Mellor, Andrew; Zia, R K P
2016-01-01
We introduce an heterogeneous nonlinear $q$-voter model with zealots and two types of susceptible voters, and study its non-equilibrium properties when the population is finite and well mixed. In this two-opinion model, each individual supports one of two parties and is either a zealot or a susceptible voter of type $q_1$ or $q_2$. While here zealots never change their opinion, a $q_i$-susceptible voter ($i=1,2$) consults a group of $q_i$ neighbors at each time step, and adopts their opinion if all group members agree. We show that this model violates the detailed balance whenever $q_1 \
A Heterogeneous Out-of-Equilibrium Nonlinear $q$-Voter Model with Zealotry
Mellor, Andrew; Zia, R K P
2016-01-01
We study the dynamics of the out-of-equilibrium nonlinear q-voter model with two types of susceptible voters and zealots, introduced in [EPL 113, 48001 (2016)]. In this model, each individual supports one of two parties and is either a susceptible voter of type $q_1$ or $q_2$, or is an inflexible zealot. At each time step, a $q_i$-susceptible voter ($i = 1,2$) consults a group of $q_i$ neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. This model violates detailed balance whenever $q_1 \
Heterogeneous out-of-equilibrium nonlinear q -voter model with zealotry
Mellor, Andrew; Mobilia, Mauro; Zia, R. K. P.
2017-01-01
We study the dynamics of the out-of-equilibrium nonlinear q -voter model with two types of susceptible voters and zealots, introduced in Mellor et al. [Europhys. Lett. 113, 48001 (2016), 10.1209/0295-5075/113/48001]. In this model, each individual supports one of two parties and is either a susceptible voter of type q1 or q2, or is an inflexible zealot. At each time step, a qi-susceptible voter (i =1 ,2 ) consults a group of qi neighbors and adopts their opinion if all group members agree, while zealots are inflexible and never change their opinion. This model violates detailed balance whenever q1≠q2 and is characterized by two distinct regimes of low and high density of zealotry. Here, by combining analytical and numerical methods, we investigate the nonequilibrium stationary state of the system in terms of its probability distribution, nonvanishing currents, and unequal-time two-point correlation functions. We also study the switching time properties of the model by exploiting an approximate mapping onto the model of Mobilia [Phys. Rev. E 92, 012803 (2015), 10.1103/PhysRevE.92.012803] that satisfies the detailed balance, and we outline some properties of the model near criticality.
Pair approximation for the q -voter model with independence on complex networks
Jedrzejewski, Arkadiusz
2017-01-01
We investigate the q -voter model with stochastic noise arising from independence on complex networks. Using the pair approximation, we provide a comprehensive, mathematical description of its behavior and derive a formula for the critical point. The analytical results are validated by carrying out Monte Carlo experiments. The pair approximation prediction exhibits substantial agreement with simulations, especially for networks with weak clustering and large average degree. Nonetheless, for the average degree close to q , some discrepancies originate. It is the first time we are aware of that the presented approach has been applied to the nonlinear voter dynamics with noise. Up till now, the analytical results have been obtained only for a complete graph. We show that in the limiting case the prediction of pair approximation coincides with the known solution on a fully connected network.
Phase transitions in the q -voter model with noise on a duplex clique
Chmiel, Anna; Sznajd-Weron, Katarzyna
2015-11-01
We study a nonlinear q -voter model with stochastic noise, interpreted in the social context as independence, on a duplex network. To study the role of the multilevelness in this model we propose three methods of transferring the model from a mono- to a multiplex network. They take into account two criteria: one related to the status of independence (LOCAL vs GLOBAL) and one related to peer pressure (AND vs OR). In order to examine the influence of the presence of more than one level in the social network, we perform simulations on a particularly simple multiplex: a duplex clique, which consists of two fully overlapped complete graphs (cliques). Solving numerically the rate equation and simultaneously conducting Monte Carlo simulations, we provide evidence that even a simple rearrangement into a duplex topology may lead to significant changes in the observed behavior. However, qualitative changes in the phase transitions can be observed for only one of the considered rules: LOCAL&AND. For this rule the phase transition becomes discontinuous for q =5 , whereas for a monoplex such behavior is observed for q =6 . Interestingly, only this rule admits construction of realistic variants of the model, in line with recent social experiments.
Phase transitions in the $q$-voter model with noise on a duplex clique
Chmiel, Anna
2015-01-01
We study a nonlinear $q$-voter model with the stochastic noise, interpreted as an independence in social psychology, on a duplex network. To study the role of the multiplex topology, we consider two criteria of level dependence -- first related to the peer pressure (\\texttt{AND} and \\texttt{OR}) and the second to the status of independence (\\texttt{LOCAL} and \\texttt{GLOBAL}). In order to examine the influence of the presence of more than one level in the social network, we perform simulations on a particularly simple multiplex -- a duplex clique, which consists of two fully overlapped complete graphs (cliques). Solving numerically the rate equation and simultaneously conducting Monte Carlo simulations, we give an evidence that even a simple rearrangement into a duplex topology leads to the significant changes in observed phase transition, in particular for the \\texttt{GLOBAL&AND} rule. In this case, which is also the most suitable from the social point of view, the phase transition becomes discontinuous ...
An analytical expression for the exit probability of the q-voter model in one dimension
Timpanaro, André Martin
2014-01-01
We present in this paper an approximation that is able to give an analytical expression for the exit probability of the $q$-voter model in one dimension. This expression gives a better fit for the more recent data about simulations in large networks, and as such, departs from the expression $\\frac{\\rho^q}{\\rho^q + (1-\\rho)^q}$ found in papers that investigated small networks only. The approximation consists in assuming a large separation on the time scales at which active groups of agents convince inactive ones and the time taken in the competition between active groups. Some interesting findings are that for $q=2$ we still have $\\frac{\\rho^2}{\\rho^2 + (1-\\rho)^2}$ as the exit probability and for large values of $q$ the difference between the result and $\\frac{\\rho^q}{\\rho^q + (1-\\rho)^q}$ becomes negligible (the difference is maximum for $q=5$ and 6)
Billings, S. A.
1988-03-01
Time and frequency domain identification methods for nonlinear systems are reviewed. Parametric methods, prediction error methods, structure detection, model validation, and experiment design are discussed. Identification of a liquid level system, a heat exchanger, and a turbocharge automotive diesel engine are illustrated. Rational models are introduced. Spectral analysis for nonlinear systems is treated. Recursive estimation is mentioned.
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-10-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-11-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
NONLINEAR STABILITY FOR EADY'S MODEL
Institute of Scientific and Technical Information of China (English)
LIU Yong-ming; QIU Ling-cun
2005-01-01
Poincaré type integral inequality plays an important role in the study of nonlinear stability ( in the sense of Arnold's second theorem) for three-dimensional quasigeostophic flow. The nonlinear stability of Eady's model is one of the most important cases in the application of the method. But the best nonlinear stability criterion obtained so far and the linear stability criterion are not coincident. The two criteria coincide only when the period of the channel is infinite.additional conservation law of momentum and by rigorous estimate of integral inequality. So the new nonlinear stability criterion was obtained, which shows that for Eady 's model in the periodic channel, the linear stable implies the nonlinear stable.
Nonlinear models for autoregressive conditional heteroskedasticity
DEFF Research Database (Denmark)
Teräsvirta, Timo
This paper contains a brief survey of nonlinear models of autore- gressive conditional heteroskedasticity. The models in question are parametric nonlinear extensions of the original model by Engle (1982). After presenting the individual models, linearity testing and parameter estimation...... are discussed. Forecasting volatility with nonlinear models is considered. Finally, parametric nonlinear models based on multi- plicative decomposition of the variance receive attention....
Nonlinear Control of Heartbeat Models
Directory of Open Access Journals (Sweden)
Witt Thanom
2011-02-01
Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.
Nonlinear time series modelling: an introduction
Simon M. Potter
1999-01-01
Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear models are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of models. Finally, forecasting and impulse response analysis is developed.
Modelling Loudspeaker Non-Linearities
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2007-01-01
This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...
Processing Approach of Non-linear Adjustment Models in the Space of Non-linear Models
Institute of Scientific and Technical Information of China (English)
LI Chaokui; ZHU Qing; SONG Chengfang
2003-01-01
This paper investigates the mathematic features of non-linear models and discusses the processing way of non-linear factors which contributes to the non-linearity of a nonlinear model. On the basis of the error definition, this paper puts forward a new adjustment criterion, SGPE.Last, this paper investigates the solution of a non-linear regression model in the non-linear model space and makes the comparison between the estimated values in non-linear model space and those in linear model space.
Nonlinear rheological models for structured interfaces
Sagis, L.M.C.
2010-01-01
The GENERIC formalism is a formulation of nonequilibrium thermodynamics ideally suited to develop nonlinear constitutive equations for the stress–deformation behavior of complex interfaces. Here we develop a GENERIC model for multiphase systems with interfaces displaying nonlinear viscoelastic stres
Adaptive regression for modeling nonlinear relationships
Knafl, George J
2016-01-01
This book presents methods for investigating whether relationships are linear or nonlinear and for adaptively fitting appropriate models when they are nonlinear. Data analysts will learn how to incorporate nonlinearity in one or more predictor variables into regression models for different types of outcome variables. Such nonlinear dependence is often not considered in applied research, yet nonlinear relationships are common and so need to be addressed. A standard linear analysis can produce misleading conclusions, while a nonlinear analysis can provide novel insights into data, not otherwise possible. A variety of examples of the benefits of modeling nonlinear relationships are presented throughout the book. Methods are covered using what are called fractional polynomials based on real-valued power transformations of primary predictor variables combined with model selection based on likelihood cross-validation. The book covers how to formulate and conduct such adaptive fractional polynomial modeling in the s...
Nonlinear Modelling of Low Frequency Loudspeakers
DEFF Research Database (Denmark)
Olsen, Erling Sandermann
1997-01-01
In the Danish LoDist project on distortion from dynamic low-frequency loudspeakers, a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...... for describing the nonlinearities have been developed. Different aspects of modelling loudspeaker nonlinearities are discussed, and the program is briefly described....
Nonlinear Modelling of Low Frequency Loudspeakers
DEFF Research Database (Denmark)
Olsen, Erling Sandermann
1997-01-01
In the Danish LoDist project on distortion from dynamic low frequency loudspeakers a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...... for describing the nonlinearities have been developed. Different aspects of modelling loudspeaker nonlinearities are discussed and the program is briefly demonstrated....
Computational Models for Nonlinear Aeroelastic Systems Project
National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate new and efficient computational methods of modeling nonlinear aeroelastic systems. The...
Model Updating Nonlinear System Identification Toolbox Project
National Aeronautics and Space Administration — ZONA Technology (ZONA) proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology that utilizes flight data with...
Mathematical modeling and applications in nonlinear dynamics
Merdan, Hüseyin
2016-01-01
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...
Optimal design for nonlinear response models
Fedorov, Valerii V
2013-01-01
Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors' many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of the key ideas, using linear models as examples. Applying the linearization in the parameter space, it then covers nonlinear models and locally optimal designs as well as minimax, optimal on average, and Bayesian designs. The authors also discuss ada
Nonlinear cumulative damage model for multiaxial fatigue
Institute of Scientific and Technical Information of China (English)
SHANG De-guang; SUN Guo-qin; DENG Jing; YAN Chu-liang
2006-01-01
On the basis of the continuum fatigue damage theory,a nonlinear uniaxial fatigue cumulative damage model is first proposed.In order to describe multiaxial fatigue damage characteristics,a nonlinear multiaxial fatigue cumulative damage model is developed based on the critical plane approach,The proposed model can consider the multiaxial fatigue limit,mean hydrostatic pressure and the unseparated characteristic for the damage variables and loading parameters.The recurrence formula of fatigue damage model was derived under multilevel loading,which is used to predict multiaxial fatigue life.The results showed that the proposed nonlinear multiaxial fatigue cumulative damage model is better than Miner's rule.
Completely integrable models of nonlinear optics
Indian Academy of Sciences (India)
Andrey I Maimistov
2001-11-01
The models of the nonlinear optics in which solitons appeared are considered. These models are of paramount importance in studies of nonlinear wave phenomena. The classical examples of phenomena of this kind are the self-focusing, self-induced transparency and parametric interaction of three waves. At present there are a number of theories based on completely integrable systems of equations, which are, both, generations of the original known models and new ones. The modiﬁed Korteweg-de Vries equation, the nonlinear Schrödinger equation, the derivative nonlinear Schrödinger equation, Sine–Gordon equation, the reduced Maxwell–Bloch equation, Hirota equation, the principal chiral ﬁeld equations, and the equations of massive Thirring model are some soliton equations, which are usually to be found in nonlinear optics theory.
Designing Experiments for Nonlinear Models - An Introduction
Johnson, Rachel T.; Montgomery, Douglas C.
2009-01-01
The article of record as published may be found at http://dx.doi.org/10.1002/qre.1063 We illustrate the construction of Bayesian D-optimal designs for nonlinear models and compare the relative efficiency of standard designs with these designs for several models and prior distributions on the parameters. Through a relative efficiency analysis, we show that standard designs can perform well in situations where the nonlinear model is intrinsically linear. However, if the model is non...
Functional uniform priors for nonlinear modeling.
Bornkamp, Björn
2012-09-01
This article considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a prior distribution that is uniform in the space of functional shapes of the underlying nonlinear function and then back-transform to obtain a prior distribution for the original model parameters. The primary application considered in this article is nonlinear regression, but the idea might be of interest beyond this case. For nonlinear regression the so constructed priors have the advantage that they are parametrization invariant and do not violate the likelihood principle, as opposed to uniform distributions on the parameters or the Jeffrey's prior, respectively. The utility of the proposed priors is demonstrated in the context of design and analysis of nonlinear regression modeling in clinical dose-finding trials, through a real data example and simulation.
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...... on the governing equations and methods of implementing....
Nonlinear Resistivity for Magnetohydrodynamical Models
Lingam, Manasvi; Pfefferlé, David; Comisso, Luca; Bhattacharjee, Amitava
2016-01-01
A nonlinear current-dependent resistivity that accurately accounts for the collisional electron-ion momentum transfer rate is derived. It is shown that the Spitzer resistivity overestimates the resistivity in certain observationally relevant regimes. The nonlinear resistivity computed herein is a strictly decreasing function of the current, in contrast to some notable previous proposals. The relative importance of the new expression with respect to the well-established electron inertia and Hall terms is also examined. The subtle implications of this current-dependent resistivity are discussed in the context of plasma systems and phenomena such as magnetic reconnection.
Nonlinear modeling of thermoacoustically driven energy cascade
Gupta, Prateek; Scalo, Carlo; Lodato, Guido
2016-11-01
We present an investigation of nonlinear energy cascade in thermoacoustically driven high-amplitude oscillations, from the initial weakly nonlinear regime to the shock wave dominated limit cycle. We develop a first principle based quasi-1D model for nonlinear wave propagation in a canonical minimal unit thermoacoustic device inspired by the experimental setup of Biwa et al.. Retaining up to quadratic nonlinear terms in the governing equations, we develop model equations for nonlinear wave propagation in the proximity of differentially heated no-slip boundaries. Furthermore, we discard the effects of acoustic streaming in the present study and focus on nonlinear energy cascade due to high amplitude wave propagation. Our model correctly predicts the observed exponential growth of the thermoacoustically amplified second harmonic, as well as the energy transfer rate to higher harmonics causing wave steepening. Moreover, we note that nonlinear coupling of local pressure with heat transfer reduces thermoacoustic amplification gradually thus causing the system to reach limit cycle exhibiting shock waves. Throughout, we verify the results from the quasi-1D model with fully compressible Navier-Stokes simulations.
Model Updating Nonlinear System Identification Toolbox Project
National Aeronautics and Space Administration — ZONA Technology proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology by adopting the flight data with state-of-the-art...
Comparing coefficients of nested nonlinear probability models
DEFF Research Database (Denmark)
Kohler, Ulrich; Karlson, Kristian Bernt; Holm, Anders
2011-01-01
In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general decomposi......In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general...... decomposition method that is unaffected by the rescaling or attenuation bias that arise in cross-model comparisons in nonlinear models. It recovers the degree to which a control variable, Z, mediates or explains the relationship between X and a latent outcome variable, Y*, underlying the nonlinear probability...
On a Nonlinear Model in Adiabatic Evolutions
Sun, Jie; Lu, Song-Feng
2016-08-01
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using. Supported by the National Natural Science Foundation of China under Grant Nos. 61402188 and 61173050. The first author also gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2014M552041
Computational Models for Nonlinear Aeroelastic Systems Project
National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate a new and efficient computational method of modeling nonlinear aeroelastic systems. The...
Non-linear Loudspeaker Unit Modelling
DEFF Research Database (Denmark)
Pedersen, Bo Rohde; Agerkvist, Finn T.
2008-01-01
Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of three...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....
Identifying nonlinear biomechanical models by multicriteria analysis
Srdjevic, Zorica; Cveticanin, Livija
2012-02-01
In this study, the methodology developed by Srdjevic and Cveticanin (International Journal of Industrial Ergonomics 34 (2004) 307-318) for the nonbiased (objective) parameter identification of the linear biomechanical model exposed to vertical vibrations is extended to the identification of n-degree of freedom (DOF) nonlinear biomechanical models. The dynamic performance of the n-DOF nonlinear model is described in terms of response functions in the frequency domain, such as the driving-point mechanical impedance and seat-to-head transmissibility function. For randomly generated parameters of the model, nonlinear equations of motion are solved using the Runge-Kutta method. The appropriate data transformation from the time-to-frequency domain is performed by a discrete Fourier transformation. Squared deviations of the response functions from the target values are used as the model performance evaluation criteria, thus shifting the problem into the multicriteria framework. The objective weights of criteria are obtained by applying the Shannon entropy concept. The suggested methodology is programmed in Pascal and tested on a 4-DOF nonlinear lumped parameter biomechanical model. The identification process over the 2000 generated sets of parameters lasts less than 20 s. The model response obtained with the imbedded identified parameters correlates well with the target values, therefore, justifying the use of the underlying concept and the mathematical instruments and numerical tools applied. It should be noted that the identified nonlinear model has an improved accuracy of the biomechanical response compared to the accuracy of a linear model.
Nonlinear model predictive control theory and algorithms
Grüne, Lars
2017-01-01
This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...
Nonlinear optical model for strip plasmonic waveguides
DEFF Research Database (Denmark)
Lysenko, Oleg; Bache, Morten; Lavrinenko, Andrei
2016-01-01
This paper presents a theoretical model of nonlinear optical properties for strip plasmonic waveguides. The particular waveguides geometry that we investigate contains a gold core, adhesion layers, and silicon dioxide cladding. It is shown that the third-order susceptibility of the gold core...... significantly depends on the layer thickness and has the dominant contribution to the effective third-order susceptibility of the long-range plasmon polariton mode. This results in two nonlinear optical effects in plasmonic waveguides, which we experimentally observed and reported in [Opt. Lett. 41, 317 (2016......)]. The first effect is the nonlinear power saturation of the plasmonic mode, and the second effect is the spectral broadening of the plasmonic mode. Both nonlinear plasmonic effects can be used for practical applications and their appropriate model will be important for further developments in communication...
Topological approximation of the nonlinear Anderson model
Milovanov, Alexander V.; Iomin, Alexander
2014-06-01
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the
Nonlinear modeling of an aerospace object dynamics
Davydov, I. E.; Davydov, E. I.
2017-01-01
Here are presented the scientific results, obtained by motion modeling of complicated technical systems of aerospace equipment with consideration of nonlinearities. Computerized panel that allows to measure mutual influence of the system's motion and stabilization device with consideration of its real characteristics has been developed. Analysis of motion stability of a system in general has been carried out and time relationships of the system's motion taking in account nonlinearities are presented.
Nonlinear chaotic model for predicting storm surges
Siek, M.; Solomatine, D.P.
This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables.
On the nonlinear modeling of ring oscillators
Elwakil, Ahmed S.
2009-06-01
We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
Modeling of the vibrating beam accelerometer nonlinearities
Romanowski, P. A.; Knop, R. C.
Successful modeling and processing of the output of a quartz Vibrating Beam Accelerometer (VBA), whose errors are inherently nonlinear with respect to input acceleration, are reported. The VBA output, with two signals that are frequencies of vibrating quartz beams, has inherent higher-order terms. In order to avoid vibration rectification errors, the signal output must be sampled at a rapid rate and the output must be reduced using a nonlinear model. The present model, with acceleration as a function of frequency, is derived by a least-squares process where the covariance matrix is obtained from simulated data. The system performance is found to be acceptable to strategic levels, and it is shown that a vibration rectification error of 400 micrograms/sq g can be reduced to 4 micrograms/sq g by using the processor electronics and a nonlinear model.
Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory
DEFF Research Database (Denmark)
Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav
Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable...
Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory
DEFF Research Database (Denmark)
Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav
Contraction theory is a recently developed nonlinear analysis tool which may be useful for solving a variety of nonlinear control problems. In this paper, using Contraction theory, a nonlinear observer is designed for a general nonlinear cable/string FEM (Finite Element Method) model. The cable...
A nonlinear constitutive model for magnetostrictive materials
Institute of Scientific and Technical Information of China (English)
Xin'en Liu; Xiaojing Zheng
2005-01-01
A general nonlinear constitutive model is proposed for magnetostrictive materials, based on the important physical fact that a nonlinear part of the elastic strain produced by a pre-stress is related to the magnetic domain rotation or movement and is responsible for the change of the maximum magnetostrictive strain with the pre-stress. To avoid the complicity of determining the tensor function describing the nonlinear elastic strain part, this paper proposes a simplified model by means of linearizing the nonlinear function.For the convenience of engineering applications, the expressions of the 3-D (bulk), 2-D (film) and 1-D (rod) models are, respectively, given for an isotropic material and their applicable ranges are also discussed. By comparison with the experimental data of a Terfenol-D rod, it is found that the proposed model can accurately predict the magnetostrictive strain curves in low, moderate and high magnetic field regions for various compressive pre-stress levels. The numerical simulation further illustrates that, for either magnetostrictive rods or thin films, the proposed model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves, while none of the known models can capture all of them. Therefore, the proposed model enjoys higher precision and wider applicability than the previous models, especially in the region of the high field.
A Nonlinear Model of Thermoacoustic Devices
Karpov, Sergey; Prosperetti, Andrea
2002-01-01
This paper presents a nonlinear, time-domain model of thermoacoustic devices based on cross-sectional averaged equations. Heat transfer perpendicular to the device axis - which lies at the core of thermoacoustic effects - is modeled in a novel and more realistic way. Heat conduction in the solid sur
Some Asymptotic Inference in Multinomial Nonlinear Models (a Geometric Approach)
Institute of Scientific and Technical Information of China (English)
WEIBOCHENG
1996-01-01
A geometric framework is proposed for multinomlat nonlinear modelsbased on a modified vemlon of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvtures for multlnomial nonlinear models. Our previous results [15] for ordlnary nonlinear regression models are extended to multlnomlal nonlinear models.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations betwee...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models.......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under...
Perturbation analysis of nonlinear matrix population models
Directory of Open Access Journals (Sweden)
Hal Caswell
2008-03-01
Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.
Nonlinear control of the Salnikov model reaction
DEFF Research Database (Denmark)
Recke, Bodil; Jørgensen, Sten Bay
1999-01-01
This paper explores different nonlinear control schemes, applied to a simple model reaction. The model is the Salnikov model, consisting of two ordinary differential equations. The control strategies investigated are I/O-linearisation, Exact linearisation, exact linearisation combined with LQR...... and Control Lyapunov Functions (CLF's). The results show that based on the lowest possible cost function and shortest settling time, the exact linearisation performs marginally better than the other methods....
Nonlinear System Identification and Behavioral Modeling
Huq, Kazi Mohammed Saidul; Kabir, A F M Sultanul
2010-01-01
The problem of determining a mathematical model for an unknown system by observing its input-output data pair is generally referred to as system identification. A behavioral model reproduces the required behavior of the original analyzed system, such as there is a one-to-one correspondence between the behavior of the original system and the simulated system. This paper presents nonlinear system identification and behavioral modeling using a work assignment.
Nonlinear distortion in wireless systems modeling and simulation with Matlab
Gharaibeh, Khaled M
2011-01-01
This book covers the principles of modeling and simulation of nonlinear distortion in wireless communication systems with MATLAB simulations and techniques In this book, the author describes the principles of modeling and simulation of nonlinear distortion in single and multichannel wireless communication systems using both deterministic and stochastic signals. Models and simulation methods of nonlinear amplifiers explain in detail how to analyze and evaluate the performance of data communication links under nonlinear amplification. The book addresses the analysis of nonlinear systems
Nonlinearity detection in hyperspectral images using a polynomial post-nonlinear mixing model.
Altmann, Yoann; Dobigeon, Nicolas; Tourneret, Jean-Yves
2013-04-01
This paper studies a nonlinear mixing model for hyperspectral image unmixing and nonlinearity detection. The proposed model assumes that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive white Gaussian noise. These nonlinear functions are approximated by polynomials leading to a polynomial post-nonlinear mixing model. We have shown in a previous paper that the parameters involved in the resulting model can be estimated using least squares methods. A generalized likelihood ratio test based on the estimator of the nonlinearity parameter is proposed to decide whether a pixel of the image results from the commonly used linear mixing model or from a more general nonlinear mixing model. To compute the test statistic associated with the nonlinearity detection, we propose to approximate the variance of the estimated nonlinearity parameter by its constrained Cramér-Rao bound. The performance of the detection strategy is evaluated via simulations conducted on synthetic and real data. More precisely, synthetic data have been generated according to the standard linear mixing model and three nonlinear models from the literature. The real data investigated in this study are extracted from the Cuprite image, which shows that some minerals seem to be nonlinearly mixed in this image. Finally, it is interesting to note that the estimated abundance maps obtained with the post-nonlinear mixing model are in good agreement with results obtained in previous studies.
