Islak, Civan
2013-01-01
This study is aimed at setting a method of experimental parameter estimation for large-deforming nonlinear viscoelastic continuous fibre-reinforced composite material model. Specifically, arterial tissue was investigated during experimental research and parameter estimation studies, due to medical, scientific and socio-economic importance of soft tissue research. Using analytical formulations for specimens under combined inflation/extension/torsion on thick-walled cylindrical tubes, in vitro experiments were carried out with fresh sheep arterial segments, and parameter estimation procedures were carried out on experimental data. Model restrictions were pointed out using outcomes from parameter estimation. Needs for further studies that can be developed are discussed.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Some theoretical methods have been reported to deal with nonlinear problems of composite materials but the accuracy is not so good. In the meantime, a lot of nonlinear problems are difficult to be managed by the theoretical methods. The present study aims to use the developed method, the random microstructure finite element method, to deal with these nonlinear problems. In this paper, the random microstructure finite element method is used to deal with all three kinds of nonlinear property problems of composite materials. The analyzed results suggest that the influences of the nonlinear phenomena on the effective properties of composite materials are significant and the random microstructure finite element method is an efficient tool to investigate the nonlinear problems.
Cigeroglu, Ender; Samandari, Hamed
2014-11-01
Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions.
Nonlinear mode decomposition: A noise-robust, adaptive decomposition method
Iatsenko, Dmytro; McClintock, Peter V. E.; Stefanovska, Aneta
2015-09-01
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool—nonlinear mode decomposition (NMD)—which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques—which, together with the adaptive choice of their parameters, make it extremely noise robust—and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.
Nonlinear mode decomposition: a noise-robust, adaptive decomposition method.
Iatsenko, Dmytro; McClintock, Peter V E; Stefanovska, Aneta
2015-09-01
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool-nonlinear mode decomposition (NMD)-which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques-which, together with the adaptive choice of their parameters, make it extremely noise robust-and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.
Implementing Kernel Methods Incrementally by Incremental Nonlinear Projection Trick.
Kwak, Nojun
2016-05-20
Recently, the nonlinear projection trick (NPT) was introduced enabling direct computation of coordinates of samples in a reproducing kernel Hilbert space. With NPT, any machine learning algorithm can be extended to a kernel version without relying on the so called kernel trick. However, NPT is inherently difficult to be implemented incrementally because an ever increasing kernel matrix should be treated as additional training samples are introduced. In this paper, an incremental version of the NPT (INPT) is proposed based on the observation that the centerization step in NPT is unnecessary. Because the proposed INPT does not change the coordinates of the old data, the coordinates obtained by INPT can directly be used in any incremental methods to implement a kernel version of the incremental methods. The effectiveness of the INPT is shown by applying it to implement incremental versions of kernel methods such as, kernel singular value decomposition, kernel principal component analysis, and kernel discriminant analysis which are utilized for problems of kernel matrix reconstruction, letter classification, and face image retrieval, respectively.
Application of nonlinear methods to the study of ionospheric plasma
Chernyshov, A. A.; Mogilevsky, M. M.; Kozelov, B. V.
2015-01-01
Most of the processes taking place in the auroral region of Earth's ionosphere are reflected in a variety of dynamic forms of the aurora borealis. In order to study these processes it is necessary to consider temporary and spatial variations of the characteristics of ionospheric plasma. Most traditional methods of classical physics are applicable mainly for stationary or quasi-stationary phenomena, but dynamic regimes, transients, fluctuations, selfsimilar scaling could be considered using the methods of nonlinear dynamics. Special interest is the development of the methods for describing the spatial structure and the temporal dynamics of auroral ionosphere based on the ideas of percolation theory and fractal geometry. The fractal characteristics (the Hausdorff fractal dimension and the index of connectivity) of Hall and Pedersen conductivities are used to the description of fractal patterns in the ionosphere. To obtain the self-consistent estimates of the parameters the Hausdorff fractal dimension and the index of connectivity in the auroral zone, an additional relation describing universal behavior of the fractal geometry of percolation at the critical threshold is applied. Also, it is shown that Tsallis statistics can be used to study auroral ionosphere
Institute of Scientific and Technical Information of China (English)
罗振东; 朱江; 王会军
2002-01-01
A nonlinear Galerkin/ Petrov- least squares mixed element (NGPLSME) method for the stationary Navier-Stokes equations is presented and analyzed. The scheme is that Petrov-least squares forms of residuals are added to the nonlinear Galerkin mixed element method so that it is stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. The existence, uniqueness and convergence ( at optimal rate ) of the NGPLSME solution is proved in the case of sufficient viscosity ( or small data).
DEFF Research Database (Denmark)
Lee, Kyo Beum; Blaabjerg, Frede
2007-01-01
-current distortion due to the nonlinearity of the matrix converter, an overmodulation strategy and a simple nonlinearity-compensation method using $PQR$ transformation are also presented. Experimental results are shown to illustrate the feasibility of the proposed strategy....... frequency and fast torque dynamics. It is possible to combine the advantages of matrix converters with the advantages of the DTC strategy using space-vector modulation and two PI controllers. To overcome the degrading of dynamic torque response compared with the basic DTC method and the phase...
Analysis of Nonlinear Vibration of Hard Coating Thin Plate by Finite Element Iteration Method
Directory of Open Access Journals (Sweden)
Hui Li
2014-01-01
Full Text Available This paper studies nonlinear vibration mechanism of hard coating thin plate based on macroscopic vibration theory and proposes finite element iteration method (FEIM to theoretically calculate its nature frequency and vibration response. First of all, strain dependent mechanical property of hard coating is briefly introduced and polynomial method is adopted to characterize the storage and loss modulus of coating material. Then, the principle formulas of inherent and dynamic response characteristics of the hard coating composite plate are derived. And consequently specific analysis procedure is proposed by combining ANSYS APDL and self-designed MATLAB program. Finally, a composite plate coated with MgO + Al2O3 is taken as a study object and both nonlinear vibration test and analysis are conducted on the plate specimen with considering strain dependent mechanical parameters of hard coating. Through comparing the resulting frequency and response results, the practicability and reliability of FEIM have been verified and the corresponding analysis results can provide an important reference for further study on nonlinear vibration mechanism of hard coating composite structure.
Nonlinear Analysis Methods for Evaluating Seismic Performance of Multi-Story RC Buildings
Tayyebi, Saeid Moussavi
2014-01-01
ABSTRACT: A major challenge in performance-based earthquake engineering is to develop simple and practical methods for estimating capacity level and seismic demand on structures by taking into account their inelastic behavior. Researchers and engineers certainly prefer to use nonlinear static methods over complicated nonlinear time-history methods. However, in Nonlinear Static procedure both predetermined target displacement and force distribution pattern are based on a false assumption that ...
Directory of Open Access Journals (Sweden)
Elsayed Mohamed Elsayed ZAYED
2014-07-01
Full Text Available In this article, many new exact solutions of the (2+1-dimensional nonlinear Boussinesq-Kadomtsev-Petviashvili equation and the (1+1-dimensional nonlinear heat conduction equation are constructed using the Riccati equation mapping method. By means of this method, many new exact solutions are successfully obtained. This method can be applied to many other nonlinear evolution equations in mathematical physics.doi:10.14456/WJST.2014.14
Analysis and Design Methods for Nonlinear Control Systems
1990-03-01
entitled "Design of Nonlinear PID Controllers ." In this paper it is demonstrated that the extended linearization approach can be applied to standard...Sciences and Systems, Baltimore, Maryland, pp. 675-680, 1987. [3] WJ. Rugh, "Design of Nonlinear PID Controllers ," AIChE Journa Vol. 33, No. 10, pp. 1738
Hu, Juju; Hu, Haijiang; Ji, Yinghua
2010-03-15
Periodic nonlinearity that ranges from tens of nanometers to a few nanometers in heterodyne interferometer limits its use in high accuracy measurement. A novel method is studied to detect the nonlinearity errors based on the electrical subdivision and the analysis method of statistical signal in heterodyne Michelson interferometer. Under the movement of micropositioning platform with the uniform velocity, the method can detect the nonlinearity errors by using the regression analysis and Jackknife estimation. Based on the analysis of the simulations, the method can estimate the influence of nonlinearity errors and other noises for the dimensions measurement in heterodyne Michelson interferometer.
Modified extended tanh-function method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Department of Physics, Faculty of Science, Theoretical Research Group, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Department of Physics, Faculty of Science, Theoretical Research Group, Mansoura University, 35516 Mansoura (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-03-15
Based on computerized symbolic computation, modified extended tanh-method for constructing multiple travelling wave solutions of nonlinear evolution equations is presented and implemented in a computer algebraic system. Applying this method, with the aid of Maple, we consider some nonlinear evolution equations in mathematical physics such as the nonlinear partial differential equation, nonlinear Fisher-type equation, ZK-BBM equation, generalized Burgers-Fisher equation and Drinfeld-Sokolov system. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods.
Directory of Open Access Journals (Sweden)
Woo-Young Jung
2013-01-01
Full Text Available An improved 8-node shell finite element applicable for the geometrically linear and nonlinear analyses of plates and shells is presented. Based on previous first-order shear deformation theory, the finite element model is further improved by the combined use of assumed natural strains and different sets of collocation points for the interpolation of the different strain components. The influence of the shell element with various conditions such as locations, number of enhanced membranes, and shear interpolation is also identified. By using assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. Furthermore, to characterize the efficiency of these modifications of the 8-node shell finite elements, numerical studies are carried out for the geometrically linear and non-linear analysis of plates and shells. In comparison to some other shell elements, numerical examples for the methodology indicate that the modified element described locking-free behavior and better performance. More specifically, the numerical examples of annular plate presented herein show good validity, efficiency, and accuracy to the developed nonlinear shell element.
Simplified Methods Applied to Nonlinear Motion of Spar Platforms
Energy Technology Data Exchange (ETDEWEB)
Haslum, Herbjoern Alf
2000-07-01
Simplified methods for prediction of motion response of spar platforms are presented. The methods are based on first and second order potential theory. Nonlinear drag loads and the effect of the pumping motion in a moon-pool are also considered. Large amplitude pitch motions coupled to extreme amplitude heave motions may arise when spar platforms are exposed to long period swell. The phenomenon is investigated theoretically and explained as a Mathieu instability. It is caused by nonlinear coupling effects between heave, surge, and pitch. It is shown that for a critical wave period, the envelope of the heave motion makes the pitch motion unstable. For the same wave period, a higher order pitch/heave coupling excites resonant heave response. This mutual interaction largely amplifies both the pitch and the heave response. As a result, the pitch/heave instability revealed in this work is more critical than the previously well known Mathieu's instability in pitch which occurs if the wave period (or the natural heave period) is half the natural pitch period. The Mathieu instability is demonstrated both by numerical simulations with a newly developed calculation tool and in model experiments. In order to learn more about the conditions for this instability to occur and also how it may be controlled, different damping configurations (heave damping disks and pitch/surge damping fins) are evaluated both in model experiments and by numerical simulations. With increased drag damping, larger wave amplitudes and more time are needed to trigger the instability. The pitch/heave instability is a low probability of occurrence phenomenon. Extreme wave periods are needed for the instability to be triggered, about 20 seconds for a typical 200m draft spar. However, it may be important to consider the phenomenon in design since the pitch/heave instability is very critical. It is also seen that when classical spar platforms (constant cylindrical cross section and about 200m draft
Application of homotopy-perturbation method to nonlinear population dynamics models
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, M.S.H. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia); Hashim, I. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)], E-mail: ishak_h@ukm.my; Abdulaziz, O. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)
2007-08-20
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)
Nonlinear PET parametric image reconstruction with MRI information using kernel method
Gong, Kuang; Wang, Guobao; Chen, Kevin T.; Catana, Ciprian; Qi, Jinyi
2017-03-01
Positron Emission Tomography (PET) is a functional imaging modality widely used in oncology, cardiology, and neurology. It is highly sensitive, but suffers from relatively poor spatial resolution, as compared with anatomical imaging modalities, such as magnetic resonance imaging (MRI). With the recent development of combined PET/MR systems, we can improve the PET image quality by incorporating MR information. Previously we have used kernel learning to embed MR information in static PET reconstruction and direct Patlak reconstruction. Here we extend this method to direct reconstruction of nonlinear parameters in a compartment model by using the alternating direction of multiplier method (ADMM) algorithm. Simulation studies show that the proposed method can produce superior parametric images compared with existing methods.
A numerical dressing method for the nonlinear superposition of solutions of the KdV equation
Trogdon, Thomas; Deconinck, Bernard
2014-01-01
In this paper we present the unification of two existing numerical methods for the construction of solutions of the Korteweg-de Vries (KdV) equation. The first method is used to solve the Cauchy initial-value problem on the line for rapidly decaying initial data. The second method is used to compute finite-genus solutions of the KdV equation. The combination of these numerical methods allows for the computation of exact solutions that are asymptotically (quasi-)periodic finite-gap solutions and are a nonlinear superposition of dispersive, soliton and (quasi-)periodic solutions in the finite (x, t)-plane. Such solutions are referred to as superposition solutions. We compute these solutions accurately for all values of x and t.
On the combination of nonlinear contracting observers and UGES controllers for output feedback
DEFF Research Database (Denmark)
Jouffroy, Jerome; Fossen, Thor I.
The paper presents a systematic method for design of observer-controllers in cascade. Uniform global exponential stability (UGES) of the resulting system is proven by assuming that the feedback control system is UGES and that the nonlinear observer can be designed using contracting analysis....... The relationship between a globally contracting and UGES observer is derived using Lyapunov analysis and a line integral which follows from Taylor's theorem....
Nonlinear Circuit Analysis via Perturbation Methods and Hardware Prototyping
Directory of Open Access Journals (Sweden)
K. Odame
2010-01-01
Full Text Available Nonlinear signal processing is necessary in many emerging applications where form factor and power are at a premium. In order to make such complex computation feasible under these constraints, it is necessary to implement the signal processors as analog circuits. Since analog circuit design is largely based on a linear systems perspective, new tools are being introduced to circuit designers that allow them to understand and exploit circuit nonlinearity for useful processing. This paper discusses two such tools, which represent nonlinear circuit behavior in a graphical way, making it easy to develop a qualitative appreciation for the circuits under study.
Elsawy, Mahmoud M. R.; Renversez, Gilles
2017-07-01
Two distinct models are developed to investigate the transverse magnetic stationary solutions propagating in one-dimensional anisotropic nonlinear plasmonic structures made from a Kerr-type nonlinear metamaterial core embedded between two semi-infinite metal claddings. The first model is semi-analytical, in which we assume that the anisotropic nonlinearity depends only on the transverse component of the electric field and that the nonlinear refractive index modification is small compared to the linear one. This method allows us to derive analytically the field profiles and nonlinear dispersion relations in terms of the Jacobi elliptical functions. The second model is fully numerical and is based on the finite element method in which all the components of the electric field are considered in the Kerr-type nonlinearity, with no presumptions as to the nonlinear refractive index change. Our finite-element-based model is valid beyond the weak nonlinearity regime and generalizes the well-known single-component fixed power algorithm that is usually used. Examples of the main cases are investigated, including those with strong spatial nonlinear effects at low power. Loss issues are reduced through the use of a gain medium in the nonlinear metamaterial core. Using anisotropic nonlinear FDTD simulations, we provide some results for the properties of the main solution.
Combined method for parallel manipulator configuration design
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Configuration design is an essential, creative and decision-making step in parallel manipulator design process, in which modeling and assembly are iterative and trivial. Combined approach with automatic parametric modeling and automatic assembly is proposed for parallel manipulator configuration design. The design process and key techniques, such as configuration design, configuration verification, poses calculation of all parts in parallel manipulator, virtual assembly and etc., are discussed and demonstrated by an example. A software package is developed for parallel manipulator configuration design based on the proposed method with Visual C+ + and UG/OPEN on Unigraphics.
Geometric methods for nonlinear many-body quantum systems
Lewin, Mathieu
2010-01-01
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr\\"odinger operators. In this paper we provide a formalism which also allows to study nonlinear systems. We start by defining a weak topology on many-body states, which appropriately describes the physical behavior of the system in the case of lack of compactness, that is when some particles are lost at infinity. We provide several important properties of this topology and use them to provide a simple proof of the famous HVZ theorem in the repulsive case. In a second step we recall the method of geometric localization in Fock space as proposed by Derezi\\'nski and G\\'erard, and we relate this tool to our weak topology. We then provide several applications. We start by studying the so-called finite-rank approximation which consists in imposing that the many-body wavefunction can be expanded using finitely many one-body functions. We thereby emphasize geometric properties of Hartree-Fock states and ...
STABILITY ANALYSIS OF RUNGE-KUTTA METHODS FOR NONLINEAR SYSTEMS OF PANTOGRAPH EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yue-xin Yu; Shou-fu Li
2005-01-01
This paper is concerned with numerical stability of nonlinear systems of pantograph equations. Numerical methods based on (k, l)-algebraically stable Runge-Kutta methods are suggested. Global and asymptotic stability conditions for the presented methods are derived.
LOCAL DISCONTINUOUS GALERKIN METHODS FOR THREE CLASSES OF NONLINEAR WAVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yan Xu; Chi-wang Shu
2004-01-01
In this paper, we further develop the local discontinuous Galerkin method to solve three classes of nonlinear wave equations formulated by the general KdV-Burgers type equations, the general fifth-order KdV type equations and the fully nonlinear K(n, n, n)equations, and prove their stability for these general classes of nonlinear equations. The schemes we present extend the previous work of Yan and Shu [30, 31] and of Levy, Shu and Yan [24] on local discontinuous Galerkin method solving partial differential equations with higher spatial derivatives. Numerical examples for nonlinear problems are shown to illustrate the accuracy and capability of the methods. The numerical experiments include stationary solitons, soliton interactions and oscillatory solitary wave solutions.The numerical experiments also include the compacton solutions of a generalized fifthorder KdV equation in which the highest order derivative term is nonlinear and the fully nonlinear K(n, n, n) equations.
Two-dimensional nonlinear geophysical data filtering using the multidimensional EEMD method
Chen, Chih-Sung; Jeng, Yih
2014-12-01
A variety of two-dimensional (2D) empirical mode decomposition (EMD) methods have been proposed in the last decade. Furthermore, the multidimensional EMD algorithm and its parallel class, multivariate EMD (MEMD), are available in recent years. From those achievements, it is possible to design an efficient 2D nonlinear filter for geophysical data processing. We introduce a robust 2D nonlinear filter which can be applied to enhance the signal of 2D geophysical data or to highlight the feature component on an image. We did this by replacing the conventionally used smooth interpolation in the ensemble empirical mode decomposition (EEMD) algorithm with a piecewise interpolation method. The one-dimensional (1D) EEMD procedures were consecutively performed in all directions, and then the comparable minimal scale combination technique was applied to the decomposed components. The theoretical derivation, model simulation, and real data applications are demonstrated in this paper. The proposed filtering method is effective in improving the image resolution by suppressing the random noise added in the simulation example and strong low frequency track corrugation noise bands with background noise in the field example. Furthermore, the algorithm can be easily extended to higher dimensions by repeating the same procedure in the succeeding dimension. To evaluate the proposed method, one data set is processed separately by using the enhanced analytic signal method and the multivariate EMD (MEMD) algorithm, and the results from these two methods are compared with that of the proposed method. A general equation for generating three-dimensional (3D) EEMD components based on the comparable minimal scale combination principle is derived for further applications.
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.
A Novel Method for Nonlinear Time Series Forecasting of Time-Delay Neural Network
Institute of Scientific and Technical Information of China (English)
JIANG Weijin; XU Yuhui
2006-01-01
Based on the idea of nonlinear prediction of phase space reconstruction, this paper presented a time delay BP neural network model, whose generalization capability was improved by Bayesian regularization.Furthermore, the model is applied to forecast the import and export trades in one industry.The results showed that the improved model has excellent generalization capabilities, which not only learned the historical curve, but efficiently predicted the trend of business.Comparing with common evaluation of forecasts, we put on a conclusion that nonlinear forecast can not only focus on data combination and precision improvement, it also can vividly reflect the nonlinear characteristic of the forecasting system.While analyzing the forecasting precision of the model, we give a model judgment by calculating the nonlinear characteristic value of the combined serial and original serial, proved that the forecasting model can reasonably catch' the dynamic characteristic of the nonlinear system which produced the origin serial.
Nonlinear generalized source method for modeling second-harmonic generation in diffraction gratings
Weismann, Martin; Panoiu, Nicolae C
2015-01-01
We introduce a versatile numerical method for modeling light diffraction in periodically patterned photonic structures containing quadratically nonlinear non-centrosymmetric optical materials. Our approach extends the generalized source method to nonlinear optical interactions by incorporating the contribution of nonlinear polarization sources to the diffracted field in the algorithm. We derive the mathematical formalism underlying the numerical method and introduce the Fourier-factorization suitable for nonlinear calculations. The numerical efficiency and runtime characteristics of the method are investigated in a set of benchmark calculations: the results corresponding to the fundamental frequency are compared to those obtained from a reference method and the beneficial effects of the modified Fourier-factorization rule on the accuracy of the nonlinear computations is demonstrated. In order to illustrate the capabilities of our method, we employ it to demonstrate strong enhancement of second-harmonic genera...
Derivation of second-order nonlinear optical conductivity by the projection-diagram method
Directory of Open Access Journals (Sweden)
Nam Lyong Kang
2012-03-01
Full Text Available A projection-diagram method is introduced for optical conductivity with lineshape functions, which takes into account the population criterion that the electron and phonon distribution functions are multiplicatively combined along with the energy conservation factors for proper interpretation of emission and absorption of phonons and photons in all the processes of electron transitions. It is further shown that the second order nonlinear optical conductivity of the system of electrons interacting with phonons, obtained using this method, is identical with that derived by using the state dependent projectors and the KC reduction identities [J. Phys. A: Math. Theor. 43, 165203 (2010]. We expect that this method can reduce the amount of many-body calculation and can be of help in providing physical intuition into solid state quantum dynamics and representing perturbation expressions for such systems.
Directory of Open Access Journals (Sweden)
Md. Nur Alam
2016-06-01
Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.
Institute of Scientific and Technical Information of China (English)
Long Shuyao; Zhang Qin
2000-01-01
In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation 2 u + u + εu3 = b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual reciprocity method(DRM) in solving nonlinear dif ferential equations.
A new method to solve the damped nonlinear Klein-Gordon equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper discusses a damped nonlinear Klein-Gordon equation in the reproducing kernel space and provides a new method for solving the damped nonlinear Klein-Gordon equation based on the reproducing kernel space.Two numerical examples are given for illustrating the feasibility and accuracy of the method.
A stabilised nodal spectral element method for fully nonlinear water waves
Engsig-Karup, A. P.; Eskilsson, C.; Bigoni, D.
2016-08-01
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively removes any aliasing driven instabilities while retaining the high-order accuracy of the numerical scheme. The additional computational cost of the over-integration is found insignificant compared to the cost of solving the Laplace problem. The model is applied to several benchmark cases in two dimensions. The results confirm the high order accuracy of the model (exponential convergence), and demonstrate the potential for accuracy and speedup. The results of numerical experiments are in excellent agreement with both analytical and experimental results for strongly nonlinear and irregular dispersive wave propagation. The benefit of using a high-order - possibly adapted - spatial discretisation for accurate water wave propagation over long times and distances is particularly attractive for marine hydrodynamics applications.
Image Encryption Using Stream Cipher Based on Nonlinear Combination Generator with Enhanced Security
Directory of Open Access Journals (Sweden)
Belmeguenaï Aîssa
2013-03-01
Full Text Available The images are very largely used in our daily life; the security of their transfer became necessary. In this work a novel image encryption scheme using stream cipher algorithm based on nonlinear combination generator is developed. The main contribution of this work is to enhance the security of encrypted image. The proposed scheme is based on the use the several linear feedback shifts registers whose feedback polynomials are primitive and of degrees are all pairwise coprimes combined by resilient function whose resiliency order, algebraic degree and nonlinearity attain Siegenthaler’s and Sarkar, al.’s bounds. This proposed scheme is simple and highly efficient. In order to evaluate performance, the proposed algorithm was measured through a series of tests. These tests included visual test and histogram analysis, key space analysis, correlation coefficient analysis, image entropy, key sensitivity analysis, noise analysis, Berlekamp-Massey attack, correlation attack and algebraic attack. Experimental results demonstrate the proposed system is highly key sensitive, highly resistance to the noises and shows a good resistance against brute-force, statistical attacks, Berlekamp-Massey attack, correlation attack, algebraic attack and a robust system which makes it a potential candidate for encryption of image.
Energy Technology Data Exchange (ETDEWEB)
Wang, Shi-bing, E-mail: wang-shibing@dlut.edu.cn, E-mail: wangxy@dlut.edu.cn [School of Computer and Information Engineering, Fuyang Normal University, Fuyang 236041 (China); Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024 (China); Wang, Xing-yuan, E-mail: wang-shibing@dlut.edu.cn, E-mail: wangxy@dlut.edu.cn [Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024 (China); Wang, Xiu-you [School of Computer and Information Engineering, Fuyang Normal University, Fuyang 236041 (China); Zhou, Yu-fei [College of Electrical Engineering and Automation, Anhui University, Hefei 230601 (China)
2016-04-15
With comprehensive consideration of generalized synchronization, combination synchronization and adaptive control, this paper investigates a novel adaptive generalized combination complex synchronization (AGCCS) scheme for different real and complex nonlinear systems with unknown parameters. On the basis of Lyapunov stability theory and adaptive control, an AGCCS controller and parameter update laws are derived to achieve synchronization and parameter identification of two real drive systems and a complex response system, as well as two complex drive systems and a real response system. Two simulation examples, namely, ACGCS for chaotic real Lorenz and Chen systems driving a hyperchaotic complex Lü system, and hyperchaotic complex Lorenz and Chen systems driving a real chaotic Lü system, are presented to verify the feasibility and effectiveness of the proposed scheme.
A SIMPLIFIED CALCULATING METHOD OF NONLINEAR FREQUENCY OF CABLE NET UNDER MEAN WIND LOAD
Institute of Scientific and Technical Information of China (English)
Feng Ruoqiang; Wu Yue; Shen Shizhao
2006-01-01
The cable net supported glass curtain wallas the most advanced technique in dot point supported glass curtain wall, is widely used in China. Because of its large deflection and high nonlinearity under wind load, the dynamic performance of the cable net is greatly different from that of the conventional linear structures. The continuous membrane theory is used to construct the nonlinear vibration differential equation of the cable net, and the harmonic balance method is used to solve the analytic formula of the nonlinear frequency. In order to verify the accuracy of the above analytic formula, the results of the formula and the nonlinear FEM time-history method are compared and found to be in good agreement. Furthermore, the nonlinear vibration differential equation and the nonlinear frequency obtained in this paper are the basis for the wind-induced response analysis of a cable net under fluctuating wind load.
Expert judgement combination using moment methods
Energy Technology Data Exchange (ETDEWEB)
Wisse, Bram [Department of Management Science, University of Strathclyde, Glasgow, Scotland (United Kingdom); TNO Defence, Security and Safety, The Hague (Netherlands)], E-mail: bram.wisse@strath.ac.uk; Bedford, Tim [Department of Management Science, University of Strathclyde, Glasgow, Scotland (United Kingdom)], E-mail: tim.bedford@strath.ac.uk; Quigley, John [Department of Management Science, University of Strathclyde, Glasgow, Scotland (United Kingdom)], E-mail: j.quigley@strath.ac.uk
2008-05-15
Moment methods have been employed in decision analysis, partly to avoid the computational burden that decision models involving continuous probability distributions can suffer from. In the Bayes linear (BL) methodology prior judgements about uncertain quantities are specified using expectation (rather than probability) as the fundamental notion. BL provides a strong foundation for moment methods, rooted in work of De Finetti and Goldstein. The main objective of this paper is to discuss in what way expert assessments of moments can be combined, in a non-Bayesian way, to construct a prior assessment. We show that the linear pool can be justified in an analogous but technically different way to linear pools for probability assessments, and that this linear pool has a very convenient property: a linear pool of experts' assessments of moments is coherent if each of the experts has given coherent assessments. To determine the weights of the linear pool we give a method of performance based weighting analogous to Cooke's classical model and explore its properties. Finally, we compare its performance with the classical model on data gathered in applications of the classical model.
Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem
Terekhov, Kirill M.; Mallison, Bradley T.; Tchelepi, Hamdi A.
2017-02-01
We present two new cell-centered nonlinear finite-volume methods for the heterogeneous, anisotropic diffusion problem. The schemes split the interfacial flux into harmonic and transversal components. Specifically, linear combinations of the transversal vector and the co-normal are used that lead to significant improvements in terms of the mesh-locking effects. The harmonic component of the flux is represented using a conventional monotone two-point flux approximation; the component along the parameterized direction is treated nonlinearly to satisfy either positivity of the solution as in [29], or the discrete maximum principle as in [9]. In order to make the method purely cell-centered, we derive a homogenization function that allows for seamless interpolation in the presence of heterogeneity following a strategy similar to [46]. The performance of the new schemes is compared with existing multi-point flux approximation methods [3,5]. The robustness of the scheme with respect to the mesh-locking problem is demonstrated using several challenging test cases.
Peng, Haijun; Wang, Xinwei; Zhang, Sheng; Chen, Biaosong
2017-07-01
Nonlinear state-delayed optimal control problems have complex nonlinear characters. To solve this complex nonlinear problem, an iterative symplectic pseudospectral method based on quasilinearization techniques, the dual variational principle and pseudospectral methods is proposed in this paper. First, the proposed method transforms the original nonlinear optimal control problem into a series of linear quadratic optimal control problems. Then, a symplectic pseudospectral method is developed to solve these converted linear quadratic state-delayed optimal control problems. Coefficient matrices in the proposed method are sparse and symmetric since the dual variational principle is used, which makes the proposed method highly efficient. Converged numerical solutions with high precision can be obtained after a few iterations due to the benefit of the local pseudospectral method and quasilinearization techniques. In the numerical simulations, other numerical methods were used for comparisons. The numerical simulation results show that the proposed method is highly accurate, efficient and robust.
Directory of Open Access Journals (Sweden)
Süleyman Öğrekçi
2015-01-01
Full Text Available We propose an efficient analytic method for solving nonlinear differential equations of fractional order. The fractional derivative is defined in the sense of modified Riemann-Liouville derivative. A new technique for calculating the generalized Taylor series coefficients (also known as “generalized differential transforms,” GDTs of nonlinear functions and a new approach of the generalized Taylor series method (GTSM are presented. This new method offers a simple algorithm for computing GDTs of nonlinear functions and avoids massive computational work that usually arises in the standard method. Several illustrative examples are demonstrated to show effectiveness of the proposed method.
A new method based on the harmonic balance method for nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Chen, Y.M. [Department of Mechanics, Zhongshan University, Guangzhou 510275 (China); Liu, J.K. [Department of Mechanics, Zhongshan University, Guangzhou 510275 (China)], E-mail: jikeliu@hotmail.com
2007-08-27
The harmonic balance (HB) method as an analytical approach is widely used for nonlinear oscillators, in which the initial conditions are generally simplified by setting velocity or displacement to be zero. Based on HB, we establish a new theory to address nonlinear conservative systems with arbitrary initial conditions, and deduce a set of over-determined algebraic equations. Since these deduced algebraic equations are not solved directly, a minimization problem is constructed instead and an iterative algorithm is employed to seek the minimization point. Taking Duffing and Duffing-harmonic equations as numerical examples, we find that these attained solutions are not only with high degree of accuracy, but also uniformly valid in the whole solution domain.
A Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem
Directory of Open Access Journals (Sweden)
Meixia Li
2012-01-01
Full Text Available Based on the smoothing function of penalized Fischer-Burmeister NCP-function, we propose a new smoothing inexact Newton algorithm with non-monotone line search for solving the generalized nonlinear complementarity problem. We view the smoothing parameter as an independent variable. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. We also establish the local superlinear (quadratic convergence of the proposed algorithm under the BD-regular assumption. Preliminary numerical experiments indicate the feasibility and efficiency of the proposed algorithm.
A novel method for extracting acoustic nonlinearity parameters with diffraction corrections
Energy Technology Data Exchange (ETDEWEB)
Jeong, Hyunjo [Wonkwang University, Iksan (Korea, Republic of); Zhang, Shuzeng; Li, Xiongbing [Central South University, Changsha (China)
2016-02-15
A new method for determining the acoustic nonlinearity parameter using a nonlinear data fitting method is proposed. Based on the quasilinear theory of Westervelt's equation, the fundamental and second harmonic beam fields are expressed as a multi-Gaussian beam model that separates the attenuation and diffraction correction terms from the propagating plane waves. A nonlinear least squares curve fitting method is developed to extract the nonlinearity parameter without knowing the attenuation coefficients of the material being tested. The nonlinearity parameter of water is determined using the proposed method, and the result agrees well with the literature value. The attenuation coefficients of the fundamental and the second harmonic are also extracted and discussed.
Enokida, Ryuta; Takewaki, Izuru; Stoten, David
2014-12-01
The problem of control system design can be conceptualised as identifying an input signal to a plant (the system to be controlled) so that the corresponding output matches that of a pre-defined reference signal. Primarily, this problem is solved via well-known techniques based upon the principle of feedback design, an essential component for ensuring stability and robustness of the controlled system. However, feedforward design techniques also have a large part to play, whereby (in the absence of feedback control and assuming that the plant is stable) a model of the plant dynamics can be used to modify the reference signal so that the resultant feedforward input signal generates a plant output signal that is sufficiently close to the original reference signal. The principal objective of this paper is to introduce a new nonlinear control method, called nonlinear signal-based control (NSBC) that can be executed as an on-line technique of feedforward compensation (used synonymously here with the phrase 'input identification') and an off-line technique of feedback compensation. NSBC determines the feedforward input signal to the plant by using an error signal, determined from the difference between the output signals from a linear model of the plant and from the nonlinear plant, under the same input signal. The efficacy of NSBC is examined via numerical examples using Matlab/Simulink and compared with alternative well-known methods based upon inverse transfer function compensation and also the method of high gain feedback control. NSBC was found to provide the most accurate input identification in all the examined cases of linear or nonlinear single-input, single-output and single-input, multi-output (SIMO) systems. Furthermore, in problems of structural and earthquake engineering, NSBC was also found to be particularly effective in estimating the original ground motion from a nonlinear SIMO system and its response.
Institute of Scientific and Technical Information of China (English)
ZHANG Juliang; ZHANG Xiangsun
2001-01-01
In this paper, we use the smoothing penalty function proposed in [1] as the merit function of SQP method for nonlinear optimization with inequality constraints. The global convergence of the method is obtained.
A Direct Algebraic Method in Finding Particular Solutions to Some Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
LIUChun-Ping; CHENJian-Kang; CAIFan
2004-01-01
Firstly, a direct algebraic method and a routine way in finding traveling wave solutions to nonlinear evolution equations are explained. And then some new exact solutions for some evolution equations are obtained by using the method.
Nonlinear dimensionality reduction methods for synthetic biology biobricks' visualization.
Yang, Jiaoyun; Wang, Haipeng; Ding, Huitong; An, Ning; Alterovitz, Gil
2017-01-19
Visualizing data by dimensionality reduction is an important strategy in Bioinformatics, which could help to discover hidden data properties and detect data quality issues, e.g. data noise, inappropriately labeled data, etc. As crowdsourcing-based synthetic biology databases face similar data quality issues, we propose to visualize biobricks to tackle them. However, existing dimensionality reduction methods could not be directly applied on biobricks datasets. Hereby, we use normalized edit distance to enhance dimensionality reduction methods, including Isomap and Laplacian Eigenmaps. By extracting biobricks from synthetic biology database Registry of Standard Biological Parts, six combinations of various types of biobricks are tested. The visualization graphs illustrate discriminated biobricks and inappropriately labeled biobricks. Clustering algorithm K-means is adopted to quantify the reduction results. The average clustering accuracy for Isomap and Laplacian Eigenmaps are 0.857 and 0.844, respectively. Besides, Laplacian Eigenmaps is 5 times faster than Isomap, and its visualization graph is more concentrated to discriminate biobricks. By combining normalized edit distance with Isomap and Laplacian Eigenmaps, synthetic biology biobircks are successfully visualized in two dimensional space. Various types of biobricks could be discriminated and inappropriately labeled biobricks could be determined, which could help to assess crowdsourcing-based synthetic biology databases' quality, and make biobricks selection.
DEFF Research Database (Denmark)
Ibsen, Lars Bo; Barari, Amin; Kimiaeifar, Amin
2010-01-01
/approximate analytical solution to strong nonlinear oscillators. Furthermore, it is shown that a large class of linear or nonlinear differential equations can be solved without the tangible restriction of sensitivity to the degree of the nonlinear term, adding that the method is quite convenient due to reduction in size...
Bias-field controlled phasing and power combination of gyromagnetic nonlinear transmission lines.
Reale, D V; Bragg, J-W B; Gonsalves, N R; Johnson, J M; Neuber, A A; Dickens, J C; Mankowski, J J
2014-05-01
Gyromagnetic Nonlinear Transmission Lines (NLTLs) generate microwaves through the damped gyromagnetic precession of the magnetic moments in ferrimagnetic material, and are thus utilized as compact, solid-state, frequency agile, high power microwave (HPM) sources. The output frequency of a NLTL can be adjusted by control of the externally applied bias field and incident voltage pulse without physical alteration to the structure of the device. This property provides a frequency tuning capability not seen in many conventional e-beam based HPM sources. The NLTLs developed and tested are mesoband sources capable of generating MW power levels in the L, S, and C bands of the microwave spectrum. For an individual NLTL the output power at a given frequency is determined by several factors including the intrinsic properties of the ferrimagnetic material and the transmission line structure. Hence, if higher power levels are to be achieved, it is necessary to combine the outputs of multiple NLTLs. This can be accomplished in free space using antennas or in a transmission line via a power combiner. Using a bias-field controlled delay, a transient, high voltage, coaxial, three port, power combiner was designed and tested. Experimental results are compared with the results of a transient COMSOL simulation to evaluate combiner performance.
Prediction of peptide bonding affinity: kernel methods for nonlinear modeling
Bergeron, Charles; Sundling, C Matthew; Krein, Michael; Katt, Bill; Sukumar, Nagamani; Breneman, Curt M; Bennett, Kristin P
2011-01-01
This paper presents regression models obtained from a process of blind prediction of peptide binding affinity from provided descriptors for several distinct datasets as part of the 2006 Comparative Evaluation of Prediction Algorithms (COEPRA) contest. This paper finds that kernel partial least squares, a nonlinear partial least squares (PLS) algorithm, outperforms PLS, and that the incorporation of transferable atom equivalent features improves predictive capability.
Comparison of alternative improved perturbative methods for nonlinear oscillations
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico)]. E-mail: paolo@ucol.mx; Raya, Alfredo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Diag. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2005-06-06
We discuss and compare two alternative perturbation approaches for the calculation of the period of nonlinear systems based on the Lindstedt-Poincare technique. As illustrative examples we choose one-dimensional anharmonic oscillators and the Van der Pol equation. Our results show that each approach is better for just one type of model considered here.
Quantifying Poincare’s Continuation Method for Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Daniel Núñez
2015-01-01
Full Text Available In the sixties, Loud obtained interesting results of continuation on periodic solutions in driven nonlinear oscillators with small parameter (Loud, 1964. In this paper Loud’s results are extended out for periodically driven Duffing equations with odd symmetry quantifying the continuation parameter for a periodic odd solution which is elliptic and emanates from the equilibrium of the nonperturbed problem.
A Novel Method for Prediction of Nonlinear Aeroelastic Responses
2010-01-01
Brian A. Freno Graduate Student, Texas A&M University Publications Journal articles: 1. Gargoloff, J. I. and Cizmas, P. G. A., “Mesh Generation and...papers: 1. Cizmas, P. G. A., Freno , B. A., Brenner, T. A., Worley, G. D., “A High-Fidelity Nonlinear Aeroelastic Model for Aircraft with Large Wing
Applied Nonlinear Dynamics Analytical, Computational, and Experimental Methods
Nayfeh, Ali H
1995-01-01
A unified and coherent treatment of analytical, computational and experimental techniques of nonlinear dynamics with numerous illustrative applications. Features a discourse on geometric concepts such as Poincaré maps. Discusses chaos, stability and bifurcation analysis for systems of differential and algebraic equations. Includes scores of examples to facilitate understanding.
DEFF Research Database (Denmark)
Rasmussen, Christian Jørgen
2001-01-01
Presents a simple and fast method for determination of the step size that exactly leads to a prescribed accuracy when signal propagation through nonlinear optical fibres is computed using the split-step Fourier method.......Presents a simple and fast method for determination of the step size that exactly leads to a prescribed accuracy when signal propagation through nonlinear optical fibres is computed using the split-step Fourier method....
A SELF-ADAPTIVE TECHNIQUE FOR A KIND OF NONLINEAR CONJUGATE GRADIENT METHODS
Institute of Scientific and Technical Information of China (English)
王丽平
2004-01-01
Conjugate gradient methods. are a class of important methods for unconstrained optimization, especially when the dimension is large. In 2001, Dai and Liao have proposed a new conjugate condition, based on it two nonlinear conjugate gradient methods are constructed. With trust region idea, this paper gives a self-adaptive technique for the two methods. The numerical results show that this technique works well for the given nonlinear optimization test problems.
A new method of determining the optimal embedding dimension based on nonlinear prediction
Institute of Scientific and Technical Information of China (English)
Meng Qing-Fang; Peng Yu-Hua; Xue Pei-Jun
2007-01-01
A new method is proposed to determine the optimal embedding dimension from a scalar time series in this paper. This method determines the optimal embedding dimension by optimizing the nonlinear autoregressive prediction model parameterized by the embedding dimension and the nonlinear degree. Simulation results show the effectiveness of this method. And this method is applicable to a short time series, stable to noise, computationally efficient, and without any purposely introduced parameters.
Analysis of factors influencing fire damage to concrete using nonlinear resonance vibration method
Energy Technology Data Exchange (ETDEWEB)
Park, Gang Kyu; Park, Sun Jong; Kwak, Hyo Gyoung [Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, KAIST, Daejeon (Korea, Republic of); Yim, Hong Jae [Dept. of Construction and Disaster Prevention Engineering, Kyungpook National University, Sangju (Korea, Republic of)
2015-04-15
In this study, the effects of different mix proportions and fire scenarios (exposure temperatures and post-fire-curing periods) on fire-damaged concrete were analyzed using a nonlinear resonance vibration method based on nonlinear acoustics. The hysteretic nonlinearity parameter was obtained, which can sensitively reflect the damage level of fire-damaged concrete. In addition, a splitting tensile strength test was performed on each fire-damaged specimen to evaluate the residual property. Using the results, a prediction model for estimating the residual strength of fire-damaged concrete was proposed on the basis of the correlation between the hysteretic nonlinearity parameter and the ratio of splitting tensile strength.