Nonlinear GARCH model and 1 / f noise
Kononovicius, A.; Ruseckas, J.
2015-06-01
Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.
Dynamical effects of overparametrization in nonlinear models
Aguirre, Luis Antonio; Billings, S. A.
1995-01-01
This paper is concemed with dynamical reconstruction for nonlinear systems. The effects of the driving function and of the complexity of a given representation on the bifurcation patter are investigated. It is shown that the use of different driving functions to excite the system may yield models with different bifurcation patterns. The complexity of the reconstructions considered is quantified by the embedding dimension and the number of estimated parameters. In this respect it appears that models which reproduce the original bifurcation behaviour are of limited complexity and that excessively complex models tend to induce ghost bifurcations and spurious dynamical regimes. Moreover, some results suggest that the effects of overparametrization on the global dynamical behaviour of a nonlinear model may be more deleterious than the presence of moderate noise levels. In order to precisely quantify the complexity of the reconstructions, global polynomials are used although the results are believed to apply to a much wider class of representations including neural networks.
Prakash, J; Srinivasan, K
2009-07-01
In this paper, the authors have represented the nonlinear system as a family of local linear state space models, local PID controllers have been designed on the basis of linear models, and the weighted sum of the output from the local PID controllers (Nonlinear PID controller) has been used to control the nonlinear process. Further, Nonlinear Model Predictive Controller using the family of local linear state space models (F-NMPC) has been developed. The effectiveness of the proposed control schemes has been demonstrated on a CSTR process, which exhibits dynamic nonlinearity.
Research on nonlinear stochastic dynamical price model
Energy Technology Data Exchange (ETDEWEB)
Li Jiaorui [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China); School of Statistics, Xi' an University of Finance and Economics, Xi' an 710061 (China)], E-mail: jiaoruili@mail.nwpu.edu.cn; Xu Wei; Xie Wenxian; Ren Zhengzheng [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2008-09-15
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies.
Simplified Model of Nonlinear Landau Damping
Energy Technology Data Exchange (ETDEWEB)
N. A. Yampolsky and N. J. Fisch
2009-07-16
The nonlinear interaction of a plasma wave with resonant electrons results in a plateau in the electron distribution function close to the phase velocity of the plasma wave. As a result, Landau damping of the plasma wave vanishes and the resonant frequency of the plasma wave downshifts. However, this simple picture is invalid when the external driving force changes the plasma wave fast enough so that the plateau cannot be fully developed. A new model to describe amplification of the plasma wave including the saturation of Landau damping and the nonlinear frequency shift is proposed. The proposed model takes into account the change of the plasma wave amplitude and describes saturation of the Landau damping rate in terms of a single fluid equation, which simplifies the description of the inherently kinetic nature of Landau damping. A proposed fluid model, incorporating these simplifications, is verified numerically using a kinetic Vlasov code.
STEW A Nonlinear Data Modeling Computer Program
Chen, H
2000-01-01
A nonlinear data modeling computer program, STEW, employing the Levenberg-Marquardt algorithm, has been developed to model the experimental sup 2 sup 3 sup 9 Pu(n,f) and sup 2 sup 3 sup 5 U(n,f) cross sections. This report presents results of the modeling of the sup 2 sup 3 sup 9 Pu(n,f) and sup 2 sup 3 sup 5 U(n,f) cross-section data. The calculation of the fission transmission coefficient is based on the double-humped-fission-barrier model of Bjornholm and Lynn. Incident neutron energies of up to 5 MeV are considered.
STEW: A Nonlinear Data Modeling Computer Program
Energy Technology Data Exchange (ETDEWEB)
Chen, H.
2000-03-04
A nonlinear data modeling computer program, STEW, employing the Levenberg-Marquardt algorithm, has been developed to model the experimental {sup 239}Pu(n,f) and {sup 235}U(n,f) cross sections. This report presents results of the modeling of the {sup 239}Pu(n,f) and {sup 235}U(n,f) cross-section data. The calculation of the fission transmission coefficient is based on the double-humped-fission-barrier model of Bjornholm and Lynn. Incident neutron energies of up to 5 MeV are considered.
Simple nonlinear models suggest variable star universality
Lindner, John F; Kia, Behnam; Hippke, Michael; Learned, John G; Ditto, William L
2015-01-01
Dramatically improved data from observatories like the CoRoT and Kepler spacecraft have recently facilitated nonlinear time series analysis and phenomenological modeling of variable stars, including the search for strange (aka fractal) or chaotic dynamics. We recently argued [Lindner et al., Phys. Rev. Lett. 114 (2015) 054101] that the Kepler data includes "golden" stars, whose luminosities vary quasiperiodically with two frequencies nearly in the golden ratio, and whose secondary frequencies exhibit power-law scaling with exponent near -1.5, suggesting strange nonchaotic dynamics and singular spectra. Here we use a series of phenomenological models to make plausible the connection between golden stars and fractal spectra. We thereby suggest that at least some features of variable star dynamics reflect universal nonlinear phenomena common to even simple systems.
Thermoviscous Model Equations in Nonlinear Acoustics
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne
Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....
Modified Nonlinear Model of Arcsin-Electrodynamics
Kruglov, S. I.
2016-07-01
A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed. We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is present. We calculate indices of refraction for two perpendicular polarizations of electromagnetic waves and estimate bounds on the parameter γ from the BMV and PVLAS experiments. It is shown that the electric field of a point-like charge is finite at the origin. We calculate the finite static electric energy of point-like particles and demonstrate that the electron mass can have the pure electromagnetic nature. The symmetrical Belinfante energy-momentum tensor and dilatation current are found. We show that the dilatation symmetry and dual symmetry are broken in the model suggested. We have investigated the gauge covariant quantization of the nonlinear electrodynamics fields as well as the gauge fixing approach based on Dirac's brackets.
Energy Technology Data Exchange (ETDEWEB)
Barus, R. P. P., E-mail: rismawan.ppb@gmail.com [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung and Centre for Material and Technical Product, Jalan Sangkuriang No. 14 Bandung (Indonesia); Tjokronegoro, H. A.; Leksono, E. [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia); Ismunandar [Chemistry Study, Faculty of Mathematics and Science, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia)
2014-09-25
Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range.
Nonlinear chaotic model for predicting storm surges
Directory of Open Access Journals (Sweden)
M. Siek
2010-09-01
Full Text Available This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables. We implemented the univariate and multivariate chaotic models with direct and multi-steps prediction techniques and optimized these models using an exhaustive search method. The built models were tested for predicting storm surge dynamics for different stormy conditions in the North Sea, and are compared to neural network models. The results show that the chaotic models can generally provide reliable and accurate short-term storm surge predictions.
The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models
Hesse, Michael; Birn, Joachim
2011-01-01
Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.
MCRG Flow for the nonlinear Sigma Model
Koerner, Daniel; Wipf, Andreas
2013-01-01
A study of the renormalization group flow in the three-dimensional nonlinear O(N) sigma model using Monte Carlo Renormalization Group (MCRG) techniques is presented. To achieve this, we combine an improved blockspin transformation with the canonical demon method to determine the flow diagram for a number of different truncations. Systematic errors of the approach are highlighted. Results are discussed with hindsight on the fixed point structure of the model and the corresponding critical exponents. Special emphasis is drawn on the existence of a nontrivial ultraviolet fixed point as required for theories modeling the asymptotic safety scenario of quantum gravity.
Forecasting with nonlinear time series models
DEFF Research Database (Denmark)
Kock, Anders Bredahl; Teräsvirta, Timo
and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with com- plex dynamic systems, albeit less frequently...... applied to economic fore- casting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a partic...
Nonlinear Modelling of Low Frequency Loudspeakers
DEFF Research Database (Denmark)
Olsen, Erling Sandermann; Christensen, Knud Bank
1996-01-01
A central part of the Danish LoDist project has been the derivation of an extended equivalent circuit and a corresponding set of differential equations suitable for the simulation of high-fidelity woofers under large and very large (clipping) signal conditions. A model including suspension creep ...... and eddy current losses seems to be sufficient, but all the parameters of the model vary with the position of the diaphragm. The model and the associated set of nonlinear differential equations and the solution of the equations are discussed....
NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES
Directory of Open Access Journals (Sweden)
R. G. SILVA
1999-03-01
Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.
Nonlinear Inertia Classification Model and Application
Directory of Open Access Journals (Sweden)
Mei Wang
2014-01-01
Full Text Available Classification model of support vector machine (SVM overcomes the problem of a big number of samples. But the kernel parameter and the punishment factor have great influence on the quality of SVM model. Particle swarm optimization (PSO is an evolutionary search algorithm based on the swarm intelligence, which is suitable for parameter optimization. Accordingly, a nonlinear inertia convergence classification model (NICCM is proposed after the nonlinear inertia convergence (NICPSO is developed in this paper. The velocity of NICPSO is firstly defined as the weighted velocity of the inertia PSO, and the inertia factor is selected to be a nonlinear function. NICPSO is used to optimize the kernel parameter and a punishment factor of SVM. Then, NICCM classifier is trained by using the optical punishment factor and the optical kernel parameter that comes from the optimal particle. Finally, NICCM is applied to the classification of the normal state and fault states of online power cable. It is experimentally proved that the iteration number for the proposed NICPSO to reach the optimal position decreases from 15 to 5 compared with PSO; the training duration is decreased by 0.0052 s and the recognition precision is increased by 4.12% compared with SVM.
Model reduction of systems with localized nonlinearities.
Energy Technology Data Exchange (ETDEWEB)
Segalman, Daniel Joseph
2006-03-01
An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.
Evaluation of model fit in nonlinear multilevel structural equation modeling
Directory of Open Access Journals (Sweden)
Karin eSchermelleh-Engel
2014-03-01
Full Text Available Evaluating model fit in nonlinear multilevel structural equation models (MSEM presents a challenge as no adequate test statistic is available. Nevertheless, using a product indicator approach a likelihood ratio test for linear models is provided which may also be useful for nonlinear MSEM. The main problem with nonlinear models is that product variables are nonnormally distributed. Although robust test statistics have been developed for linear SEM to ensure valid results under the condition of nonnormality, they were not yet investigated for nonlinear MSEM. In a Monte Carlo study, the performance of the robust likelihood ratio test was investigated for models with single-level latent interaction effects using the unconstrained product indicator approach. As overall model fit evaluation has a potential limitation in detecting the lack of fit at a single level even for linear models, level-specific model fit evaluation was also investigated using partially saturated models. Four population models were considered: a model with interaction effects at both levels, an interaction effect at the within-group level, an interaction effect at the between-group level, and a model with no interaction effects at both levels. For these models the number of groups, predictor correlation, and model misspecification was varied. The results indicate that the robust test statistic performed sufficiently well. Advantages of level-specific model fit evaluation for the detection of model misfit are demonstrated.
Evaluation of model fit in nonlinear multilevel structural equation modeling.
Schermelleh-Engel, Karin; Kerwer, Martin; Klein, Andreas G
2014-01-01
Evaluating model fit in nonlinear multilevel structural equation models (MSEM) presents a challenge as no adequate test statistic is available. Nevertheless, using a product indicator approach a likelihood ratio test for linear models is provided which may also be useful for nonlinear MSEM. The main problem with nonlinear models is that product variables are non-normally distributed. Although robust test statistics have been developed for linear SEM to ensure valid results under the condition of non-normality, they have not yet been investigated for nonlinear MSEM. In a Monte Carlo study, the performance of the robust likelihood ratio test was investigated for models with single-level latent interaction effects using the unconstrained product indicator approach. As overall model fit evaluation has a potential limitation in detecting the lack of fit at a single level even for linear models, level-specific model fit evaluation was also investigated using partially saturated models. Four population models were considered: a model with interaction effects at both levels, an interaction effect at the within-group level, an interaction effect at the between-group level, and a model with no interaction effects at both levels. For these models the number of groups, predictor correlation, and model misspecification was varied. The results indicate that the robust test statistic performed sufficiently well. Advantages of level-specific model fit evaluation for the detection of model misfit are demonstrated.
Nonlinear trading models through Sharpe Ratio maximization.
Choey, M; Weigend, A S
1997-08-01
While many trading strategies are based on price prediction, traders in financial markets are typically interested in optimizing risk-adjusted performance such as the Sharpe Ratio, rather than the price predictions themselves. This paper introduces an approach which generates a nonlinear strategy that explicitly maximizes the Sharpe Ratio. It is expressed as a neural network model whose output is the position size between a risky and a risk-free asset. The iterative parameter update rules are derived and compared to alternative approaches. The resulting trading strategy is evaluated and analyzed on both computer-generated data and real world data (DAX, the daily German equity index). Trading based on Sharpe Ratio maximization compares favorably to both profit optimization and probability matching (through cross-entropy optimization). The results show that the goal of optimizing out-of-sample risk-adjusted profit can indeed be achieved with this nonlinear approach.
Nonlinear Model of non-Debye Relaxation
Zon, Boris A
2010-01-01
We present a simple nonlinear relaxation equation which contains the Debye equation as a particular case. The suggested relaxation equation results in power-law decay of fluctuations. This equation contains a parameter defining the frequency dependence of the dielectric permittivity similarly to the well-known one-parameter phenomenological equations of Cole-Cole, Davidson-Cole and Kohlrausch-Williams-Watts. Unlike these models, the obtained dielectric permittivity (i) obeys to the Kramers-Kronig relation; (ii) has proper behaviour at large frequency; (iii) its imaginary part, conductivity, shows a power-law frequency dependence \\sigma ~ \\omega^n where n1 is also observed in several experiments. The nonlinear equation proposed may be useful in various fields of relaxation theory.
Residual models for nonlinear partial differential equations
Directory of Open Access Journals (Sweden)
Garry Pantelis
2005-11-01
Full Text Available Residual terms that appear in nonlinear PDEs that are constructed to generate filtered representations of the variables of the fully resolved system are examined by way of a consistency condition. It is shown that certain commonly used empirical gradient models for the residuals fail the test of consistency and therefore cannot be validated as approximations in any reliable sense. An alternate method is presented for computing the residuals. These residual models are independent of free or artificial parameters and there direct link with the functional form of the system of PDEs which describe the fully resolved system are established.
Model of anisotropic nonlinearity in self-defocusing photorefractive media.
Barsi, C; Fleischer, J W
2015-09-21
We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.
Model updating of nonlinear structures from measured FRFs
Canbaloğlu, Güvenç; Özgüven, H. Nevzat
2016-12-01
There are always certain discrepancies between modal and response data of a structure obtained from its mathematical model and experimentally measured ones. Therefore it is a general practice to update the theoretical model by using experimental measurements in order to have a more accurate model. Most of the model updating methods used in structural dynamics are for linear systems. However, in real life applications most of the structures have nonlinearities, which restrict us applying model updating techniques available for linear structures, unless they work in linear range. Well-established frequency response function (FRF) based model updating methods would easily be extended to a nonlinear system if the FRFs of the underlying linear system (linear FRFs) could be experimentally measured. When frictional type of nonlinearity co-exists with other types of nonlinearities, it is not possible to obtain linear FRFs experimentally by using low level forcing. In this study a method (named as Pseudo Receptance Difference (PRD) method) is presented to obtain linear FRFs of a nonlinear structure having multiple nonlinearities including friction type of nonlinearity. PRD method, calculates linear FRFs of a nonlinear structure by using FRFs measured at various forcing levels, and simultaneously identifies all nonlinearities in the system. Then, any model updating method can be used to update the linear part of the mathematical model. In this present work, PRD method is used to predict the linear FRFs from measured nonlinear FRFs, and the inverse eigensensitivity method is employed to update the linear finite element (FE) model of the nonlinear structure. The proposed method is validated with different case studies using nonlinear lumped single-degree of freedom system, as well as a continuous system. Finally, a real nonlinear T-beam test structure is used to show the application and the accuracy of the proposed method. The accuracy of the updated nonlinear model of the
From spiking neuron models to linear-nonlinear models.
Directory of Open Access Journals (Sweden)
Srdjan Ostojic
Full Text Available Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF, exponential integrate-and-fire (EIF and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.
Fallacies of composition in nonlinear marketing models
Bischi, Gian Italo; Cerboni Baiardi, Lorenzo
2015-01-01
In this paper we consider some nonlinear discrete-time dynamic models proposed in the literature to represent marketing competition, and we use these models to critically discuss the statement, often made in economic literature, that identical agents behave identically and quasi-identical ones behave in a similar way. We show, through examples and some general mathematical statements, that the one-dimensional model of a representative agent, whose dynamics summarize the common behavior of identical interacting agents, may be misleading. In order to discuss these topics some simple methods for the study of local stability and bifurcations are employed, as well as numerical examples where some results taken from the literature on chaos synchronization are applied to two-dimensional marketing models that exhibit riddling, blowout and other global phenomena related to the existence of measure-theoretic attractors.
Nonlinear regime-switching state-space (RSSS) models.
Chow, Sy-Miin; Zhang, Guangjian
2013-10-01
Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases--namely, latent "regimes" or classes--during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.
Model Reduction of Nonlinear Fire Dynamics Models
Lattimer, Alan Martin
2016-01-01
Due to the complexity, multi-scale, and multi-physics nature of the mathematical models for fires, current numerical models require too much computational effort to be useful in design and real-time decision making, especially when dealing with fires over large domains. To reduce the computational time while retaining the complexity of the domain and physics, our research has focused on several reduced-order modeling techniques. Our contributions are improving wildland fire reduced-order mod...
Modeling of unusual nonlinear behaviors in superconducting microstrip transmission lines
Energy Technology Data Exchange (ETDEWEB)
Javadzadeh, S. Mohammad Hassan, E-mail: smh_javadzadeh@ee.sharif.edu [School of Electrical Engineering, Sharif University of Technology, P.O. Box 11365-9363, Tehran (Iran, Islamic Republic of); Farzaneh, Forouhar; Fardmanesh, Mehdi [School of Electrical Engineering, Sharif University of Technology, P.O. Box 11365-9363, Tehran (Iran, Islamic Republic of)
2013-03-15
Highlights: ► Avoiding of considering just quadratic or modulus nonlinearity. ► Proposing a nonlinear model to predict unusual nonlinear behaviors at low temperatures. ► Description of temperature dependency of nonlinear behaviors in superconducting lines. ► Analytical formulation for each parameter in our proposed model. ► Obtaining very good results which shows this model can predict unusual nonlinear behavior. -- Abstract: There are unusual nonlinear behaviors in superconducting materials, especially at low temperatures. This paper describes the procedure to reliably predict this nonlinearity in superconducting microstrip transmission lines (SMTLs). An accurate nonlinear distributed circuit model, based on simultaneously considering of both quadratic and modulus nonlinearity dependences, is proposed. All parameters of the equivalent circuit can be calculated analytically using proposed closed-form expressions. A numerical method based on Harmonic Balance approach is used to predict nonlinear phenomena like intermodulation distortions and third harmonic generations. Nonlinear analyses of the SMTLs at the different temperatures and the input powers have been presented. This proposed model can describe the unusual behaviors of the nonlinearity at low temperatures, which are frequently observed in the SMTLs.
Model Reduction for Nonlinear Systems by Incremental Balanced Truncation
Besselink, Bart; van de Wouw, Nathan; Scherpen, Jacquelien M. A.; Nijmeijer, Henk
2014-01-01
In this paper, the method of incremental balanced truncation is introduced as a tool for model reduction of nonlinear systems. Incremental balanced truncation provides an extension of balanced truncation for linear systems towards the nonlinear case and differs from existing nonlinear balancing tech
Model Reduction for Nonlinear Systems by Incremental Balanced Truncation
Besselink, Bart; van de Wouw, Nathan; Scherpen, Jacquelien M. A.; Nijmeijer, Henk
2014-01-01
In this paper, the method of incremental balanced truncation is introduced as a tool for model reduction of nonlinear systems. Incremental balanced truncation provides an extension of balanced truncation for linear systems towards the nonlinear case and differs from existing nonlinear balancing tech
A nonlinear RDF model for waves propagating in shallow water
Institute of Scientific and Technical Information of China (English)
王厚杰; 杨作升; 李瑞杰; 张军
2001-01-01
In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs’s relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refracti
Nonlinear structural finite element model updating and uncertainty quantification
Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.
2015-04-01
This paper presents a framework for nonlinear finite element (FE) model updating, in which state-of-the-art nonlinear structural FE modeling and analysis techniques are combined with the maximum likelihood estimation method (MLE) to estimate time-invariant parameters governing the nonlinear hysteretic material constitutive models used in the FE model of the structure. The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem. A proof-of-concept example, consisting of a cantilever steel column representing a bridge pier, is provided to verify the proposed nonlinear FE model updating framework.
Nonlinear system modeling based on experimental data
Energy Technology Data Exchange (ETDEWEB)
PAEZ,THOMAS L.; HUNTER,NORMAN F.
2000-02-02
The canonical variate analysis technique is used in this investigation, along with a data transformation algorithm, to identify a system in a transform space. The transformation algorithm involves the preprocessing of measured excitation/response data with a zero-memory-nonlinear transform, specifically, the Rosenblatt transform. This transform approximately maps the measured excitation and response data from its own space into the space of uncorrelated, standard normal random variates. Following this transform, it is appropriate to model the excitation/response relation as linear since Gaussian inputs excite Gaussian responses in linear structures. The linear model is identified in the transform space using the canonical variate analysis approach, and system responses in the original space are predicted using inverse Rosenblatt transformation. An example is presented.
Modified nonlinear model of arcsin-electrodynamics
Kruglov, S I
2015-01-01
A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed. We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is present. We calculate indices of refraction for two perpendicular polarizations of electromagnetic waves and estimate bounds on the parameter $\\gamma$ from the BMV and PVLAS experiments. It is shown that the electric field of a point-like charge is finite at the origin. We calculate the finite static electric energy of point-like particles and demonstrate that the electron mass can have the pure electromagnetic nature. The symmetrical Belinfante energy-momentum tensor and dilatation current are found. We show that the dilatation symmetry and dual symmetry are broken in the model suggested.
Nonlinear time reversal of classical waves: experiment and model.
Frazier, Matthew; Taddese, Biniyam; Xiao, Bo; Antonsen, Thomas; Ott, Edward; Anlage, Steven M
2013-12-01
We consider time reversal of electromagnetic waves in a closed, wave-chaotic system containing a discrete, passive, harmonic-generating nonlinearity. An experimental system is constructed as a time-reversal mirror, in which excitations generated by the nonlinearity are gathered, time-reversed, transmitted, and directed exclusively to the location of the nonlinearity. Here we show that such nonlinear objects can be purely passive (as opposed to the active nonlinearities used in previous work), and we develop a higher data rate exclusive communication system based on nonlinear time reversal. A model of the experimental system is developed, using a star-graph network of transmission lines, with one of the lines terminated by a model diode. The model simulates time reversal of linear and nonlinear signals, demonstrates features seen in the experimental system, and supports our interpretation of the experimental results.
Nonlinear dynamical model of an automotive dual mass flywheel
Directory of Open Access Journals (Sweden)
Lei Chen
2015-06-01
Full Text Available The hysteresis, stick–slip, and rotational speed-dependent characteristics in a basic dual mass flywheel are obtained from a static and a dynamic experiments. Based on the experimental results, a nonlinear model of the transferred torque in this dual mass flywheel is developed, with the overlying form of nonlinear elastic torque and frictional torque. The nonlinearities of stiffness are investigated, deriving a nonlinear model to describe the rotational speed-dependent stiffness. In addition, Bouc–Wen model is used to model the hysteretic frictional torque. Thus, the nonlinear 2-degree-of-freedom system of this dual mass flywheel is set up. Then, the Levenberg–Marquardt method is adopted for the parameter estimation of the frictional torque. Finally, taking the nonlinear stiffness in this model into account, the parameters of Bouc–Wen model are estimated based on the dynamic test data.
Recovering map static nonlinearities from chaotic data using dynamical models
Aguirre, Luis Antonio
1997-02-01
This paper is concerned with the estimation from chaotic data of maps with static nonlinearities. A number of issues concerning model construction such as structure selection, over-parametrization and model validation are discussed in the light of the shape of the static non-linearities reproduced by the estimated maps. A new interpretation of term clusters and cluster coefficients of polynomial models is provided based on this approach. The paper discusses model limitations and some useful principles to select the structure of nonlinear maps. Some of the ideas have been tested using several nonlinear systems including a boost voltage regulator map and a set of real data from a chaotic circuit.
Variational modelling of nonlinear water waves
Kalogirou, Anna; Bokhove, Onno
2015-11-01
Mathematical modelling of water waves is demonstrated by investigating variational methods. A potential flow water wave model is derived using variational techniques and extented to include explicit time-dependence, leading to non-autonomous dynamics. As a first example, we consider the problem of a soliton splash in a long wave channel with a contraction at its end, resulting after a sluice gate is removed at a finite time. The removal of the sluice gate is included in the variational principle through a time-dependent gravitational potential. A second example involving non-autonomous dynamics concerns the motion of a free surface in a vertical Hele-Shaw cell. Explicit time-dependence now enters the model through a linear damping term due to the effect of wall friction and a term representing the motion of an artificially driven wave pump. In both cases, the model is solved numerically using a Galerkin FEM and the numerical results are compared to wave structures observed in experiments. The water wave model is also adapted to accommodate nonlinear ship dynamics. The novelty is this case is the coupling between the water wave dynamics, the ship dynamics and water line dynamics on the ship. For simplicity, we consider a simple ship structure consisting of V-shaped cross-sections.