Zhao, Zhanqi; Guttmann, Josef; Möller, Knut
2012-01-01
The objective of this paper is to introduce and evaluate the adaptive SLICE method (ASM) for continuous determination of intratidal nonlinear dynamic compliance and resistance. The tidal volume is subdivided into a series of volume intervals called slices. For each slice, one compliance and one resistance are calculated by applying a least-squares-fit method. The volume window (width) covered by each slice is determined based on the confidence interval of the parameter estimation. The method was compared to the original SLICE method and evaluated using simulation and animal data. The ASM was also challenged with separate analysis of dynamic compliance during inspiration. If the signal-to-noise ratio (SNR) in the respiratory data decreased from +∞ to 10 dB, the relative errors of compliance increased from 0.1% to 22% for the ASM and from 0.2% to 227% for the SLICE method. Fewer differences were found in resistance. When the SNR was larger than 40 dB, the ASM delivered over 40 parameter estimates (42.2 ± 1.3). When analyzing the compliance during inspiration separately, the estimates calculated with the ASM were more stable. The adaptive determination of slice bounds results in consistent and reliable parameter values. Online analysis of nonlinear respiratory mechanics will profit from such an adaptive selection of interval size.
Kádár, Roland; Abbasi, Mahdi; Figuli, Roxana; Rigdahl, Mikael; Wilhelm, Manfred
2017-01-01
The linear and nonlinear oscillatory shear, extensional and combined rheology-dielectric spectroscopy of hybrid polymer nanocomposites for semiconductive applications were investigated in this study. The main focus was the influence of processing conditions on percolated poly(ethylene-butyl acrylate) (EBA) nanocomposite hybrids containing graphite nanoplatelets (GnP) and carbon black (CB). The rheological response of the samples was interpreted in terms of dispersion properties, filler distortion from processing, filler percolation, as well as the filler orientation and distribution dynamics inside the matrix. Evidence of the influence of dispersion properties was found in linear viscoelastic dynamic frequency sweeps, while the percolation of the nanocomposites was detected in nonlinearities developed in dynamic strain sweeps. Using extensional rheology, hybrid samples with better dispersion properties lead to a more pronounced strain hardening behavior, while samples with a higher volume percentage of fillers caused a drastic reduction in strain hardening. The rheo-dielectric time-dependent response showed that in the case of nanocomposites containing only GnP, the orientation dynamics leads to non-conductive samples. However, in the case of hybrids, the orientation of the GnP could be offset by the dispersing of the CB to bridge the nanoplatelets. The results were interpreted in the framework of a dual PE-BA model, where the fillers would be concentrated mainly in the BA regions. Furthermore, better dispersed hybrids obtained using mixing screws at the expense of filler distortion via extrusion processing history were emphasized through the rheo-dielectric tests. PMID:28336857
Kádár, Roland; Abbasi, Mahdi; Figuli, Roxana; Rigdahl, Mikael; Wilhelm, Manfred
2017-01-24
The linear and nonlinear oscillatory shear, extensional and combined rheology-dielectric spectroscopy of hybrid polymer nanocomposites for semiconductive applications were investigated in this study. The main focus was the influence of processing conditions on percolated poly(ethylene-butyl acrylate) (EBA) nanocomposite hybrids containing graphite nanoplatelets (GnP) and carbon black (CB). The rheological response of the samples was interpreted in terms of dispersion properties, filler distortion from processing, filler percolation, as well as the filler orientation and distribution dynamics inside the matrix. Evidence of the influence of dispersion properties was found in linear viscoelastic dynamic frequency sweeps, while the percolation of the nanocomposites was detected in nonlinearities developed in dynamic strain sweeps. Using extensional rheology, hybrid samples with better dispersion properties lead to a more pronounced strain hardening behavior, while samples with a higher volume percentage of fillers caused a drastic reduction in strain hardening. The rheo-dielectric time-dependent response showed that in the case of nanocomposites containing only GnP, the orientation dynamics leads to non-conductive samples. However, in the case of hybrids, the orientation of the GnP could be offset by the dispersing of the CB to bridge the nanoplatelets. The results were interpreted in the framework of a dual PE-BA model, where the fillers would be concentrated mainly in the BA regions. Furthermore, better dispersed hybrids obtained using mixing screws at the expense of filler distortion via extrusion processing history were emphasized through the rheo-dielectric tests.
Measurement of nonlinear elastic response in rock by the resonant bar method
Energy Technology Data Exchange (ETDEWEB)
Johnson, P.A. [Los Alamos National Lab., NM (United States); Rasolofosaon, P.; Zinszner, B. [Institut Francais du Petrole (IFP), 92 - Rueil-Malmaison (France)
1993-04-01
In this work we are studying the behavior of the fundamental (Young`s) mode resonant peak as a function of drive amplitude in rock samples. Our goal from these studies is to obtain nonlinear moduli for many rock types, and to study the nonlinear moduli as a function of water saturation and other changes in physical properties. Measurements were made on seven different room dry rock samples. For one sample measurements were taken at 16 saturation levels between 1 and 98%. All samples display a ``softening`` nonlinearity, that is, the resonant frequency shifts downward with increasing drive amplitude. In extreme cases, the resonant frequency changes by as much as 25% over a strain interval of 10{sup {minus}7} to {approximately}4 {times} 10{sup {minus}5}. Measurements indicate that the nonlinear response is extremely sensitive to saturation. Estimates of a combined cubic and quartic nonlinear parameter {Gamma} range from approximately {minus}300 to {minus}10{sup 9} for the rock samples.
Institute of Scientific and Technical Information of China (English)
WangLin; NiQiao; HuangYuying
2003-01-01
This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support. The nonlinear equation of motion is derived by forces equilibrium on microelement of the system under consideration. The spatial coordinate of the system is discretized by the differential quadrature method and then the dynamic equation is solved by the Newton-Raphson method. The numerical solutions show that the inner fluid velocity of the Hopf bifurcation point of the curved pipe varies with different values of the parameter,nonlinear spring stiffness. Based on this, the cycle and divergent motions are both found to exist at specific fluid flow velocities with a given value of the nonlinear spring stiffness. The results are useful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.
Institute of Scientific and Technical Information of China (English)
赵应桥; 朱鹤元; 刘建华; 孙迭篪; 李富铭
1997-01-01
A time-resolved cross-phase modulation method combined with a modified nonlinear Schrodinger equation is used to study the effects of nonlinear response time on the propagation of ultrashort pulses in nonlinear dispersion media. Evolution of cross-phase modulation spectrum with the different time delay between the probe pulse and pump pulse is simulated using split-step Fourier method. It is shown that both normal self-frequency-shift-red-shift and abnormal self-frequency-shift-blue-shift can occur in the frequency domain for the probe pulse, and a satisfactory theoretical interpretation is given.
Applications of algebraic method to exactly solve some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Darwish, A.A. [Department of Mathematics, Faculty of Science, Helwan University (Egypt)]. E-mail: profdarwish@yahoo.com; Ramady, A. [Department of Mathematics, Faculty of Science, Beni-Suef University (Egypt)]. E-mail: aramady@yahoo.com
2007-08-15
A direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear evolution equations is used and implemented in a computer algebraic system. New solutions for some nonlinear partial differential equations (NLPDE's) are obtained. Graphs of the solutions are displayed.
Indian Academy of Sciences (India)
Jalil Manafian; Mehrdad Lakestani
2015-07-01
An application of the (′/)-expansion method to search for exact solutions of nonlinear partial differential equations is analysed. This method is used for Burgers, Fisher, Huxley equations and combined forms of these equations. The (′/)-expansion method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. It is shown that the (′/)-expansion method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear partial differential equations.
Polymers on disordered hierarchical lattices: A nonlinear combination of random variables
Energy Technology Data Exchange (ETDEWEB)
Cook, J. (Commissariat a l' Energie Atomique, Gif-sur-Yvette (France) Univ. of Edinburgh (England)); Derrida, B. (Commissariat a l' Energie Atomique, Gif-sur-Yvette (France))
1989-10-01
The problem of directed polymers on disordered hierarchical and hypercubic lattices is considered. For the hierarchical lattices the problem can be reduced to the study of the stable laws for combining random variables in a nonlinear way. The authors present the results of numerical simulations of two hierarchical lattices, finding evidence of a phase transition in one case. For a limiting case they extend the perturbation theory developed by Derrida and Griffiths to nonzero temperature and to higher order and use this approach to calculate thermal and geometrical properties (overlaps) of the model. In this limit they obtain an interpolation formula, allowing one to obtain the noninteger moments of the partition function from the integer moments. They obtain bounds for the transition temperature for hierarchical and hypercubic lattices, and some similarities between the problem on the two different types of lattice are discussed.
Fang, Xiaohui; Wai, P K A; Lu, Chao; Chen, Jinhua
2014-02-10
A pulse-width-tunable 10 GHz flattop pulse (FTP) train is generated based on the combined action of active mode locking and nonlinear polarization rotation pulse shaping. Although the setup was previously used for other applications, the mechanism of FTP generation based on it is first analyzed and confirmed in the experiment. An FTP with pulse width tunable from 12 to 20 ps by changing polarization controllers is generated within the wavelength tuning range of 20 nm. The generated pulse reveals good stability, with the side mode suppression ratio of 65 dB, timing jitter of 92 fs, and amplitude fluctuation of 0.36%.
Sousa, Vagner Candido de; Silva, Tarcísio Marinelli Pereira; De Marqui Junior, Carlos
2017-10-01
In this paper, the combined effects of semi-passive control using shunted piezoelectric material and passive pseudoelastic hysteresis of shape memory springs on the aerolastic behavior of a typical section is investigated. An aeroelastic model that accounts for the presence of both smart materials employed as mechanical energy dissipation devices is presented. The Brinson model is used to simulate the shape memory material. New expressions for the modeling of the synchronized switch damping on inductor technique (developed for enhanced piezoelectric damping) are presented, resulting in better agreement with experimental data. The individual effects of each nonlinear mechanism on the aeroelastic behavior of the typical section are first verified. Later, the combined effects of semi-passive piezoelectric control and passive shape memory alloy springs on the post-critical behavior of the system are discussed in details. The range of post-flutter airflow speeds with stable limit cycle oscillations is significantly increased due to the combined effects of both sources of energy dissipation, providing an effective and autonomous way to modify the behavior of aeroelastic systems using smart materials.
A NUMERICAL CALCULATION METHOD FOR EIGENVALUE PROBLEMS OF NONLINEAR INTERNAL WAVES
Institute of Scientific and Technical Information of China (English)
SHI Xin-gang; FAN Zhi-song; LIU Hai-long
2009-01-01
Generally speaking, the background shear current U(z)must be taken into account in eigenvalue problems of nonlinear internal waves in ocean, as is different from those of linear internal waves. A numerical calculation method for eigenvalue problems of nonlinear internal waves is presented in this paper on the basis of the Thompson-Haskell's calculation method. As an application of this method, at a station (21°N, 117°15′E) in the South China Sea, a modal structure and parameters of nonlinear internal waves are calculated, and the results closely agree with the calculated results based on observation by Yang et al..
Directory of Open Access Journals (Sweden)
Shaheed N. Huseen
2013-01-01
Full Text Available A modified q-homotopy analysis method (mq-HAM was proposed for solving nth-order nonlinear differential equations. This method improves the convergence of the series solution in the nHAM which was proposed in (see Hassan and El-Tawil 2011, 2012. The proposed method provides an approximate solution by rewriting the nth-order nonlinear differential equation in the form of n first-order differential equations. The solution of these n differential equations is obtained as a power series solution. This scheme is tested on two nonlinear exactly solvable differential equations. The results demonstrate the reliability and efficiency of the algorithm developed.
Directory of Open Access Journals (Sweden)
Hasibun Naher
2014-10-01
Full Text Available In this article, new extension of the generalized and improved (G′/G-expansion method is proposed for constructing more general and a rich class of new exact traveling wave solutions of nonlinear evolution equations. To demonstrate the novelty and motivation of the proposed method, we implement it to the Korteweg-de Vries (KdV equation. The new method is oriented toward the ease of utilize and capability of computer algebraic system and provides a more systematic, convenient handling of the solution process of nonlinear equations. Further, obtained solutions disclose a wider range of applicability for handling a large variety of nonlinear partial differential equations.
Nonlinear time series theory, methods and applications with R examples
Douc, Randal; Stoffer, David
2014-01-01
FOUNDATIONSLinear ModelsStochastic Processes The Covariance World Linear Processes The Multivariate Cases Numerical Examples ExercisesLinear Gaussian State Space Models Model Basics Filtering, Smoothing, and Forecasting Maximum Likelihood Estimation Smoothing Splines and the Kalman Smoother Asymptotic Distribution of the MLE Missing Data Modifications Structural Component Models State-Space Models with Correlated Errors Exercises Beyond Linear ModelsNonlinear Non-Gaussian Data Volterra Series Expansion Cumulants and Higher-Order Spectra Bilinear Models Conditionally Heteroscedastic Models Thre
An Efficient Pseudospectral Method for Solving a Class of Nonlinear Optimal Control Problems
Emran Tohidi; Atena Pasban; Kilicman, A.; S. Lotfi Noghabi
2013-01-01
This paper gives a robust pseudospectral scheme for solving a class of nonlinear optimal control problems (OCPs) governed by differential inclusions. The basic idea includes two major stages. At the first stage, we linearize the nonlinear dynamical system by an interesting technique which is called linear combination property of intervals. After this stage, the linearized dynamical system is transformed into a multi domain dynamical system via computational interval partitioning. Moreover,...
Song, Jia; Wang, Lun; Cai, Guobiao; Qi, Xiaoqiang
2015-06-01
Near space hypersonic vehicle model is nonlinear, multivariable and couples in the reentry process, which are challenging for the controller design. In this paper, a nonlinear fractional order proportion integral derivative (NFOPIλDμ) active disturbance rejection control (ADRC) strategy based on a natural selection particle swarm (NSPSO) algorithm is proposed for the hypersonic vehicle flight control. The NFOPIλDμ ADRC method consists of a tracking-differentiator (TD), an NFOPIλDμ controller and an extended state observer (ESO). The NFOPIλDμ controller designed by combining an FOPIλDμ method and a nonlinear states error feedback control law (NLSEF) is to overcome concussion caused by the NLSEF and conversely compensate the insufficiency for relatively simple and rough signal processing caused by the FOPIλDμ method. The TD is applied to coordinate the contradiction between rapidity and overshoot. By attributing all uncertain factors to unknown disturbances, the ESO can achieve dynamic feedback compensation for these disturbances and thus reduce their effects. Simulation results show that the NFOPIλDμ ADRC method can make the hypersonic vehicle six-degree-of-freedom nonlinear model track desired nominal signals accurately and fast, has good stability, dynamic properties and strong robustness against external environmental disturbances.
A NUMERICAL EMBEDDING METHOD FOR SOLVING THE NONLINEAR COMPLEMENTARITY PROBLEM(Ⅰ)--THEORY
Institute of Scientific and Technical Information of China (English)
Jian-jun Zhang; De-ren Wang
2002-01-01
In this paper, we extend the numerical embedding method for solving the smooth equations to the nonlinear complementarity problem. By using the nonsmooth theory,we prove the existence and the continuation of the following path for the corresponding homotopy equations. Therefore the basic theory of the numerical embedding method for solving the nonlinear complementarity problem is established. In part Ⅱ of this paper, we will further study the implementation of the method and give some numerical exapmles.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A trial equation method to nonlinear evolution equation with rank inhomogeneous is given. As applications, the exact traveling wave solutions to some higher-order nonlinear equations such as generalized Boussinesq equation,generalized Pochhammer-Chree equation, KdV-Burgers equation, and KS equation and so on, are obtained. Among these, some results are new. The proposed method is based on the idea of reduction of the order of ODE. Some mathematical details of the proposed method are discussed.
Institute of Scientific and Technical Information of China (English)
ZHANGJin-Liang; WANGMing-Liang
2004-01-01
The complex tanh-function expansion method was presented recently, and it can be applied to derive exact solutions to the Schroedinger-type nonlinear evolution equations directly without transformation. In this paper,the complex tanh-function expansion method is applied to derive the exact solutions to the general coupled nonlinear evolution equations. Zakharov system and a long-short-wave interaction system are considered as examples, and the new applications of the complex tanh-function expansion method are shown.
NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Cheng-jian Zhang
2002-01-01
This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDEs,are given. In particular, it is shown that the (k, l)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.
Directory of Open Access Journals (Sweden)
Sohrab Bazm
2016-11-01
Full Text Available Alternative Legendre polynomials (ALPs are used to approximate the solution of a class of nonlinear Volterra-Hammerstein integral equations. For this purpose, the operational matrices of integration and the product for ALPs are derived. Then, using the collocation method, the considered problem is reduced into a set of nonlinear algebraic equations. The error analysis of the method is given and the efficiency and accuracy are illustrated by applying the method to some examples.
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-Liang; WANG Ming-Liang
2004-01-01
The complex tanh-function expansion method was presented recently, and it can be applied to derive exact solutions to the Schrodinger-type nonlinear evolution equations directly without transformation. In this paper,the complex tanh-function expansion method is applied to derive the exact solutions to the general coupled nonlinear evolution equations. Zakharov system and a long-short-wave interaction system are considered as examples, and the new applications of the complex tanh-function expansion method are shown.
An extended harmonic balance method based on incremental nonlinear control parameters
Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.
2017-02-01
A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.
A NUMERICAL METHOD FOR SIMULATING NONLINEAR FLUID-RIGID STRUCTURE INTERACTION PROBLEMS
Institute of Scientific and Technical Information of China (English)
XingJ.T; PriceW.G; ChenY.G
2005-01-01
A numerical method for simulating nonlinear fluid-rigid structure interaction problems is developed. The structure is assumed to undergo large rigid body motions and the fluid flow is governed by nonlinear, viscous or non-viscous, field equations with nonlinear boundary conditions applied to the free surface and fluid-solid interaction interfaces. An Arbitrary-Lagrangian-Eulerian (ALE) mesh system is used to construct the numerical model. A multi-block numerical scheme of study is adopted allowing for the relative motion between moving overset grids, which are independent of one another. This provides a convenient method to overcome the difficulties in matching fluid meshes with large solid motions. Nonlinear numerical equations describing nonlinear fluid-solid interaction dynamics are derived through a numerical discretization scheme of study. A coupling iteration process is used to solve these numerical equations. Numerical examples are presented to demonstrate applications of the model developed.
Directory of Open Access Journals (Sweden)
Shadan Sadigh Behzadi
2011-12-01
Full Text Available In this paper, Adomian decomposition method (ADM and homotopy analysis method (HAM are proposed to solving the fuzzy nonlinear Volterra-Fredholm integral equation of the second kind$(FVFIE-2$. we convert a fuzzy nonlinear Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. we use ADM , HAM and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the nonlinear fuzzy Volterra-Fredholm integral equation. Also, the existence and uniqueness of the solution and convergence of the proposed methods are proved. Examples is given and the results reveal that homotopy analysis method is very effective and simple compared with the Adomian decomposition method.
Indian Academy of Sciences (India)
Zaiyun Zhang; Jianhua Huang; Juan Zhong; Sha-Sha Dou; Jiao Liu; Dan Peng; Ting Gao
2014-06-01
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 (′/)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.
Simple Weighting Methods to Combine Multimodel Projections
Lorenz, R.; Sedlacek, J.; Knutti, R.
2016-12-01
Multimodel ensembles of global climate models are very heterogeneous and some models perform better than others for a certain purpose. Nevertheless, weighting of models is rarely performed and there is a debate about whether and how to weight model projections when combining simulations. We argue that the growing number of models with different characteristics and considerable interdependence, at least for cases where relevant metrics of model performance are clear, requires to make use of model constraints to decrease uncertainties in model projections. Steps towards this should involve a) showing unweighted results along with weighted ones, b) testing the robustness of the results towards different metrics or constraints to maximize transparency and comparability across studies, c) an explicit discussion of the choice of metrics, including the physical reasoning why those quantities matter, d) an assessment of the uncertainties in observations, e) testing the sensitivity towards different datasets, time periods, seasonal vs. annual mean values, grid point vs. spatially aggregated data, etc., and f) exploring whether the choice of metric may lead to overconfident results. Several prerequisites need to be met for such approaches to work. For instance, we need available observations, a certain degree of model skill as well as observable relationships that relate to the projections in question. Here we explore projections of summer temperature over central North America. Many CMIP5 models show a pronounced bias of summer temperature over central North America in present climate. We investigate possible causes for this bias and possibilities to constrain the CMIP5 ensemble. We will show if and how uncertainties of projections change depending on weighting method, observational dataset and constraint used.
Neural networks for emulation variational method for data assimilation in nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Morais Furtado, Helaine Cristina; Fraga de Campos Velho, Haroldo; Macau, Elbert E N, E-mail: helaine.furtado@lac.inpe.br, E-mail: haroldo@lac.inpe.br, E-mail: elbert@lac.inpe.br [Laboratorio Associado de Computacao e Matematica Aplicada, Sao Jose dos Campos (Brazil)
2011-03-01
Description of a physical phenomenon through differential equations has errors involved, since the mathematical model is always an approximation of reality. For an operational prediction system, one strategy to improve the prediction is to add some information from the real dynamics into mathematical model. This additional information consists of observations on the phenomenon. However, the observational data insertion should be done carefully, for avoiding a worse performance of the prediction. Technical data assimilation are tools to combine data from physical-mathematics model with observational data to obtain a better forecast. The goal of this work is to present the performance of the Neural Network Multilayer Perceptrons trained to emulate a Variational method in context of data assimilation. Techniques for data assimilation are applied for the Lorenz systems; which presents a strong nonlinearity and chaotic nature.
Nonlinear Simulations of Coalescence Instability Using a Flux Difference Splitting Method
Ma, Jun; Qin, Hong; Yu, Zhi; Li, Dehui
2016-07-01
A flux difference splitting numerical scheme based on the finite volume method is applied to study ideal/resistive magnetohydrodynamics. The ideal/resistive MHD equations are cast as a set of hyperbolic conservation laws, and we develop a numerical capability to solve the weak solutions of these hyperbolic conservation laws by combining a multi-state Harten-Lax-Van Leer approximate Riemann solver with the hyperbolic divergence cleaning technique, high order shock-capturing reconstruction schemes, and a third order total variance diminishing Runge-Kutta time evolving scheme. The developed simulation code is applied to study the long time nonlinear evolution of the coalescence instability. It is verified that small structures in the instability oscillate with time and then merge into medium structures in a coherent manner. The medium structures then evolve and merge into large structures, and this trend continues through all scale-lengths. The physics of this interesting nonlinear dynamics is numerically analyzed. supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2013GB111002, 2013GB105003, 2013GB111000, 2014GB124005, 2015GB111003), National Natural Science Foundation of China (Nos. 11305171, 11405208), JSPS-NRF-NSFC A3 Foresight Program in the field of Plasma Physics (NSFC-11261140328), the Science Foundation of the Institute of Plasma Physics, Chinese Academy of Sciences (DSJJ-15-JC02) and the CAS Program for the Interdisciplinary Collaboration Team
Rashidi, M. M.; Erfani, E.
2009-09-01
In this study, we present a numerical comparison between the differential transform method (DTM) and the homotopy analysis method (HAM) for solving Burgers' and nonlinear heat transfer problems. The first differential equation is the Burgers' equation serves as a useful model for many interesting problems in applied mathematics. The second one is the modeling equation of a straight fin with a temperature dependent thermal conductivity. In order to show the effectiveness of the DTM, the results obtained from the DTM is compared with available solutions obtained using the HAM [M.M. Rashidi, G. Domairry, S. Dinarvand, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 708-717; G. Domairry, M. Fazeli, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 489-499] and whit exact solutions. The method can easily be applied to many linear and nonlinear problems. It illustrates the validity and the great potential of the differential transform method in solving nonlinear partial differential equations. The obtained results reveal that the technique introduced here is very effective and convenient for solving nonlinear partial differential equations and nonlinear ordinary differential equations that we are found to be in good agreement with the exact solutions.
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
Cerro, J. A.; Scotti, S. J.
1991-01-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
Tajaldini, Mehdi; Mat Jafri, Mohd Zubir Mat
2013-05-01
In this study, we propose a novel approach that is called nonlinear modal propagation analysis method (NMPA) in MMI coupler via the enhances of nonlinear wave propagation in terms of guided modes interferences in nonlinear regimes, such that the modal fields are measurable at any point of coupler and output facets. Then, the ultra-short MMI coupler is optimized as a building block in micro ring resonator to investigate the method efficiency against the already used method. Modeling results demonstrate more efficiency and accuracy in shorter lengths of multimode interference coupler. Therefore, NMPA can be used as a method to study the compact dimension coupler and for developing the performance in applications. Furthermore, the possibility of access tothe all-optical switching is assumed due to one continuous MMI for proof of the development of performances in nonlinear regimes.
NONLINEAR GALERKIN METHODS FOR SOLVING TWO DIMENSIONAL NEWTON-BOUSSINESQ EQUATIONS
Institute of Scientific and Technical Information of China (English)
GUOBOLING
1995-01-01
The nonlinear Galerkin methods for solving two-dimensional Newton-Boussinesq equations are proposed. The existence and uniqueness of global generalized solution of these equations,and the convergence of approximate solutions are also obtained.
On the freezing method for nonlinear nonautonomous systems with delay
Directory of Open Access Journals (Sweden)
Michael I. Gil'
2001-01-01
Full Text Available Nonlinear nonautonomous differential systems with delaying argument are considered. Explicit conditions for absolute stability are derived. The proposed approach is based on the generalization of the freezing method for ordinary differential equations.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
The Full—Discrete Mixed Finite Element Methods for Nonlinear Hyperbolic Equations
Institute of Scientific and Technical Information of China (English)
YanpingCHEN; YunqingHUANG
1998-01-01
This article treats mixed finite element methods for second order nonlinear hyperbolic equations.A fully discrete scheme is presented and improved L2-error estimates are established.The convergence of both the function value andthe flux is demonstrated.
Stability analysis of Runge-Kutta methods for nonlinear neutral delay integro-differential equations
Institute of Scientific and Technical Information of China (English)
2007-01-01
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.
Nonlinear Time Reversal Acoustic Method of Friction Stir Weld Assessment Project
National Aeronautics and Space Administration — The goal of the project is demonstration of the feasibility of Friction Stir Weld (FSW) assessment by novel Nonlinear Time Reversal Acoustic (TRA) method. Time...
Wang, Qing; Yao, Jing-Zheng
2010-12-01
Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.
Determining the minimum embedding dimension of nonlinear time series based on prediction method
Institute of Scientific and Technical Information of China (English)
Bian Chun-Hua; Ning Xin-Bao
2004-01-01
Determining the embedding dimension of nonlinear time series plays an important role in the reconstruction of nonlinear dynamics. The paper first summarizes the current methods for determining the embedding dimension.Then, inspired by the fact that the optimum modelling dimension of nonlinear autoregressive (NAR) prediction model can characterize the embedding feature of the dynamics, the paper presents a new idea that the optimum modelling dimension of the NAR model can be taken as the minimum embedding dimension. Some validation examples and results are given and the present method shows its advantage for short data series.
H∞ Synthesis Method for Control of Non-linear Flexible Joint Models
Axelsson, Patrik; Pipeleers, Goele; Helmersson, Anders; Norrlöf, Mikael
2014-01-01
An H∞ synthesis method for control of a flexible joint, with non-linear spring characteristic, is proposed. The first step of the synthesis method is to extend the joint model with an uncertainty description of the stiffness parameter. In the second step, a non-linear optimisation problem, based on nominal performance and robust stability requirements, has to be solved. Using the Lyapunov shaping paradigm and a change of variables, the non-linear optimisation problem can be rewritten as a con...
DEFF Research Database (Denmark)
Barari, Amin; Ganjavi, B.; Jeloudar, M. Ghanbari
2010-01-01
Purpose – In the last two decades with the rapid development of nonlinear science, there has appeared ever-increasing interest of scientists and engineers in the analytical techniques for nonlinear problems. This paper considers linear and nonlinear systems that are not only regarded as general...... and fluid mechanics. Design/methodology/approach – Two new but powerful analytical methods, namely, He's VIM and HPM, are introduced to solve some boundary value problems in structural engineering and fluid mechanics. Findings – Analytical solutions often fit under classical perturbation methods. However...
Nonlinear dynamics of rotating shallow water methods and advances
Zeitlin, Vladimir
2007-01-01
The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wa
DOUBLE TRIALS METHOD FOR NONLINEAR PROBLEMS ARISING IN HEAT TRANSFER
Directory of Open Access Journals (Sweden)
Chun-Hui He
2011-01-01
Full Text Available According to an ancient Chinese algorithm, the Ying Buzu Shu, in about second century BC, known as the rule of double false position in West after 1202 AD, two trial roots are assumed to solve algebraic equations. The solution procedure can be extended to solve nonlinear differential equations by constructing an approximate solution with an unknown parameter, and the unknown parameter can be easily determined using the Ying Buzu Shu. An example in heat transfer is given to elucidate the solution procedure.
Prescott, Aaron M.; Abel, Steven M.
2016-12-01
The rational design of network behavior is a central goal of synthetic biology. Here, we combine in silico evolution with nonlinear dimensionality reduction to redesign the responses of fixed-topology signaling networks and to characterize sets of kinetic parameters that underlie various input-output relations. We first consider the earliest part of the T cell receptor (TCR) signaling network and demonstrate that it can produce a variety of input-output relations (quantified as the level of TCR phosphorylation as a function of the characteristic TCR binding time). We utilize an evolutionary algorithm (EA) to identify sets of kinetic parameters that give rise to: (i) sigmoidal responses with the activation threshold varied over 6 orders of magnitude, (ii) a graded response, and (iii) an inverted response in which short TCR binding times lead to activation. We also consider a network with both positive and negative feedback and use the EA to evolve oscillatory responses with different periods in response to a change in input. For each targeted input-output relation, we conduct many independent runs of the EA and use nonlinear dimensionality reduction to embed the resulting data for each network in two dimensions. We then partition the results into groups and characterize constraints placed on the parameters by the different targeted response curves. Our approach provides a way (i) to guide the design of kinetic parameters of fixed-topology networks to generate novel input-output relations and (ii) to constrain ranges of biological parameters using experimental data. In the cases considered, the network topologies exhibit significant flexibility in generating alternative responses, with distinct patterns of kinetic rates emerging for different targeted responses.
Directory of Open Access Journals (Sweden)
Roland Kádár
2017-01-01
Full Text Available The linear and nonlinear oscillatory shear, extensional and combined rheology-dielectric spectroscopy of hybrid polymer nanocomposites for semiconductive applications were investigated in this study. The main focus was the influence of processing conditions on percolated poly(ethylene-butyl acrylate (EBA nanocomposite hybrids containing graphite nanoplatelets (GnP and carbon black (CB. The rheological response of the samples was interpreted in terms of dispersion properties, filler distortion from processing, filler percolation, as well as the filler orientation and distribution dynamics inside the matrix. Evidence of the influence of dispersion properties was found in linear viscoelastic dynamic frequency sweeps, while the percolation of the nanocomposites was detected in nonlinearities developed in dynamic strain sweeps. Using extensional rheology, hybrid samples with better dispersion properties lead to a more pronounced strain hardening behavior, while samples with a higher volume percentage of fillers caused a drastic reduction in strain hardening. The rheo-dielectric time-dependent response showed that in the case of nanocomposites containing only GnP, the orientation dynamics leads to non-conductive samples. However, in the case of hybrids, the orientation of the GnP could be offset by the dispersing of the CB to bridge the nanoplatelets. The results were interpreted in the framework of a dual PE-BA model, where the fillers would be concentrated mainly in the BA regions. Furthermore, better dispersed hybrids obtained using mixing screws at the expense of filler distortion via extrusion processing history were emphasized through the rheo-dielectric tests.
Indian Academy of Sciences (India)
M Mirzazadeh; M Eslami
2013-12-01
Studying compactons, solitons, solitary patterns and periodic solutions is important in nonlinear phenomena. In this paper we study nonlinear variants of the Kadomtsev–Petviashvili (KP) and the Korteweg–de Vries (KdV) equations with positive and negative exponents. The functional variable method is used to establish compactons, solitons, solitary patterns and periodic solutions for these variants. This method is a powerful tool for searching exact travelling solutions in closed form.
In vivo characterization of skin using a Weiner nonlinear stochastic system identification method.
Chen, Yi; Hunter, Ian W
2009-01-01
This paper describes an indentometer device used to identify the linear dynamic and nonlinear properties of skin and underlying tissue using an in vivo test. The device uses a Lorentz force actuator to apply a dynamic force to the skin and measures the resulting displacement. It was found that the skin could be modeled as a Wiener system (i.e. a linear dynamic system followed by a static nonlinearity). Using a stochastic nonlinear system identification technique, the method presented in this paper was able to identify the dynamic linear and static nonlinear mechanical parameters of the indentometer-skin system within 2 to 4 seconds. The shape of the nonlinearity was found to vary depending on the area of the skin that was tested. We show that the device can repeatably distinguish between different areas of human tissue for multiple test subjects.
Directory of Open Access Journals (Sweden)
Shahriari
2017-02-01
Full Text Available In this work, the optical properties dependence of Multi-Walled Carbon Nanotubes (MWNT on concentration was discussed. MWNT samples were prepared in polypyrrole by an electrochemical polymerization of monomers, in the presence of different concentrations of MWNTs, using Sodium Dodecyl-Benzen-Sulfonate (SDBS as surfactant at room temperature. The nonlinear refractive and nonlinear absorbtion indices were measured using a low power CW laser beam operated at 532 nm using z-scan method. The results show that nonlinear refractive and nonlinear absorbtion indices tend to be increased with increasing the concentration of carbon nanotubes. Optical properties of carbone nanotubes indicate that they are good candidates for nonlinear optical devices
Investigation of nonlinear optical properties of various organic materials by the Z-scan method
Ganeev, R. A.; Boltaev, G. S.; Tugushev, R. I.; Usmanov, T.
2012-06-01
We have studied the nonlinear optical properties of various organic materials (vegetable oil, juice, wine, cognac, Coca-Cola and Fanta drinks, Nescafé coffee, tea, gasoline, clock oil, glycerol, and polyphenyl ether) that are used in everyday life. Their nonlinearities have been studied by the Z-scan method in the near-IR and visible spectral ranges. We have shown that the majority of samples possess a nonlinear absorption; however, some of the studied materials show a strong saturated absorption and nonlinear refraction. Red wine and glycerol proved to be the most interesting materials. For these samples, we have observed a change in the sign of the nonlinear absorption with increasing laser intensity, which was attributed to the competition between two-photon absorption and saturated absorption.
Analytical exploration of γ-function explicit method for pseudodynamic testing of nonlinear systems
Institute of Scientific and Technical Information of China (English)
Shuenn-Yih Chang; Yu-Chi Sung
2005-01-01
It has been well studied that the γ-function explicit method can be effective in providing favorable numerical dissipation for linear elastic systems. However, its performance for nonlinear systems is unclear due to a lack of analytical evaluation techniques. Thus, a novel technique is proposed herein to evaluate its efficiency for application to nonlinear systems by introducing two parameters to describe the stiffness change. As a result, the numerical properties and error propagation characteristics of the γ-function explicit method for the pseudodynamic testing of a nonlinear system are analytically assessed. It is found that the upper stability limit decreases as the step degree of nonlinearity increases; and it increases as the current degree of nonlinearity increases. It is also shown that this integration method provides favorable numerical dissipation not only for linear elastic systems but also for nonlinear systems. Furthermore, error propagation analysis reveals that the numerical dissipation can effectively suppress the severe error propagation of high frequency modes while the low frequency responses are almost unaffected for both linear elastic and nonlinear systems.
Third-order nonlinear optical properties of acid green 25 dye by Z-scan method
Jeyaram, S.; Geethakrishnan, T.
2017-03-01
Third-order nonlinear optical (NLO) properties of aqueous solutions of an anthraquinone dye (Acid green 25 dye, color index: 61570) have been studied by Z-scan method with a 5 mW continuous wave (CW) diode laser operating at 635 nm. The nonlinear refractive index (n2) and the absorption coefficient (β) have been evaluated respectively from the closed and open aperture Z-scan data and the values of these parameters are found to increase with increase in concentration of the dye solution. The negative sign of the observed nonlinear refractive index (n2) indicates that the aqueous solution of acid green 25 dye exhibits self-defocusing type optical nonlinearity. The mechanism of the observed nonlinear absorption (NLA) and nonlinear refraction (NLR) is attributed respectively to reverse saturable absorption (RSA) and thermal nonlinear effects. The magnitudes of n2 and β are found to be of the order of 10-7 cm2/W and 10-3 cm/W respectively. With these experimental results, the authors suggest that acid green 25 dye may have potential applications in nonlinear optics.
Three-step iterative methods with eighth-order convergence for solving nonlinear equations
Directory of Open Access Journals (Sweden)
Mashallah Matinfar
2013-01-01
Full Text Available A family of eighth-order iterative methods for solution of nonlinear equations is presented. We propose an optimal three-step method with eight-order convergence for finding the simple roots of nonlinear equations by Hermite interpolation method. Per iteration of this method requires two evaluations of the function and two evaluations of its first derivative, which implies that the efficiency index of the developed methods is 1.682. Some numerical examples illustrate that the algorithms are more efficient and performs better than the other methods.
Image segmentation combining non-linear diffusion and the Nystrom extension
Izquierdo, Ebroul
2005-07-01
An approach for image segmentation is presented. Images are first preprocessed using multiscale simplification by nonlinear diffusion. Subsequently image segmentation of the resulting smoothed images is carried out. The actual segmentation step is based on the estimation of the Eigenvectors and Eigenvalues of a matrix derived from both the total dissimilarity and the total similarity between different groups of pixels in the image. This algorithm belong to the class of spectral methods, specifically, the Nystron extension introduced by Fowlkes et al in [1]. Stability analysis of the approximation of the underlying spectral partitioning is presented. Modifications of Fowlkes technique are proposed to improve the stability of the algorithm. The proposed modifications include a criterion for the selection of the initial sample and numerically stable estimations of ill-posed inverse matrices for the solution of the underlying mathematical problem. Results of selected computer experiments are reported to validate the superiority of the proposed approach when compared with the technique proposed in [1].
Non-linear time series analysis: methods and applications to atrial fibrillation.
Hoekstra, B P; Diks, C G; Allessie, M A; Degoede, J
2001-01-01
We apply methods from non-linear statistical time series analysis to characterize electrograms of atrial fibrillation. These are based on concepts originating from the theory of non-linear dynamical systems and use the empirical reconstruction density in reconstructed phase space. Application of these methods is not restricted to deterministic chaos but is valid in a general time series context. We illustrate this by applying three recently proposed non-linear time series methods to fibrillation electrograms: 1) a test for time reversibility in atrial electrograms during paroxysmal atrial fibrillation in patients; 2) a test to detect differences in the dynamical behaviour during the pharmacological conversion of sustained atrial fibrillation in instrumented conscious goats; 3) a test for general Granger causality to identify couplings and information transport in the atria during fibrillation. We conclude that a characterization of the dynamics via the reconstruction density offers a useful framework for the non-linear analysis of electrograms of atrial fibrillation.
Ren, Shijin
2003-01-01
Response surface models based on multiple linear regression had previously been developed for the toxicity of aromatic chemicals to Tetrahymena pyriformis. However, a nonlinear relationship between toxicity and one of the molecular descriptors in the response surface model was observed. In this study, response surface models were established using six nonlinear modeling methods to handle the nonlinearity exhibited in the aromatic chemicals data set. All models were validated using the method of cross-validation, and prediction accuracy was tested on an external data set. Results showed that response surface models based on locally weighted regression scatter plot smoothing (LOESS), multivariate adaptive regression splines (MARS), neural networks (NN), and projection pursuit regression (PPR) provided satisfactory power of model fitting and prediction and had similar applicabilities. The response surface models based on nonlinear methods were difficult to interpret and conservative in discriminating toxicity mechanisms.
Exact travelling solutions for some nonlinear physical models by (′/)-expansion method
Indian Academy of Sciences (India)
B Salim Bahrami; H Abdollahzadeh; I M Berijani; D D Ganji; M Abdollahzadeh
2011-08-01
In this paper, we establish exact solutions for some special nonlinear partial differential equations. The (′/)-expansion method is used to construct travelling wave solutions of the twodimensional sine-Gordon equation, Dodd–Bullough–Mikhailov and Schrödinger–KdV equations, which appear in many ﬁelds such as, solid-state physics, nonlinear optics, ﬂuid dynamics, ﬂuid ﬂow, quantum ﬁeld theory, electromagnetic waves and so on. In this method we take the advantage of general solutions of second-order linear ordinary differential equation (LODE) to solve many nonlinear evolution equations effectively. The (′/)-expansion method is direct, concise and elementary and can be used with a wider applicability for handling many nonlinear wave equations.
A novel order reduction method for nonlinear dynamical system under external periodic excitations
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The concept of approximate inertial manifold (AIM) is extended to develop a kind of nonlinear order reduction technique for non-autonomous nonlinear systems in second-order form in this paper.Using the modal transformation,a large nonlinear dynamical system is split into a ’master’ subsystem,a ’slave’ subsystem,and a ’negligible’ subsystem.Accordingly,a novel order reduction method (Method I) is developed to construct a low order subsystem by neglecting the ’negligible’ subsystem and slaving the ’slave’ subsystem into the ’master’ subsystem using the extended AIM.As a comparison,Method II accounting for the effects of both ’slave’ subsystem and the ’negligible’ subsystem is also applied to obtain the reduced order subsystem.Then,a typical 5-degree-of-freedom nonlinear dynamical system is given to compare the accuracy and efficiency of the traditional Galerkin truncation (ignoring the contributions of the slave and negligible subsystems),Method I and Method II.It is shown that Method I gives a considerable increase in accuracy for little computational cost in comparison with the standard Galerkin method,and produces almost the same accuracy as Method II.Finally,a 3-degree-of-freedom nonlinear dynamical system is analyzed by using the analytic method for showing predominance and convenience of Method I to obtain the analytically reduced order system.
Three novel high-resolution nonlinear methods for fast signal processing
Belkić, Dž.; Dando, P. A.; Main, J.; Taylor, H. S.
2000-10-01
Three novel nonlinear parameter estimators are devised and implemented for accurate and fast processing of experimentally measured or theoretically generated time signals of arbitrary length. The new techniques can also be used as powerful tools for diagonalization of large matrices that are customarily encountered in quantum chemistry and elsewhere. The key to the success and the common denominator of the proposed methods is a considerably reduced dimensionality of the original data matrix. This is achieved in a preprocessing stage called beamspace windowing or band-limited decimation. The methods are decimated signal diagonalization (DSD), decimated linear predictor (DLP), and decimated Padé approximant (DPA). Their mutual equivalence is shown for the signals that are modeled by a linear combination of time-dependent damped exponentials with stationary amplitudes. The ability to obtain all the peak parameters first and construct the required spectra afterwards enables the present methods to phase correct the absorption mode. Additionally, a new noise reduction technique, based upon the stabilization method from resonance scattering theory, is proposed. The results obtained using both synthesized and experimental time signals show that DSD/DLP/DPA exhibit an enhanced resolution power relative to the standard fast Fourier transform. Of the three methods, DPA is found to be the most efficient computationally.