Nonlinear Eddy Viscosity Models applied to Wind Turbine Wakes
DEFF Research Database (Denmark)
Laan, van der, Paul Maarten; Sørensen, Niels N.; Réthoré, Pierre-Elouan;
2013-01-01
The linear k−ε eddy viscosity model and modified versions of two existing nonlinear eddy viscosity models are applied to single wind turbine wake simulations using a Reynolds Averaged Navier-Stokes code. Results are compared with field wake measurements. The nonlinear models give better results...
A simple numerical model of a geometrically nonlinear Timoshenko beam
Keijdener, C.; Metrikine, A.
2015-01-01
In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and tran
Non-Linear Sigma Model on Conifolds
Parthasarathy, R
2002-01-01
Explicit solutions to the conifold equations with complex dimension $n=3,4$ in terms of {\\it{complex coordinates (fields)}} are employed to construct the Ricci-flat K\\"{a}hler metrics on these manifolds. The K\\"{a}hler 2-forms are found to be closed. The complex realization of these conifold metrics are used in the construction of 2-dimensional non-linear sigma model with the conifolds as target spaces. The action for the sigma model is shown to be bounded from below. By a suitable choice of the 'integration constants', arising in the solution of Ricci flatness requirement, the metric and the equations of motion are found to be {\\it{non-singular}}. As the target space is Ricci flat, the perturbative 1-loop counter terms being absent, the model becomes topological. The inherent U(1) fibre over the base of the conifolds is shown to correspond to a gauge connection in the sigma model. The same procedure is employed to construct the metric for the resolved conifold, in terms of complex coordinates and the action ...
Explicit Nonlinear Model Predictive Control Theory and Applications
Grancharova, Alexandra
2012-01-01
Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...
Highly Nonlinear Ising Model and Social Segregation
Sumour, M A; Shabat, M M
2011-01-01
The usual interaction energy of the random field Ising model in statistical physics is modified by complementing the random field by added to the energy of the usual Ising model a nonlinear term S^n were S is the sum of the neighbor spins, and n=0,1,3,5,7,9,11. Within the Schelling model of urban segregation, this modification corresponds to housing prices depending on the immediate neighborhood. Simulations at different temperatures, lattice size, magnetic field, number of neighbors and different time intervals showed that results for all n are similar, expect for n=3 in violation of the universality principle and the law of corresponding states. In order to find the critical temperatures, for large n we no longer start with all spins parallel but instead with a random configuration, in order to facilitate spin flips. However, in all cases we have a Curie temperature with phase separation or long-range segregation only below this Curie temperature, and it is approximated by a simple formula: Tc is proportion...
Asymmetric and common absorption of shocks in nonlinear autoregressive models
Dijk, Dick van; Franses, Philip Hans; Boswijk, Peter
2000-01-01
textabstractA key feature of many nonlinear time series models is that they allow for the possibility that the model structure experiences changes, depending on for example the state of the economy or of the financial market. A common property of these models is that it generally is not possible to fully understand the structure of the model by considering the estimated values of the model parameters only. Put differently, it often is difficult to interpret a specific nonlinear model. To shed...
Fuzzy Modeling for Uncertainty Nonlinear Systems with Fuzzy Equations
Directory of Open Access Journals (Sweden)
Raheleh Jafari
2017-01-01
Full Text Available The uncertain nonlinear systems can be modeled with fuzzy equations by incorporating the fuzzy set theory. In this paper, the fuzzy equations are applied as the models for the uncertain nonlinear systems. The nonlinear modeling process is to find the coefficients of the fuzzy equations. We use the neural networks to approximate the coefficients of the fuzzy equations. The approximation theory for crisp models is extended into the fuzzy equation model. The upper bounds of the modeling errors are estimated. Numerical experiments along with comparisons demonstrate the excellent behavior of the proposed method.
A NEW SOLUTION MODEL OF NONLINEAR DYNAMIC LEAST SQUARE ADJUSTMENT
Institute of Scientific and Technical Information of China (English)
陶华学; 郭金运
2000-01-01
The nonlinear least square adjustment is a head object studied in technology fields. The paper studies on the non-derivative solution to the nonlinear dynamic least square adjustment and puts forward a new algorithm model and its solution model. The method has little calculation load and is simple. This opens up a theoretical method to solve the linear dynamic least square adjustment.
Lattice Boltzmann model for nonlinear convection-diffusion equations.
Shi, Baochang; Guo, Zhaoli
2009-01-01
A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.
Nonlinear lower hybrid modeling in tokamak plasmas
Energy Technology Data Exchange (ETDEWEB)
Napoli, F.; Schettini, G. [Università Roma Tre, Dipartimento di Ingegneria, Roma (Italy); Castaldo, C.; Cesario, R. [Associazione EURATOM/ENEA sulla Fusione, Centro Ricerche Frascati (Italy)
2014-02-12
We present here new results concerning the nonlinear mechanism underlying the observed spectral broadening produced by parametric instabilities occurring at the edge of tokamak plasmas in present day LHCD (lower hybrid current drive) experiments. Low frequency (LF) ion-sound evanescent modes (quasi-modes) are the main parametric decay channel which drives a nonlinear mode coupling of lower hybrid (LH) waves. The spectrum of the LF fluctuations is calculated here considering the beating of the launched LH wave at the radiofrequency (RF) operating line frequency (pump wave) with the noisy background of the RF power generator. This spectrum is calculated in the frame of the kinetic theory, following a perturbative approach. Numerical solutions of the nonlinear LH wave equation show the evolution of the nonlinear mode coupling in condition of a finite depletion of the pump power. The role of the presence of heavy ions in a Deuterium plasma in mitigating the nonlinear effects is analyzed.
A Modal Model to Simulate Typical Structural Dynamic Nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Pacini, Benjamin Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Mayes, Randall L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Roettgen, Daniel R [Univ. of Wisconsin, Madison, WI (United States)
2015-10-01
Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.
ASYMPTOTIC EFFICIENT ESTIMATION IN SEMIPARAMETRIC NONLINEAR REGRESSION MODELS
Institute of Scientific and Technical Information of China (English)
ZhuZhongyi; WeiBocheng
1999-01-01
In this paper, the estimation method based on the “generalized profile likelihood” for the conditionally parametric models in the paper given by Severini and Wong (1992) is extendedto fixed design semiparametrie nonlinear regression models. For these semiparametrie nonlinear regression models,the resulting estimator of parametric component of the model is shown to beasymptotically efficient and the strong convergence rate of nonparametric component is investigated. Many results (for example Chen (1988) ,Gao & Zhao (1993), Rice (1986) et al. ) are extended to fixed design semiparametric nonlinear regression models.
Control design approaches for nonlinear systems using multiple models
Institute of Scientific and Technical Information of China (English)
Junyong ZHAI; Shumin FEI; Feipeng DA
2007-01-01
It is difficult to realize control for some complex nonlinear systems operated in different operating regions.Based on developing local models for different operating regions of the process, a novel algorithm using multiple models is proposed. It utilizes dynamic model bank to establish multiple local models, and their membership functions are defined according to respective regions. Then the nonlinear system is approximated to a weighted combination of the local models.The stability of the nonlinear system is proven. Finally, simulations are given to demonstrate the validity of the proposed method.
TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS
Institute of Scientific and Technical Information of China (English)
LinJinguan; WeiBocheng; ZhangNansong
2003-01-01
It is necessary to test for varying dispersion in generalized nonlinear models. Wei ,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models. This type of problem in the framework of general discrete exponential family nonlinear models is discussed. Two types of varying dispersion, which are random coefficients model and random effects model, are proposed,and corresponding score test statistics are constructed and expressed in simple ,easy to use ,matrix formulas.
Nonlinear flow model for well production in an underground formation
Directory of Open Access Journals (Sweden)
J. C. Guo
2013-05-01
Full Text Available Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water. The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.
Model reduction of nonlinear systems subject to input disturbances
Ndoye, Ibrahima
2017-07-10
The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order nonlinear system with similar disturbance-output properties to the original plant. The proposed model reduction strategy preserves the nonlinearity and the input disturbance nature of the model. It guarantees a sufficiently small error between the outputs of the original and the reduced-order systems, and also maintains the properties of input-to-state stability. The matrices of the reduced order system are given in terms of a set of linear matrix inequalities (LMIs). The paper concludes with a demonstration of the proposed approach on model reduction of a nonlinear electronic circuit with additive disturbances.
Nonlinear and Non Normal Regression Models in Physiological Research
1984-01-01
Applications of nonlinear and non normal regression models are in increasing order for appropriate interpretation of complex phenomenon of biomedical sciences. This paper reviews critically some applications of these models physiological research.
Nonlinear Dynamic Model Explains The Solar Dynamic
Kuman, Maria
Nonlinear mathematical model in torus representation describes the solar dynamic. Its graphic presentation shows that without perturbing force the orbits of the planets would be circles; only perturbing force could elongate the circular orbits into ellipses. Since the Hubble telescope found that the planetary orbits of other stars in the Milky Way are also ellipses, powerful perturbing force must be present in our galaxy. Such perturbing force is the Sagittarius Dwarf Galaxy with its heavy Black Hole and leftover stars, which we see orbiting around the center of our galaxy. Since observations of NASA's SDO found that magnetic fields rule the solar activity, we can expect when the planets align and their magnetic moments sum up, the already perturbed stars to reverse their magnetic parity (represented graphically as periodic looping through the hole of the torus). We predict that planets aligned on both sides of the Sun, when their magnetic moments sum-up, would induce more flares in the turbulent equatorial zone, which would bulge. When planets align only on one side of the Sun, the strong magnetic gradient of their asymmetric pull would flip the magnetic poles of the Sun. The Sun would elongate pole-to-pole, emit some energy through the poles, and the solar activity would cease. Similar reshaping and emission was observed in stars called magnetars and experimentally observed in super-liquid fast-spinning Helium nanodroplets. We are certain that NASA's SDO will confirm our predictions.
Nonlinear State Space Modeling and System Identification for Electrohydraulic Control
Directory of Open Access Journals (Sweden)
Jun Yan
2013-01-01
Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.
Modelling and Estimation of Hammerstein System with Preload Nonlinearity
Directory of Open Access Journals (Sweden)
Khaled ELLEUCH
2010-12-01
Full Text Available This paper deals with modelling and parameter identification of nonlinear systems described by Hammerstein model having asymmetric static nonlinearities known as preload nonlinearity characteristic. The simultaneous use of both an easy decomposition technique and the generalized orthonormal bases leads to a particular form of Hammerstein model containing a minimal parameters number. The employ of orthonormal bases for the description of the linear dynamic block conducts to a linear regressor model, so that least squares techniques can be used for the parameter estimation. Singular Values Decomposition (SVD technique has been applied to separate the coupled parameters. To demonstrate the feasibility of the identification method, an illustrative example is included.
Applications of Nonlinear Dynamics Model and Design of Complex Systems
In, Visarath; Palacios, Antonio
2009-01-01
This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.
Extended models of nonlinear waves in liquid with gas bubbles
Kudryashov, Nikolay A
2016-01-01
In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for nonlinear waves. We also take into consideration high order terms with respect to the small parameter. Two new nonlinear differential equations are derived for long weakly nonlinear waves in a liquid with gas bubbles by the reductive perturbation method considering both high order terms with respect to the small parameter and the above mentioned physical properties. One of these equations is the perturbation of the Burgers equation and corresponds to main influence of dissipation on nonlinear waves propagation. The other equation is the perturbation of the Burgers--Korteweg--de Vries equation and corresponds to main influence of dispersion on nonlinear waves propagation.
Nonlinear Mixed-Effects Models for Repairable Systems Reliability
Institute of Scientific and Technical Information of China (English)
TAN Fu-rong; JIANG Zhi-bin; KUO Way; Suk Joo BAE
2007-01-01
Mixed-effects models, also called random-effects models, are a regression type of analysis which enables the analyst to not only describe the trend over time within each subject, but also to describe the variation among different subjects. Nonlinear mixed-effects models provide a powerful and flexible tool for handling the unbalanced count data. In this paper, nonlinear mixed-effects models are used to analyze the failure data from a repairable system with multiple copies. By using this type of models, statistical inferences about the population and all copies can be made when accounting for copy-to-copy variance. Results of fitting nonlinear mixed-effects models to nine failure-data sets show that the nonlinear mixed-effects models provide a useful tool for analyzing the failure data from multi-copy repairable systems.
A Boussinesq model with alleviated nonlinearity and dispersion
Institute of Scientific and Technical Information of China (English)
ZHANG Dian-xin; TAO Jian-hua
2008-01-01
The classical Boussinesq equation is a weakly nonlinear and weakly dispersive equation, which has been widely applied to simulate wave propagation in off-coast shallow waters. A new form of the Boussinesq model for an uneven bottoms is derived in this paper. In the new model, nonlinearity is reduced without increasing the order of the highest derivative in the differential equations. Dispersion relationship of the model is improved to the order of Pade (2,2) by adjusting a parameter in the model based on the long wave approximation. Analysis of the linear dispersion, linear shoaling and nonlinearity of the present model shows that the performances in terms of nonlinearity, dispersion and shoaling of this model are improved. Numerical results obtained with the present model are in agreement with experimental data.
Employment of CB models for non-linear dynamic analysis
Klein, M. R. M.; Deloo, P.; Fournier-Sicre, A.
1990-01-01
The non-linear dynamic analysis of large structures is always very time, effort and CPU consuming. Whenever possible the reduction of the size of the mathematical model involved is of main importance to speed up the computational procedures. Such reduction can be performed for the part of the structure which perform linearly. Most of the time, the classical Guyan reduction process is used. For non-linear dynamic process where the non-linearity is present at interfaces between different structures, Craig-Bampton models can provide a very rich information, and allow easy selection of the relevant modes with respect to the phenomenon driving the non-linearity. The paper presents the employment of Craig-Bampton models combined with Newmark direct integration for solving non-linear friction problems appearing at the interface between the Hubble Space Telescope and its solar arrays during in-orbit maneuvers. Theory, implementation in the FEM code ASKA, and practical results are shown.
Linear and Nonlinear Thinking: A Multidimensional Model and Measure
Groves, Kevin S.; Vance, Charles M.
2015-01-01
Building upon previously developed and more general dual-process models, this paper provides empirical support for a multidimensional thinking style construct comprised of linear thinking and multiple dimensions of nonlinear thinking. A self-report assessment instrument (Linear/Nonlinear Thinking Style Profile; LNTSP) is presented and…
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
Temperature effects in a nonlinear model of monolayer Scheibe aggregates
DEFF Research Database (Denmark)
Bang, Ole; Christiansen, Peter Leth; If, F.
1994-01-01
A nonlinear dynamical model of molecular monolayers arranged in Scheibe aggregates is derived from a proper Hamiltonian. Thermal fluctuations of the phonons are included. The resulting equation for the excitons is the two dimensional nonlinear Schrodinger equation with noise. Two limits...
Linear and Nonlinear Thinking: A Multidimensional Model and Measure
Groves, Kevin S.; Vance, Charles M.
2015-01-01
Building upon previously developed and more general dual-process models, this paper provides empirical support for a multidimensional thinking style construct comprised of linear thinking and multiple dimensions of nonlinear thinking. A self-report assessment instrument (Linear/Nonlinear Thinking Style Profile; LNTSP) is presented and…
DEFF Research Database (Denmark)
Fournier, David A.; Skaug, Hans J.; Ancheta, Johnoel
2011-01-01
Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem.Automatic Differentiation Model Builder (ADMB) is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number...
Nonlinear Economic Model Predictive Control Strategy for Active Smart Buildings
DEFF Research Database (Denmark)
Santos, Rui Mirra; Zong, Yi; Sousa, Joao M. C.
2016-01-01
Nowadays, the development of advanced and innovative intelligent control techniques for energy management in buildings is a key issue within the smart grid topic. A nonlinear economic model predictive control (EMPC) scheme, based on the branch-and-bound tree search used as optimization algorithm...... for solving the nonconvex optimization problem is proposed in this paper. A simulation using the nonlinear model-based controller to control the temperature levels of an intelligent office building (PowerFlexHouse) is addressed. Its performance is compared with a linear model-based controller. The nonlinear...
Local Influence Analysis for Semiparametric Reproductive Dispersion Nonlinear Models
Institute of Scientific and Technical Information of China (English)
Xue-dong CHEN; Nian-sheng TANG; Xue-ren WANG
2012-01-01
The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM)which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models.Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented.Assessment of local influence for various perturbation schemes are investigated.Some local influence diagnostics are given.A simulation study and a real example are used to illustrate the proposed methodologies.
General expression for linear and nonlinear time series models
Institute of Scientific and Technical Information of China (English)
Ren HUANG; Feiyun XU; Ruwen CHEN
2009-01-01
The typical time series models such as ARMA, AR, and MA are founded on the normality and stationarity of a system and expressed by a linear difference equation; therefore, they are strictly limited to the linear system. However, some nonlinear factors are within the practical system; thus, it is difficult to fit the model for real systems with the above models. This paper proposes a general expression for linear and nonlinear auto-regressive time series models (GNAR). With the gradient optimization method and modified AIC information criteria integrated with the prediction error, the parameter estimation and order determination are achieved. The model simulation and experiments show that the GNAR model can accurately approximate to the dynamic characteristics of the most nonlinear models applied in academics and engineering. The modeling and prediction accuracy of the GNAR model is superior to the classical time series models. The proposed GNAR model is flexible and effective.
Bayesian model comparison in nonlinear BOLD fMRI hemodynamics
DEFF Research Database (Denmark)
Jacobsen, Danjal Jakup; Hansen, Lars Kai; Madsen, Kristoffer Hougaard
2008-01-01
Nonlinear hemodynamic models express the BOLD (blood oxygenation level dependent) signal as a nonlinear, parametric functional of the temporal sequence of local neural activity. Several models have been proposed for both the neural activity and the hemodynamics. We compare two such combined models......: the original balloon model with a square-pulse neural model (Friston, Mechelli, Turner, & Price, 2000) and an extended balloon model with a more sophisticated neural model (Buxton, Uludag, Dubowitz, & Liu, 2004). We learn the parameters of both models using a Bayesian approach, where the distribution...
Coupled Oscillator Model for Nonlinear Gravitational Perturbations
Yang, Huan; Green, Stephen R; Lehner, Luis
2015-01-01
Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a collection of nonlinearly-coupled harmonic oscillators. These oscillators correspond to the quasinormal or normal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism within the context of perturbed asymptotically anti-de Sitter black brane spacetimes. We confirm in this case that the boundary fluid dynamics are equivalent to those of the hydrodynamic quasinormal modes of the bulk spacetime. We expect this formalism to remain valid in more general spacetimes, including those without a fluid dual. In other words, although borne out of the gravity/fluid correspondence, the formalism is fully independent and it has a much wider range of applicability. In particular, as this formalism inspires an especially transparent physical intuition, w...
Reduced Noise Effect in Nonlinear Model Estimation Using Multiscale Representation
Directory of Open Access Journals (Sweden)
Mohamed N. Nounou
2010-01-01
Full Text Available Nonlinear process models are widely used in various applications. In the absence of fundamental models, it is usually relied on empirical models, which are estimated from measurements of the process variables. Unfortunately, measured data are usually corrupted with measurement noise that degrades the accuracy of the estimated models. Multiscale wavelet-based representation of data has been shown to be a powerful data analysis and feature extraction tool. In this paper, these characteristics of multiscale representation are utilized to improve the estimation accuracy of the linear-in-the-parameters nonlinear model by developing a multiscale nonlinear (MSNL modeling algorithm. The main idea in this MSNL modeling algorithm is to decompose the data at multiple scales, construct multiple nonlinear models at multiple scales, and then select among all scales the model which best describes the process. The main advantage of the developed algorithm is that it integrates modeling and feature extraction to improve the robustness of the estimated model to the presence of measurement noise in the data. This advantage of MSNL modeling is demonstrated using a nonlinear reactor model.
Blind channel identication of nonlinear folding mixing model
Institute of Scientific and Technical Information of China (English)
Su Yong; Xu Shangzhi; Ye Zhongfu
2006-01-01
Signals from multi-sensor systems are often mixtures of (statistically) independent sources by unknown mixing method. Blind source separation(BSS) and independent component analysis(ICA) are the methods to identify/recover the channels and the sources. BSS/ICA of nonlinear mixing models are difficult problems. For instance, the post-nonlinear model has been studied by several authors. It is noticed that in most cases, the proposed models are always with an invertible mixing. According to this fact there is an interesting question: how about the situation of the non-invertible non-linear mixing in BSS or ICA? A new simple non-linear mixing model is proposed with a kind of non-invertible mixing, the folding mixing, and method to identify its channel, blindly.
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).
Exact travelling wave solutions for some important nonlinear physical models
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2013-05-01
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.
A reduced order model for nonlinear vibroacoustic problems
Directory of Open Access Journals (Sweden)
Ouisse Morvan
2012-07-01
Full Text Available This work is related to geometrical nonlinearities applied to thin plates coupled with fluid-filled domain. Model reduction is performed to reduce the computation time. Reduced order model (ROM is issued from the uncoupled linear problem and enriched with residues to describe the nonlinear behavior and coupling effects. To show the efficiency of the proposed method, numerical simulations in the case of an elastic plate closing an acoustic cavity are presented.
A Comment on the Renormalization of the Nonlinear Sigma Model
Bettinelli, D; Quadri, A; Bettinelli, Daniele; Ferrari, Ruggero; Quadri, Andrea
2007-01-01
We consider the recently proposed renormalization procedure for the nonlinear sigma model, consisting in the recursive subtraction of the divergences in a symmetric fashion. We compare this subtraction with the conventional procedure in power counting renormalizable (PCR) theories. We argue that symmetric subtraction in the nonlinear sigma model does not follow the lore by which nonrenormalizable theories require an infinite number of parameter fixings. Our conclusion is that only two parameters can be consistently used as physical constants.
Robust Designs for Three Commonly Used Nonlinear Models
Xu, Xiaojian; Chen, Arnold
2011-11-01
In this paper, we study the robust designs for a few nonlinear models, including an exponential model with an intercept, a compartmental model, and a Michaelis-Menten model, when these models are possibly misspecified. The minimax robust designs we considered in this paper are under consideration of not only minimizing the variances but also reducing the possible biases in estimation. Both prediction and extrapolation cases are discussed. The robust designs are found incorporating the approximation of these models with several situations such as homoscedasticity, and heteroscedasticity. Both ordinary and weighted nonlinear least squares methods are utilized.
RECENT PROGRESS IN NONLINEAR EDDY-VISCOSITY TURBULENCE MODELING
Institute of Scientific and Technical Information of China (English)
符松; 郭阳; 钱炜祺; 王辰
2003-01-01
This article presents recent progresses in turbulence modeling in the Unit for Turbulence Simulation in the Department of Engineering Mechanics at Tsinghua University. The main contents include: compact Non-Linear Eddy-Viscosity Model (NLEVM) based on the second-moment closure, near-wall low-Re non-linear eddy-viscosity model and curvature sensitive turbulence model.The models have been validated in a wide range of complex flow test cases and the calculated results show that the present models exhibited overall good performance.
Modeling of nonlinear responses for reciprocal transducers involving polarization switching
DEFF Research Database (Denmark)
Willatzen, Morten; Wang, Linxiang
2007-01-01
Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled....... We present numerical results for the reciprocal-transducer system and identify the influence of nonlinearities on the system dynamics at high and low frequency as well as electrical impedance effects due to tuning by a series inductance. It is found that nonlinear effects are not important at high...... by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled...
Nonlinear unmixing of hyperspectral images: models and algorithms
Dobigeon, Nicolas; Richard, Cédric; Bermudez, José C M; McLaughlin, Stephen; Hero, Alfred O
2013-01-01
When considering the problem of unmixing hyperspectral images, most of the literature in the geoscience and image processing areas rely on the widely acknowledged linear mixing model (LMM). However, in specific but common contexts, the LMM may be not valid and other nonlinear models should be invoked. Consequently, over the last few years, several significant contributions have been proposed to overcome the limitations inherent in the LMM. In this paper, we present an overview of recent advances that deal with the nonlinear unmixing problem. The main nonlinear models are introduced and their validity discussed. Then, we describe the main classes of unmixing strategies designed to solve the problem in supervised and unsupervised frameworks. Finally, the problem of detecting nonlinear mixtures in hyperspectral images is addressed.
A Study of Thermal Contact using Nonlinear System Identification Models
Directory of Open Access Journals (Sweden)
M. H. Shojaeefard
2008-01-01
Full Text Available One interesting application of system identification method is to identify and control the heat transfer from the exhaust valve to the seat to keep away the valve from being damaged. In this study, two co-axial cylindrical specimens are used as exhaust valve and its seat. Using the measured temperatures at different locations of the specimens and with a semi-analytical method, the temperature distribution of the specimens is calculated and consequently, the thermal contact conductance is calculated. By applying the system identification method and having the temperatures at both sides of the contact surface, the temperature transfer function is calculated. With regard to the fact that the thermal contact has nonlinear behavior, two nonlinear black-box models called nonlinear ARX and NLN Hammerstein-Wiener models are taken for accurate estimation. Results show that the NLN Hammerstein-Wiener models with wavelet network nonlinear estimator is the best.
A Simple Holographic Model of Nonlinear Conductivity
Horowitz, Gary T; Santos, Jorge E
2013-01-01
We present a simple analytic gravitational solution which describes the holographic dual of a 2+1-dimensional conductor which goes beyond the usual linear response. In particular it includes Joule heating. We find that the nonlinear frequency-dependent conductivity is a constant. Surprisingly, the pressure remains isotropic. We also apply an electric field to a holographic insulator and show that there is a maximum electric field below which it can remain an insulator. Above this critical value, we argue that it becomes a conductor due to pair creation of charged particles. Finally, we study 1+1 and 3+1 dimensional conductors at the nonlinear level; here exact solutions are not available and a perturbative analysis shows that the current becomes time dependent, but in a way that is captured by a time-dependent effective temperature.
Nonlinear dynamics new directions models and applications
Ugalde, Edgardo
2015-01-01
This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynam...
Modeling of nonlinear propagation in fiber tapers
DEFF Research Database (Denmark)
Lægsgaard, Jesper
2012-01-01
A full-vectorial nonlinear propagation equation for short pulses in tapered optical fibers is developed. Specific emphasis is placed on the importance of the field normalization convention for the structure of the equations, and the interpretation of the resulting field amplitudes. Different...... numerical schemes for interpolation of fiber parameters along the taper are discussed and tested in numerical simulations on soliton propagation and generation of continuum radiation in short photonic-crystal fiber tapers....
Practical Soil-Shallow Foundation Model for Nonlinear Structural Analysis
Directory of Open Access Journals (Sweden)
Moussa Leblouba
2016-01-01
Full Text Available Soil-shallow foundation interaction models that are incorporated into most structural analysis programs generally lack accuracy and efficiency or neglect some aspects of foundation behavior. For instance, soil-shallow foundation systems have been observed to show both small and large loops under increasing amplitude load reversals. This paper presents a practical macroelement model for soil-shallow foundation system and its stability under simultaneous horizontal and vertical loads. The model comprises three spring elements: nonlinear horizontal, nonlinear rotational, and linear vertical springs. The proposed macroelement model was verified using experimental test results from large-scale model foundations subjected to small and large cyclic loading cases.
Geometrically nonlinear creeping mathematic models of shells with variable thickness
Directory of Open Access Journals (Sweden)
V.M. Zhgoutov
2012-08-01
Full Text Available Calculations of strength, stability and vibration of shell structures play an important role in the design of modern devices machines and structures. However, the behavior of thin-walled structures of variable thickness during which geometric nonlinearity, lateral shifts, viscoelasticity (creep of the material, the variability of the profile take place and thermal deformation starts up is not studied enough.In this paper the mathematical deformation models of variable thickness shells (smoothly variable and ribbed shells, experiencing either mechanical load or permanent temperature field and taking into account the geometrical nonlinearity, creeping and transverse shear, were developed. The refined geometrical proportions for geometrically nonlinear and steadiness problems are given.
Haar basis and nonlinear modeling of complex systems
García, P.; Merlitti, A.
2007-04-01
In this work we introduce a technique to perform nonlinear modeling of chaotic time series using the kernel method. The basic idea behind this method is to map the data into a high dimensional space via nonlinear mapping and do a linear regression in this space. Here we use a Haar wavelet-like kernel to achieve the task. This strategy, in contrast to Support Vector Machines technique, shows the conceptual simplicity of least mean square algoritm for linear regression but allows local nonlinear aproximation of the system evolution, with low computational cost.
Physical mechanisms of nonlinear conductivity: A model analysis
Heuer, Andreas; Lühning, Lars
2014-03-01
Nonlinear effects are omnipresent in thin films of ion conducting materials showing up as a significant increase of the conductivity. For a disordered hopping model general physical mechanisms are identified giving rise to the occurrence of positive or negative nonlinear effects, respectively. Analytical results are obtained in the limit of high but finite dimensions. They are compared with the numerical results for 3D up to 6D systems. A very good agreement can be found, in particular for higher dimensions. The results can also be used to rationalize previous numerical simulations. The implications for the interpretation of nonlinear conductivity experiments on inorganic ion conductors are discussed.
Nonlinear analysis of lipid tubules by nonlocal beam model.
Shen, Hui-Shen
2011-05-07
Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for lipid tubules. The lipid tubule is modeled as a nonlocal micro/nano-beam which contains small scale effect. The material properties are assumed to be size-dependent. The governing equation is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e₀a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of lipid tubules. In contrast, it increases the nonlinear to linear frequency ratios slightly for the lipid tubule with immovable end conditions.
Numerical modelling of nonlinear full-wave acoustic propagation
Energy Technology Data Exchange (ETDEWEB)
Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx [Grupo de Acústica y Vibraciones, Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Ciudad Universitaria, Apartado Postal 70-186, C.P. 04510, México D.F., México (Mexico)
2015-10-28
The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on a GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.
Residual Minimizing Model Reduction for Parameterized Nonlinear Dynamical Systems
Constantine, Paul G
2010-01-01
We present a method for approximating the solution of a parameterized, nonlinear dynamical (or static) system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the dynamical system. The approximation properties of this residual minimizing scheme are comparable to existing reduced basis and POD-Galerkin model reduction methods, but its implementation requires only independent evaluations of the nonlinear forcing function. We prove some interesting characteristics of the scheme including uniqueness and an interpolatory property, and we present heuristics for mitigating the effects of the ill-conditioning and reducing the overall cost of the method. We apply the method to representative numerical examples from kinetics - a three state system with one parameter controlling the stiffness - and groundwater modeling - a nonlinear parabolic PDE w...
2010-09-30
Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING
Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbek, Anders
In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing...... symmetric non-linear error correction are considered. A simulation study shows that the finite sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes....
Recent Advances in Explicit Multiparametric Nonlinear Model Predictive Control
Domínguez, Luis F.
2011-01-19
In this paper we present recent advances in multiparametric nonlinear programming (mp-NLP) algorithms for explicit nonlinear model predictive control (mp-NMPC). Three mp-NLP algorithms for NMPC are discussed, based on which novel mp-NMPC controllers are derived. The performance of the explicit controllers are then tested and compared in a simulation example involving the operation of a continuous stirred-tank reactor (CSTR). © 2010 American Chemical Society.
Inference of a nonlinear stochastic model of the cardiorespiratory interaction
Smelyanskiy, V N; Stefanovska, A; McClintock, P V E
2005-01-01
A new technique is introduced to reconstruct a nonlinear stochastic model of the cardiorespiratory interaction. Its inferential framework uses a set of polynomial basis functions representing the nonlinear force governing the system oscillations. The strength and direction of coupling, and the noise intensity are simultaneously inferred from a univariate blood pressure signal, monitored in a clinical environment. The technique does not require extensive global optimization and it is applicable to a wide range of complex dynamical systems subject to noise.
Asymmetric and common absorption of shocks in nonlinear autoregressive models
D.J.C. van Dijk (Dick); Ph.H.B.F. Franses (Philip Hans); H.P. Boswijk (Peter)
2000-01-01
textabstractA key feature of many nonlinear time series models is that they allow for the possibility that the model structure experiences changes, depending on for example the state of the economy or of the financial market. A common property of these models is that it generally is not possible to
Asymmetric and common absorption of shocks in nonlinear autoregressive models
D.J.C. van Dijk (Dick); Ph.H.B.F. Franses (Philip Hans); H.P. Boswijk (Peter)
2000-01-01
textabstractA key feature of many nonlinear time series models is that they allow for the possibility that the model structure experiences changes, depending on for example the state of the economy or of the financial market. A common property of these models is that it generally is not possible to
Modeling and nonlinear heading control for sailing yachts
DEFF Research Database (Denmark)
Xiao, Lin; Jouffroy, Jerome
2011-01-01
This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen's compact notation for marine vehicles, we first describe a nonlinear 4-DOF dynamic model for a sailing yacht, including roll. Starting from this model, we then design ...
Modeling and nonlinear heading control for sailing yachts
DEFF Research Database (Denmark)
Xiao, Lin; Jouffroy, Jerome
2014-01-01
This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen’s compact notation for marine vehicles, we first describe a nonlinear four-degree-of-freedom (DOF) dynamic model for a sailing yacht, including roll. Our model also inc...
Modeling of Nonlinear Signal Distortion in Fiber-Optical Networks
Johannisson, Pontus
2013-01-01
A low-complexity model for signal quality prediction in a nonlinear fiber-optical network is developed. The model, which builds on the Gaussian noise model, takes into account the signal degradation caused by a combination of chromatic dispersion, nonlinear signal distortion, and amplifier noise. The center frequencies, bandwidths, and transmit powers can be chosen independently for each channel, which makes the model suitable for analysis and optimization of resource allocation, routing, and scheduling in large-scale optical networks applying flexible-grid wavelength-division multiplexing.
An Improved Nonlinear Five-Point Model for Photovoltaic Modules
Directory of Open Access Journals (Sweden)
Sakaros Bogning Dongue
2013-01-01
Full Text Available This paper presents an improved nonlinear five-point model capable of analytically describing the electrical behaviors of a photovoltaic module for each generic operating condition of temperature and solar irradiance. The models used to replicate the electrical behaviors of operating PV modules are usually based on some simplified assumptions which provide convenient mathematical model which can be used in conventional simulation tools. Unfortunately, these assumptions cause some inaccuracies, and hence unrealistic economic returns are predicted. As an alternative, we used the advantages of a nonlinear analytical five-point model to take into account the nonideal diode effects and nonlinear effects generally ignored, which PV modules operation depends on. To verify the capability of our method to fit PV panel characteristics, the procedure was tested on three different panels. Results were compared with the data issued by manufacturers and with the results obtained using the five-parameter model proposed by other authors.
Non-linear Growth Models in Mplus and SAS.
Grimm, Kevin J; Ram, Nilam
2009-10-01
Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included.
Earthquake analysis of structures using nonlinear models
Cemalovic, Miran
2015-01-01
Throughout the governing design codes, several different methods are presented for the evaluation of seismic problems. This thesis assesses the non-linear static and dynamic procedures presented in EN 1998-1 through the structural response of a RC wall-frame building. The structure is designed in detail according to the guidelines for high ductility (DCH) in EN 1998-1. The applied procedures are meticulously evaluated and the requirements in EN 1998-1 are reviewed. In addition, the finite ele...
Similarity transformation approach to identifiability analysis of nonlinear compartmental models.
Vajda, S; Godfrey, K R; Rabitz, H
1989-04-01
Through use of the local state isomorphism theorem instead of the algebraic equivalence theorem of linear systems theory, the similarity transformation approach is extended to nonlinear models, resulting in finitely verifiable sufficient and necessary conditions for global and local identifiability. The approach requires testing of certain controllability and observability conditions, but in many practical examples these conditions prove very easy to verify. In principle the method also involves nonlinear state variable transformations, but in all of the examples presented in the paper the transformations turn out to be linear. The method is applied to an unidentifiable nonlinear model and a locally identifiable nonlinear model, and these are the first nonlinear models other than bilinear models where the reason for lack of global identifiability is nontrivial. The method is also applied to two models with Michaelis-Menten elimination kinetics, both of considerable importance in pharmacokinetics, and for both of which the complicated nature of the algebraic equations arising from the Taylor series approach has hitherto defeated attempts to establish identifiability results for specific input functions.
Bayesian parameter estimation for nonlinear modelling of biological pathways
Directory of Open Access Journals (Sweden)
Ghasemi Omid
2011-12-01
Full Text Available Abstract Background The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. Results We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC method. We applied this approach to the biological pathways involved in the left ventricle (LV response to myocardial infarction (MI and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly
Variable structure control of nonlinear systems through simplified uncertain models
Sira-Ramirez, Hebertt
1986-01-01
A variable structure control approach is presented for the robust stabilization of feedback equivalent nonlinear systems whose proposed model lies in the same structural orbit of a linear system in Brunovsky's canonical form. An attempt to linearize exactly the nonlinear plant on the basis of the feedback control law derived for the available model results in a nonlinearly perturbed canonical system for the expanded class of possible equivalent control functions. Conservatism tends to grow as modeling errors become larger. In order to preserve the internal controllability structure of the plant, it is proposed that model simplification be carried out on the open-loop-transformed system. As an example, a controller is developed for a single link manipulator with an elastic joint.
A Simple Model for Nonlinear Confocal Ultrasonic Beams
Institute of Scientific and Technical Information of China (English)
ZHANG Dong; ZHOU Lin; SI Li-Sheng; GONG Xiu-Fen
2007-01-01
@@ A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented.Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.
Nonlinear dispersion effects in elastic plates: numerical modelling and validation
Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2017-04-01
Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.
Notes on holographic superconductor models with the nonlinear electrodynamics
Zhao, Zixu; Chen, Songbai; Jing, Jiliang
2013-01-01
We investigate systematically the effect of the nonlinear correction to the usual Maxwell electrodynamics on the holographic dual models in the backgrounds of AdS black hole and AdS soliton. Considering three types of typical nonlinear electrodynamics, we observe that in the black hole background the higher nonlinear electrodynamics correction makes the condensation harder to form and changes the expected relation in the gap frequency, which is similar to that caused by the curvature correction. However, in strong contrast to the influence of the curvature correction, we find that in the AdS soliton background the nonlinear electrodynamics correction will not affect the properties of the holographic superconductor and insulator phase transitions, which may be a quite general feature for the s-wave holographic superconductor/insulator system.
The fractional-nonlinear robotic manipulator: Modeling and dynamic simulations
David, S. A.; Balthazar, J. M.; Julio, B. H. S.; Oliveira, C.
2012-11-01
In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional-order nonlinear dynamics equations of a two link robotic manipulator. The aformentioned equations have been simulated for several cases involving: integer and non-integer order analysis, with and without external forcing acting and some different initial conditions. The fractional nonlinear governing equations of motion are coupled and the time evolution of the angular positions and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the dynamics equations of a two link robotic manipulator have been modeled with the fractional Euler-Lagrange dynamics approach. The results reveal that the fractional-nonlinear robotic manipulator can exhibit different and curious behavior from those obtained with the standard dynamical system and can be useful for a better understanding and control of such nonlinear systems.
Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity
Directory of Open Access Journals (Sweden)
Isao Ishida
2015-01-01
Full Text Available We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor’s 500 (S&P 500 and several other indices, we obtained good performance using these models in an out-of-sample forecasting exercise compared with the forecasts obtained based on the usual linear heterogeneous autoregressive and other models of realized volatility.
A propagation model of computer virus with nonlinear vaccination probability
Gan, Chenquan; Yang, Xiaofan; Liu, Wanping; Zhu, Qingyi
2014-01-01
This paper is intended to examine the effect of vaccination on the spread of computer viruses. For that purpose, a novel computer virus propagation model, which incorporates a nonlinear vaccination probability, is proposed. A qualitative analysis of this model reveals that, depending on the value of the basic reproduction number, either the virus-free equilibrium or the viral equilibrium is globally asymptotically stable. The results of simulation experiments not only demonstrate the validity of our model, but also show the effectiveness of nonlinear vaccination strategies. Through parameter analysis, some effective strategies for eradicating viruses are suggested.
Nonlinear model predictive control of a packed distillation column
Energy Technology Data Exchange (ETDEWEB)
Patwardhan, A.A.; Edgar, T.F. (Univ. of Texas, Austin, TX (United States). Dept. of Chemical Engineering)
1993-10-01
A rigorous dynamic model based on fundamental chemical engineering principles was formulated for a packed distillation column separating a mixture of cyclohexane and n-heptane. This model was simplified to a form suitable for use in on-line model predictive control calculations. A packed distillation column was operated at several operating conditions to estimate two unknown model parameters in the rigorous and simplified models. The actual column response to step changes in the feed rate, distillate rate, and reboiler duty agreed well with dynamic model predictions. One unusual characteristic observed was that the packed column exhibited gain-sign changes, which are very difficult to treat using conventional linear feedback control. Nonlinear model predictive control was used to control the distillation column at an operating condition where the process gain changed sign. An on-line, nonlinear model-based scheme was used to estimate unknown/time-varying model parameters.
Finite element model calibration of a nonlinear perforated plate
Ehrhardt, David A.; Allen, Matthew S.; Beberniss, Timothy J.; Neild, Simon A.
2017-03-01
This paper presents a case study in which the finite element model for a curved circular plate is calibrated to reproduce both the linear and nonlinear dynamic response measured from two nominally identical samples. The linear dynamic response is described with the linear natural frequencies and mode shapes identified with a roving hammer test. Due to the uncertainty in the stiffness characteristics from the manufactured perforations, the linear natural frequencies are used to update the effective modulus of elasticity of the full order finite element model (FEM). The nonlinear dynamic response is described with nonlinear normal modes (NNMs) measured using force appropriation and high speed 3D digital image correlation (3D-DIC). The measured NNMs are used to update the boundary conditions of the full order FEM through comparison with NNMs calculated from a nonlinear reduced order model (NLROM). This comparison revealed that the nonlinear behavior could not be captured without accounting for the small curvature of the plate from manufacturing as confirmed in literature. So, 3D-DIC was also used to identify the initial static curvature of each plate and the resulting curvature was included in the full order FEM. The updated models are then used to understand how the stress distribution changes at large response amplitudes providing a possible explanation of failures observed during testing.
Geometry of exponential family nonlinear models and some asymptotic inference
Institute of Scientific and Technical Information of China (English)
韦博成
1995-01-01
A differential geometric framework in Euclidean space for exponential family nonlinear models is presented. Based on this framework, some asymptotic inference related to statistical curvatures and Fisher information are studied. This geometric framework can also be extended to more genera) dass of models and used to study some other problems.
A Novel Nonlinear Programming Model for Distribution Protection Optimization
Zambon, Eduardo; Bossois, Débora Z.; Garcia, Berilhes B.; Azeredo, Elias F.
2009-01-01
This paper presents a novel nonlinear binary programming model designed to improve the reliability indices of a distribution network. This model identifies the type and location of protection devices that should be installed in a distribution feeder and is a generalization of the classical optimizat
STABILITY OF INNOVATION DIFFUSION MODEL WITH NONLINEAR ACCEPTANCE
Institute of Scientific and Technical Information of China (English)
Yu Yumei; Wang Wendi
2007-01-01
In this article, an innovation diffusion model with the nonlinear acceptance is proposed to describe the dynamics of three competing products in a market. It is proved that the model admits a unique positive equilibrium, which is globally stable by excluding the existence of periodic solutions and by using the theory of three dimensional competition systems.
Modeling of Nonlinear Marine Cooling Systems with Closed Circuit Flow
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
of container ships. The purpose of the model is to describe the important dynamics of the system, such as nonlinearities, transport delays and closed circuit flow dynamics to enable the model to be used for control design and simulation. The control challenge is related to the highly non-standard type of step...
A toolkit for analyzing nonlinear dynamic stochastic models easily
Uhlig, H.F.H.V.S.
1995-01-01
Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the meth
A toolkit for analyzing nonlinear dynamic stochastic models easily
Uhlig, H.F.H.V.S.
1995-01-01
Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the meth
Locally supersymmetric D=3 non-linear sigma models
Wit, B. de; Tollsten, A. K.; Nicolai, H.
1992-01-01
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it general
Structure and Asymptotic theory for Nonlinear Models with GARCH Errors
F. Chan (Felix); M.J. McAleer (Michael); M.C. Medeiros (Marcelo)
2011-01-01
textabstractNonlinear time series models, especially those with regime-switching and conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with li
An Alternative Approach for Nonlinear Latent Variable Models
Mooijaart, Ab; Bentler, Peter M.
2010-01-01
In the last decades there has been an increasing interest in nonlinear latent variable models. Since the seminal paper of Kenny and Judd, several methods have been proposed for dealing with these kinds of models. This article introduces an alternative approach. The methodology involves fitting some third-order moments in addition to the means and…
A Multilevel Nonlinear Profile Analysis Model for Dichotomous Data
Culpepper, Steven Andrew
2009-01-01
This study linked nonlinear profile analysis (NPA) of dichotomous responses with an existing family of item response theory models and generalized latent variable models (GLVM). The NPA method offers several benefits over previous internal profile analysis methods: (a) NPA is estimated with maximum likelihood in a GLVM framework rather than…
Nonlinear Kalman Filtering in Affine Term Structure Models
DEFF Research Database (Denmark)
Christoffersen, Peter; Dorion, Christian; Jacobs, Kris;
When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi…ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze...... Monte Carlo experiment demonstrates that the unscented Kalman fi…lter is much more accurate than its extended counterpart in fi…ltering the states and forecasting swap rates and caps. Our fi…ndings suggest that the unscented Kalman fi…lter may prove to be a good approach for a number of other problems...... in fi…xed income pricing with nonlinear relationships between the state vector and the observations, such as the estimation of term structure models using coupon bonds and the estimation of quadratic term structure models....
Interval standard neural network models for nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design approach employs a neural network, whose activation functions satisfy the sector conditions, to approximate the nonlinear system. To improve the approximation performance and to account for the parameter perturbations during operation, a novel neural network model termed standard neural network model (SNNM) is proposed. If the uncertainty is bounded, the SNNM is called an interval SNNM (ISNNM). A state-feedback control law is designed for the nonlinear system modelled by an ISNNM such that the closed-loop system is globally, robustly, and asymptotically stable. The control design equations are shown to be a set of linear matrix inequalities (LMIs) that can be easily solved by available convex optimization algorithms. An example is given to illustrate the control design procedure, and the performance of the proposed approach is compared with that of a related method reported in literature.
Adaptive modeling of shallow fully nonlinear gravity waves
Dutykh, Denys; Mitsotakis, Dimitrios
2014-01-01
This paper presents an extended version of the celebrated Serre-Green-Naghdi (SGN) system. This extension is based on the well-known Bona-Smith-Nwogu trick which aims to improve the linear dispersion properties. We show that in the fully nonlinear setting it results in modifying the vertical acceleration. Even if this technique is well-known, the effect of this modification on the nonlinear properties of the model is not clear. The first goal of this study is to shed some light on the properties of solitary waves, as the most important class of nonlinear permanent solutions. Then, we propose a simple adaptive strategy to choose the optimal value of the free parameter at every instance of time. This strategy is validated by comparing the model prediction with the reference solutions of the full Euler equations and its classical counterpart. Numerical simulations show that the new adaptive model provides a much better accuracy for the same computational complexity.
Nonlinear Modeling and Neuro-Fuzzy Control of PEMFC
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The proton exchange membrane generation technology is highly efficient, and clean and is considered as the most hopeful "green" power technology. The operating principles of proton exchange membrane fuel cell (PEMFC) system involve thermodynamics, electrochemistry, hydrodynamics and mass transfer theory, which comprise a complex nonlinear system, for which it is difficult to establish a mathematical model and control online.This paper analyzed the characters of the PEMFC; and used the approach and self-study ability of artificial neural networks to build the model of nonlinear system, and adopted the adaptive neural-networks fuzzy infer system to build the temperature model of PEMFC which is used as the reference model of the control system, and adjusted the model parameters to control online. The model and control were implemented in SIMULINK environment.The results of simulation show the test data and model have a good agreement. The model is useful for the optimal and real time control of PEMFC system.
Groundwater transport modeling with nonlinear sorption and intraparticle diffusion
Singh, Anshuman; Allen-King, Richelle M.; Rabideau, Alan J.
2014-08-01
Despite recent advances in the mechanistic understanding of sorption in groundwater systems, most contaminant transport models provide limited support for nonideal sorption processes such as nonlinear isotherms and/or diffusion-limited sorption. However, recent developments in the conceptualization of "dual mode" sorption for hydrophobic organic contaminants have provided more realistic and mechanistically sound alternatives to the commonly used Langmuir and Freundlich models. To support the inclusion of both nonlinear and diffusion-limited sorption processes in groundwater transport models, this paper presents two numerical algorithms based on the split operator approach. For the nonlinear equilibrium scenario, the commonly used two-step split operator algorithm has been modified to provide a more robust treatment of complex multi-parameter isotherms such as the Polanyi-partitioning model. For diffusion-limited sorption, a flexible three step split-operator procedure is presented to simulate intraparticle diffusion in multiple spherical particles with different sizes and nonlinear isotherms. Numerical experiments confirmed the accuracy of both algorithms for several candidate isotherms. However, the primary advantages of the algorithms are: (1) flexibility to accommodate any isotherm equation including "dual mode" and similar expressions, and (2) ease of adapting existing grid-based transport models of any dimensionality to include nonlinear sorption and/or intraparticle diffusion. Comparisons are developed for one-dimensional transport scenarios with different isotherms and particle configurations. Illustrative results highlight (1) the potential influence of isotherm model selection on solute transport predictions, and (2) the combined effects of intraparticle diffusion and nonlinear sorption on the plume transport and flushing for both single-particle and multi-particle scenarios.
Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers
Directory of Open Access Journals (Sweden)
Nicolás Peréz Alvarez
2015-11-01
Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.
Parallel Evolutionary Modeling for Nonlinear Ordinary Differential Equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
We introduce a new parallel evolutionary algorithm in modeling dynamic systems by nonlinear higher-order ordinary differential equations (NHODEs). The NHODEs models are much more universal than the traditional linear models. In order to accelerate the modeling process, we propose and realize a parallel evolutionary algorithm using distributed CORBA object on the heterogeneous networking. Some numerical experiments show that the new algorithm is feasible and efficient.
Likelihood-Based Inference in Nonlinear Error-Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbæk, Anders
We consider a class of vector nonlinear error correction models where the transfer function (or loadings) of the stationary relation- ships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties...... and a linear trend in general. Gaussian likelihood-based estimators are considered for the long- run cointegration parameters, and the short-run parameters. Asymp- totic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normaity can be found. A simulation study...
Modeling and stability analysis of the nonlinear reactive sputtering process
Directory of Open Access Journals (Sweden)
György Katalin
2011-12-01
Full Text Available The model of the reactive sputtering process has been determined from the dynamic equilibrium of the reactive gas inside the chamber and the dynamic equilibrium of the sputtered metal atoms which form the compound with the reactive gas atoms on the surface of the substrate. The analytically obtained dynamical model is a system of nonlinear differential equations which can result in a histeresis-type input/output nonlinearity. The reactive sputtering process has been simulated by integrating these differential equations. Linearization has been applied for classical analysis of the sputtering process and control system design.