Finding zeros of nonlinear functions using the hybrid parallel cell mapping method
Xiong, Fu-Rui; Schütze, Oliver; Ding, Qian; Sun, Jian-Qiao
2016-05-01
Analysis of nonlinear dynamical systems including finding equilibrium states and stability boundaries often leads to a problem of finding zeros of vector functions. However, finding all the zeros of a set of vector functions in the domain of interest is quite a challenging task. This paper proposes a zero finding algorithm that combines the cell mapping methods and the subdivision techniques. Both the simple cell mapping (SCM) and generalized cell mapping (GCM) methods are used to identify a covering set of zeros. The subdivision technique is applied to enhance the solution resolution. The parallel implementation of the proposed method is discussed extensively. Several examples are presented to demonstrate the application and effectiveness of the proposed method. We then extend the study of finding zeros to the problem of finding stability boundaries of potential fields. Examples of two and three dimensional potential fields are studied. In addition to the effectiveness in finding the stability boundaries, the proposed method can handle several millions of cells in just a few seconds with the help of parallel computing in graphics processing units (GPUs).
A Family of Fifth-order Iterative Methods for Solving Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
Liu Tian-Bao; Cai Hua
2013-01-01
In this paper, we present and analyze a family of fifth-order iterative methods free from second derivative for solving nonlinear equations. It is established that the family of iterative methods has convergence order five. Numerical examples show that the new methods are comparable with the well known existing methods and give better results in many aspects.
An analysis of a new nonlinear estimation technique: The state-dependent Ricatti equation method
Ewing, Craig Michael
1999-10-01
Research into nonlinear estimation techniques for terminal homing missiles has been conducted for many decades. The terminal state estimator, also called the guidance filter, is responsible for providing accurate estimates of target motion for use in guiding the missile to a collision course with the target. Some form of the extended-Kalman filter (EKF) has become the standard estimation technique employed in most modern weapon guidance systems. EKF linearization of nonlinear dynamics and/or measurements can cause problems of divergence when confronted by highly nonlinear conditions. The objective of this dissertation is to analyze a new nonlinear estimation technique that is based on the parameterization of the nonlinearities. This parameterization converts the nonlinear estimation problem into the form of a steady-state continuous Kalman filtering problem with state-dependent coefficients. This new technique, called the state-dependent Ricatti equation filter (SDREF), allows the nonlinearities of the system to be fully incorporated into the filter design, before stochastic uncertainties are imposed, without the need for linearization. The SDREF was investigated in three problems: an exoatmospheric, terminal homing, ballistic-missile intercept problem; a highly nonlinear pendulum example; and an algorithmic loss of observability problem. The exoatmospheric guidance problem examined nonlinear measurements with linear dynamics. To investigate the SDREF when used with a combination of nonlinear dynamics and nonlinear measurements, a highly nonlinear, two-state pendulum problem was also examined. While these problems were useful in gaining insight into the performance characteristics of the SDREF, no formal proof of stability could be determined for the original formulation of the estimator. The original SDREF solved an algebraic SDRE that arose from an infinite-time horizon formulation of the nonlinear filtering problem. A modification to the SDREF formulation was
Institute of Scientific and Technical Information of China (English)
TAO Hua-xue (陶华学); GUO Jin-yun (郭金运)
2003-01-01
Data are very important to build the digital mine. Data come from many sources, have different types and temporal states. Relations between one class of data and the other one, or between data and unknown parameters are more nonlinear. The unknown parameters are non-random or random, among which the random parameters often dynamically vary with time. Therefore it is not accurate and reliable to process the data in building the digital mine with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method to process data in building the digital mine is put forward. In the meantime, the corresponding mathematical model is also given. The generalized nonlinear least squares problem is more complex than the common nonlinear least squares problem and its solution is more difficultly obtained because the dimensions of data and parameters in the former are bigger. So a new solution model and the method are put forward to solve the generalized nonlinear dynamic least squares problem. In fact, the problem can be converted to two sub-problems, each of which has a single variable. That is to say, a complex problem can be separated and then solved. So the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations. The method lessens the calculating load and opens up a new way to process the data in building the digital mine, which have more sources, different types and more temporal states.
Method and system for training dynamic nonlinear adaptive filters which have embedded memory
Rabinowitz, Matthew (Inventor)
2002-01-01
Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.
NONLINEAR ESTIMATION METHODS FOR AUTONOMOUS TRACKED VEHICLE WITH SLIP
Institute of Scientific and Technical Information of China (English)
ZHOU Bo; HAN Jianda
2007-01-01
In order to achieve precise, robust autonomous guidance and control of a tracked vehicle, a kinematic model with longitudinal and lateral slip is established. Four different nonlinear filters are used to estimate both state vector and time-varying parameter vector of the created model jointly. The first filter is the well-known extended Kalman filter. The second filter is an unscented version of the Kalman filter. The third one is a particle filter using the unscented Kalman filter to generate the importance proposal distribution. The last one is a novel and guaranteed filter that uses a linear set-membership estimator and can give an ellipsoid set in which the true state lies. The four different approaches have different complexities, behavior and advantages that are surveyed and compared.
Modified Semi-Classical Methods for Nonlinear Quantum Oscillations Problems
Moncrief, Vincent; Maitra, Rachel
2012-01-01
We develop a modified semi-classical approach to the approximate solution of Schrodinger's equation for certain nonlinear quantum oscillations problems. At lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. Under smoothness, convexity and coercivity hypotheses on its potential energy function, we prove, using the calculus of variations together with the Banach space implicit function theorem, the existence of a global, smooth `fundamental solution'. Higher order quantum corrections, for ground and excited states, are computed through the integration of associated systems of linear transport equations, and formal expansions for the corresponding energy eigenvalues obtained by imposing smoothness on the quantum corrections to the eigenfunctions. For linear oscillators our expansions naturally truncate, reproducing the well-known solutions for the energy eigenfunctions and eigenvalues. As an application, w...
A hybrid nonlinear programming method for design optimization
Rajan, S. D.
1986-01-01
Solutions to engineering design problems formulated as nonlinear programming (NLP) problems usually require the use of more than one optimization technique. Moreover, the interaction between the user (analysis/synthesis) program and the NLP system can lead to interface, scaling, or convergence problems. An NLP solution system is presented that seeks to solve these problems by providing a programming system to ease the user-system interface. A simple set of rules is used to select an optimization technique or to switch from one technique to another in an attempt to detect, diagnose, and solve some potential problems. Numerical examples involving finite element based optimal design of space trusses and rotor bearing systems are used to illustrate the applicability of the proposed methodology.
Application of new novel energy balance method to strongly nonlinear oscillator systems
Directory of Open Access Journals (Sweden)
Md. Abdur Razzak
2015-01-01
Full Text Available In this paper, a new novel energy balance method based on the harmonic balance method is proposed to obtain higher-order approximations of strongly nonlinear problems arising in engineering. Especially, second-order approximation is considered in this paper. Results found in this paper are compared with the exact result and other existing results. The results show that the proposed method gives better result for both small and large amplitudes of oscillation than other existing results. The method is illustrated by examples. It has been shown that the proposed method is very effective, convenient and quite accurate to nonlinear engineering problems.
A Novel in situ Trigger Combination Method
Buzatu, Adrian; Krumnack, Nils; Yao, Wei-Ming
2012-01-01
Searches for rare physics processes using particle detectors in high-luminosity colliding hadronic beam environments require the use of multi-level trigger systems to reject colossal background rates in real time. In analyses like the search for the Higgs boson, there is a need to maximize the signal acceptance by combining multiple different trigger chains when forming the offline data sample. In such statistically limited searches, datasets are often amassed over periods of several years, during which the trigger characteristics evolve and their performance can vary significantly. Reliable production cross-section measurements and upper limits must take into account a detailed understanding of the effective trigger inefficiency for every selected candidate event. We present as an example the complex situation of three trigger chains, based on missing energy and jet energy, to be combined in the context of the search for the Higgs (H) boson produced in association with a W boson at the Collider Detector at F...
Nonlinear system identification NARMAX methods in the time, frequency, and spatio-temporal domains
Billings, Stephen A
2013-01-01
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) modelThe orthogonal least squares algorithm that allows models to be built term by
The (′/)-expansion method for a discrete nonlinear Schrödinger equation
Indian Academy of Sciences (India)
Sheng Zhang; Ling Dong; Jin-Mei Ba; Ying-Na Sun
2010-02-01
An improved algorithm is devised for using the (′/)-expansion method to solve nonlinear differential-difference equations. With the aid of symbolic computation, we choose a discrete nonlinear Schrödinger equation to illustrate the validity and advantages of the improved algorithm. As a result, hyperbolic function solutions, trigonometric function solutions and rational solutions with parameters are obtained, from which some special solutions including the known solitary wave solution are derived by setting the parameters as appropriate values. It is shown that the improved algorithm is effective and can be used for many other nonlinear differential-difference equations in mathematical physics.
Control design for the nonlinear benchmark problem via the output regulation method
Institute of Scientific and Technical Information of China (English)
Jie HUANG; Guoqiang HU
2004-01-01
The problem of designing a feedback controller to achieve asymptotic disturbance rejection / attenuation while maintaining good transient response in the RTAC system is known as a benchmark nonlinear control problem, which has been an intensive research subject since 1995. In this paper, we will further investigate the solvability of the robust disturbance rejection problem of the RTAC system by the measurement output feedback control based on the robust output regulation method. We have obtained a design by overcoming two major obstacles: find a closed-form solution of the regulator equations; and devise a nonlinear internal model to account for non-polynomial nonlinearities.
Application of nonlinear systems in nanomechanics and nanofluids analytical methods and applications
Ganji, Davood Domairry
2015-01-01
With Application of Nonlinear Systems in Nanomechanics and Nanofluids the reader gains a deep and practice-oriented understanding of nonlinear systems within areas of nanotechnology application as well as the necessary knowledge enabling the handling of such systems. The book helps readers understand relevant methods and techniques for solving nonlinear problems, and is an invaluable reference for researchers, professionals and PhD students interested in research areas and industries where nanofluidics and dynamic nano-mechanical systems are studied or applied. The book is useful in areas suc
GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yin-nian He; Yan-ren Hou; Li-quan Mei
2001-01-01
A global finite element nonlinear Galerkin method for the penalized Navier-Stokes equations is presented. This method is based on two finite element spaces XH and Xh,defined respectively on one coarse grid with grid size H and one fine grid with grid size h ＜＜ H. Comparison is also made with the finite element Galerkin method. If we choose H = O(ε-1/4h1/2), ε＞ 0 being the penalty parameter, then two methods are of the same order of approximation. However, the global finite element nonlinear Galerkin method is much cheaper than the standard finite element Galerkin method. In fact, in the finite element Galerkin method the nonlinearity is treated on the fine grid finite element space Xh and while in the global finite element nonlinear Galerkin method the similar nonlinearity is treated on the coarse grid finite element space XH and only the linearity needs to be treated on the fine grid increment finite element space Wh. Finally, we provide numerical test which shows above results stated.
Application of nonlinear ultrasonic method for monitoring of stress state in concrete
Energy Technology Data Exchange (ETDEWEB)
Kim, Gyu Jin; Kwak, Hyo Gyoung [Dept. of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Park, Sun Jong [Dept. of Structural System and Site Safety Evaluation, Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of)
2016-04-15
As the lifespan of concrete structures increases, their load carrying capacity decreases owing to cyclic loads and long-term effects such as creep and shrinkage. For these reasons, there is a necessity for stress state monitoring of concrete members. Particularly, it is necessary to evaluate the concrete structures for behavioral changes by using a technique that can overcome the measuring limitations of usual ultrasonic nondestructive evaluation methods. This paper proposes the use of a nonlinear ultrasonic method, namely, nonlinear resonant ultrasonic spectroscopy (NRUS) for the measurement of nonlinearity parameters for stress monitoring. An experiment compared the use of NRUS method and a linear ultrasonic method, namely, ultrasonic pulse velocity (UPV) to study the effects of continuously increasing loads and cyclic loads on the nonlinearity parameter. Both NRUS and UPV methods found a similar direct relationship between load level and that parameter. The NRUS method showed a higher sensitivity to micro-structural changes of concrete than UPV method. Thus, the experiment confirms the possibility of using the nonlinear ultrasonic method for stress state monitoring of concrete members.
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2016-07-01
Full Text Available In this paper, we improve the extended trial equation method to construct the exact solutions for nonlinear coupled system of partial differential equations in mathematical physics. We use the extended trial equation method to find some different types of exact solutions such as the Jacobi elliptic function solutions, soliton solutions, trigonometric function solutions and rational, exact solutions to the nonlinear coupled Schrodinger Boussinesq equations when the balance number is a positive integer. The performance of this method is reliable, effective and powerful for solving more complicated nonlinear partial differential equations in mathematical physics. The balance number of this method is not constant as we have in other methods. This method allows us to construct many new types of exact solutions. By using the Maple software package we show that all obtained solutions satisfy the original partial differential equations.
Acceleration of the AFEN method by two-node nonlinear iteration
Energy Technology Data Exchange (ETDEWEB)
Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)
1998-12-31
A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)
Directory of Open Access Journals (Sweden)
Kohei Arai
2013-01-01
Full Text Available Method for image prediction with nonlinear control lines which are derived from extracted feature points from the previously acquired imagery data based on Kriging method and morphing method is proposed. Through comparisons between the proposed method and the conventional linear interpolation and widely used Cubic Spline interpolation methods, it is found that the proposed method is superior to the conventional methods in terms of prediction accuracy.
Nonlinear Spline Kernel-based Partial Least Squares Regression Method and Its Application
Institute of Scientific and Technical Information of China (English)
JIA Jin-ming; WEN Xiang-jun
2008-01-01
Inspired by the traditional Wold's nonlinear PLS algorithm comprises of NIPALS approach and a spline inner function model,a novel nonlinear partial least squares algorithm based on spline kernel(named SK-PLS)is proposed for nonlinear modeling in the presence of multicollinearity.Based on the iuner-product kernel spanned by the spline basis functions with infinite numher of nodes,this method firstly maps the input data into a high dimensional feature space,and then calculates a linear PLS model with reformed NIPALS procedure in the feature space and gives a unified framework of traditional PLS"kernel"algorithms in consequence.The linear PLS in the feature space corresponds to a nonlinear PLS in the original input (primal)space.The good approximating property of spline kernel function enhances the generalization ability of the novel model,and two numerical experiments are given to illustrate the feasibility of the proposed method.
Tremblay-Darveau, Charles; Williams, Ross; Milot, Laurent; Bruce, Matthew; Burns, Peter N
2014-12-01
Plane-wave imaging offers image acquisition rates at the pulse repetition frequency, effectively increasing the imaging frame rates by up to two orders of magnitude over conventional line-by-line imaging. This form of acquisition can be used to achieve very long ensemble lengths in nonlinear modes such as pulse inversion Doppler, which enables new imaging trade-offs that were previously unattainable. We first demonstrate in this paper that the coherence of microbubble signals under repeated exposure to acoustic pulses of low mechanical index can be as high as 204 ± 5 pulses, which is long enough to allow an accurate power Doppler measurement. We then show that external factors, such as tissue acceleration, restrict the detection of perfusion at the capillary level with linear Doppler, even if long Doppler ensembles are considered. Hence, perfusion at the capillary level can only be detected with ultrasound through combined microbubbles and Doppler imaging. Finally, plane-wave contrast-enhanced power and color Doppler are performed on a rabbit kidney in vivo as a proof of principle. We establish that long pulse-inversion Doppler sequences and conventional wall-filters can create an image that simultaneously resolves both the vascular morphology of veins and arteries, and perfusion at the capillary level with frame rates above 100 Hz.
Institute of Scientific and Technical Information of China (English)
Pan Jun-Ting; Gong Lun-Xun
2008-01-01
Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation,and by converting it into a new expansion form,this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations.Being concise and straightforward,themethod is applied to modified Benjamin-Bona-Mahony (mBBM) model,and some new exact solutions to the system are obtained.The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.
A One-parameter Filled Function Method for Nonlinear Integer Programming
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
This paper gives a new definition of the filled function for nonlinear integer programming problem. A filled function satisfying our definition is presented. This function contains only one parameter. The properties of the proposed filled function and the method using this filled function to solve nonlinear integer programming problem are also discussed. Numerical results indicate the efficiency and reliability of the proposed filled function algorithm.
Singular perturbation methods for nonlinear dynamic systems with time delays
Energy Technology Data Exchange (ETDEWEB)
Hu, H.Y. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)], E-mail: hhyae@nuaa.edu.cn; Wang, Z.H. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)
2009-04-15
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.
A stabilised nodal spectral element method for fully nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, C.; Bigoni, Daniele
2016-01-01
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although...... the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions...
He-Laplace Method for Linear and Nonlinear Partial Differential Equations
Directory of Open Access Journals (Sweden)
Hradyesh Kumar Mishra
2012-01-01
Full Text Available A new treatment for homotopy perturbation method is introduced. The new treatment is called He-Laplace method which is the coupling of the Laplace transform and the homotopy perturbation method using He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. The method is implemented on linear and nonlinear partial differential equations. It is found that the proposed scheme provides the solution without any discretization or restrictive assumptions and avoids the round-off errors.
Directory of Open Access Journals (Sweden)
Banan Maayah
2014-01-01
Full Text Available A new algorithm called multistep reproducing kernel Hilbert space method is represented to solve nonlinear oscillator’s models. The proposed scheme is a modification of the reproducing kernel Hilbert space method, which will increase the intervals of convergence for the series solution. The numerical results demonstrate the validity and the applicability of the new technique. A very good agreement was found between the results obtained using the presented algorithm and the Runge-Kutta method, which shows that the multistep reproducing kernel Hilbert space method is very efficient and convenient for solving nonlinear oscillator’s models.
Solution of (3+1-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method
Directory of Open Access Journals (Sweden)
Hassan A. Zedan
2012-01-01
Full Text Available Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.
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.
Energy Technology Data Exchange (ETDEWEB)
Ravi Kanth, A.S.V. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)], E-mail: asvravikanth@yahoo.com; Aruna, K. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)
2008-11-17
In this Letter, we propose a reliable algorithm to develop exact and approximate solutions for the linear and non-linear systems of partial differential equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.
Directory of Open Access Journals (Sweden)
Sahar Zakeri
2017-02-01
Full Text Available Objective: Interest in the subject of creativity and its impacts on human life is growing extensively. However, only a few surveys pay attention to the relation between creativity and physiological changes. This paper presents a novel approach to distinguish between creativity states from electrocardiogram signals. Nineteen linear and nonlinear features of the cardiac signal were extracted to detect creativity states. Method: ECG signals of 52 participants were recorded while doing three tasks of Torrance Tests of Creative Thinking (TTCT/ figural B. To remove artifacts, notch filter 50 Hz and Chebyshev II were applied. According to TTCT scores, participants were categorized into the high and low creativity groups: Participants with scores higher than 70 were assigned into the high creativity group and those with scores less than 30 were considered as low creativity group. Some linear and nonlinear features were extracted from the ECGs. Then, Support Vector Machine (SVM and Adaptive Neuro-Fuzzy Inference System (ANFIS were used to classify the groups.Results: Applying the Wilcoxon test, significant differences were observed between rest and each three tasks of creativity. However, better discrimination was performed between rest and the first task. In addition, there were no statistical differences between the second and third task of the test. The results indicated that the SVM effectively detects all the three tasks from the rest, particularly the task 1 and reached the maximum accuracy of 99.63% in the linear analysis. In addition, the high creative group was separated from the low creative group with the accuracy of 98.41%.Conclusion: the combination of SVM classifier with linear features can be useful to show the relation between creativity and physiological changes.
Zakeri, Sahar; Abbasi, Ataollah; Goshvarpour, Ateke
2017-01-01
Objective: Interest in the subject of creativity and its impacts on human life is growing extensively. However, only a few surveys pay attention to the relation between creativity and physiological changes. This paper presents a novel approach to distinguish between creativity states from electrocardiogram signals. Nineteen linear and nonlinear features of the cardiac signal were extracted to detect creativity states. Method: ECG signals of 52 participants were recorded while doing three tasks of Torrance Tests of Creative Thinking (TTCT/ figural B). To remove artifacts, notch filter 50 Hz and Chebyshev II were applied. According to TTCT scores, participants were categorized into the high and low creativity groups: Participants with scores higher than 70 were assigned into the high creativity group and those with scores less than 30 were considered as low creativity group. Some linear and nonlinear features were extracted from the ECGs. Then, Support Vector Machine (SVM) and Adaptive Neuro-Fuzzy Inference System (ANFIS) were used to classify the groups. Results: Applying the Wilcoxon test, significant differences were observed between rest and each three tasks of creativity. However, better discrimination was performed between rest and the first task. In addition, there were no statistical differences between the second and third task of the test. The results indicated that the SVM effectively detects all the three tasks from the rest, particularly the task 1 and reached the maximum accuracy of 99.63% in the linear analysis. In addition, the high creative group was separated from the low creative group with the accuracy of 98.41%. Conclusion: the combination of SVM classifier with linear features can be useful to show the relation between creativity and physiological changes.