Modeling and equalization of nonlinear bandlimited satellite channels
Konstantinides, K.; Yao, K.
1986-01-01
The problem of modeling and equalization of a nonlinear satellite channel is considered. The channel is assumed to be bandlimited and exhibits both amplitude and phase nonlinearities. A discrete time satellite link is modeled under both uplink and downlink white Gaussian noise. Under conditions of practical interest, a simple and computationally efficient design technique for the minimum mean square error linear equalizer is presented. The bit error probability and some numerical results for a binary phase shift keyed (BPSK) system demonstrate that the proposed equalization technique outperforms standard linear receiver structures.
A Nonlinear Vortex Induced Vibration Model of Marine Risers
Institute of Scientific and Technical Information of China (English)
LIU Juan; HUANG Weiping
2013-01-01
With the exploitation of oil and gas in deep water,the traditional vortex induced vibration (VIV) theory is challenged by the unprecedented flexibility of risers.A nonlinear time-dependent VIV model is developed in this paper based on a VIV lift force model and the Morison equation.Both the inline vibration induced by the flow due to vortex shedding and the fluid-structure interaction in the transverse direction are included in the model.One of the characteristics of the model is the response-dependent lift force with nonlinear damping,which is different from other VIV models.The calculations show that the model can well describe the VIV of deepwater risers with the results agreeing with those calculated by other models.
A Stochastic Nonlinear Water Wave Model for Efficient Uncertainty Quantification
Bigoni, Daniele; Eskilsson, Claes
2014-01-01
A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a stochastic formulation of a fully nonlinear and dispersive potential flow water wave model for the probabilistic description of the evolution waves. This model is discretized using the Stochastic Collocation Method (SCM), which provides an approximate surrogate of the model. This can be used to accurately and efficiently estimate the probability distribution of the unknown time dependent stochastic solution after the forward propagation of uncertainties. We revisit experimental benchmarks often used for validation of deterministic water wave models. We do this using a fully nonlinear and dispersive model and show how uncertainty in the model input can influence the model output. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in compa...
Testing linearity against nonlinear moving average models
de Gooijer, J.G.; Brännäs, K.; Teräsvirta, T.
1998-01-01
Lagrange multiplier (LM) test statistics are derived for testing a linear moving average model against an additive smooth transition moving average model. The latter model is introduced in the paper. The small sample performance of the proposed tests are evaluated in a Monte Carlo study and compared
Mathematical models for suspension bridges nonlinear structural instability
Gazzola, Filippo
2015-01-01
This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.
Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbek, Anders
In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing...... for linearity is of particular interest as parameters of non-linear components vanish under the null. To solve the latter type of testing, we use the so-called sup tests, which here requires development of new (uniform) weak convergence results. These results are potentially useful in general for analysis...... of non-stationary non-linear time series models. Thus the paper provides a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated...
Non-linear calibration models for near infrared spectroscopy.
Ni, Wangdong; Nørgaard, Lars; Mørup, Morten
2014-02-27
Different calibration techniques are available for spectroscopic applications that show nonlinear behavior. This comprehensive comparative study presents a comparison of different nonlinear calibration techniques: kernel PLS (KPLS), support vector machines (SVM), least-squares SVM (LS-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS-SVM is also attractive due to its good predictive performance for both linear and nonlinear calibrations.
Modeling and non-linear responses of MEMS capacitive accelerometer
Directory of Open Access Journals (Sweden)
Sri Harsha C.
2014-01-01
Full Text Available A theoretical investigation of an electrically actuated beam has been illustrated when the electrostatic-ally actuated micro-cantilever beam is separated from the electrode by a moderately large gap for two distinct types of geometric configurations of MEMS accelerometer. Higher order nonlinear terms have been taken into account for studying the pull in voltage analysis. A nonlinear model of gas film squeezing damping, another source of nonlinearity in MEMS devices is included in obtaining the dynamic responses. Moreover, in the present work, the possible source of nonlinearities while formulating the mathematical model of a MEMS accelerometer and their influences on the dynamic responses have been investigated. The theoretical results obtained by using MATLAB has been verified with the results obtained in FE software and has been found in good agreement. Criterion towards stable micro size accelerometer for each configuration has been investigated. This investigation clearly provides an understanding of nonlinear static and dynamics characteristics of electrostatically micro cantilever based device in MEMS.
Nonlinear Pressure Wave Analysis by Concentrated Mass Model
Ishikawa, Satoshi; Kondou, Takahiro; Matsuzaki, Kenichiro
A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effect of fluid. Analyzing this phenomenon by the finite difference method requires high computational cost. To lessen the computational cost, a concentrated mass model is proposed. This model consists of masses, connecting nonlinear springs, connecting dampers, and base support dampers. The characteristic of a connecting nonlinear spring is derived from the adiabatic change of fluid, and the equivalent mass and equivalent damping coefficient of the base support damper are derived from the equation of motion of fluid in a cylindrical tube. Pressure waves generated in a hydraulic oil tube, a sound tube and a plane-wave tube are analyzed numerically by the proposed model to confirm the validity of the model. All numerical computational results agree very well with the experimental results carried out by Okamura, Saenger and Kamakura. Especially, the numerical analysis reproduces the phenomena that a pressure wave with large amplitude propagating in a sound tube or in a plane tube changes to a shock wave. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem.
Full Hydrodynamic Model of Nonlinear Electromagnetic Response in Metallic Metamaterials
Fang, Ming; Sha, Wei E I; Xiong, Xiaoyan Y Z; Wu, Xianliang
2016-01-01
Applications of metallic metamaterials have generated significant interest in recent years. Electromagnetic behavior of metamaterials in the optical range is usually characterized by a local-linear response. In this article, we develop a finite-difference time-domain (FDTD) solution of the hydrodynamic model that describes a free electron gas in metals. Extending beyond the local-linear response, the hydrodynamic model enables numerical investigation of nonlocal and nonlinear interactions between electromagnetic waves and metallic metamaterials. By explicitly imposing the current continuity constraint, the proposed model is solved in a self-consistent manner. Charge, energy and angular momentum conservation laws of high-order harmonic generation have been demonstrated for the first time by the Maxwell-hydrodynamic FDTD model. The model yields nonlinear optical responses for complex metallic metamaterials irradiated by a variety of waveforms. Consequently, the multiphysics model opens up unique opportunities f...
Estimating Nonlinear Structural Models: EMM and the Kenny-Judd Model
Lyhagen, Johan
2007-01-01
The estimation of nonlinear structural models is not trivial. One reason for this is that a closed form solution of the likelihood may not be feasible or does not exist. We propose to estimate nonlinear structural models using the efficient method of moments, as generating data according to the models is often very easy. A simulation study of the…
The Nonlinear Sigma Model With Distributed Adaptive Mesh Refinement
Liebling, S L
2004-01-01
An adaptive mesh refinement (AMR) scheme is implemented in a distributed environment using Message Passing Interface (MPI) to find solutions to the nonlinear sigma model. Previous work studied behavior similar to black hole critical phenomena at the threshold for singularity formation in this flat space model. This work is a follow-up describing extensions to distribute the grid hierarchy and presenting tests showing the correctness of the model.
INFLUENCE ANALYSIS ON EXPONENTIAL NONLINEAR MODELS WITH RANDOM EFFECTS
Institute of Scientific and Technical Information of China (English)
宗序平; 赵俊; 王海斌; 韦博成
2003-01-01
This paper presents a unified diagnostic method for exponential nonlinear models with random effects based upon the joint likelihood given by Robinson in 1991.The authors show that the case deletion model is equivalent to mean shift outlier model.From this point of view,several diagnostic measures,such as Cook distance,score statistics are derived.The local influence measure of Cook is also presented.Numerical example illustrates that our method is available.
INFLUENCE ANALYSIS IN NONLINEAR MODELS WITH RANDOM EFFECTS
Institute of Scientific and Technical Information of China (English)
WeiBocheng; ZhongXuping
2001-01-01
Abstract. In this paper,a unified diagnostic method for the nonlinear models with random ef-fects based upon the joint likelihood given by Robinson in 1991 is presented. It is shown that thecase deletion model is equivalent to the mean shift outlier model. From this point of view ,sever-al diagnostic measures, such as Cook distance, score statistics are derived. The local influencemeasure of Cook is also presented. A numerical example illustrates that the method is avail-able
Analyzing the Dynamics of Nonlinear Multivariate Time Series Models
Institute of Scientific and Technical Information of China (English)
DenghuaZhong; ZhengfengZhang; DonghaiLiu; StefanMittnik
2004-01-01
This paper analyzes the dynamics of nonlinear multivariate time series models that is represented by generalized impulse response functions and asymmetric functions. We illustrate the measures of shock persistences and asymmetric effects of shocks derived from the generalized impulse response functions and asymmetric function in bivariate smooth transition regression models. The empirical work investigates a bivariate smooth transition model of US GDP and the unemployment rate.
Nonlinear diffusion model for Rayleigh-Taylor mixing.
Boffetta, G; De Lillo, F; Musacchio, S
2010-01-22
The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusivity models for the mean temperature profile. It is found that a nonlinear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows us to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.
Nonlinear diffusion model for Rayleigh-Taylor mixing
Boffetta, G; Musacchio, S
2010-01-01
The complex evolution of turbulent mixing in Rayleigh-Taylor convection is studied in terms of eddy diffusiviy models for the mean temperature profile. It is found that a non-linear model, derived within the general framework of Prandtl mixing theory, reproduces accurately the evolution of turbulent profiles obtained from numerical simulations. Our model allows to give very precise predictions for the turbulent heat flux and for the Nusselt number in the ultimate state regime of thermal convection.
Hybrid nonlinear model of the angular vestibulo-ocular reflex.
Ranjbaran, Mina; Galiana, Henrietta L
2013-01-01
A hybrid nonlinear bilateral model for the horizontal angular vestibulo-ocular reflex (AVOR) is presented in this paper. The model relies on known interconnections between saccadic burst circuits in the brainstem and ocular premotor areas in the vestibular nuclei during slow and fast phase intervals. A viable switching strategy for the timing of nystagmus events is proposed. Simulations show that this hybrid model replicates AVOR nystagmus patterns that are observed in experimentally recorded data.
Nonlinear stochastic inflation modelling using SEASETARs
de Gooijer, J.G.; Vidiella-i-Anguera, A.
2003-01-01
The development of stochastic inflation models for actuarial and investment applications has become an important topic to actuaries since Wilkie [Transactions of the Faculty of Actuaries 39 (1986) 341] introduced his first investment model. Two empirical features of monthly inflation rates are dynam
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.
Nonlinear dynamics of incommensurately contacting surfaces : a model study
Consoli, Luca
2002-01-01
This PhD thesis is about the nonlinear dynamics of contacting surfaces. More specifically, it deals with the problem of modelling at the microscopic level some of the contributions that lead to the macroscopic effect of dry sliding friction. In chapter 1, we try to give an overview of the physical q
RF Circuit linearity optimization using a general weak nonlinearity model
Cheng, W.; Oude Alink, M.S.; Annema, Anne J.; Croon, Jeroen A.; Nauta, Bram
2012-01-01
This paper focuses on optimizing the linearity in known RF circuits, by exploring the circuit design space that is usually available in today’s deep submicron CMOS technologies. Instead of using brute force numerical optimizers we apply a generalized weak nonlinearity model that only involves AC
UAV Formation Flight Based on Nonlinear Model Predictive Control
Directory of Open Access Journals (Sweden)
Zhou Chao
2012-01-01
Full Text Available We designed a distributed collision-free formation flight control law in the framework of nonlinear model predictive control. Formation configuration is determined in the virtual reference point coordinate system. Obstacle avoidance is guaranteed by cost penalty, and intervehicle collision avoidance is guaranteed by cost penalty combined with a new priority strategy.
Dynamics of breathers in discrete nonlinear Schrodinger models
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge
1998-01-01
We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized...
Control mechanisms for a nonlinear model of international relations
Energy Technology Data Exchange (ETDEWEB)
Pentek, A.; Kadtke, J. [Univ. of California, San Diego, La Jolla, CA (United States). Inst. for Pure and Applied Physical Sciences; Lenhart, S. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.
1997-07-15
Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race.
Two-dimensional effects in nonlinear Kronig-Penney models
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Christiansen, Peter Leth; Rasmussen, Kim
1997-01-01
An analysis of two-dimensional (2D) effects in the nonlinear Kronig-Penney model is presented. We establish an effective one-dimensional description of the 2D effects, resulting in a set of pseudodifferential equations. The stationary states of the 2D system and their stability is studied...
Maximum Likelihood Estimation of Nonlinear Structural Equation Models.
Lee, Sik-Yum; Zhu, Hong-Tu
2002-01-01
Developed an EM type algorithm for maximum likelihood estimation of a general nonlinear structural equation model in which the E-step is completed by a Metropolis-Hastings algorithm. Illustrated the methodology with results from a simulation study and two real examples using data from previous studies. (SLD)
Case-Deletion Diagnostics for Nonlinear Structural Equation Models
Lee, Sik-Yum; Lu, Bin
2003-01-01
In this article, a case-deletion procedure is proposed to detect influential observations in a nonlinear structural equation model. The key idea is to develop the diagnostic measures based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm. An one-step pseudo approximation is proposed to reduce the…
Local Influence Analysis of Nonlinear Structural Equation Models
Lee, Sik-Yum; Tang, Nian-Sheng
2004-01-01
By regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm, we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model. The basic building blocks of local influence analysis…
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
). In the present paper we use a single layer of quadratic (in 2D) and prismatic (in 3D) elements. The model has been stabilized through a combination of over-integration of the Galerkin projections and a mild modal filter. We present numerical tests of nonlinear waves serving as a proof-of-concept validation...
S-AMP for non-linear observation models
DEFF Research Database (Denmark)
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2015-01-01
Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement...
A nonlinear regression model-based predictive control algorithm.
Dubay, R; Abu-Ayyad, M; Hernandez, J M
2009-04-01
This paper presents a unique approach for designing a nonlinear regression model-based predictive controller (NRPC) for single-input-single-output (SISO) and multi-input-multi-output (MIMO) processes that are common in industrial applications. The innovation of this strategy is that the controller structure allows nonlinear open-loop modeling to be conducted while closed-loop control is executed every sampling instant. Consequently, the system matrix is regenerated every sampling instant using a continuous function providing a more accurate prediction of the plant. Computer simulations are carried out on nonlinear plants, demonstrating that the new approach is easily implemented and provides tight control. Also, the proposed algorithm is implemented on two real time SISO applications; a DC motor, a plastic injection molding machine and a nonlinear MIMO thermal system comprising three temperature zones to be controlled with interacting effects. The experimental closed-loop responses of the proposed algorithm were compared to a multi-model dynamic matrix controller (MPC) with improved results for various set point trajectories. Good disturbance rejection was attained, resulting in improved tracking of multi-set point profiles in comparison to multi-model MPC.
Nonlinear Hyperbolic-Parabolic System Modeling Some Biological Phenomena
Institute of Scientific and Technical Information of China (English)
WU Shaohua; CHEN Hua
2011-01-01
In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N = 1, the global existence of the weak solution will be established by the bootstrap argument.
Visualization of nonlinear kernel models in neuroimaging by sensitivity maps
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup; Madsen, Kristoffer Hougaard; Lund, Torben Ellegaard
2011-01-01
There is significant current interest in decoding mental states from neuroimages. In this context kernel methods, e.g., support vector machines (SVM) are frequently adopted to learn statistical relations between patterns of brain activation and experimental conditions. In this paper we focus......, and conclude that the sensitivity map is a versatile and computationally efficient tool for visualization of nonlinear kernel models in neuroimaging....
An Adaptive Neural Network Model for Nonlinear Programming Problems
Institute of Scientific and Technical Information of China (English)
Xiang-sun Zhang; Xin-jian Zhuo; Zhu-jun Jing
2002-01-01
In this paper a canonical neural network with adaptively changing synaptic weights and activation function parameters is presented to solve general nonlinear programming problems. The basic part of the model is a sub-network used to find a solution of quadratic programming problems with simple upper and lower bounds. By sequentially activating the sub-network under the control of an external computer or a special analog or digital processor that adjusts the weights and parameters, one then solves general nonlinear programming problems. Convergence proof and numerical results are given.
NONLINEAR MICRO－MECHANICAL MODEL FOR PLAIN WOVEN FABRIC
Institute of Scientific and Technical Information of China (English)
ZhangYitong; XieYuxin
2003-01-01
The warp yarns and weft yarns of plain woven fabric which, being the principal axes of material of fabric, are orthogonal in the original configuration, but are obliquely crossed in the deformed configuration in general. The orthotropic constitutive model is unsuitable for fabric. In the oblique principal axes system the relations between loaded stress vectors and stress tensor are investigated, the stress fields of micro-weaving structures of fabric due to pure shear are carefully studied and, finally, a nonlinear micro-mechanical model for plain woven fabric is proposed. This model can accurately describe the nonlinear mechanical behavior of fabric observed in experiments. Under the assumption of small deformation and linearity of mechanical properties of fabric the model will degenerate into the existing linear model.
Nonlinear Model Identification from Operating Records.
1980-11-01
34, Submitted July 1979 to Proc. IEEE. [13] Wellstead , P., "Model Order Identification Using an Auxillary System," Proc. IEEE, vol. 123, No. 12, December...C and Systems, Nov. 1979 . I I ~I lt( -~ I -l.. .... .. . ... . .. . . , _. . - -"
Population mixture model for nonlinear telomere dynamics
Itzkovitz, Shalev; Shlush, Liran I.; Gluck, Dan; Skorecki, Karl
2008-12-01
Telomeres are DNA repeats protecting chromosomal ends which shorten with each cell division, eventually leading to cessation of cell growth. We present a population mixture model that predicts an exponential decrease in telomere length with time. We analytically solve the dynamics of the telomere length distribution. The model provides an excellent fit to available telomere data and accounts for the previously unexplained observation of telomere elongation following stress and bone marrow transplantation, thereby providing insight into the nature of the telomere clock.
Validating a quasi-linear transport model versus nonlinear simulations
Casati, A.; Bourdelle, C.; Garbet, X.; Imbeaux, F.; Candy, J.; Clairet, F.; Dif-Pradalier, G.; Falchetto, G.; Gerbaud, T.; Grandgirard, V.; Gürcan, Ö. D.; Hennequin, P.; Kinsey, J.; Ottaviani, M.; Sabot, R.; Sarazin, Y.; Vermare, L.; Waltz, R. E.
2009-08-01
In order to gain reliable predictions on turbulent fluxes in tokamak plasmas, physics based transport models are required. Nonlinear gyrokinetic electromagnetic simulations for all species are still too costly in terms of computing time. On the other hand, interestingly, the quasi-linear approximation seems to retain the relevant physics for fairly reproducing both experimental results and nonlinear gyrokinetic simulations. Quasi-linear fluxes are made of two parts: (1) the quasi-linear response of the transported quantities and (2) the saturated fluctuating electrostatic potential. The first one is shown to follow well nonlinear numerical predictions; the second one is based on both nonlinear simulations and turbulence measurements. The resulting quasi-linear fluxes computed by QuaLiKiz (Bourdelle et al 2007 Phys. Plasmas 14 112501) are shown to agree with the nonlinear predictions when varying various dimensionless parameters, such as the temperature gradients, the ion to electron temperature ratio, the dimensionless collisionality, the effective charge and ranging from ion temperature gradient to trapped electron modes turbulence.
Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation
Abdelkefi, Abdessattar
2013-06-18
In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.
Nonlinear analysis of traffic jams in an anisotropic continuum model
Institute of Scientific and Technical Information of China (English)
Arvind Kumar Gupta; Sapna Sharma
2010-01-01
This paper presents our study of the nonlinear stability of a new anisotropic continuum traffic flow model in which the dimensionless parameter or anisotropic factor controls the non-isotropic character and diffusive influence. In order to establish traffic flow stability criterion or to know the critical parameters that lead, on one hand, to a stable response to perturbations or disturbances or, on the other hand, to an unstable response and therefore to a possible congestion, a nonlinear stability criterion is derived by using a wavefront expansion technique. The stability criterion is illustrated by numerical results using the finite difference method for two different values of anisotropic parameter. It is also been observed that the newly derived stability results are consistent with previously reported results obtained using approximate linearisation methods. Moreover, the stability criterion derived in this paper can provide more refined information from the perspective of the capability to reproduce nonlinear traffic flow behaviors observed in real traffic than previously established methodologies.
Nonlinear Dynamical Modeling and Forecast of ENSO Variability
Feigin, Alexander; Mukhin, Dmitry; Gavrilov, Andrey; Seleznev, Aleksey; Loskutov, Evgeny
2017-04-01
New methodology of empirical modeling and forecast of nonlinear dynamical system variability [1] is applied to study of ENSO climate system. The methodology is based on two approaches: (i) nonlinear decomposition of data [2], that provides low-dimensional embedding for further modeling, and (ii) construction of empirical model in the form of low dimensional random dynamical ("stochastic") system [3]. Three monthly data sets are used for ENSO modeling and forecast: global sea surface temperature anomalies, troposphere zonal wind speed, and thermocline depth; all data sets are limited by 30 S, 30 N and have horizontal resolution 10x10 . We compare results of optimal data decomposition as well as prognostic skill of the constructed models for different combinations of involved data sets. We also present comparative analysis of ENSO indices forecasts fulfilled by our models and by IRI/CPC ENSO Predictions Plume. [1] A. Gavrilov, D. Mukhin, E. Loskutov, A. Feigin, 2016: Construction of Optimally Reduced Empirical Model by Spatially Distributed Climate Data. 2016 AGU Fall Meeting, Abstract NG31A-1824. [2] D. Mukhin, A. Gavrilov, E. Loskutov , A.Feigin, J.Kurths, 2015: Principal nonlinear dynamical modes of climate variability, Scientific Reports, rep. 5, 15510; doi: 10.1038/srep15510. [3] Ya. Molkov, D. Mukhin, E. Loskutov, A. Feigin, 2012: Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.
Adaptive Predistortion Using Cubic Spline Nonlinearity Based Hammerstein Modeling
Wu, Xiaofang; Shi, Jianghong
In this paper, a new Hammerstein predistorter modeling for power amplifier (PA) linearization is proposed. The key feature of the model is that the cubic splines, instead of conventional high-order polynomials, are utilized as the static nonlinearities due to the fact that the splines are able to represent hard nonlinearities accurately and circumvent the numerical instability problem simultaneously. Furthermore, according to the amplifier's AM/AM and AM/PM characteristics, real-valued cubic spline functions are utilized to compensate the nonlinear distortion of the amplifier and the following finite impulse response (FIR) filters are utilized to eliminate the memory effects of the amplifier. In addition, the identification algorithm of the Hammerstein predistorter is discussed. The predistorter is implemented on the indirect learning architecture, and the separable nonlinear least squares (SNLS) Levenberg-Marquardt algorithm is adopted for the sake that the separation method reduces the dimension of the nonlinear search space and thus greatly simplifies the identification procedure. However, the convergence performance of the iterative SNLS algorithm is sensitive to the initial estimation. Therefore an effective normalization strategy is presented to solve this problem. Simulation experiments were carried out on a single-carrier WCDMA signal. Results show that compared to the conventional polynomial predistorters, the proposed Hammerstein predistorter has a higher linearization performance when the PA is near saturation and has a comparable linearization performance when the PA is mildly nonlinear. Furthermore, the proposed predistorter is numerically more stable in all input back-off cases. The results also demonstrate the validity of the convergence scheme.
Nonclassical measurements errors in nonlinear models
DEFF Research Database (Denmark)
Madsen, Edith; Mulalic, Ismir
Discrete choice models and in particular logit type models play an important role in understanding and quantifying individual or household behavior in relation to transport demand. An example is the choice of travel mode for a given trip under the budget and time restrictions that the individuals...... estimates of the income effect it is of interest to investigate the magnitude of the estimation bias and if possible use estimation techniques that take the measurement error problem into account. We use data from the Danish National Travel Survey (NTS) and merge it with administrative register data...... of a households face. In this case an important policy parameter is the effect of income (reflecting the household budget) on the choice of travel mode. This paper deals with the consequences of measurement error in income (an explanatory variable) in discrete choice models. Since it is likely to give misleading...
Nonlinear dynamic phenomena in the beer model
DEFF Research Database (Denmark)
Mosekilde, Erik; Laugesen, Jakob Lund
2007-01-01
The production-distribution system or "beer game" is one of the most well-known system dynamics models. Notorious for the complex dynamics it produces, the beer game has been used for nearly five decades to illustrate how structure generates behavior and to explore human decision making. Here we...
Defects in the discrete non-linear Schroedinger model
Energy Technology Data Exchange (ETDEWEB)
Doikou, Anastasia, E-mail: adoikou@upatras.gr [University of Patras, Department of Engineering Sciences, Physics Division, GR-26500 Patras (Greece)
2012-01-01
The discrete non-linear Schroedinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.
Non-linear models: coal combustion efficiency and emissions control
Energy Technology Data Exchange (ETDEWEB)
Bulsari, A.; Wemberg, A.; Anttila, A.; Multas, A. [Nonlinear Solutions Oy, Turku (Finland)
2009-04-15
Today's power plants feel the pressure to limit their NOx emissions and improve their production economics. The article describes how nonlinear models are effective for process guidance of various kinds of processes, including coal fired boilers. These models were developed for the Naantati 2 boiler at the electricity and heat generating coal-fired plant in Naantali, near Turku, Finland. 4 refs., 6 figs.
Nonlinear modeling of neural population dynamics for hippocampal prostheses
Song, Dong; Chan, Rosa H.M.; Vasilis Z Marmarelis; Hampson, Robert E.; Deadwyler, Sam A.; Berger, Theodore W.
2009-01-01
Developing a neural prosthesis for the damaged hippocampus requires restoring the transformation of population neural activities performed by the hippocampal circuitry. To bypass a damaged region, output spike trains need to be predicted from the input spike trains and then reinstated through stimulation. We formulate a multiple-input, multiple-output (MIMO) nonlinear dynamic model for the input–output transformation of spike trains. In this approach, a MIMO model comprises a series of physio...
Geometric Properties of AR（q） Nonlinear Regression Models
Institute of Scientific and Technical Information of China (English)
LIUYing-ar; WEIBo-cheng
2004-01-01
This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].
Solutions to a nonlinear drift-diffusion model for semiconductors
Directory of Open Access Journals (Sweden)
Weifu Fang
1999-05-01
Full Text Available A nonlinear drift-diffusion model for semiconductors is analyzed to show the existence of non-vacuum global solutions and stationary solutions. The long time behavior of the solutions is studied by establishing the existence of an absorbing set and a compact attractor of the dynamical system. Parallel results on vacuum solutions are also obtained under weaker conditions on model parameters.
CONSERVATIVE ESTIMATING FUNCTIONIN THE NONLINEAR REGRESSION MODEL WITHAGGREGATED DATA
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When this function happens to be conservative, it is projection of the true score function onto a class of estimation functions. By constructing, the potential function for the projected score with aggregated data is obtained, which have some properties of log-likelihood function.
Supersymmetric Q-Lumps in the Grassmannian nonlinear sigma models
Bak, D; Lee, J; Oh, P; Bak, Dongsu; Hahn, Sang-Ok; Lee, Joohan; Oh, Phillial
2007-01-01
We construct the N=2 supersymmetric Grassmannian nonlinear sigma model for the massless case and extend it to massive N=2 model by adding an appropriate superpotential. We then study their BPS equations leading to supersymmetric Q-lumps carrying both topological and Noether charges. These solutions are shown to be always time dependent even sometimes involving multiple frequencies. Thus we illustrate explicitly that the time dependence is consistent with remaining supersymmetries of solitons.
Nonlinear Dynamic Model of PMBLDC Motor Considering Core Losses
DEFF Research Database (Denmark)
Fasil, Muhammed; Mijatovic, Nenad; Jensen, Bogi Bech
2017-01-01
The phase variable model is used commonly when simulating a motor drive system with a three-phase permanent magnet brushless DC (PMBLDC) motor. The phase variable model neglects core losses and this affects its accuracy when modelling fractional-slot machines. The inaccuracy of phase variable model...... on the detailed analysis of the flux path and the variation of flux in different components of the machine. A prototype of fractional slot axial flux PMBLDC in-wheel motor is used to assess the proposed nonlinear dynamic model....
Robust nonlinear system identification using neural-network models.
Lu, S; Basar, T
1998-01-01
We study the problem of identification for nonlinear systems in the presence of unknown driving noise, using both feedforward multilayer neural network and radial basis function network models. Our objective is to resolve the difficulty associated with the persistency of excitation condition inherent to the standard schemes in the neural identification literature. This difficulty is circumvented here by a novel formulation and by using a new class of identification algorithms recently obtained by Didinsky et al. We show how these algorithms can be exploited to successfully identify the nonlinearity in the system using neural-network models. By embedding the original problem in one with noise-perturbed state measurements, we present a class of identifiers (under L1 and L2 cost criteria) which secure a good approximant for the system nonlinearity provided that some global optimization technique is used. In this respect, many available learning algorithms in the current neural-network literature, e.g., the backpropagation scheme and the genetic algorithms-based scheme, with slight modifications, can ensure the identification of the system nonlinearity. Subsequently, we address the same problem under a third, worst case L(infinity) criterion for an RBF modeling. We present a neural-network version of an H(infinity)-based identification algorithm from Didinsky et al and show how, along with an appropriate choice of control input to enhance excitation, under both full-state-derivative information (FSDI) and noise-perturbed full-state-information (NPFSI), it leads to satisfaction of a relevant persistency of excitation condition, and thereby to robust identification of the nonlinearity. Results from several simulation studies have been included to demonstrate the effectiveness of these algorithms.
Reduced Complexity Volterra Models for Nonlinear System Identification
Directory of Open Access Journals (Sweden)
Hacıoğlu Rıfat
2001-01-01
Full Text Available A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter′s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a Fixed Pole Expansion Technique (FPET within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed in the paper.
Structure and asymptotic theory for nonlinear models with GARCH errors
Directory of Open Access Journals (Sweden)
Felix Chan
2015-01-01
Full Text Available Nonlinear time series models, especially those with regime-switching and/or conditionally heteroskedastic errors, have become increasingly popular in the economics and finance literature. However, much of the research has concentrated on the empirical applications of various models, with little theoretical or statistical analysis associated with the structure of the processes or the associated asymptotic theory. In this paper, we derive sufficient conditions for strict stationarity and ergodicity of three different specifications of the first-order smooth transition autoregressions with heteroskedastic errors. This is essential, among other reasons, to establish the conditions under which the traditional LM linearity tests based on Taylor expansions are valid. We also provide sufficient conditions for consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator for a general nonlinear conditional mean model with first-order GARCH errors.
Modeling and study of nonlinear effects in electrodynamic shakers
Saraswat, Abhishek; Tiwari, Nachiketa
2017-02-01
An electrodynamic shaker is inherently a nonlinear electro-mechanical system. In this work, we have developed a lumped parameter model for the entire electromechanical system, developed an approach to non-destructively determine these parameters, and predict the nonlinear response of the shaker. This predicted response has been validated using experimental data. Through such an approach, we have been able to accurately predict the resulting distortions in the response of the shaker and other nonlinear effects like DC offset in the displacement response. Our approach offers a key advantage vis-à-vis other approaches which rely on techniques involving Volterra Series expansions or techniques based on blackbox models like neural networks, which is that in our approach, apart from predicting the response of the shaker, the model parameters obtained have a physical significance and changes in the parameters can be directly mapped to modification in key design parameters of the shaker. The proposed approach is also advantageous in one more way: it requires measurement of only four parameters, voltage, current, displacement and acceleration for estimating shaker model parameters non-destructively. The proposed model can be used for the design of linearization controllers, prototype testing and simulation of new shaker designs as well as for performance prediction of shakers under testing conditions.
A data driven nonlinear stochastic model for blood glucose dynamics.
Zhang, Yan; Holt, Tim A; Khovanova, Natalia
2016-03-01
The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles.
Large-N Analysis of Three Dimensional Nonlinear Sigma Models
Higashijima, K; Tsuzuki, M; Higashijima, Kiyoshi; Itou, Etsuko; Tsuzuki, Makoto
2005-01-01
Non-perturbative renormalization group approach suggests that a large class of nonlinear sigma models are renormalizable in three dimensional space-time, while they are non-renormalizable in perturbation theory. ${\\cal N}=2$ supersymmetric nonlinear sigma models whose target spaces are Einstein-K\\"{a}hler manifolds with positive scalar curvature belongs to this class. hermitian symmetric spaces, being homogeneous, are specially simple examples of these manifolds. To find an independent evidence of the nonperturbative renormalizability of these models, the large N method, another nonperturbative method, is applied to 3-dimensional ${\\cal N}=2$ supersymmetric nonlinear sigma models on the target spaces $CP^{N-1}=SU(N)/[SU(N-1)\\times U(1)]$ and $Q^{N-2}=SO(N)/[SO(N-2)\\times SO(2)]$, two typical examples of hermitian symmetric spaces. We find that $\\beta$ functions in these models agree with the results of the nonperturbative renormalization group approach in the next-to-leading order of 1/N expansion, and have n...
Reduction of the curvature of a class of nonlinear regression models
Institute of Scientific and Technical Information of China (English)
吴翊; 易东云
2000-01-01
It is proved that the curvature of nonlinear model can be reduced to zero by increasing measured data for a class of nonlinear regression models. The result is important to actual problem and has obtained satisfying effect on data fusing.
Estimation of Nonlinear DC-Motor Models Using a Sensitivity Approach
DEFF Research Database (Denmark)
Knudsen, Morten; Jensen, J.G.
1995-01-01
A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed.......A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed....
Enhanced Model of Nonlinear Spiral High Voltage Divider
Directory of Open Access Journals (Sweden)
V. Panko
2015-04-01
Full Text Available This paper deals with the enhanced accurate DC and RF model of nonlinear spiral polysilicon voltage divider. The high resistance polysilicon divider is a sensing part of the high voltage start-up MOSFET transistor that can operate up to 700 V. This paper presents the structure of a proposed model, implemented voltage, frequency and temperature dependency, and scalability. A special attention is paid to the ability of the created model to cover the mismatch and influence of a variation of process parameters on the device characteristics. Finally, the comparison of measured data vs. simulation is presented in order to confirm the model validity and a typical application is demonstrated.
Spatio-temporal modeling of nonlinear distributed parameter systems
Li, Han-Xiong
2011-01-01
The purpose of this volume is to provide a brief review of the previous work on model reduction and identifi cation of distributed parameter systems (DPS), and develop new spatio-temporal models and their relevant identifi cation approaches. In this book, a systematic overview and classifi cation on the modeling of DPS is presented fi rst, which includes model reduction, parameter estimation and system identifi cation. Next, a class of block-oriented nonlinear systems in traditional lumped parameter systems (LPS) is extended to DPS, which results in the spatio-temporal Wiener and Hammerstein s
Nonlinear Reynolds stress models and the renormalization group
Rubinstein, Robert; Barton, J. Michael
1990-01-01
The renormalization group is applied to derive a nonlinear algebraic Reynolds stress model of anisotropic turbulence in which the Reynolds stresses are quadratic functions of the mean velocity gradients. The model results from a perturbation expansion that is truncated systematically at second order with subsequent terms contributing no further information. The resulting turbulence model applied to both low and high Reynolds number flows without requiring wall functions or ad hoc modifications of the equations. All constants are derived from the renormalization group procedure; no adjustable constants arise. The model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in noncircular ducts.
Discrete state space modeling and control of nonlinear unknown systems.
Savran, Aydogan
2013-11-01
A novel procedure for integrating neural networks (NNs) with conventional techniques is proposed to design industrial modeling and control systems for nonlinear unknown systems. In the proposed approach, a new recurrent NN with a special architecture is constructed to obtain discrete-time state-space representations of nonlinear dynamical systems. It is referred as the discrete state-space neural network (DSSNN). In the DSSNN, the outputs of the hidden layer neurons of the DSSNN represent the system's (pseudo) state. The inputs are fed to output neurons and the delayed outputs of the hidden layer neurons are fed to their inputs via adjustable weights. The discrete state space model of the actual system is directly obtained by training the DSSNN with the input-output data. A training procedure based on the back-propagation through time (BPTT) algorithm is developed. The Levenberg-Marquardt (LM) method with a trust region approach is used to update the DSSNN weights. Linear state space models enable to use well developed conventional analysis and design techniques. Thus, building a linear model of a system has primary importance in industrial applications. Thus, a suitable linearization procedure is proposed to derive the linear state space model from the nonlinear DSSNN representation. The controllability, observability and stability properties are examined. The state feedback controllers are designed with both the linear quadratic regulator (LQR) and the pole placement techniques. The regulator and servo control problems are both addressed. A full order observer is also designed to estimate the state variables. The performance of the proposed procedure is demonstrated by applying for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) nonlinear control problems. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
NONLINEAR EXTENSION OF ASYMMETRIC GARCH MODEL WITHIN NEURAL NETWORK FRAMEWORK
Directory of Open Access Journals (Sweden)
Josip Arnerić
2016-05-01
Full Text Available The importance of volatility for all market participants has led to the development and application of various econometric models. The most popular models in modelling volatility are GARCH type models because they can account excess kurtosis and asymmetric effects of financial time series. Since standard GARCH(1,1 model usually indicate high persistence in the conditional variance, the empirical researches turned to GJR-GARCH model and reveal its superiority in fitting the asymmetric heteroscedasticity in the data. In order to capture both asymmetry and nonlinearity in data, the goal of this paper is to develop a parsimonious NN model as an extension to GJR-GARCH model and to determine if GJR-GARCH-NN outperforms the GJR-GARCH model.
Nonlinear Mathematical Modeling in Pneumatic Servo Position Applications
Directory of Open Access Journals (Sweden)
Antonio Carlos Valdiero
2011-01-01
Full Text Available This paper addresses a new methodology for servo pneumatic actuators mathematical modeling and selection from the dynamic behavior study in engineering applications. The pneumatic actuator is very common in industrial application because it has the following advantages: its maintenance is easy and simple, with relatively low cost, self-cooling properties, good power density (power/dimension rate, fast acting with high accelerations, and installation flexibility. The proposed fifth-order nonlinear mathematical model represents the main characteristics of this nonlinear dynamic system, as servo valve dead zone, air flow-pressure relationship through valve orifice, air compressibility, and friction effects between contact surfaces in actuator seals. Simulation results show the dynamic performance for different pneumatic cylinders in order to see which features contribute to a better behavior of the system. The knowledge of this behavior allows an appropriate choice of pneumatic actuator, mainly contributing to the success of their precise control in several applications.
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
Directory of Open Access Journals (Sweden)
Hasan YILDIZ
2004-03-01
Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.
A Linearization Approach for Rational Nonlinear Models in Mathematical Physics
Institute of Scientific and Technical Information of China (English)
Robert A. Van Gorder
2012-01-01
In this paper, a novel method for linearization of rational second order nonlinear models is discussed. In particular, we discuss an application of the 5 expansion method （created to deal with problems in Quantum Field Theory） which will enable both the linearization and perturbation expansion of such equations. Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations. Higher order perturbation theories can then be obtained in terms of such special functions. One benefit to such a method is that it may be applied even to models without small physical parameters, as the perturbation is given in terms of the degree of nonlinearity, rather than any physical parameter. As an application, we discuss a method of linearizing the six Painlev~ equations by an application of the method. In addition to highlighting the benefits of the method, we discuss certain shortcomings of the method.
A non-linear model of economic production processes
Ponzi, A.; Yasutomi, A.; Kaneko, K.
2003-06-01
We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.
Off-shell BCJ Relation in Nonlinear Sigma Model
Chen, Gang; Liu, Hanqing
2016-01-01
We investigate relations among tree-level off-shell currents in nonlinear sigma model. Under Cayley parametrization, we propose and prove a general revised BCJ relation for even-point currents. Unlike the on-shell BCJ relation, the off-shell one behaves quite differently from Yang-Mills theory although the algebraic structure is the same. After performing the permutation summation in the revised BCJ relation, the sum is non-vanishing, instead, it equals to the sum of sub-current products with the BCJ coefficients under a specific ordering, which is presented by an explicit formula. Taking on-shell limit, this identity is reduced to the on-shell BCJ relation, and thus provides the full off-shell correspondence of tree-level BCJ relation in nonlinear sigma model.
Likelihood-Based Inference in Nonlinear Error-Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbæk, Anders
We consider a class of vector nonlinear error correction models where the transfer function (or loadings) of the stationary relation- ships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties...... of the process in terms of stochastic and deter- ministic trends as well as stationary components. In particular, the behaviour of the cointegrating relations is described in terms of geo- metric ergodicity. Despite the fact that no deterministic terms are included, the process will have both stochastic trends...... and a linear trend in general. Gaussian likelihood-based estimators are considered for the long- run cointegration parameters, and the short-run parameters. Asymp- totic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normaity can be found. A simulation study...
SIVS EPIDEMIC MODELS WITH INFECTION AGE AND NONLINEAR VACCINATION RATE
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Vaccination is a very important strategy for the elimination of infectious diseaVaccination is a very important strategy for the elimination of infectious diseases. A SIVS epidemic model with infection age and nonlinear vaccination has been formulated in this paper. Using the theory of differential and integral equation, we show the local asymptotic stability of the infection-free equilibrium and the endemic equilibrium under some assumptions.
Nonlinear dynamics mathematical models for rigid bodies with a liquid
Lukovsky, Ivan A
2015-01-01
This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities partly filled by liquid. It combines several methods and compares the results with experimental data. It is useful for experienced and early-stage readers interested in analytical approaches to fluid-structure interaction problems, the fundamental mathematical background and modeling the dynamics of such complex mechanical systems.
A Nonlinear Viscous Model for Sn-Whisker Growth
Yang, Fuqian
2016-12-01
Based on the mechanism of the grain boundary fluid flow, a nonlinear viscous model for the growth of Sn-whiskers is proposed. This model consists of two units, one with a stress exponent of one and one with a stress exponent of n -1. By letting one of the constants be zero in the model, the constitutive relationship reduces to a linear flow relation or a power-law relation, representing the flow behavior of various metals. Closed-form solutions for the growth behavior of a whisker are derived, which can be used to predict the whisker growth and the stress evolution.
A nonlinear poroelastic model for the periodontal ligament
Favino, Marco; Bourauel, Christoph; Krause, Rolf
2016-05-01
A coupled elastic-poroelastic model for the simulation of the PDL and the adjacent tooth is presented. A poroelastic constitutive material model for the periodontal ligament (PDL) is derived. The solid phase is modeled by means of a Fung material law, accounting for large displacements and strains. Numerical solutions are performed by means of a multigrid Newton method to solve the arising large nonlinear system. Finally, by means of numerical experiments, the biomechanical response of the PDL is studied. In particular, the effect of the hydraulic conductivity and of the mechanical parameters of a Fung potential is investigated in two realistic applications.
Linear and nonlinear viscoelastic arterial wall models: application on animals
Ghigo, Arthur; Armentano, Ricardo; Lagrée, Pierre-Yves; Fullana, Jose-Maria
2016-01-01
This work deals with the viscoelasticity of the arterial wall and its influence on the pulse waves. We describe the viscoelasticity by a non-linear Kelvin-Voigt model in which the coefficients are fitted using experimental time series of pressure and radius measured on a sheep's arterial network. We obtained a good agreement between the results of the nonlinear Kelvin-Voigt model and the experimental measurements. We found that the viscoelastic relaxation time-defined by the ratio between the viscoelastic coefficient and the Young's modulus-is nearly constant throughout the network. Therefore, as it is well known that smaller arteries are stiffer, the viscoelastic coefficient rises when approaching the peripheral sites to compensate the rise of the Young's modulus, resulting in a higher damping effect. We incorporated the fitted viscoelastic coefficients in a nonlinear 1D fluid model to compute the pulse waves in the network. The damping effect of viscoelasticity on the high frequency waves is clear especiall...
A numerical model for pipelaying on nonlinear soil stiffness seabed
Institute of Scientific and Technical Information of China (English)
昝英飞; 韩端锋; 袁利毫; 李志刚
2016-01-01
The J-lay method is regarded as one of the most feasible methods to lay a pipeline in deep water and ultra-deep water. A numerical model that accounts for the nonlinear soil stiffness is developed in this study to evaluate a J-lay pipeline. The pipeline considered in this model is divided into two parts: the part one is suspended in water, and the part two is laid on the seabed. In addition to the boundary conditions at the two end points of the pipeline, a special set of the boundary conditions is required at the touchdown point that connects the two parts of the pipeline. The two parts of the pipeline are solved by a numerical iterative method and the finite difference method, respectively. The proposed numerical model is validated for a special case using a catenary model and a numerical model with linear soil stiffness. A good agreement in the pipeline configuration, the tension force and the bending moment is obtained among these three models. Furthermore, the present model is used to study the importance of the nonlinear soil stiffness. Finally, the parametric study is performed to study the effect of the mudline shear strength, the gradient of the soil shear strength, and the outer diameter of the pipeline on the pipelaying solution.
Wu, Hao; Noé, Frank
2011-03-01
Diffusion processes are relevant for a variety of phenomena in the natural sciences, including diffusion of cells or biomolecules within cells, diffusion of molecules on a membrane or surface, and diffusion of a molecular conformation within a complex energy landscape. Many experimental tools exist now to track such diffusive motions in single cells or molecules, including high-resolution light microscopy, optical tweezers, fluorescence quenching, and Förster resonance energy transfer (FRET). Experimental observations are most often indirect and incomplete: (1) They do not directly reveal the potential or diffusion constants that govern the diffusion process, (2) they have limited time and space resolution, and (3) the highest-resolution experiments do not track the motion directly but rather probe it stochastically by recording single events, such as photons, whose properties depend on the state of the system under investigation. Here, we propose a general Bayesian framework to model diffusion processes with nonlinear drift based on incomplete observations as generated by various types of experiments. A maximum penalized likelihood estimator is given as well as a Gibbs sampling method that allows to estimate the trajectories that have caused the measurement, the nonlinear drift or potential function and the noise or diffusion matrices, as well as uncertainty estimates of these properties. The approach is illustrated on numerical simulations of FRET experiments where it is shown that trajectories, potentials, and diffusion constants can be efficiently and reliably estimated even in cases with little statistics or nonequilibrium measurement conditions.
Application of nonlinear forecasting techniques for meteorological modeling
Directory of Open Access Journals (Sweden)
V. Pérez-Muñuzuri
Full Text Available A nonlinear forecasting method was used to predict the behavior of a cloud coverage time series several hours in advance. The method is based on the reconstruction of a chaotic strange attractor using four years of cloud absorption data obtained from half-hourly Meteosat infrared images from Northwestern Spain. An exhaustive nonlinear analysis of the time series was carried out to reconstruct the phase space of the underlying chaotic attractor. The forecast values are used by a non-hydrostatic meteorological model ARPS for daily weather prediction and their results compared with surface temperature measurements from a meteorological station and a vertical sounding. The effect of noise in the time series is analyzed in terms of the prediction results.
Key words: Meterology and atmospheric dynamics (mesoscale meteorology; general – General (new fields
The inherent complexity in nonlinear business cycle model in resonance
Energy Technology Data Exchange (ETDEWEB)
Ma Junhai [School of Management, Tianjin University, Tianjin 300072 (China) and Tianjin University of Finance and Economics, Tianjin 300222 (China)], E-mail: lzqsly@126.com; Sun Tao; Liu Lixia [School of Management, Tianjin University, Tianjin 300072 (China)
2008-08-15
Based on Abraham C.-L. Chian's research, we applied nonlinear dynamic system theory to study the first-order and second-order approximate solutions to one category of the nonlinear business cycle model in resonance condition. We have also analyzed the relation between amplitude and phase of second-order approximate solutions as well as the relation between outer excitements' amplitude, frequency approximate solutions, and system bifurcation parameters. Then we studied the system quasi-periodical solutions, annulus periodical solutions and the path leading to system bifurcation and chaotic state with different parameter combinations. Finally, we conducted some numerical simulations for various complicated circumstances. Therefore this research will lay solid foundation for detecting the complexity of business cycles and systems in the future.
Vainshtein mechanism in massive gravity nonlinear sigma models
Aoki, Katsuki
2016-01-01
We study the stability of the Vainshtein screening solution of the massive/bi-gravity based on the massive nonlinear sigma model as the effective action inside the Vainshtein radius. The effective action is obtained by taking the $\\Lambda_2$ decoupling limit around a curved spacetime. First we derive a general consequence that any Ricci flat Vainshtein screening solution is unstable when we take into account the excitation of the scalar graviton only. This instability suggests that the nonlinear excitation of the scalar graviton is not sufficient to obtain a successful Vainshtein screening in massive/bi-gravity. Then to see the role of the excitation of the vector graviton, we study perturbations around the static and spherically symmetric solution obtained in bigravity explicitly. As a result, we find that linear excitations of the vector graviton cannot be helpful and the solution still suffers from a ghost and/or a gradient instability for any parameters of the theory for this background.
Augmented twin-nonlinear two-box behavioral models for multicarrier LTE power amplifiers.
Hammi, Oualid
2014-01-01
A novel class of behavioral models is proposed for LTE-driven Doherty power amplifiers with strong memory effects. The proposed models, labeled augmented twin-nonlinear two-box models, are built by cascading a highly nonlinear memoryless function with a mildly nonlinear memory polynomial with cross terms. Experimental validation on gallium nitride based Doherty power amplifiers illustrates the accuracy enhancement and complexity reduction achieved by the proposed models. When strong memory effects are observed, the augmented twin-nonlinear two-box models can improve the normalized mean square error by up to 3 dB for the same number of coefficients when compared to state-of-the-art twin-nonlinear two-box models. Furthermore, the augmented twin-nonlinear two-box models lead to the same performance as previously reported twin-nonlinear two-box models while requiring up to 80% less coefficients.
Augmented Twin-Nonlinear Two-Box Behavioral Models for Multicarrier LTE Power Amplifiers
Directory of Open Access Journals (Sweden)
Oualid Hammi
2014-01-01
Full Text Available A novel class of behavioral models is proposed for LTE-driven Doherty power amplifiers with strong memory effects. The proposed models, labeled augmented twin-nonlinear two-box models, are built by cascading a highly nonlinear memoryless function with a mildly nonlinear memory polynomial with cross terms. Experimental validation on gallium nitride based Doherty power amplifiers illustrates the accuracy enhancement and complexity reduction achieved by the proposed models. When strong memory effects are observed, the augmented twin-nonlinear two-box models can improve the normalized mean square error by up to 3 dB for the same number of coefficients when compared to state-of-the-art twin-nonlinear two-box models. Furthermore, the augmented twin-nonlinear two-box models lead to the same performance as previously reported twin-nonlinear two-box models while requiring up to 80% less coefficients.
Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit
Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie
2015-09-01
The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity
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...
Probability bounds analysis for nonlinear population ecology models.