Li, Cheng; Zhao, Tianlun; Li, Cong; Mei, Lei; Yu, En; Dong, Yating; Chen, Jinhong; Zhu, Shuijin
2017-04-15
Near infrared (NIR) spectroscopy combined with Monte Carlo uninformative variable elimination (MC-UVE) and nonlinear calibration methods employed to determine gossypol content in cottonseeds were investigated. The reference method was performed by high performance liquid chromatography coupled to an ultraviolet detector (HPLC-UV). MC-UVE was employed to extract the effective information from the full NIR spectra. Nonlinear calibration methods were applied to establish the models compared with the linear method. The optimal model for gossypol content was obtained by MC-UVE-WLS-SVM, with root mean squares error of prediction (RMSEP) of 0.0422, coefficient of determination (R(2)) of 0.9331, and residual predictive deviation (RPD) of 3.8374, respectively, which was accurate and robust enough to substitute for traditional gossypol measurements. The nonlinear methods performed more reliable than linear method during the development of calibration models. Furthermore, MC-UVE could provide better and simpler calibration models than full spectra.
Nonlinear viscosity derived by means of Grad's moment method
Eu, Byung Chan
2002-03-01
In this paper we examine the stress tensor component evolution equations recently derived by Uribe and Garcia-Colin [Phys. Rev. E 60, 4052 (1999)] for unidirectional flow at uniform temperature under the assumption/approximation of vanishing transversal velocity gradients. By removing this assumption/approximation we derive the stress tensor evolution equation from the Boltzmann equation within the framework of the Grad moment expansion for the case of uniform temperature (the same condition as theirs). Specializing the evolution equation to the case of steady unidirectional flow in a square channel, we obtain a set of steady state evolution equations for the components of the stress tensor. Because the transversal velocity gradients are not assumed to vanish in this paper in contrast to their paper, the present result is more general than theirs. Its special case corresponding to the one-dimensional flow considered by Uribe and Garcia-Colin is at variance with theirs because of a missing term in their stress evolution equation for the xy component. The nonlinear viscosity formulas are also different. A general remark is given with regard to the relation of dimensionalities of hydrodynamic equations and the kinetic equation underlying the former. They are not necessarily the same.
A new method for observing the running states of a single-variable nonlinear system.
Meng, Yu; Chen, Hong; Chen, Cheng
2015-03-01
In order to timely grasp a single variable nonlinear system running states, a new method called Scatter Point method is put forward in this paper. It can be used to observe or monitor the running states of a single variable nonlinear system in real-time. In this paper, the definition of the method is given at first, and then its working principle is expounded theoretically, after this, some physical experiments based on Chua's nonlinear system are conducted. At the same time, many scatter point graphs are measured by a general analog oscilloscope. The motion, number, and distribution of these scatter points shown on the oscilloscope screen can directly reflect the current states of the tested system. The experimental results further confirm that the method is effective and practical, in which the system running states are not easily lost. In addition, this method is not only suitable for single variable systems but also for multivariable systems.
Demi, L; van Dongen, K W A; Verweij, M D
2011-03-01
Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation.
A time stepping method in analysis of nonlinear structural dynamics
Directory of Open Access Journals (Sweden)
Gholampour A. A.
2011-12-01
Full Text Available In this paper a new method is proposed for the direct time integration method for structural dynamics problems. The proposed method assumes second order variations of the acceleration at each time step. Therefore more terms in the Taylor series expansion were used compared to other methods. Because of the increase in order of variations of acceleration, this method has higher accuracy than classical methods. The displacement function is a polynomial with five constants and they are calculated using: two equations for initial conditions (from the end of previous time step, two equations for satisfying the equilibrium at both ends of the time step, and one equation for the weighted residual integration. Proposed method has higher stability and order of accuracy than the other methods.
On Newton-Like Methods for Solving Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we present a family of general Newton-like methods with a parametric function for finding a zero of a univariate function, permitting f′(x)=0 in some points. The case of multiple roots is not treated. The methods are proved to be quadratically convergent provided the weak condition. Thus the methods remove the severe condition f′(x)≠0. Based on the general form of the Newton-like methods, a family of new iterative methods with a variable parameter are developed.
Stability analysis of nonlinear systems by multiple time scaling. [using perturbation methods
Morino, L.
1974-01-01
The asymptotic solution for the transient analysis of a general nonlinear system in the neighborhood of the stability boundary was obtained by using the multiple-time-scaling asymptotic-expansion method. The nonlinearities are assumed to be of algebraic nature. Terms of order epsilon to the 3rd power (where epsilon is the order of amplitude of the unknown) are included in the solution. The solution indicates that there is always a limit cycle which is stable (unstable) and exists above (below) the stability boundary if the nonlinear terms are stabilizing (destabilizing). Extension of the solution to include fifth order nonlinear terms is also presented. Comparisons with harmonic balance and with multiple-time-scaling solution of panel flutter equations are also included.
Directory of Open Access Journals (Sweden)
Sarvesh Kumar
2014-01-01
Full Text Available The incompressible miscible displacement problem in porous media is modeled by a coupled system of two nonlinear partial differential equations, the pressure-velocity equation and the concentration equation. In this paper, we present a mixed finite volume element method (FVEM for the approximation of the pressure-velocity equation. Since modified method of characteristics (MMOC minimizes the grid orientation effect, for the approximation of the concentration equation, we apply a standard FVEM combined with MMOC. A priori error estimates in L∞(L2 norm are derived for velocity, pressure and concentration. Numerical results are presented to substantiate the validity of the theoretical results.
Image quality assessment method based on nonlinear feature extraction in kernel space
Institute of Scientific and Technical Information of China (English)
Yong DING‡; Nan LI; Yang ZHAO; Kai HUANG
2016-01-01
To match human perception, extracting perceptual features effectively plays an important role in image quality assessment. In contrast to most existing methods that use linear transformations or models to represent images, we employ a complex mathematical expression of high dimensionality to reveal the statistical characteristics of the images. Furthermore, by introducing kernel methods to transform the linear problem into a nonlinear one, a full-reference image quality assessment method is proposed based on high-dimensional nonlinear feature extraction. Experiments on the LIVE, TID2008, and CSIQ databases demonstrate that nonlinear features offer competitive performance for image inherent quality representation and the proposed method achieves a promising performance that is consistent with human subjective evaluation.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A. [Departamento de Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2008-09-22
An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency 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, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. 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 with complex nonlinearities.
Method of Green’s function of nonlinear vibration of corrugated shallow shells
Institute of Scientific and Technical Information of China (English)
2008-01-01
Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution, the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated. The nonlinear partial differential equations of shallow shell were re-duced to the nonlinear integral-differential equations by using the method of Green’s function. To solve the integral-differential equations, the expansion method was used to obtain Green’s function. Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green’s function as a series of characteristic function. Therefore, the integral-differential equations be-came nonlinear ordinary differential equations with regard to time. The ampli-tude-frequency relation, with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force, were obtained by considering single mode vibration. As a numerical example, nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied. The obtained solutions are available for reference to the design of corrugated shells.
Method of Green's function of nonlinear vibration of corrugated shallow shells
Institute of Scientific and Technical Information of China (English)
YUAN Hong
2008-01-01
Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution,the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated.The nonlinear partial differential equations of shallow shell were re-duced to the nonlinear integral-differential equations by using the method of Green's function.To solve the integral-differential equations,the expansion method was used to obtain Green's function.Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green's function as a series of characteristic function.Therefore,the integral-differential equations be-came nonlinear ordinary differential equations with regard to time.The ampli-tude-frequency relation,with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force,were obtained by considering single mode vibration.As a numerical example,nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied.The obtained solutions are available for reference to the design of corrugated shells.
Institute of Scientific and Technical Information of China (English)
DUAN Wan-suo; MU Mu
2005-01-01
Linear singular vector and linear singular value can only describe the evolution of sufficiently small perturbations during the period in which the tangent linear model is valid.With this in mind, the applications of nonlinear optimization methods to the atmospheric and oceanic sciences are introduced, which include nonlinear singular vector (NSV) and nonlinear singular value (NSVA), conditional nonlinear optimal perturbation (CNOP), and their applications to the studies of predictability in numerical weather and climate prediction.The results suggest that the nonlinear characteristics of the motions of atmosphere and oceans can be explored by NSV and CNOP. Also attentions are paid to the introduction of the classification of predictability problems, which are related to the maximum predictable time,the maximum prediction error, and the maximum allowing error of initial value and the parameters. All the information has the background of application to the evaluation of products of numerical weather and climate prediction. Furthermore the nonlinear optimization methods of the sensitivity analysis with numerical model are also introduced, which can give a quantitative assessment whether a numerical model is able to simulate the observations and find the initial field that yield the optimal simulation. Finally, the difficulties in the lack of ripe algorithms are also discussed, which leave future work to both computational mathematics and scientists in geophysics.
Institute of Scientific and Technical Information of China (English)
WANG Mei-Jiao; WANG Qi
2006-01-01
In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons & Fractals 25 (2005) 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions' soliton-like solutions and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.
Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics
Wu, Shen R
2012-01-01
A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit FiniteElement Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in master
A new variable coefficient algebraic method and non-traveling wave solutions of nonlinear equations
Institute of Scientific and Technical Information of China (English)
Lu Bin; Zhang Hong-Qing
2008-01-01
In this paper,a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics,which is direct and more powerful than projective Riccati equation method.In order to illustrate the validity and the advantages of the method,(2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained.This algorithm can also be applied to other nonlinear differential equations.
Application of nonlinear optimization method to sensitivity analysis of numerical model
Institute of Scientific and Technical Information of China (English)
XU Hui; MU Mu; LUO Dehai
2004-01-01
A nonlinear optimization method is applied to sensitivity analysis of a numerical model. Theoretical analysis and numerical experiments indicate that this method can give not only a quantitative assessment whether the numerical model is able to simulate the observations or not, but also the initial field that yields the optimal simulation. In particular, when the simulation results are apparently satisfactory, and sometimes both model error and initial error are considerably large, the nonlinear optimization method, under some conditions, can identify the error that plays a dominant role.
Directory of Open Access Journals (Sweden)
H. M. Abdelhafez
2016-03-01
Full Text Available The modified differential transform method (MDTM, Laplace transform and Padé approximants are used to investigate a semi-analytic form of solutions of nonlinear oscillators in a large time domain. Forced Duffing and forced van der Pol oscillators under damping effect are studied to investigate semi-analytic forms of solutions. Moreover, solutions of the suggested nonlinear oscillators are obtained using the fourth-order Runge-Kutta numerical solution method. A comparison of the result by the numerical Runge-Kutta fourth-order accuracy method is compared with the result by the MDTM and plotted in a long time domain.
A new method of thermal network modeling - A nonlinear programming approach
Adachi, M.; Miyaoka, S.; Muramatsu, A.; Funabashi, M.; Nakajima, T.
A new method for correcting thermal network model coefficients is described. This method sharply reduces discrepancies obtained by the nonlinear programming approach in the conductance coefficients and radiation coefficients for determining the heat balance of a spacecraft. The method consists of an experimental design and a nonlinear parameter identification. An experimental design for obtaining useful data for the thermal network model correction is discussed. A simulation study has shown that the standard deviation of the estimated temperature and estimation error of the parameters are reduced by 50 percent and 70 percent respectively.
A weak condition for secant method to solve systems of nonlinear equations
Institute of Scientific and Technical Information of China (English)
LIANG Ke-wei; HAN Dan-fu; ZHANG Hong; ZHU Cheng-yan
2009-01-01
In this paper, a new weak condition for the convergence of secant method to solve the systems of nonlinear equations is proposed. A convergence ball with the center x0 is replaced by that with X1, the first approximation generated by the secant method with the initial data x-1 and x0. Under the bounded conditions of the divided difference, a convergence theorem is obtained and two examples to illustrate the weakness of convergence conditions are provided.Moreover, the secant method is applied to a system of nonlinear equations to demonstrate the viability and effectiveness of the results in the paper.
Simple equation method for nonlinear partial differential equations and its applications
Directory of Open Access Journals (Sweden)
Taher A. Nofal
2016-04-01
Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.
An iterative regularization method for nonlinear problems based on Bregman projections
Maaß, Peter; Strehlow, Robin
2016-11-01
In this paper, we present an iterative method for the regularization of ill-posed, nonlinear problems. The approach is based on the Bregman projection onto stripes the width of which is controlled by both the noise level and the structure of the operator. In our investigations, we follow (Lorenz et al 2014 SIAM J. Imaging Sci. 7 1237-62) and extend the respective method to the setting of nonlinear operators. Furthermore, we present a proof for the regularizing properties of the method.
A NOTE ON THE NONLINEAR CONJUGATE GRADIENT METHOD
Institute of Scientific and Technical Information of China (English)
Yu-hong Dai; Ya-xiang Yuan
2002-01-01
The conjugate gradient method for unconstrained optimization problems varies with a scalar. In this note, a general condition concerning the scalar is given, which ensures the global convergence of the method in the case of strong Wolfe line searches. It is also discussed how to use the result to obtain the convergence of the famous Fletcher-Reeves, and Polak-Ribiere-Polyak conjugate gradient methods. That the condition cannot be relaxed in some sense is mentioned.
Multi-Symplectic Splitting Method for Two-Dimensional Nonlinear Schriidinger Equation
Institute of Scientific and Technical Information of China (English)
陈亚铭; 朱华君; 宋松和
2011-01-01
Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.
Three-Step Iterative Methods with Sixth-Order Convergence for Solving Nonlinear Equations
Directory of Open Access Journals (Sweden)
Behzad GHANBARI
2012-09-01
Full Text Available In this paper, we develop new families of sixth-order methods for solving simple zeros of non-linear equations. These methods are constructed such that the convergence is of order six. Each member of the families requires two evaluations of the given function and two of its derivative per iteration. These methods have more advantages than Newton’s method and other methods with the same convergence order, as shown in the illustration examples.
A nonlinearity compensation method for a matrix converter drive
DEFF Research Database (Denmark)
Lee, Kyo-Beum; Blaabjerg, Frede
2005-01-01
converter model using the direction of current. The proposed method does not need any additional hardware or complicated software and it is easy to realize by applying the algorithm to the conventional vector control. The proposed compensation method is applied for high-performance induction motor drives...
4th Workshop on Combinations of Intelligent Methods and Applications
Palade, Vasile; Prentzas, Jim
2016-01-01
This volume includes extended and revised versions of the papers presented at the 4th Workshop on “Combinations of Intelligent Methods and Applications” (CIMA 2014) which was intended to become a forum for exchanging experience and ideas among researchers and practitioners dealing with combinations of different intelligent methods in Artificial Intelligence. The aim is to create integrated or hybrid methods that benefit from each of their components. Some of the existing presented efforts combine soft computing methods (fuzzy logic, neural networks and genetic algorithms). Another stream of efforts integrates case-based reasoning or machine learning with soft-computing methods. Some of the combinations have been more widely explored, like neuro-symbolic methods, neuro-fuzzy methods and methods combining rule-based and case-based reasoning. CIMA 2014 was held in conjunction with the 26th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2014). .
A Projection-Programming Method of Combination Weighting
Institute of Scientific and Technical Information of China (English)
ZeshuiXu; LiLi
2004-01-01
This paper proposes a projection programming method of combination weighting. The method combines subjective weights and objective weights, and derives the weights of attributes by solving a projection-programming model. The method is simple, practical and easy to implement on computer. A numerical example is also given.
Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K
2016-08-08
In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.
Tiffany, Sherwood H.; Adams, William M., Jr.
1988-01-01
The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.
Shi, Zhong-Ke; Wu, Fang-Xiang
2013-06-01
A common assumption is that the model structure is known for modelling high performance aircraft. In practice, this is not the case. Actually, structure identification plays the most important role in the processing of nonlinear system modelling. The integration of mode structure identification and parameter estimation is an efficient method to construct the model for high performance aircraft, which is nonlinear and also contains uncertainties. This article presents an efficient method for identifying nonlinear model structure and estimating parameters for high-performance aircraft model, which contains uncertainties. The parameters associated with nonlinear terms are considered one after the other if they should be included in the nonlinear model until a stopping criterion is met, which is based on Akaike's information criterion. A numerically efficient U-D factorisation is presented to avoid complex computation of high-order matrices. The proposed method is applied to flight test data of a high-performance aircraft. The results demonstrate that the proposed method could obtain the good aircraft model with a reasonably good fidelity based on the comparison with flight test data.
Meshkat, Nicolette; Anderson, Chris; Distefano, Joseph J
2011-09-01
When examining the structural identifiability properties of dynamic system models, some parameters can take on an infinite number of values and yet yield identical input-output data. These parameters and the model are then said to be unidentifiable. Finding identifiable combinations of parameters with which to reparameterize the model provides a means for quantitatively analyzing the model and computing solutions in terms of the combinations. In this paper, we revisit and explore the properties of an algorithm for finding identifiable parameter combinations using Gröbner Bases and prove useful theoretical properties of these parameter combinations. We prove a set of M algebraically independent identifiable parameter combinations can be found using this algorithm and that there exists a unique rational reparameterization of the input-output equations over these parameter combinations. We also demonstrate application of the procedure to a nonlinear biomodel.
Nonlinear system identification with global and local soft computing methods
Energy Technology Data Exchange (ETDEWEB)
Runkler, T.A. [Siemens AG, Muenchen (Germany). Zentralabt. Technik Information und Kommunikation
2000-10-01
An important step in the design of control systems is system identification. Data driven system identification finds functional models for the system's input output behavior. Regression methods are simple and effective, but may cause overshoots for complicated characteristics. Neural network approaches such as the multilayer perceptron yield very accurate models, but are black box approaches which leads to problems in system and stability analysis. In contrast to these global modeling methods crisp and fuzzy rule bases represent local models that can be extracted from data by clustering methods. Depending on the type and number of models different degrees of model accuracy can be achieved. (orig.)
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In this paper, we extend the mapping transformation method through introducing variable coefficients.By means of the extended mapping transformation method, many explicit and exact general solutions with arbitrary functions for some nonlinear partial differential equations, which contain solitary wave solutions, trigonometric function solutions, and rational solutions, are obtained.
A new method to obtain approximate symmetry of nonlinear evolution equation from perturbations
Institute of Scientific and Technical Information of China (English)
Zhang Zhi-Yong; Yong Xue-Lin; Chen Yu-Fu
2009-01-01
A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.
Institute of Scientific and Technical Information of China (English)
CHEN Jiang; HE Hong-Sheng; YANG Kong-Qing
2005-01-01
A generalized F-expansion method is introduced and applied to (3+ 1)-dimensional Kadomstev-Petviashvili(KP) equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the trigonometric function solutions and the solitary wave solutions can be obtained. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.
Indian Academy of Sciences (India)
Wenjun Liu; Kewang Chen
2013-09-01
In this paper, we implemented the functional variable method and the modified Riemann–Liouville derivative for the exact solitary wave solutions and periodic wave solutions of the time-fractional Klein–Gordon equation, and the time-fractional Hirota–Satsuma coupled KdV system. This method is extremely simple but effective for handling nonlinear time-fractional differential equations.
A Smooth Newton Method for Nonlinear Programming Problems with Inequality Constraints
Directory of Open Access Journals (Sweden)
Vasile Moraru
2012-02-01
Full Text Available The paper presents a reformulation of the Karush-Kuhn-Tucker (KKT system associated nonlinear programming problem into an equivalent system of smooth equations. Classical Newton method is applied to solve the system of equations. The superlinear convergence of the primal sequence, generated by proposed method, is proved. The preliminary numerical results with a problems test set are presented.
Asymptotic Analysis to Two Nonlinear Equations in Fluid Mechanics by Homotopy Renormalisation Method
Guan, Jiang; Kai, Yue
2016-09-01
By the homotopy renormalisation method, the global approximate solutions to Falkner-Skan equation and Von Kármá's problem of a rotating disk in an infinite viscous fluid are obtained. The homotopy renormalisation method is simple and powerful for finding global approximate solutions to nonlinear perturbed differential equations arising in mathematical physics.
Variational space–time (dis)continuous Galerkin method for nonlinear free surface water waves
Gagarina, E.; Ambati, V.R.; Vegt, van der J.J.W.; Bokhove, O.
2014-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves using the potential flow approximation. This method also handles waves generated by a wave maker. Its formulation stems from Miles’ variational principle for water waves together with a finite element
Variational space-time (dis)continuous Galerkin method for nonlinear free surface waves
Gagarina, E.; Vegt, van der J.J.W.; Ambati, V.R.; Bokhove, O.
2013-01-01
A new variational finite element method is developed for nonlinear free surface gravity water waves. This method also handles waves generated by a wave maker. Its formulation stems from Miles' variational principle for water waves together with a space-time finite element discretization that is cont
Energy Technology Data Exchange (ETDEWEB)
Zhang Huiqun [College of Mathematical Science, Qingdao University, Qingdao, Shandong 266071 (China)], E-mail: hellozhq@yahoo.com.cn
2009-02-15
By using some exact solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct the exact complex solutions for nonlinear partial differential equations. The method is implemented for the NLS equation, a new Hamiltonian amplitude equation, the coupled Schrodinger-KdV equations and the Hirota-Maccari equations. New exact complex solutions are obtained.
Directory of Open Access Journals (Sweden)
Abaker. A. Hassaballa.
2015-10-01
Full Text Available - In recent years, many more of the numerical methods were used to solve a wide range of mathematical, physical, and engineering problems linear and nonlinear. This paper applies the homotopy perturbation method (HPM to find exact solution of partial differential equation with the Dirichlet and Neumann boundary conditions.
Numerical Analysis of Strongly Nonlinear Oscillation Systems using He's Max-Min Method
DEFF Research Database (Denmark)
Babazadeh, H; Domairry, G; Barari, Amin;
2011-01-01
Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method...
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation an
Indian Academy of Sciences (India)
Yusuf Gurefe; Abdullah Sonmezoglu; Emine Misirli
2011-12-01
In this paper some exact solutions including soliton solutions for the KdV equation with dual power law nonlinearity and the (, ) equation with generalized evolution are obtained using the trial equation method. Also a more general trial equation method is proposed.