Enszer, Joshua A; Andrei Măceș, D; Stadtherr, Mark A
2015-09-01
Mathematical models in population ecology often involve parameters that are empirically determined and inherently uncertain, with probability distributions for the uncertainties not known precisely. Propagating such imprecise uncertainties rigorously through a model to determine their effect on model outputs can be a challenging problem. We illustrate here a method for the direct propagation of uncertainties represented by probability bounds though nonlinear, continuous-time, dynamic models in population ecology. This makes it possible to determine rigorous bounds on the probability that some specified outcome for a population is achieved, which can be a core problem in ecosystem modeling for risk assessment and management. Results can be obtained at a computational cost that is considerably less than that required by statistical sampling methods such as Monte Carlo analysis. The method is demonstrated using three example systems, with focus on a model of an experimental aquatic food web subject to the effects of contamination by ionic liquids, a new class of potentially important industrial chemicals.
Nonlinear modeling of PEMFC based on neural networks identification
Institute of Scientific and Technical Information of China (English)
SUN Tao; CAO Guang-yi; ZHU Xin-jian
2005-01-01
The proton exchange membrane generation technology is highly efficient and clean, and is considered as the most hopeful "green" power technology. The operating principles of proton exchange membrane fuel cell (PEMFC) system involve thermodynamics, electrochemistry, hydrodynamics and mass transfer theory, which comprise a complex nonlinear system, for which it is difficult to establish a mathematical model. This paper first simply analyzes the necessity of the PEMFC generation technology, then introduces the generating principle from four aspects: electrode, single cell, stack, system; and then uses the approach and self-study ability of artificial neural network to build the model of nonlinear system, and adapts the Levenberg-Marquardt BP (LMBP) to build the electric characteristic model of PEMFC. The model uses experimental data as training specimens, on the condition the system is provided enough hydrogen. Considering the flow velocity of air (or oxygen) and the cell operational temperature as inputs, the cell voltage and current density as the outputs and establishing the electric characteristic model of PEMFC according to the different cell temperatures. The voltage-current output curves of model has some guidance effect for improving the cell performance, and provide basic data for optimizing cell performance that have practical significance.
Nonlinear Time Series Model for Shape Classification Using Neural Networks
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A complex nonlinear exponential autoregressive (CNEAR) model for invariant feature extraction is developed for recognizing arbitrary shapes on a plane. A neural network is used to calculate the CNEAR coefficients. The coefficients, which constitute the feature set, are proven to be invariant to boundary transformations such as translation, rotation, scale and choice of starting point in tracing the boundary. The feature set is then used as the input to a complex multilayer perceptron (C-MLP) network for learning and classification. Experimental results show that complicated shapes can be accurately recognized even with the low-order model and that the classification method has good fault tolerance when noise is present.
Stability Analysis of Some Nonlinear Anaerobic Digestion Models
Directory of Open Access Journals (Sweden)
Ivan Simeonov
2010-04-01
Full Text Available Abstract: The paper deals with local asymptotic stability analysis of some mass balance dynamic models (based on one and on two-stage reaction schemes of the anaerobic digestion (AD in CSTR. The equilibrium states for models based on one (with Monod, Contois and Haldane shapes for the specific growth rate and on two-stage (only with Monod shapes for both the specific growth rate of acidogenic and methanogenic bacterial populations reaction schemes have been determined solving sets of nonlinear algebraic equations using Maples. Their stability has been analyzed systematically, which provides insight and guidance for AD bioreactors design, operation and control.
Linear and non-linear perturbations in dark energy models
Escamilla-Rivera, Celia; Fabris, Julio C; Alcaniz, Jailson S
2016-01-01
In this work we discuss observational aspects of three time-dependent parameterisations of the dark energy equation of state $w(z)$. In order to determine the dynamics associated with these models, we calculate their background evolution and perturbations in a scalar field representation. After performing a complete treatment of linear perturbations, we also show that the non-linear contribution of the selected $w(z)$ parameterisations to the matter power spectra is almost the same for all scales, with no significant difference from the predictions of the standard $\\Lambda$CDM model.
Elimination of Nonlinear Deviations in Thermal Lattice BGK Models
Chen, Y; Hongo, T; Chen, Yu; Ohashi, Hirotada; Akiyam, Mamoru
1993-01-01
Abstracet: We present a new thermal lattice BGK model in D-dimensional space for the numerical calculation of fluid dynamics. This model uses a higher order expansion of equilibrium distribution in Maxwellian type. In the mean time the lattice symmetry is upgraded to ensure the isotropy of 6th order tensor. These manipulations lead to macroscopic equations free from nonlinear deviations. We demonstrate the improvements by conducting classical Chapman-Enskog analysis and by numerical simulation of shear wave flow. The transport coefficients are measured numerically, too.
Extended nonlinear feedback model for describing episodes of high inflation
Szybisz, M A; Szybisz, L.
2016-01-01
An extension of the nonlinear feedback (NLF) formalism to describe regimes of hyper- and high-inflation in economy is proposed in the present work. In the NLF model the consumer price index (CPI) exhibits a finite time singularity of the type $1/(t_c -t)^{(1- \\beta)/\\beta}$, with $\\beta>0$, predicting a blow up of the economy at a critical time $t_c$. However, this model fails in determining $t_c$ in the case of weak hyperinflation regimes like, e.g., that occurred in Israel. To overcome this...
The Precession Index and a Nonlinear Energy Balance Climate Model
Rubincam, David
2004-01-01
A simple nonlinear energy balance climate model yields a precession index-like term in the temperature. Despite its importance in the geologic record, the precession index e sin (Omega)S, where e is the Earth's orbital eccentricity and (Omega)S is the Sun's perigee in the geocentric frame, is not present in the insolation at the top of the atmosphere. Hence there is no one-for-one mapping of 23,000 and 19,000 year periodicities from the insolation to the paleoclimate record; a nonlinear climate model is needed to produce these long periods. A nonlinear energy balance climate model with radiative terms of form T n, where T is surface temperature and n less than 1, does produce e sin (omega)S terms in temperature; the e sin (omega)S terms are called Seversmith psychroterms. Without feedback mechanisms, the model achieves extreme values of 0.64 K at the maximum orbital eccentricity of 0.06, cooling one hemisphere while simultaneously warming the other; the hemisphere over which perihelion occurs is the cooler. In other words, the nonlinear energy balance model produces long-term cooling in the northern hemisphere when the Sun's perihelion is near northern summer solstice and long-term warming in the northern hemisphere when the aphelion is near northern summer solstice. (This behavior is similar to the inertialess gray body which radiates like T 4, but the amplitude is much lower for the energy balance model because of its thermal inertia.) This seemingly paradoxical behavior works against the standard Milankovitch model, which requires cool northern summers (Sun far from Earth in northern summer) to build up northern ice sheets, so that if the standard model is correct it must be more efficient than previously thought. Alternatively, the new mechanism could possibly be dominant and indicate southern hemisphere control of the northern ice sheets, wherein the southern oceans undergo a long-term cooling when the Sun is far from the Earth during northern summer. The cold
Filtering nonlinear dynamical systems with linear stochastic models
Harlim, J.; Majda, A. J.
2008-06-01
An important emerging scientific issue is the real time filtering through observations of noisy signals for nonlinear dynamical systems as well as the statistical accuracy of spatio-temporal discretizations for filtering such systems. From the practical standpoint, the demand for operationally practical filtering methods escalates as the model resolution is significantly increased. For example, in numerical weather forecasting the current generation of global circulation models with resolution of 35 km has a total of billions of state variables. Numerous ensemble based Kalman filters (Evensen 2003 Ocean Dyn. 53 343-67 Bishop et al 2001 Mon. Weather Rev. 129 420-36 Anderson 2001 Mon. Weather Rev. 129 2884-903 Szunyogh et al 2005 Tellus A 57 528-45 Hunt et al 2007 Physica D 230 112-26) show promising results in addressing this issue; however, all these methods are very sensitive to model resolution, observation frequency, and the nature of the turbulent signals when a practical limited ensemble size (typically less than 100) is used. In this paper, we implement a radical filtering approach to a relatively low (40) dimensional toy model, the L-96 model (Lorenz 1996 Proc. on Predictability (ECMWF, 4-8 September 1995) pp 1-18) in various chaotic regimes in order to address the 'curse of ensemble size' for complex nonlinear systems. Practically, our approach has several desirable features such as extremely high computational efficiency, filter robustness towards variations of ensemble size (we found that the filter is reasonably stable even with a single realization) which makes it feasible for high dimensional problems, and it is independent of any tunable parameters such as the variance inflation coefficient in an ensemble Kalman filter. This radical filtering strategy decouples the problem of filtering a spatially extended nonlinear deterministic system to filtering a Fourier diagonal system of parametrized linear stochastic differential equations (Majda and Grote
Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties
Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon
2012-01-01
Purpose: The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F[subscript 0]) during anterior-posterior stretching. Method: Three materially linear and 3 materially nonlinear models were…
Sridhar, Upasana Manimegalai; Govindarajan, Anand; Rhinehart, R Russell
2016-01-01
This work reveals the applicability of a relatively new optimization technique, Leapfrogging, for both nonlinear regression modeling and a methodology for nonlinear model-predictive control. Both are relatively simple, yet effective. The application on a nonlinear, pilot-scale, shell-and-tube heat exchanger reveals practicability of the techniques.
Nonlinear stochastic modeling of river dissolved-oxygen
Energy Technology Data Exchange (ETDEWEB)
Tabios, G.Q. III.
1984-01-01
An important aspect of water quality modeling is forecasting water quality variables for real-time management and control applications to enhance, maintain and sustain desirable water qualities. The major objective of this research is to develop daily time series models for forecasting river dissolved-oxygen (DO). The modeling approach adopted herein combines deterministic and stochastic concepts for determining properties of the DO process based on time series data and dynamic mechanisms governing the said process. This is accomplished by deriving a general DO stochastic model structure based on a modified Streeter-Phelps DO-BOD dynamic model. Then some types of nonlinear models namely, self-exciting threshold autoregressive-moving average (SETARMA), amplitude-dependent autoregressive (ADAR) and bilinear (BL) models, and the class of linear autoregressive-moving average (ARMA) models are adopted for model identification and parameter estimation. Six stream-water quality gaging stations located in the eastern portion of the continental U.S.A. are utilized in this study. Various orders of ARMA, SETARMA, ADAR and BL models are fitted to the data. Results obtained indicated that ADAR and BL models are superior for one-step ahead forecasts, while SETARMA models are better for forecasts of longer lead times. In general, the SETARMA, ADAR and BL models show promise as alternative models for river DO time series modeling and forecasting with unique advantages in each.
Recent advances in estimating nonlinear models with applications in economics and finance
Ma, Jun
2013-01-01
Featuring current research in economics, finance and management, this book surveys nonlinear estimation techniques and offers new methods and insights into nonlinear time series analysis. Covers Markov Switching Models for analyzing economics series and more.
On Models of Nonlinear Evolution Paths in Adiabatic Quantum Algorithms
Institute of Scientific and Technical Information of China (English)
SUN Jie; LU Song-Feng; Samuel L.Braunstein
2013-01-01
In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model — an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.
A non-linear model of information seeking behaviour
Directory of Open Access Journals (Sweden)
Allen E. Foster
2005-01-01
Full Text Available The results of a qualitative, naturalistic, study of information seeking behaviour are reported in this paper. The study applied the methods recommended by Lincoln and Guba for maximising credibility, transferability, dependability, and confirmability in data collection and analysis. Sampling combined purposive and snowball methods, and led to a final sample of 45 inter-disciplinary researchers from the University of Sheffield. In-depth semi-structured interviews were used to elicit detailed examples of information seeking. Coding of interview transcripts took place in multiple iterations over time and used Atlas-ti software to support the process. The results of the study are represented in a non-linear Model of Information Seeking Behaviour. The model describes three core processes (Opening, Orientation, and Consolidation and three levels of contextual interaction (Internal Context, External Context, and Cognitive Approach, each composed of several individual activities and attributes. The interactivity and shifts described by the model show information seeking to be non-linear, dynamic, holistic, and flowing. The paper concludes by describing the whole model of behaviours as analogous to an artist's palette, in which activities remain available throughout information seeking. A summary of key implications of the model and directions for further research are included.
A nonlinear inversion for the velocity background and perturbation models
Wu, Zedong
2015-08-19
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect diving waves, which is an important source of information for extracting the long wavelength components of the velocity model. Thus, we propose a new optimization problem through breaking the velocity model into the background and the perturbation in the wave equation directly. In this case, the perturbed model is no longer the single scattering model, but includes all scattering. We optimize both components simultaneously, and thus, the objective function is nonlinear with respect to both the background and perturbation. The new introduced w can absorb the non-smooth update of background naturally. Application to the Marmousi model with frequencies that start at 5 Hz shows that this method can converge to the accurate velocity starting from a linearly increasing initial velocity. Application to the SEG2014 demonstrates the versatility of the approach.
A nonlinear model of gold production in Malaysia
Ramli, Norashikin; Muda, Nora; Umor, Mohd Rozi
2014-06-01
Malaysia is a country which is rich in natural resources and one of it is a gold. Gold has already become an important national commodity. This study is conducted to determine a model that can be well fitted with the gold production in Malaysia from the year 1995-2010. Five nonlinear models are presented in this study which are Logistic model, Gompertz, Richard, Weibull and Chapman-Richard model. These model are used to fit the cumulative gold production in Malaysia. The best model is then selected based on the model performance. The performance of the fitted model is measured by sum squares error, root mean squares error, coefficient of determination, mean relative error, mean absolute error and mean absolute percentage error. This study has found that a Weibull model is shown to have significantly outperform compare to the other models. To confirm that Weibull is the best model, the latest data are fitted to the model. Once again, Weibull model gives the lowest readings at all types of measurement error. We can concluded that the future gold production in Malaysia can be predicted according to the Weibull model and this could be important findings for Malaysia to plan their economic activities.
Validation of a Hertzian contact model with nonlinear damping
Sierakowski, Adam
2015-11-01
Due to limited spatial resolution, most disperse particle simulation methods rely on simplified models for incorporating short-range particle interactions. In this presentation, we introduce a contact model that combines the Hertz elastic restoring force with a nonlinear damping force, requiring only material properties and no tunable parameters. We have implemented the model in a resolved-particle flow solver that implements the Physalis method, which accurately captures hydrodynamic interactions by analytically enforcing the no-slip condition on the particle surface. We summarize the results of a few numerical studies that suggest the validity of the contact model over a range of particle interaction intensities (i.e., collision Stokes numbers) when compared with experimental data. This work was supported by the National Science Foundation under Grant Number CBET1335965 and the Johns Hopkins University Modeling Complex Systems IGERT program.
Nonlinear oscillations in a muscle pacemaker cell model
González-Miranda, J. M.
2017-02-01
This article presents a numerical simulation study of the nonlinear oscillations displayed by the Morris-Lecar model [Biophys. J. 35 (1981) 193] for the oscillations experimentally observed in the transmembrane potential of a muscle fiber subject to an external electrical stimulus. We consider the model in the case when there is no external stimulation, aiming to establish the ability of the model to display biophysically reasonable pacemaker dynamics. We obtain 2D bifurcation diagrams showing that indeed the model presents oscillatory dynamics, displaying the two main types of action potentials that are observed in muscle fibers. The results obtained are shown to be structurally stable; that is, robust against changes in the values of system parameters. Moreover, it is demonstrated how the model is appropriate to analyze the action potentials observed in terms of the transmembrane currents creating them.
Digital simulation and modeling of nonlinear stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Richardson, J M; Rowland, J R
1981-04-01
Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions that result from different integration algorithms and then comparing the moments to those arising from various stochastic integral definitions. This algorithm-dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases in which unique solutions are determined by any convergent numerical algorithm. Consequences of the relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. Monte Carlo simulations and statistical tests are applied to the example to illustrate the determining role which computational procedures play in generating solutions.
Digital simulation and modeling of nonlinear stochastic systems
Energy Technology Data Exchange (ETDEWEB)
Richardson, J M; Rowland, J R
1980-01-01
Digitally generated solutions of nonlinear stochastic systems are not unique, but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system, but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions resulting from different integration algorithms and comparing the moments to those arising from various stochastic integral definitions. Monte Carlo simulations and statistical tests are applied to illustrate the determining role that computational procedures play in generating solutions. This algorithm dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases, in which unique solutions are determined by any convergent numerical algorithm. Consequences of this relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. 2 figures.
Reduced nonlinear prognostic model construction from high-dimensional data
Gavrilov, Andrey; Mukhin, Dmitry; Loskutov, Evgeny; Feigin, Alexander
2017-04-01
Construction of a data-driven model of evolution operator using universal approximating functions can only be statistically justified when the dimension of its phase space is small enough, especially in the case of short time series. At the same time in many applications real-measured data is high-dimensional, e.g. it is space-distributed and multivariate in climate science. Therefore it is necessary to use efficient dimensionality reduction methods which are also able to capture key dynamical properties of the system from observed data. To address this problem we present a Bayesian approach to an evolution operator construction which incorporates two key reduction steps. First, the data is decomposed into a set of certain empirical modes, such as standard empirical orthogonal functions or recently suggested nonlinear dynamical modes (NDMs) [1], and the reduced space of corresponding principal components (PCs) is obtained. Then, the model of evolution operator for PCs is constructed which maps a number of states in the past to the current state. The second step is to reduce this time-extended space in the past using appropriate decomposition methods. Such a reduction allows us to capture only the most significant spatio-temporal couplings. The functional form of the evolution operator includes separately linear, nonlinear (based on artificial neural networks) and stochastic terms. Explicit separation of the linear term from the nonlinear one allows us to more easily interpret degree of nonlinearity as well as to deal better with smooth PCs which can naturally occur in the decompositions like NDM, as they provide a time scale separation. Results of application of the proposed method to climate data are demonstrated and discussed. The study is supported by Government of Russian Federation (agreement #14.Z50.31.0033 with the Institute of Applied Physics of RAS). 1. Mukhin, D., Gavrilov, A., Feigin, A., Loskutov, E., & Kurths, J. (2015). Principal nonlinear dynamical
Nonlinear structure formation in the Cubic Galileon gravity model
Barreira, Alexandre; Hellwing, Wojciech A; Baugh, Carlton M; Pascoli, Silvia
2013-01-01
We model the linear and nonlinear growth of large scale structure in the Cubic Galileon gravity model, by running a suite of N-body cosmological simulations using the {\\tt ECOSMOG} code. Our simulations include the Vainshtein screening effect, which reconciles the Cubic Galileon model with local tests of gravity. In the linear regime, the amplitude of the matter power spectrum increases by $\\sim 25%$ with respect to the standard $\\Lambda$CDM model today. The modified expansion rate accounts for $\\sim 20%$ of this enhancement, while the fifth force is responsible for only $\\sim 5%$. This is because the effective unscreened gravitational strength deviates from standard gravity only at late times, even though it can be twice as large today. In the nonlinear regime ($k \\gtrsim 0.1 h\\rm{Mpc}^{-1}$), the fifth force leads to only a modest increase ($\\lesssim 8%$) in the clustering power on all scales due to the very efficient operation of the Vainshtein mechanism. Such a strong effect is typically not seen in other...
On the Identifiability of the Post-Nonlinear Causal Model
Zhang, Kun
2012-01-01
By taking into account the nonlinear effect of the cause, the inner noise effect, and the measurement distortion effect in the observed variables, the post-nonlinear (PNL) causal model has demonstrated its excellent performance in distinguishing the cause from effect. However, its identifiability has not been properly addressed, and how to apply it in the case of more than two variables is also a problem. In this paper, we conduct a systematic investigation on its identifiability in the two-variable case. We show that this model is identifiable in most cases; by enumerating all possible situations in which the model is not identifiable, we provide sufficient conditions for its identifiability. Simulations are given to support the theoretical results. Moreover, in the case of more than two variables, we show that the whole causal structure can be found by applying the PNL causal model to each structure in the Markov equivalent class and testing if the disturbance is independent of the direct causes for each va...
Chaotic Inflation from Nonlinear Sigma Models in Supergravity
Hellerman, Simeon; Yanagida, Tsutomu T
2014-01-01
We present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu-Goldstone boson (NGB) of a nonlinear sigma model. However, it is well known that nonlinear sigma models (NLSMs) with nontrivial K\\"ahler transformations are problematic to couple to supergravity. An additional field is necessary to make the K\\"ahler potential of the NLSM invariant in supergravity. This field must have a shift symmetry --- making it a candidate for the inflaton (or axion). We give an explicit example of such a model for the coset space $SU(3)/SU(2) \\times U(1)$, with the Higgs as the NGB, including breaking the inflaton's shift symmetry and producing a chaotic inflation potential. This construction can also be applied to other models, such as one based on $E_7/SO(10) \\times U(1) \\times U(1)$ which incorporates the first two ge...
Models of the delayed nonlinear Raman response in diatomic gases
Palastro, J. P.; Antonsen, T. M., Jr.; Pearson, A.
2011-07-01
We examine the delayed response of a diatomic gas to a polarizing laser field with the goal of obtaining computationally efficient methods for use with laser pulse propagation simulations. We demonstrate that for broadband pulses, heavy molecules such as O2 and N2, and typical atmospheric temperatures, the initial delayed response requires only classical physics. The linear kinetic Green's function is derived from the Boltzmann equation and shown to be in excellent agreement with full density-matrix calculations. A straightforward perturbation approach for the fully nonlinear, kinetic impulse response is also presented. With the kinetic theory a reduced fluid model of the diatomic gas’ orientation is derived. Transport coefficients are introduced to model the kinetic phase mixing of the delayed response. In addition to computational rapidity, the fluid model provides intuition through the use of familiar macroscopic quantities. Both the kinetic and the fluid descriptions predict a nonlinear steady-state alignment after passage of the laser pulse, which in the fluid model is interpreted as an anisotropic temperature of the diatomic fluid with respect to motion about the polarization axis.
On the nonlinear models of the vibrating string
Watzky, Alexandre
2005-09-01
Vibrations of strings (threads, wires, cables...) are of great interest because of their various domains of application. In musical acoustics, phenomena which could have been neglected elsewhere take a particular importance since perception, which is very sensitive to nonlinear effects, is involved. Some phenomena can also be emphasized when a string is coupled to a sound-radiating structure. Reliable physical models are thus necessary to account for these phenomena, and to understand the true behavior of a vibrating string. Despite the fact that the first nonlinear models were published more than one century ago, and that accurate equations of motion can be naturally achieved within a finite displacement continuum mechanics framework, general models never received the attention they deserved, most authors focusing on particular phenomena and often settling on approximate models. This can be explained by the awkward multiplicity of the involved phenomena. The aim of this presentation is to discuss the consequences of some common assumptions and the true nature of some observed couplings. Particular attention will be paid to the preponderance of the spatial shape of the modes, which are usually underestimated with respect to their temporal form.
Nonlinear Sigma Models with Compact Hyperbolic Target Spaces
Gubser, Steven; Schoenholz, Samuel S; Stoica, Bogdan; Stokes, James
2015-01-01
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the $O(2)$ model. Unlike in the $O(2)$ case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggest...
Fault Diagnosis of Nonlinear Systems Using Structured Augmented State Models
Institute of Scientific and Technical Information of China (English)
Jochen Aβfalg; Frank Allg(o)wer
2007-01-01
This paper presents an internal model approach for modeling and diagnostic functionality design for nonlinear systems operating subject to single- and multiple-faults. We therefore provide the framework of structured augmented state models. Fault characteristics are considered to be generated by dynamical exosystems that are switched via equality constraints to overcome the augmented state observability limiting the number of diagnosable faults. Based on the proposed model, the fault diagnosis problem is specified as an optimal hybrid augmented state estimation problem. Sub-optimal solutions are motivated and exemplified for the fault diagnosis of the well-known three-tank benchmark. As the considered class of fault diagnosis problems is large, the suggested approach is not only of theoretical interest but also of high practical relevance.
Nonlinear Thermoelastic Model for SMAs and SMA Hybrid Composites
Turner, Travis L.
2004-01-01
A constitutive mathematical model has been developed that predicts the nonlinear thermomechanical behaviors of shape-memory-alloys (SMAs) and of shape-memory-alloy hybrid composite (SMAHC) structures, which are composite-material structures that contain embedded SMA actuators. SMAHC structures have been investigated for their potential utility in a variety of applications in which there are requirements for static or dynamic control of the shapes of structures, control of the thermoelastic responses of structures, or control of noise and vibrations. The present model overcomes deficiencies of prior, overly simplistic or qualitative models that have proven ineffective or intractable for engineering of SMAHC structures. The model is sophisticated enough to capture the essential features of the mechanics of SMAHC structures yet simple enough to accommodate input from fundamental engineering measurements and is in a form that is amenable to implementation in general-purpose structural analysis environments.
Modelling of nonlinear shoaling based on stochastic evolution equations
DEFF Research Database (Denmark)
Kofoed-Hansen, Henrik; Rasmussen, Jørgen Hvenekær
1998-01-01
A one-dimensional stochastic model is derived to simulate the transformation of wave spectra in shallow water including generation of bound sub- and super-harmonics, near-resonant triad wave interaction and wave breaking. Boussinesq type equations with improved linear dispersion characteristics...... are recast into evolution equations for the complex amplitudes, and serve as the underlying deterministic model. Next, a set of evolution equations for the cumulants is derived. By formally introducing the well-known Gaussian closure hypothesis, nonlinear evolution equations for the power spectrum...... and bispectrum are derived. A simple description of depth-induced wave breaking is incorporated in the model equations, assuming that the total rate of dissipation may be distributed in proportion to the spectral energy density on each discrete frequency. The proposed phase-averaged model is compared...
Improved Methodology for Parameter Inference in Nonlinear, Hydrologic Regression Models
Bates, Bryson C.