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation
Boosting iterative stochastic ensemble method for nonlinear calibration of subsurface flow models
Elsheikh, Ahmed H.
2013-06-01
A novel parameter estimation algorithm is proposed. The inverse problem is formulated as a sequential data integration problem in which Gaussian process regression (GPR) is used to integrate the prior knowledge (static data). The search space is further parameterized using Karhunen-Loève expansion to build a set of basis functions that spans the search space. Optimal weights of the reduced basis functions are estimated by an iterative stochastic ensemble method (ISEM). ISEM employs directional derivatives within a Gauss-Newton iteration for efficient gradient estimation. The resulting update equation relies on the inverse of the output covariance matrix which is rank deficient.In the proposed algorithm we use an iterative regularization based on the ℓ2 Boosting algorithm. ℓ2 Boosting iteratively fits the residual and the amount of regularization is controlled by the number of iterations. A termination criteria based on Akaike information criterion (AIC) is utilized. This regularization method is very attractive in terms of performance and simplicity of implementation. The proposed algorithm combining ISEM and ℓ2 Boosting is evaluated on several nonlinear subsurface flow parameter estimation problems. The efficiency of the proposed algorithm is demonstrated by the small size of utilized ensembles and in terms of error convergence rates. © 2013 Elsevier B.V.
Harmonic balance finite element method applications in nonlinear electromagnetics and power systems
Lu, Junwei; Yamada, Sotoshi
2016-01-01
The first book applying HBFEM to practical electronic nonlinear field and circuit problems * Examines and solves wide aspects of practical electrical and electronic nonlinear field and circuit problems presented by HBFEM * Combines the latest research work with essential background knowledge, providing an all-encompassing reference for researchers, power engineers and students of applied electromagnetics analysis * There are very few books dealing with the solution of nonlinear electric- power-related problems * The contents are based on the authors' many years' research and industry experience; they approach the subject in a well-designed and logical way * It is expected that HBFEM will become a more useful and practical technique over the next 5 years due to the HVDC power system, renewable energy system and Smart Grid, HF magnetic used in DC/DC converter, and Multi-pulse transformer for HVDC power supply * HBFEM can provide effective and economic solutions to R&D product development * Includes Matlab e...
Application of a new method of nonlinear dynamical system identification to biochemical problems.
Karnaukhov, A V; Karnaukhova, E V
2003-03-01
The system identification method for a variety of nonlinear dynamic models is elaborated. The problem of identification of an original nonlinear model presented as a system of ordinary differential equations in the Cauchy explicit form with a polynomial right part reduces to the solution of the system of linear equations for the constants of the dynamical model. In other words, to construct an integral model of the complex system (phenomenon), it is enough to collect some data array characterizing the time-course of dynamical parameters of the system. Collection of such a data array has always been a problem. However difficulties emerging are, as a rule, not principal and may be overcome almost without exception. The potentialities of the method under discussion are demonstrated by the example of the test problem of multiparametric nonlinear oscillator identification. The identification method proposed may be applied to the study of different biological systems and in particular the enzyme kinetics of complex biochemical reactions.
Directory of Open Access Journals (Sweden)
Fukang Yin
2013-01-01
Full Text Available This paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs. The approximate solutions of PDEs are calculated in the form of a series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The main advantage of the new method is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. The results show that the proposed method is very effective and easy to implement.
Hein, Matthias
2010-01-01
Many problems in machine learning and statistics can be formulated as (generalized) eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding critical points of a quadratic function subject to quadratic constraints. In this paper we show that a certain class of constrained optimization problems with nonquadratic objective and constraints can be understood as nonlinear eigenproblems. We derive a generalization of the inverse power method which is guaranteed to converge to a nonlinear eigenvector. We apply the inverse power method to 1-spectral clustering and sparse PCA which can naturally be formulated as nonlinear eigenproblems. In both applications we achieve state-of-the-art results in terms of solution quality and runtime. Moving beyond the standard eigenproblem should be useful also in many other applications and our inverse power method can be easily adapted to new problems.
Stability for a class of nonlinear time-delay systems via Hamiltonian functional method
Institute of Scientific and Technical Information of China (English)
YANG RenMing; WANG YuZhen
2012-01-01
This paper investigates the stability of a class of nonlinear time-delay systems via Hamiltonian functional method,and proposes a number of new results on generalized Hamiltonian realization (GHR) and stability analysis for this class of systems.Firstly,the concept of GHR of general nonlinear time-delay systems is proposed,and several new GHR methods are given.Then,based on the new GHR methods obtained,the stability of time-delay systems is investigated,and several delay-dependent sufficient conditions in term of matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov-Krasovskii (L-K) functionals.Finally,an illustrative example shows that the results obtained in this paper have less conservatism,and work very well in the stability analysis of some nonlinear time-delay Hamiltonian systems.
Directory of Open Access Journals (Sweden)
Mahsa Khoeiniha
2012-01-01
Full Text Available This paper investigated study of dynamics of nonlinear electrical circuit by means of modern nonlinear techniques and the control of a class of chaotic system by using backstepping method based on Lyapunov function. The behavior of such nonlinear system when they are under the influence of external sinusoidal disturbances with unknown amplitudes has been considered. The objective is to analyze the performance of this system at different amplitudes of disturbances. We illustrate the proposed approach for controlling duffing oscillator problem to stabilize this system at the equilibrium point. Also Genetic Algorithm method (GA for computing the parameters of controller has been used. GA can be successfully applied to achieve a better controller. Simulation results have shown the effectiveness of the proposed method.
The Optical Nonlinearity of Au and Ag Nanoparticle Prepared by the Γ-Radiation Method
Directory of Open Access Journals (Sweden)
Esmaeil Shahriari
2010-01-01
Full Text Available Problem statement: The third order nonlinear optical properties of metal nanoparticles have been of interest in physical chemistry, medical diagnostics and optical devices. Gold colloidal nanoparticles are responsible for the brilliant reds seen in stained glass windows and silver particles are typically yellow. The purpose of the study was to determine the nonlinear refraction and absorption coefficient of the Au and Ag nanoparticles in PVP solution. Approach: The samples were prepared by Γ-radiation method and the nonlinear optical properties of the composites were investigated using a single beam Z-scan technique with a beam power of 40 mW and operated at wavelength of 532 nm. The measurements were carried out for both Open and closed aperture Z-scan arrangements. Results: For both Au/PVP and Ag/PVP samples the results exhibited reverse saturable absorption. The closed aperture Z-scan of the nano-fluid samples revealed self-defocusing effect while the open aperture Z-scan of the samples show a reversible saturable absorption. Conclusion: The Z-scan measurement showed that silver and gold nano-fluid prepared by gamma radiation exhibited large thermal nonlinear refractive index n2 as -8.78×10-7 and -2.478×10-6 cm2/W, respectively. We have also investigated nonlinear absorption of these samples and we found a large value of nonlinear absorption for Ag nanoparticle and a weak absorption for Au nanoparticle. In conclusion, the experimental result shows a good nonlinear refractive index at low laser power in which encouraging for possible applications in nonlinear optical devices.
Directory of Open Access Journals (Sweden)
Uswah Qasim
2016-03-01
Full Text Available A homotopy method is presented for the construction of frozen Jacobian iterative methods. The frozen Jacobian iterative methods are attractive because the inversion of the Jacobian is performed in terms of LUfactorization only once, for a single instance of the iterative method. We embedded parameters in the iterative methods with the help of the homotopy method: the values of the parameters are determined in such a way that a better convergence rate is achieved. The proposed homotopy technique is general and has the ability to construct different families of iterative methods, for solving weakly nonlinear systems of equations. Further iterative methods are also proposed for solving general systems of nonlinear equations.
Yelve, Nitesh P; Mitra, Mira; Mujumdar, P M; Ramadas, C
2016-08-01
A new hybrid method based upon nonlinear Lamb wave response in time and frequency domains is introduced to locate a delamination in composite laminates. In Lamb wave based nonlinear method, the presence of damage is shown by the appearance of higher harmonics in the Lamb wave response. The proposed method not only uses this spectral information but also the corresponding temporal response data, for locating the delamination. Thus, the method is termed as a hybrid method. The paper includes formulation of the method and its application to locate a Barely Visible Impact Damage (BVID) induced delamination in a Carbon Fiber Reinforced Polymer (CFRP) laminate. The method gives the damage location fairly well. It is a baseline free method, as it does not need data from the pristine specimen.
Combined methods for elliptic equations with singularities, interfaces and infinities
Li, Zi Cai
1998-01-01
In this book the author sets out to answer two important questions: 1. Which numerical methods may be combined together? 2. How can different numerical methods be matched together? In doing so the author presents a number of useful combinations, for instance, the combination of various FEMs, the combinations of FEM-FDM, REM-FEM, RGM-FDM, etc. The combined methods have many advantages over single methods: high accuracy of solutions, less CPU time, less computer storage, easy coupling with singularities as well as the complicated boundary conditions. Since coupling techniques are essential to combinations, various matching strategies among different methods are carefully discussed. The author provides the matching rules so that optimal convergence, even superconvergence, and optimal stability can be achieved, and also warns of the matching pitfalls to avoid. Audience: The book is intended for both mathematicians and engineers and may be used as text for advanced students.
Measurement of nonlinear elastic response in rock by the resonant bar method
Energy Technology Data Exchange (ETDEWEB)
Johnson, P.A. (Los Alamos National Lab., NM (United States)); Rasolofosaon, P.; Zinszner, B. (Institut Francais du Petrole (IFP), 92 - Rueil-Malmaison (France))
1993-01-01
In this work we are studying the behavior of the fundamental (Young's) mode resonant peak as a function of drive amplitude in rock samples. Our goal from these studies is to obtain nonlinear moduli for many rock types, and to study the nonlinear moduli as a function of water saturation and other changes in physical properties. Measurements were made on seven different room dry rock samples. For one sample measurements were taken at 16 saturation levels between 1 and 98%. All samples display a softening'' nonlinearity, that is, the resonant frequency shifts downward with increasing drive amplitude. In extreme cases, the resonant frequency changes by as much as 25% over a strain interval of 10[sup [minus]7] to [approximately]4 [times] 10[sup [minus]5]. Measurements indicate that the nonlinear response is extremely sensitive to saturation. Estimates of a combined cubic and quartic nonlinear parameter [Gamma] range from approximately [minus]300 to [minus]10[sup 9] for the rock samples.
Measurement of heart rate variability by methods based on nonlinear dynamics.
Huikuri, Heikki V; Mäkikallio, Timo H; Perkiömäki, Juha
2003-01-01
Heart rate (HR) variability has been conventionally analyzed with time and frequency domain methods, which measure the overall magnitude of R-R interval fluctuations around its mean value or the magnitude of fluctuations in some predetermined frequencies. Analysis of HR dynamics by methods based on chaos theory and nonlinear system theory has gained recent interest. This interest is based on observations suggesting that the mechanisms involved in cardiovascular regulation likely interact with each other in a nonlinear way. Furthermore, recent observational studies suggest that some indexes describing nonlinear HR dynamics, such as fractal scaling exponents, may provide more powerful prognostic information than the traditional HR variability indexes. In particular, short-term fractal scaling exponent measured by detrended fluctuation analysis method has been shown to predict fatal cardiovascular events in various populations. Approximate entropy, a nonlinear index of HR dynamics, which describes the complexity of R-R interval behavior, has provided information on the vulnerability to atrial fibrillation. There are many other nonlinear indexes, eg, Lyapunov exponent and correlation dimensions, which also give information on the characteristics of HR dynamics, but their clinical utility is not well established. Although concepts of chaos theory, fractal mathematics, and complexity measures of HR behavior in relation to cardiovascular physiology or various cardiovascular events are still far away from clinical medicine, they are a fruitful area for future research to expand our knowledge concerning the behavior of cardiovascular oscillations in normal healthy conditions as well as in disease states.
Li, Xingfeng; Coyle, Damien; Maguire, Liam; McGinnity, Thomas M; Benali, Habib
2011-07-01
In this paper a model selection algorithm for a nonlinear system identification method is proposed to study functional magnetic resonance imaging (fMRI) effective connectivity. Unlike most other methods, this method does not need a pre-defined structure/model for effective connectivity analysis. Instead, it relies on selecting significant nonlinear or linear covariates for the differential equations to describe the mapping relationship between brain output (fMRI response) and input (experiment design). These covariates, as well as their coefficients, are estimated based on a least angle regression (LARS) method. In the implementation of the LARS method, Akaike's information criterion corrected (AICc) algorithm and the leave-one-out (LOO) cross-validation method were employed and compared for model selection. Simulation comparison between the dynamic causal model (DCM), nonlinear identification method, and model selection method for modelling the single-input-single-output (SISO) and multiple-input multiple-output (MIMO) systems were conducted. Results show that the LARS model selection method is faster than DCM and achieves a compact and economic nonlinear model simultaneously. To verify the efficacy of the proposed approach, an analysis of the dorsal and ventral visual pathway networks was carried out based on three real datasets. The results show that LARS can be used for model selection in an fMRI effective connectivity study with phase-encoded, standard block, and random block designs. It is also shown that the LOO cross-validation method for nonlinear model selection has less residual sum squares than the AICc algorithm for the study.
A mixed Newton-Tikhonov method for nonlinear ill-posed problems
Institute of Scientific and Technical Information of China (English)
Chuan-gang KANG; Guo-qiang HE
2009-01-01
Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems,which have attracted extensive attention.However,computational cost of Newton type methods is high because practical problems are complicated.We propose a mixed Newton-Tikhonov method,i.e.,one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method.Convergence and stability of this method are proved under some conditions.Numerical experiments show that the proposed method has obvious advantages over the classical Newton method in terms of computational costs.
Extension of the homotopy pertubation method for solving nonlinear differential-difference equations
Energy Technology Data Exchange (ETDEWEB)
Mousa, Mohamed Medhat [Benha Univ. (Egypt). Benha High Inst. of Technology; Al-Farabi Kazakh National Univ., Almaty (Kazakhstan); Kaltayev, Aidarkan [Al-Farabi Kazakh National Univ., Almaty (Kazakhstan); Bulut, Hasan [Firat Univ., Elazig (Turkey). Dept. of Mathematics
2010-12-15
In this paper, we have extended the homotopy perturbation method (HPM) to find approximate analytical solutions for some nonlinear differential-difference equations (NDDEs). The discretized modified Korteweg-de Vries (mKdV) lattice equation and the discretized nonlinear Schroedinger equation are taken as examples to demonstrate the validity and the great potential of the HPM in solving such NDDEs. Comparisons are made between the results of the presented method and exact solutions. The obtained results reveal that the HPM is a very effective and convenient tool for solving such kind of equations. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Hagstrom, T. [Univ. of New Mexico, Albuquerque, NM (United States); Radhakrishnan, K. [Sverdrup Technology, Brook Park, OH (United States)
1994-12-31
The authors report on some iterative methods which they have tested for use in combustion simulations. In particular, they have developed a code to solve zero Mach number reacting flow equations with complex reaction and diffusion physics. These equations have the form of a nonlinear parabolic system coupled with constraints. In semi-discrete form, one obtains DAE`s of index two or three depending on the number of spatial dimensions. The authors have implemented a fourth order (fully implicit) BDF method in time, coupled with a suite of fourth order explicit and implicit spatial difference approximations. Most codes they know of for simulating reacting flows use a splitting strategy to march in time. This results in a sequence of nonlinear systems to solve, each of which has a simpler structure than the one they are faced with. The rapid and robust solution of the coupled system is the essential requirement for the success of their approach. They have implemented and analyzed nonlinear generalizations of conjugate gradient-like methods for nonsymmetric systems, including CGS and the quasi-Newton based method of Eirola and Nevanlinna. They develop a general framework for the nonlinearization of linear methods in terms of the acceleration of fixed-point iterations, where the latter is assumed to include the {open_quote}preconditioning{open_quote}. Their preconditioning is a single step of a split method, using lower order spatial difference approximations as well as simplified (Fickian) approximations of the diffusion physics.
An assessment of a semi analytical AG method for solving nonlinear oscillators
Directory of Open Access Journals (Sweden)
Hadi Mirgolbabaee
2016-02-01
Based on the comparison between AGM and numerical methods, AGM can be successfully applied for a broad range of nonlinear equations. One of the important reasons of selecting AGM for solving differential equations in miscellaneous fields not only in vibrations but also in different fields of sciences for instance fluid mechanics, solid mechanics, chemical engineering, etc. The main benefit of this method in comparison with the other approaches are as follows: normally according to the order of differential equations, we need boundary conditions so in the case of the number of boundary conditions is less than the order of the differential equation, AGM can create additional new boundary conditions in regard to the own differential equation and its derivatives. Results illustrate that method is efficient and has enough accuracy in comparison with other semi analytical and numerical methods because of the simplicity of this method. Moreover results demonstrate that AGM could be applicable through other methods in nonlinear problems with high nonlinearity. Furthermore convergence problems for solving nonlinear equations by using AGM appear small.
Nonlinear simulation of arch dam cracking with mixed finite element method
Directory of Open Access Journals (Sweden)
Ren Hao
2008-06-01
Full Text Available This paper proposes a new, simple and efficient method for nonlinear simulation of arch dam cracking from the construction period to the operation period, which takes into account the arch dam construction process and temperature loads. In the calculation mesh, the contact surface of pair nodes is located at places on the arch dam where cracking is possible. A new effective iterative method, the mixed finite element method for friction-contact problems, is improved and used for nonlinear simulation of the cracking process. The forces acting on the structure are divided into two parts: external forces and contact forces. The displacement of the structure is chosen as the basic variable and the nodal contact force in the possible contact region of the local coordinate system is chosen as the iterative variable, so that the nonlinear iterative process is only limited within the possible contact surface and is much more economical. This method was used to simulate the cracking process of the Shuanghe Arch Dam in Southwest China. In order to prove the validity and accuracy of this method and to study the effect of thermal stress on arch dam cracking, three schemes were designed for calculation. Numerical results agree with actual measured data, proving that it is feasible to use this method to simulate the entire process of nonlinear arch dam cracking.
A conservative Fourier pseudo-spectral method for the nonlinear Schrödinger equation
Gong, Yuezheng; Wang, Qi; Wang, Yushun; Cai, Jiaxiang
2017-01-01
A Fourier pseudo-spectral method that conserves mass and energy is developed for a two-dimensional nonlinear Schrödinger equation. By establishing the equivalence between the semi-norm in the Fourier pseudo-spectral method and that in the finite difference method, we are able to extend the result in Ref. [56] to prove that the optimal rate of convergence of the new method is in the order of O (N-r +τ2) in the discrete L2 norm without any restrictions on the grid ratio, where N is the number of modes used in the spectral method and τ is the time step size. A fast solver is then applied to the discrete nonlinear equation system to speed up the numerical computation for the high order method. Numerical examples are presented to show the efficiency and accuracy of the new method.
A LQP BASED INTERIOR PREDICTION-CORRECTION METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS
Institute of Scientific and Technical Information of China (English)
Bing-sheng He; Li-zhi Liao; Xiao-ming Yuan
2006-01-01
To solve nonlinear complementarity problems (NCP), at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the LogarithmicQuadratic Proximal (LQP) method solves a system of nonlinear equations (LQP system). This paper presents a practical LQP method-based prediction-correction method for NCP.The predictor is obtained via solving the LQP system approximately under significantly relaxed restriction, and the new iterate (the corrector) is computed directly by an explicit formula derived from the original LQP method. The implementations are very easy to be carried out. Global convergence of the method is proved under the same mild assumptions as the original LQP method. Finally, numerical results for traffic equilibrium problems are provided to verify that the method is effective for some practical problems.
Adaptive discontinuous Galerkin methods for non-linear reactive flows
Uzunca, Murat
2016-01-01
The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with internal/boundary layers in an accurate and efficient way. After introducing the ADR equations and discontinuous Galerkin discretization, robust residual-based a posteriori error estimators in space and time are derived. The elliptic reconstruction technique is then utilized to derive the a posteriori error bounds for the fully discrete system and to obtain optimal orders of convergence. As coupled surface and subsurface flow over large space and time scales is described by (ADR) equation the methods described in this book are of high importance in many areas of Geosciences including oil and gas recovery, groundwater contamination and sustainable use of groundwater resources, storing greenhouse gases or radioactive waste in the subsurface.
Nonlinear Least Squares Methods for Joint DOA and Pitch Estimation
DEFF Research Database (Denmark)
Jensen, Jesper Rindom; Christensen, Mads Græsbøll; Jensen, Søren Holdt
2013-01-01
In this paper, we consider the problem of joint direction-of-arrival (DOA) and fundamental frequency estimation. Joint estimation enables robust estimation of these parameters in multi-source scenarios where separate estimators may fail. First, we derive the exact and asymptotic Cram\\'{e}r-Rao...... estimation. Moreover, simulations on real-life data indicate that the NLS and aNLS methods are applicable even when reverberation is present and the noise is not white Gaussian....
Material nonlinear analysis via mixed-iterative finite element method
Sutjahjo, Edhi; Chamis, Christos C.
1992-01-01
The performance of elastic-plastic mixed-iterative analysis is examined through a set of convergence studies. Membrane and bending behaviors are tested using 4-node quadrilateral finite elements. The membrane result is excellent, which indicates the implementation of elastic-plastic mixed-iterative analysis is appropriate. On the other hand, further research to improve bending performance of the method seems to be warranted.
Controlling Beam Halo-chaos Using a Special Nonlinear Method
Institute of Scientific and Technical Information of China (English)
2002-01-01
Beam halo-chaos in high-current accelerators has become a key concerned issue because it can cause excessive radioactivity from the accelerators therefore significantly limits their applications in industry,medicine, and national defense. Some general engineering methods for chaos control have been developedin recent years, but they generally are unsuccessful for beam halo-chaos suppression due to manytechnical constraints. Beam halo-chaos is essentially a spatotemporal chaotic motion within a high power
Easy-to-implement method to target nonlinear systems
Baptista, Murilo S.; Caldas, Iberê L.
1998-03-01
In this work we present a method to rapidly direct a chaotic system, to an aimed state or target, through a sequence of control perturbations, with few different amplitudes chosen according to the allowed control-parameter changes. We applied this procedure to the one-dimensional Logistic map, to the two-dimensional Hénon map, and to the Double Scroll circuit described by a three-dimensional system of differential equations. Furthermore, for the Logistic map, we show numerically that the resulting trajectory (from the starting point to the target) goes along a stable manifold of the target. Moreover, using the Hénon map, we create and stabilize unstable periodic orbits, and also verify the procedure robustness in the presence of noise. We apply our method to the Double Scroll circuit, without using any low-dimensional mapping to represent its dynamics, an improvement with respect to previous targeting methods only applied for experimental systems that are mapping-modeled.
Nonlinear preprocessing method for detecting peaks from gas chromatograms
Directory of Open Access Journals (Sweden)
Min Hyeyoung
2009-11-01
Full Text Available Abstract Background The problem of locating valid peaks from data corrupted by noise frequently arises while analyzing experimental data. In various biological and chemical data analysis tasks, peak detection thus constitutes a critical preprocessing step that greatly affects downstream analysis and eventual quality of experiments. Many existing techniques require the users to adjust parameters by trial and error, which is error-prone, time-consuming and often leads to incorrect analysis results. Worse, conventional approaches tend to report an excessive number of false alarms by finding fictitious peaks generated by mere noise. Results We have designed a novel peak detection method that can significantly reduce parameter sensitivity, yet providing excellent peak detection performance and negligible false alarm rates from gas chromatographic data. The key feature of our new algorithm is the successive use of peak enhancement algorithms that are deliberately designed for a gradual improvement of peak detection quality. We tested our approach with real gas chromatograms as well as intentionally contaminated spectra that contain Gaussian or speckle-type noise. Conclusion Our results demonstrate that the proposed method can achieve near perfect peak detection performance while maintaining very small false alarm probabilities in case of gas chromatograms. Given the fact that biological signals appear in the form of peaks in various experimental data and that the propose method can easily be extended to such data, our approach will be a useful and robust tool that can help researchers highlight valid signals in their noisy measurements.
Zhang, Songchuan; Xia, Youshen
2016-12-28
Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an ℓ₁-norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms.
Analysis of search-extension method for finding multiple solutions of nonlinear problem
Institute of Scientific and Technical Information of China (English)
2008-01-01
For numerical computations of multiple solutions of the nonlinear elliptic problemΔu+ f（u）=0 inΩ, u=0 onΓ, a search-extension method （SEM） was proposed and systematically studied by the authors. This paper shall complete its theoretical analysis. It is assumed that the nonlinearity is non-convex and its solution is isolated, under some conditions the corresponding linearized problem has a unique solution. By use of the compactness of the solution family and the contradiction argument, in general conditions, the high order regularity of the solution u∈H1+α,α>0 is proved. Assume that some initial value searched by suitably many eigenbases is already fallen into the neighborhood of the isolated solution, then the optimal error estimates of its nonlinear finite element approximation are shown by the duality argument and continuation method.
An efficient and accurate method for calculating nonlinear diffraction beam fields
Energy Technology Data Exchange (ETDEWEB)
Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)
2016-04-15
This study develops an efficient and accurate method for calculating nonlinear diffraction beam fields propagating in fluids or solids. The Westervelt equation and quasilinear theory, from which the integral solutions for the fundamental and second harmonics can be obtained, are first considered. A computationally efficient method is then developed using a multi-Gaussian beam (MGB) model that easily separates the diffraction effects from the plane wave solution. The MGB models provide accurate beam fields when compared with the integral solutions for a number of transmitter-receiver geometries. These models can also serve as fast, powerful modeling tools for many nonlinear acoustics applications, especially in making diffraction corrections for the nonlinearity parameter determination, because of their computational efficiency and accuracy.
NONLINEAR FILTER METHOD OF GPS DYNAMIC POSITIONING BASED ON BANCROFT ALGORITHM
Institute of Scientific and Technical Information of China (English)
ZHANGQin; TAOBen-zao; ZHAOChao-ying; WANGLi
2005-01-01
Because of the ignored items after linearization, the extended Kalman filter (EKF) becomes a form of suboptimal gradient descent algorithm. The emanative tendency exists in GPS solution when the filter equations are ill-posed. The deviation in the estimation cannot be avoided. Furthermore, the true solution may be lost in pseudorange positioning because the linearized pseudorange equations are partial solutions. To solve the above problems in GPS dynamic positioning by using EKF, a closed-form Kalman filter method called the two-stage algorithm is presented for the nonlinear algebraic solution of GPS dynamic positioning based on the global nonlinear least squares closed algorithm--Bancroft numerical algorithm of American. The method separates the spatial parts from temporal parts during processing the GPS filter problems, and solves the nonlinear GPS dynamic positioning, thus getting stable and reliable dynamic positioning solutions.
Energy Technology Data Exchange (ETDEWEB)
Etchepareborda, Andres [Department of Nuclear Engineering, Argentine National Atomic Energy Commission, Centro Atomico Bariloche, Av. E. Bustillo 9500, Bariloche 8400 (Argentina)]. E-mail: etche@cab.cnea.gov.ar; Lolich, Jose [INVAP S.E., Moreno 1089, Bariloche 8400 (Argentina)
2007-02-15
A constrained, output feedback nonlinear receding horizon control (NRHC) method is applied to design a research reactor power controller. The method uses a nonlinear plant model subject to state, control and terminal set constraints; a nonlinear cost function; and a high gain observer. The controller regulates reactor power from 1% to 100% of full power; considers known disturbances, such as reactivity insertions and changes in core inlet flow and temperature; and includes upper limits constraints on neutron flux, neutron flux rate, core outlet temperature and core inlet-outlet temperature difference. Simulation results show an excellent performance for power regulation and known disturbances rejection: all process variables are kept within the admissible limits avoiding the actuation of the safety systems.
Directory of Open Access Journals (Sweden)
Aijia Ouyang
2015-01-01
Full Text Available Nonlinear Muskingum models are important tools in hydrological forecasting. In this paper, we have come up with a class of new discretization schemes including a parameter θ to approximate the nonlinear Muskingum model based on general trapezoid formulas. The accuracy of these schemes is second order, if θ≠1/3, but interestingly when θ=1/3, the accuracy of the presented scheme gets improved to third order. Then, the present schemes are transformed into an unconstrained optimization problem which can be solved by a hybrid invasive weed optimization (HIWO algorithm. Finally, a numerical example is provided to illustrate the effectiveness of the present methods. The numerical results substantiate the fact that the presented methods have better precision in estimating the parameters of nonlinear Muskingum models.
DEFF Research Database (Denmark)
Ibsen, Lars Bo; Barari, Amin; Kimiaeifar, Amin
2010-01-01
/approximate analytical solution to strong nonlinear oscillators. Furthermore, it is shown that a large class of linear or nonlinear differential equations can be solved without the tangible restriction of sensitivity to the degree of the nonlinear term, adding that the method is quite convenient due to reduction in size...
New implicit method for analysis of problems in nonlinear structural dynamics
Directory of Open Access Journals (Sweden)
Gholampour A. A.
2011-06-01
Full Text Available In this paper a new method is proposed for direct time integration of nonlinear structural dynamics problems. In the proposed method the order of time integration scheme is higher than the conventional Newmark’s family of methods. This method assumes second order variation of the acceleration at each time step. Two variable parameters are used to increase the stability and accuracy of the method. The result obtained from this new higher order method is compared with two implicit methods; namely the Wilson-θ and the Newmark’s average acceleration methods.
Application of the G'/G Expansion Method in Ultrashort Pulses in Nonlinear Optical Fibers
Directory of Open Access Journals (Sweden)
Jiang Xing-Fang
2013-01-01
Full Text Available With the increasing input power in optical fibers, the dispersion problem is becoming a severe restriction on wavelength division multiplexing (WDM. With the aid of solitons, in which the shape and speed can remain constant during propagation, it is expected that the transmission of nonlinear ultrashort pulses in optical fibers can effectively control the dispersion. The propagation of a nonlinear ultrashort laser pulse in an optical fiber, which fits the high-order nonlinear Schrödinger equation (NLSE, has been solved using the G'/G expansion method. Group velocity dispersion, self-phase modulation, the fourth-order dispersion, and the fifth-order nonlinearity of the high-order NLSE were taken into consideration. A series of solutions has been obtained such as the solitary wave solutions of kink, inverse kink, the tangent trigonometric function, and the cotangent trigonometric function. The results have shown that the G'/G expansion method is an effective way to obtain the exact solutions for the high-order NLSE, and it provides a theoretical basis for the transmission of ultrashort pulses in nonlinear optical fibers.
Sequential Monte Carlo methods for nonlinear discrete-time filtering
Bruno, Marcelo GS
2013-01-01
In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable.We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in line
Institute of Scientific and Technical Information of China (English)
倪力军; 钟霖; 张鑫; 张立国; 黄士新
2014-01-01
the content levels of the adulterants indi-cated that near infrared spectroscopy combined with non-linear pattern recognition methods can distinguish dextrin and starch in milks with higher concentration levels (>0.15% ) ,but do not work well on identifying the adulterants with lower concentrations such as melamine (365.5 to 1 096.5 mg · kg -1 ) ,urea (524 to 1 572 mg · kg -1 ) ,ammonium nitrate (700 to 2 100 mg · kg -1 ) . Therefore near Infrared Spectroscopy is not suitable for identifying the adulterants with concentrations are below 0.1% .
Indian Academy of Sciences (India)
Ibrahim Eren
2008-02-01
In this study, large deﬂection of cantilever beams of Ludwick type material subjected to a combined loading consisting of a uniformly distributed load and one vertical concentrated load at the free end was investigated. In calculations, both material and geometrical non-linearity have been considered. Horizontal and vertical deﬂections magnitudes were calculated throughout Euler–Bernoulli curvature-moment relationship assuming different arc lengths. Vertical deﬂections were calculated by using Runge–Kutta method. More simple and easily understandable results have been obtained compared to the previous studies about the issue and compatible values have been obtained for most of the compared values.
Directory of Open Access Journals (Sweden)
Syed Tauseef Mohyud-Din
2015-01-01
Full Text Available This paper witnesses the coupling of an analytical series expansion method which is called reduced differential transform with fractional complex transform. The proposed technique is applied on three mathematical models, namely, fractional Kaup-Kupershmidt equation, generalized fractional Drinfeld-Sokolov equations, and system of coupled fractional Sine-Gordon equations subject to the appropriate initial conditions which arise frequently in mathematical physics. The derivatives are defined in Jumarie’s sense. The accuracy, efficiency, and convergence of the proposed technique are demonstrated through the numerical examples. It is observed that the presented coupling is an alternative approach to overcome the demerit of complex calculation of fractional differential equations. The proposed technique is independent of complexities arising in the calculation of Lagrange multipliers, Adomian’s polynomials, linearization, discretization, perturbation, and unrealistic assumptions and hence gives the solution in the form of convergent power series with elegantly computed components. All the examples show that the proposed combination is a powerful mathematical tool to solve other nonlinear equations also.
Institute of Scientific and Technical Information of China (English)
R.Mokhtari; A.Samadi Toodar; N.G.Chegini
2011-01-01
@@ We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schr(o)dinger equations.The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method.The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly.Some comparisons with the methods applied in the literature are carried out.%We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrodinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out.
Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.
1989-01-01
In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.
A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems
Directory of Open Access Journals (Sweden)
S. S. Motsa
2013-01-01
Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.
A Theoretical Method for Characterizing Nonlinear Effects in Paul Traps with Added Octopole Field.
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Chen, Suming; Nie, Zongxiu
2015-08-01
In comparison with numerical methods, theoretical characterizations of ion motion in the nonlinear Paul traps always suffer from low accuracy and little applicability. To overcome the difficulties, the theoretical harmonic balance (HB) method was developed, and was validated by the numerical fourth-order Runge-Kutta (4th RK) method. Using the HB method, analytical ion trajectory and ion motion frequency in the superimposed octopole field, ε, were obtained by solving the nonlinear Mathieu equation (NME). The obtained accuracy of the HB method was comparable with that of the 4th RK method at the Mathieu parameter, q = 0.6, and the applicable q values could be extended to the entire first stability region with satisfactory accuracy. Two sorts of nonlinear effects of ion motion were studied, including ion frequency shift, Δβ, and ion amplitude variation, Δ(C(2n)/C0) (n ≠ 0). New phenomena regarding Δβ were observed, although extensive studies have been performed based on the pseudo-potential well (PW) model. For instance, the |Δβ| at ε = 0.1 and ε = -0.1 were found to be different, but they were the same in the PW model. This is the first time the nonlinear effects regarding Δ(C(2n)/C0) (n ≠ 0) are studied, and the associated study has been a challenge for both theoretical and numerical methods. The nonlinear effects of Δ(C(2n)/C0) (n ≠ 0) and Δβ were found to share some similarities at q < 0.6: both of them were proportional to ε, and the square of the initial ion displacement, z(0)(2).
Tene, Yair; Tene, Noam; Tene, G.
1993-08-01
An interactive data fusion methodology of video, audio, and nonlinear structural dynamic analysis for potential application in forensic engineering is presented. The methodology was developed and successfully demonstrated in the analysis of heavy transportable bridge collapse during preparation for testing. Multiple bridge elements failures were identified after the collapse, including fracture, cracks and rupture of high performance structural materials. Videotape recording by hand held camcorder was the only source of information about the collapse sequence. The interactive data fusion methodology resulted in extracting relevant information form the videotape and from dynamic nonlinear structural analysis, leading to full account of the sequence of events during the bridge collapse.
Institute of Scientific and Technical Information of China (English)
Rui QI; Cheng-jian ZHANG; Yu-jie ZHANG
2012-01-01
This paper is concerned with the numerical dissipativity of multistep Runge-Kutta methods for nonlinear Volterra delay-integro-differential equations. We investigate the dissipativity properties of (k,l)-algebraically stable multistep Runge-Kutta methods with constrained grid and an uniform grid.The finitedimensional and infinite-dimensional dissipativity results of (k,l)-algebraically stable Runge-Kutta methods are obtained.
Directory of Open Access Journals (Sweden)
Behzad Ghanbari
2014-01-01
Full Text Available We aim to study the convergence of the homotopy analysis method (HAM in short for solving special nonlinear Volterra-Fredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.
Kutev, N.; Kolkovska, N.; Dimova, M.
2013-10-01
The Cauchy problem to the generalized Boussinesq equation with Bernoulli type nonlinearities is studied. Global solvability of the solutions with sub-critical initial energy is proved by means of different techniques - nonstandard potential well method and method of the conservation low of the energy. In the framework of the nonstandard potential well method a new critical energy constant is introduced and estimated. The performed numerical experiments support the theoretical results.
Evaluation of a physically based quasi-linear and a conceptually based nonlinear Muskingum methods
Perumal, Muthiah; Tayfur, Gokmen; Rao, C. Madhusudana; Gurarslan, Gurhan
2017-03-01
Two variants of the Muskingum flood routing method formulated for accounting nonlinearity of the channel routing process are investigated in this study. These variant methods are: (1) The three-parameter conceptual Nonlinear Muskingum (NLM) method advocated by Gillin 1978, and (2) The Variable Parameter McCarthy-Muskingum (VPMM) method recently proposed by Perumal and Price in 2013. The VPMM method does not require rigorous calibration and validation procedures as required in the case of NLM method due to established relationships of its parameters with flow and channel characteristics based on hydrodynamic principles. The parameters of the conceptual nonlinear storage equation used in the NLM method were calibrated using the Artificial Intelligence Application (AIA) techniques, such as the Genetic Algorithm (GA), the Differential Evolution (DE), the Particle Swarm Optimization (PSO) and the Harmony Search (HS). The calibration was carried out on a given set of hypothetical flood events obtained by routing a given inflow hydrograph in a set of 40 km length prismatic channel reaches using the Saint-Venant (SV) equations. The validation of the calibrated NLM method was investigated using a different set of hypothetical flood hydrographs obtained in the same set of channel reaches used for calibration studies. Both the sets of solutions obtained in the calibration and validation cases using the NLM method were compared with the corresponding solutions of the VPMM method based on some pertinent evaluation measures. The results of the study reveal that the physically based VPMM method is capable of accounting for nonlinear characteristics of flood wave movement better than the conceptually based NLM method which requires the use of tedious calibration and validation procedures.
On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations
Directory of Open Access Journals (Sweden)
H. Montazeri
2012-01-01
Full Text Available We consider a system of nonlinear equations F(x=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.
Institute of Scientific and Technical Information of China (English)
Dongyang Shi; Haihong Wang; Yuepeng Du
2009-01-01
An anisotropic nonconforming finite element method is presented for a class of nonlinear Sobolev equations. The optimal error estimates and supercloseness are obtained for both semi-discrete and fully-discrete approximate schemes, which are the same as the traditional finite element methods. In addition, the global superconvergence is derived through the postprocessing technique. Numerical experiments are included to illustrate the feasibility of the proposed method.
A New UKF Based Fault Detection Method in Non-linear Systems
Institute of Scientific and Technical Information of China (English)
GE Zhe-xue; YANG Yong-min; HU Zheng
2006-01-01
To detect the bias fault in stochastic non-linear dynamic systems, a new Unscented Kalman Filtering(UKF) based real-time recursion detection method is brought forward with the consideration of the flaws of traditional Extended Kalman Filtering(EKF). It uses the UKF as the residual generation method and the Weighted-Sum Squared Residual (WSSR) as the fault detection strategy. The simulation results are provided which demonstrate better effectiveness and a higher detection ratio of the developed methods.
Modeling Solution of Nonlinear Dispersive Partial Differential Equations using the Marker Method
Energy Technology Data Exchange (ETDEWEB)
Jerome L.V. Lewandowski
2005-01-25
A new method for the solution of nonlinear dispersive partial differential equations is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details.
Combining building thermal simulation methods and LCA methods
DEFF Research Database (Denmark)
Pedersen, Frank; Hansen, Klaus; Wittchen, Kim Bjarne
2008-01-01
Thsi paper describes recent efforts made by the Danish Building Research Institute regarding the integration of a life cycle assessment (LCA) method into a whole building hygro-thermal simulation tool. The motivation for the work is that the increased requirements to the energy performance...
3rd Workshop on "Combinations of Intelligent Methods and Applications"
Palade, Vasile
2013-01-01
The combination of different intelligent methods is a very active research area in Artificial Intelligence (AI). The aim is to create integrated or hybrid methods that benefit from each of their components. The 3rd Workshop on “Combinations of Intelligent Methods and Applications” (CIMA 2012) was intended to become a forum for exchanging experience and ideas among researchers and practitioners who are dealing with combining intelligent methods either based on first principles or in the context of specific applications. CIMA 2012 was held in conjunction with the 22nd European Conference on Artificial Intelligence (ECAI 2012).This volume includes revised versions of the papers presented at CIMA 2012. .
Stupishin, L.; Nikitin, K.; Kolesnikov, A.
2017-05-01
A methodology for shell stability research and determining buckling load, based on the mixed finite element method are proposed. Axisymmetric geometrically nonlinear shallow shells made of orthotropic material are considered. The results of numerical research of stability by changing the shape of shells, ratio of elastic modulus of the material and parameters of the support contour are presented.
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.
A Kernel Time Structure Independent Component Analysis Method for Nonlinear Process Monitoring☆
Institute of Scientific and Technical Information of China (English)
Lianfang Cai; Xuemin Tian; Ni Zhang
2014-01-01
Kernel independent component analysis (KICA) is a newly emerging nonlinear process monitoring method, which can extract mutually independent latent variables cal ed independent components (ICs) from process var-iables. However, when more than one IC have Gaussian distribution, it cannot extract the IC feature effectively and thus its monitoring performance will be degraded drastical y. To solve such a problem, a kernel time struc-ture independent component analysis (KTSICA) method is proposed for monitoring nonlinear process in this paper. The original process data are mapped into a feature space nonlinearly and then the whitened data are calculated in the feature space by the kernel trick. Subsequently, a time structure independent component analysis algorithm, which has no requirement for the distribution of ICs, is proposed to extract the IC feature. Finally, two monitoring statistics are built to detect process faults. When some fault is detected, a nonlinear fault identification method is developed to identify fault variables based on sensitivity analysis. The proposed monitoring method is applied in the Tennessee Eastman benchmark process. Applications demonstrate the superiority of KTSICA over KICA.
An Assessment of Linear Versus Non-linear Multigrid Methods for Unstructured Mesh Solvers
2001-05-01
problems is investigated. The first case consists of a transient radiation-diffusion problem for which an exact linearization is available, while the...to the Jacobian of a second-order accurate discretization. When an exact linearization is employed, the linear and non-linear multigrid methods
Adaptive Wavelet Methods for Linear and Nonlinear Least-Squares Problems
Stevenson, R.
2014-01-01
The adaptive wavelet Galerkin method for solving linear, elliptic operator equations introduced by Cohen et al. (Math Comp 70:27-75, 2001) is extended to nonlinear equations and is shown to converge with optimal rates without coarsening. Moreover, when an appropriate scheme is available for the appr