1992-01-01
A new method is developed for the construction of reliable marginal confidence intervals and joint confidence regions for the parameters of nonlinear, hydrologic regression models. A parameter power transformation is combined with measures of the asymptotic bias and asymptotic skewness of maximum likelihood estimators to determine the transformation constants which cause the bias or skewness to vanish. These optimized constants are used to construct confidence intervals and regions for the transformed model parameters using linear regression theory. The resulting confidence intervals and regions can be easily mapped into the original parameter space to give close approximations to likelihood method confidence intervals and regions for the model parameters. Unlike many other approaches to parameter transformation, the procedure does not use a grid search to find the optimal transformation constants. An example involving the fitting of the Michaelis-Menten model to velocity-discharge data from an Australian gauging station is used to illustrate the usefulness of the methodology.
Nonlinear elastic model for compacted clay concrete interface
Institute of Scientific and Technical Information of China (English)
R. R. SHAKIR; Jungao ZHU
2009-01-01
In this paper, a nonlinear elastic model was developed to simulate the behavior of compacted clay concrete interface (CCCI) based on the principle of transition mechanism failure (TMF). A number of simple shear tests were conducted on CCCI to demonstrate different failure mechanisms; i.e., sliding failure and deformation failure. The clay soil used in the test was collected from the "Shuang Jang Kou" earth rockfill dam project. It was found that the behavior of the interface depends on the critical water contents by which two failure mechanisms can be recognized. Mathematical relations were proposed between the shear at failure and water content in addition to the transition mechanism indicator.The mathematical relations were then incorporated into the interface model. The performance of the model is verified with the experimental results. The verification shows that the proposed model is capable of predicting the interface shear stress versus the total shear displacement very well.
Non-linear DSGE Models and The Optimized Particle Filter
DEFF Research Database (Denmark)
Andreasen, Martin Møller
This paper improves the accuracy and speed of particle filtering for non-linear DSGE models with potentially non-normal shocks. This is done by introducing a new proposal distribution which i) incorporates information from new observables and ii) has a small optimization step that minimizes...... the distance to the optimal proposal distribution. A particle filter with this proposal distribution is shown to deliver a high level of accuracy even with relatively few particles, and this filter is therefore much more efficient than the standard particle filter....
Dynamics in a nonlinear Keynesian good market model
Energy Technology Data Exchange (ETDEWEB)
Naimzada, Ahmad, E-mail: ahmad.naimzada@unimib.it [Department of Economics, Quantitative Methods and Management, University of Milano-Bicocca, U7 Building, Via Bicocca degli Arcimboldi 8, 20126 Milano (Italy); Pireddu, Marina, E-mail: marina.pireddu@unimib.it [Department of Mathematics and Applications, University of Milano-Bicocca, U5 Building, Via Cozzi 55, 20125 Milano (Italy)
2014-03-15
In this paper, we show how a rich variety of dynamical behaviors can emerge in the standard Keynesian income-expenditure model when a nonlinearity is introduced, both in the cases with and without endogenous government spending. A specific sigmoidal functional form is used for the adjustment mechanism of income with respect to the excess demand, in order to bound the income variation. With the aid of analytical and numerical tools, we investigate the stability conditions, bifurcations, as well as periodic and chaotic dynamics. Globally, we study multistability phenomena, i.e., the coexistence of different kinds of attractors.
Modeling highly-dispersive transparency in planar nonlinear metamaterials
Potravkin, N. N.; Makarov, V. A.; Perezhogin, I. A.
2017-02-01
We consider propagation of light in planar optical metamaterial, which basic element is composed of two silver stripes, and it possesses strong dispersion in optical range. Our method of numerical modeling allows us to take into consideration the nonlinearity of the material and the effects of light self-action without considerable increase of the calculation time. It is shown that plasmonic resonances originating in such a structure result in multiple enhancement of local field and high sensitivity of the transmission coefficient to the intensity of incident monochromatic wave.
Nonzero solutions of nonlinear integral equations modeling infectious disease
Energy Technology Data Exchange (ETDEWEB)
Williams, L.R. (Indiana Univ., South Bend); Leggett, R.W.
1982-01-01
Sufficient conditions to insure the existence of periodic solutions to the nonlinear integral equation, x(t) = ..integral../sup t//sub t-tau/f(s,x(s))ds, are given in terms of simple product and product integral inequalities. The equation can be interpreted as a model for the spread of infectious diseases (e.g., gonorrhea or any of the rhinovirus viruses) if x(t) is the proportion of infectives at time t and f(t,x(t)) is the proportion of new infectives per unit time.
A Nonlinear k-ε Turbulence Model Applicable to High Pressure Gradient and Large Curvature Flow
Directory of Open Access Journals (Sweden)
Xiyao Gu
2014-01-01
Full Text Available Most of the RANS turbulence models solve the Reynolds stress by linear hypothesis with isotropic model. They can not capture all kinds of vortexes in the turbomachineries. In this paper, an improved nonlinear k-ε turbulence model is proposed, which is modified from the RNG k-ε turbulence model and Wilcox's k-ω turbulence model. The Reynolds stresses are solved by nonlinear methods. The nonlinear k-ε turbulence model can calculate the near wall region without the use of wall functions. The improved nonlinear k-ε turbulence model is used to simulate the flow field in a curved rectangular duct. The results based on the improved nonlinear k-ε turbulence model agree well with the experimental results. The calculation results prove that the nonlinear k-ε turbulence model is available for high pressure gradient flows and large curvature flows, and it can be used to capture complex vortexes in a turbomachinery.
Institute of Scientific and Technical Information of China (English)
GUO Qintao; ZHANG Lingmi; TAO Zheng
2008-01-01
Thin wall component is utilized to absorb impact energy of a structure. However, the dynamic behavior of such thin-walled structure is highly non-linear with material, geometry and boundary non-linearity. A model updating and validation procedure is proposed to build accurate finite element model of a frame structure with a non-linear thin-walled component for dynamic analysis. Design of experiments (DOE) and principal component decomposition (PCD) approach are applied to extract dynamic feature from nonlinear impact response for correlation of impact test result and FE model of the non-linear structure. A strain-rate-dependent non-linear model updating method is then developed to build accurate FE model of the structure. Computer simulation and a real frame structure with a highly non-linear thin-walled component are employed to demonstrate the feasibility and effectiveness of the proposed approach.
Empirical intrinsic geometry for nonlinear modeling and time series filtering.
Talmon, Ronen; Coifman, Ronald R
2013-07-30
In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.
On concurvity in nonlinear and nonparametric regression models
Directory of Open Access Journals (Sweden)
Sonia Amodio
2014-12-01
Full Text Available When data are affected by multicollinearity in the linear regression framework, then concurvity will be present in fitting a generalized additive model (GAM. The term concurvity describes nonlinear dependencies among the predictor variables. As collinearity results in inflated variance of the estimated regression coefficients in the linear regression model, the result of the presence of concurvity leads to instability of the estimated coefficients in GAMs. Even if the backfitting algorithm will always converge to a solution, in case of concurvity the final solution of the backfitting procedure in fitting a GAM is influenced by the starting functions. While exact concurvity is highly unlikely, approximate concurvity, the analogue of multicollinearity, is of practical concern as it can lead to upwardly biased estimates of the parameters and to underestimation of their standard errors, increasing the risk of committing type I error. We compare the existing approaches to detect concurvity, pointing out their advantages and drawbacks, using simulated and real data sets. As a result, this paper will provide a general criterion to detect concurvity in nonlinear and non parametric regression models.
2-D Composite Model for Numerical Simulations of Nonlinear Waves
Institute of Scientific and Technical Information of China (English)
2000-01-01
－ A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational region Ω is divided into two subregions. In the near-field around a structure, Ω2, the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulence closure model of k-ε equations and numerically solved by the improved VOF method; whereas in the subregion Ω1 (Ω1 = Ω - Ω2) the flow is governed by one-D Boussinesq equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundary of the two subregions. Numerical tests have been conducted for the case of wave propagation and interaction with a wave barrier. It is shown that the composite model can help perform efficient computation of nonlinear waves in a large region with the complicated flow fields near structures taken into account.
Nonlinear turbulence models for predicting strong curvature effects
Institute of Scientific and Technical Information of China (English)
XU Jing-lei; MA Hui-yang; HUANG Yu-ning
2008-01-01
Prediction of the characteristics of turbulent flows with strong streamline curvature, such as flows in turbomachines, curved channel flows, flows around airfoils and buildings, is of great importance in engineering applicatious and poses a very practical challenge for turbulence modeling. In this paper, we analyze qualitatively the curvature effects on the structure of turbulence and conduct numerical simulations of a turbulent U- duct flow with a number of turbulence models in order to assess their overall performance. The models evaluated in this work are some typical linear eddy viscosity turbulence models, nonlinear eddy viscosity turbulence models (NLEVM) (quadratic and cubic), a quadratic explicit algebraic stress model (EASM) and a Reynolds stress model (RSM) developed based on the second-moment closure. Our numerical results show that a cubic NLEVM that performs considerably well in other benchmark turbulent flows, such as the Craft, Launder and Suga model and the Huang and Ma model, is able to capture the major features of the highly curved turbulent U-duct flow, including the damping of turbulence near the convex wall, the enhancement of turbulence near the concave wall, and the subsequent turbulent flow separation. The predictions of the cubic models are quite close to that of the RSM, in relatively good agreement with the experimental data, which suggests that these inodels may be employed to simulate the turbulent curved flows in engineering applications.
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...
New holographic dark energy model with non-linear interaction
Oliveros, A
2014-01-01
In this paper the cosmological evolution of a holographic dark energy model with a non-linear interaction between the dark energy and dark matter components in a FRW type flat universe is analysed. In this context, the deceleration parameter $q$ and the equation state $w_{\\Lambda}$ are obtained. We found that, as the square of the speed of sound remains positive, the model is stable under perturbations since early times; it also shows that the evolution of the matter and dark energy densities are of the same order for a long period of time, avoiding the so--called coincidence problem. We have also made the correspondence of the model with the dark energy densities and pressures for the quintessence and tachyon fields. From this correspondence we have reconstructed the potential of scalar fields and their dynamics.
Nonlinear sensor fault diagnosis using mixture of probabilistic PCA models
Sharifi, Reza; Langari, Reza
2017-02-01
This paper presents a methodology for sensor fault diagnosis in nonlinear systems using a Mixture of Probabilistic Principal Component Analysis (MPPCA) models. This methodology separates the measurement space into several locally linear regions, each of which is associated with a Probabilistic PCA (PPCA) model. Using the transformation associated with each PPCA model, a parity relation scheme is used to construct a residual vector. Bayesian analysis of the residuals forms the basis for detection and isolation of sensor faults across the entire range of operation of the system. The resulting method is demonstrated in its application to sensor fault diagnosis of a fully instrumented HVAC system. The results show accurate detection of sensor faults under the assumption that a single sensor is faulty.
Sensor Fault Tolerant Generic Model Control for Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A modified Strong Tracking Filter (STF) is used to develop a new approach to sensor fault tolerant control. Generic Model Control (GMC) is used to control the nonlinear process while the process runs normally because of its robust control performance. If a fault occurs in the sensor, a sensor bias vector is then introduced to the output equation of the process model. The sensor bias vector is estimated on-line during every control period using the STF. The estimated sensor bias vector is used to develop a fault detection mechanism to supervise the sensors. When a sensor fault occurs, the conventional GMC is switched to a fault tolerant control scheme, which is, in essence, a state estimation and output prediction based GMC. The laboratory experimental results on a three-tank system demonstrate the effectiveness of the proposed Sensor Fault Tolerant Generic Model Control (SFTGMC) approach.
Nonlinear model accounting for minor hysteresis of embedded SMA actuators
Institute of Scientific and Technical Information of China (English)
YANG Kai; GU Chenglin
2007-01-01
A quantitative index martensite fraction was used to describe the phase transformation degree of shape memory alloy (SMA).On the basis of the martensite fraction,a nonlinear analysis model for major and minor hysteresis loops was developed.The model adopted two exponential equations to calculate the martensite fractions for cooling and heating,respectively.The martensite fractions were derived as the relative parameters were adjusted timely according to continuous,common initial and common limit constraints.By use of the linear relationship between the curvature of embedded SMA actuator and SMA's martensite fraction,the curvature was determined.The results of the simulations and experiments prove the validity and veracity of the model.
A NONLINEAR MATHEMATICAL MODEL FOR ASTHMA: EFFECT OF ENVIRONMENTAL POLLUTION
Directory of Open Access Journals (Sweden)
NARESHA RAM
2009-04-01
Full Text Available In this paper, we explore a nonlinear mathematical model to study the spread of asthma due to inhaled pollutants from industry as well as tobacco smoke from smokers in a variable size population. The model is analyzed using stability theory of differential equations and computer simulation. It is shown that with an increase in the level of air pollutants concentration, the asthmatic (diseased population increases. It is also shown that along with pollutants present in the environment, smoking (active or passive also helps in the spread of asthma. Moreover, with the increase in the rate of interaction between susceptibles and smokers, the persistence of the spread of asthma is higher. A numerical study of the model is also performed to see the role of certain key parameters on the spread of asthma and to support the analytical results.
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.
Nonlinear dynamic modeling of multicomponent batch distillation: a case study
Directory of Open Access Journals (Sweden)
Jiménez L.
2002-01-01
Full Text Available The aim of this work is to compare several of the commercial dynamic models for batch distillation available worldwide. In this context, BATCHFRAC(TM, CHEMCAD(TM BATCH, and HYSYS.Plant® software performances are compared to experimental data. The software can be used as soft sensors, playing the roll of ad-hoc observers or estimators for control objectives. Rigorous models were used as an alternative to predict the concentration profile and to specify the optimal switching time from products to slop cuts. The performance of a nonlinear model obtained using a novel identification algorithm was also studied. In addition, the strategy for continuous separation was revised with residue curve map analysis using Aspen SPLIT(TM.
Estimation of Nonlinear Dynamic Panel Data Models with Individual Effects
Directory of Open Access Journals (Sweden)
Yi Hu
2014-01-01
Full Text Available This paper suggests a generalized method of moments (GMM based estimation for dynamic panel data models with individual specific fixed effects and threshold effects simultaneously. We extend Hansen’s (Hansen, 1999 original setup to models including endogenous regressors, specifically, lagged dependent variables. To address the problem of endogeneity of these nonlinear dynamic panel data models, we prove that the orthogonality conditions proposed by Arellano and Bond (1991 are valid. The threshold and slope parameters are estimated by GMM, and asymptotic distribution of the slope parameters is derived. Finite sample performance of the estimation is investigated through Monte Carlo simulations. It shows that the threshold and slope parameter can be estimated accurately and also the finite sample distribution of slope parameters is well approximated by the asymptotic distribution.
Design Intelligent Model base Online Tuning Methodology for Nonlinear System
Directory of Open Access Journals (Sweden)
Ali Roshanzamir
2014-04-01
Full Text Available In various dynamic parameters systems that need to be training on-line adaptive control methodology is used. In this paper fuzzy model-base adaptive methodology is used to tune the linear Proportional Integral Derivative (PID controller. The main objectives in any systems are; stability, robust and reliability. However PID controller is used in many applications but it has many challenges to control of continuum robot. To solve these problems nonlinear adaptive methodology based on model base fuzzy logic is used. This research is used to reduce or eliminate the PID controller problems based on model reference fuzzy logic theory to control of flexible robot manipulator system and testing of the quality of process control in the simulation environment of MATLAB/SIMULINK Simulator.
Modelling of an ASR countercurrent pyrolysis reactor with nonlinear kinetics
Energy Technology Data Exchange (ETDEWEB)
Chiarioni, A.; Reverberi, A.P.; Dovi, V.G. [Universita degli Studi di Genova (Italy). Dipartimento di Ingegneria Chimica e di Processo ' G.B. Bonino' ; El-Shaarawi, A.H. [National Water Research Institute, Burlington, Ont. (Canada)
2003-10-01
The main objective of this work is focused on the modelling of a steady-state reactor where an automotive shredder residue (ASR) is subject to pyrolysis. The gas and solid temperature inside the reactor and the relevant density profiles of both phases are simulated for fixed values of the geometry of the apparatus and a lumped kinetic model is adopted to take into account the high heterogeneity of the ASR material. The key elements for the simulation are the inlet solid temperature and the outlet gas temperature. The problem is modelled by a system of first-order boundary-value ordinary differential equations and it is solved by means of a relaxation technique owing to the nonlinearities contained in the chemical kinetic expression. (author)
A note on nonlinear σ-models in noncommutative geometry
Lee, Hyun Ho
2016-03-01
We study nonlinear σ-models defined on a noncommutative torus as a two-dimensional string worldsheet. We consider (i) a two-point space, (ii) a circle, (iii) a noncommutative torus, (iv) a classical group SU(2, ℂ) as examples of space-time. Based on established results, the trivial harmonic unitaries of the noncommutative chiral model known as local minima are shown not to be global minima by comparing them to the symmetric unitaries derived from instanton solutions of the noncommutative Ising model corresponding to a two-point space. In addition, a ℤ2-action on field maps is introduced to a noncommutative torus, and its action on solutions of various Euler-Lagrange equations is described.
Quasilinear Extreme Learning Machine Model Based Internal Model Control for Nonlinear Process
Directory of Open Access Journals (Sweden)
Dazi Li
2015-01-01
Full Text Available A new strategy for internal model control (IMC is proposed using a regression algorithm of quasilinear model with extreme learning machine (QL-ELM. Aimed at the chemical process with nonlinearity, the learning process of the internal model and inverse model is derived. The proposed QL-ELM is constructed as a linear ARX model with a complicated nonlinear coefficient. It shows some good approximation ability and fast convergence. The complicated coefficients are separated into two parts. The linear part is determined by recursive least square (RLS, while the nonlinear part is identified through extreme learning machine. The parameters of linear part and the output weights of ELM are estimated iteratively. The proposed internal model control is applied to CSTR process. The effectiveness and accuracy of the proposed method are extensively verified through numerical results.
Riedl, M.; Suhrbier, A.; Malberg, H.; Penzel, T.; Bretthauer, G.; Kurths, J.; Wessel, N.
2008-07-01
The parameters of heart rate variability and blood pressure variability have proved to be useful analytical tools in cardiovascular physics and medicine. Model-based analysis of these variabilities additionally leads to new prognostic information about mechanisms behind regulations in the cardiovascular system. In this paper, we analyze the complex interaction between heart rate, systolic blood pressure, and respiration by nonparametric fitted nonlinear additive autoregressive models with external inputs. Therefore, we consider measurements of healthy persons and patients suffering from obstructive sleep apnea syndrome (OSAS), with and without hypertension. It is shown that the proposed nonlinear models are capable of describing short-term fluctuations in heart rate as well as systolic blood pressure significantly better than similar linear ones, which confirms the assumption of nonlinear controlled heart rate and blood pressure. Furthermore, the comparison of the nonlinear and linear approaches reveals that the heart rate and blood pressure variability in healthy subjects is caused by a higher level of noise as well as nonlinearity than in patients suffering from OSAS. The residue analysis points at a further source of heart rate and blood pressure variability in healthy subjects, in addition to heart rate, systolic blood pressure, and respiration. Comparison of the nonlinear models within and among the different groups of subjects suggests the ability to discriminate the cohorts that could lead to a stratification of hypertension risk in OSAS patients.
Identification of a Class of Non-linear State Space Models using RPE Techniques
DEFF Research Database (Denmark)
Zhou, Wei-Wu; Blanke, Mogens
1989-01-01
The RPE (recursive prediction error) method in state-space form is developed in the nonlinear systems and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions...... of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows a quite convincing performance of the filter as combined parameter and state estimator...
Output tracking and regulation of nonlinear system based on Takagi-Sugeno fuzzy model.
Ma, X J; Sun, Z Q
2000-01-01
On the basis of the Takagi-Sugeno (TS) fuzzy model, this paper discusses in detail the following three problems: (1) output tracking of the nonlinear system; (2) output regulation of the nonlinear system via a state feedback; (3) output regulation of the nonlinear system via a error feedback. Numerical simulations are given to illustrate the soundness of these results and the effectiveness of the new methodology solving the output tracking and regulation problem of the nonlinear system.
Study of Super-Twisting sliding mode control for U model based nonlinear system
Zhang, Jianhua; Li, Yang; Xueli WU; Jianan HUO; Shenyang ZHUANG
2016-01-01
The Super-Twisting control algorithm is adopted to analyze the U model based nonlinear control system in order to solve the controller design problems of non-affine nonlinear systems. The non-affine nonlinear systems are studied, the neural network approximation of the nonlinear function is performed, and the Super-Twisting control algorithm is used to control. The convergence of the Super-Twisting algorithm is proved by selecting an appropriate Lyapunov function. The Matlab simulation is car...
Fredette, Luke; Dreyer, Jason T.; Rook, Todd E.; Singh, Rajendra
2016-06-01
The dynamic stiffness properties of automotive hydraulic bushings exhibit significant amplitude sensitivity which cannot be captured by linear time-invariant models. Quasi-linear and nonlinear models are therefore proposed with focus on the amplitude sensitivity in magnitude and loss angle spectra (up to 50 Hz). Since production bushing model parameters are unknown, dynamic stiffness tests and laboratory experiments are utilized to extract model parameters. Nonlinear compliance and resistance elements are incorporated, including their interactions in order to improve amplitude sensitive predictions. New solution approximations for the new nonlinear system equations refine the multi-term harmonic balance term method. Quasi-linear models yield excellent accuracy but cannot predict trends in amplitude sensitivity since they rely on available dynamic stiffness measurements. Nonlinear models containing both nonlinear resistance and compliance elements yield superior predictions to those of prior models (with a single nonlinearity) while also providing more physical insight. Suggestion for further work is briefly mentioned.
Chaotic inflation from nonlinear sigma models in supergravity
Directory of Open Access Journals (Sweden)
Simeon Hellerman
2015-03-01
Full Text Available We present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu–Goldstone boson (NGB of a nonlinear sigma model. However, it is well known that nonlinear sigma models (NLSMs with nontrivial Kähler transformations are problematic to couple to supergravity. An additional field is necessary to make the Kähler potential of the NLSM invariant in supergravity. This field must have a shift symmetry — making it a candidate for the inflaton (or axion. We give an explicit example of such a model for the coset space SU(3/SU(2×U(1, with the Higgs as the NGB, including breaking the inflaton's shift symmetry and producing a chaotic inflation potential. This construction can also be applied to other models, such as one based on E7/SO(10×U(1×U(1 which incorporates the first two generations of (light quarks as the Nambu–Goldstone multiplets, and has an axion in addition to the inflaton. Along the way we clarify and connect previous work on understanding NLSMs in supergravity and the origin of the extra field (which is the inflaton here, including a connection to Witten–Bagger quantization. This framework has wide applications to model building; a light particle from a NLSM requires, in supergravity, exactly the structure for chaotic inflaton or an axion.
Chaotic inflation from nonlinear sigma models in supergravity
Hellerman, Simeon; Kehayias, John; Yanagida, Tsutomu T.
2015-03-01
We present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu-Goldstone boson (NGB) of a nonlinear sigma model. However, it is well known that nonlinear sigma models (NLSMs) with nontrivial Kähler transformations are problematic to couple to supergravity. An additional field is necessary to make the Kähler potential of the NLSM invariant in supergravity. This field must have a shift symmetry - making it a candidate for the inflaton (or axion). We give an explicit example of such a model for the coset space SU (3) / SU (2) × U (1), with the Higgs as the NGB, including breaking the inflaton's shift symmetry and producing a chaotic inflation potential. This construction can also be applied to other models, such as one based on E7 / SO (10) × U (1) × U (1) which incorporates the first two generations of (light) quarks as the Nambu-Goldstone multiplets, and has an axion in addition to the inflaton. Along the way we clarify and connect previous work on understanding NLSMs in supergravity and the origin of the extra field (which is the inflaton here), including a connection to Witten-Bagger quantization. This framework has wide applications to model building; a light particle from a NLSM requires, in supergravity, exactly the structure for chaotic inflaton or an axion.
Non-linear calibration models for near infrared spectroscopy
DEFF Research Database (Denmark)
Ni, Wangdong; Nørgaard, Lars; Mørup, Morten
2014-01-01
Different calibration techniques are available for spectroscopic applications that show nonlinear behavior. This comprehensive comparative study presents a comparison of different nonlinear calibration techniques: kernel PLS (KPLS), support vector machines (SVM), least-squares SVM (LS-SVM), relev...
Nonlinear Fuzzy Model Predictive Control for a PWR Nuclear Power Plant
Directory of Open Access Journals (Sweden)
Xiangjie Liu
2014-01-01
Full Text Available Reliable power and temperature control in pressurized water reactor (PWR nuclear power plant is necessary to guarantee high efficiency and plant safety. Since the nuclear plants are quite nonlinear, the paper presents nonlinear fuzzy model predictive control (MPC, by incorporating the realistic constraints, to realize the plant optimization. T-S fuzzy modeling on nuclear power plant is utilized to approximate the nonlinear plant, based on which the nonlinear MPC controller is devised via parallel distributed compensation (PDC scheme in order to solve the nonlinear constraint optimization problem. Improved performance compared to the traditional PID controller for a TMI-type PWR is obtained in the simulation.
Min-max model predictive control for constrained nonlinear systems via multiple LPV embeddings
Institute of Scientific and Technical Information of China (English)
ZHAO Min; LI Ning; LI ShaoYuan
2009-01-01
A min-max model predictive control strategy is proposed for a class of constrained nonlinear system whose trajectories can be embedded within those of a bank of linear parameter varying (LPV) models. The embedding LPV models can yield much better approximation of the nonlinear system dynamics than a single LTV model. For each LPV model, a parameter-dependent Lyapunov function is introduced to obtain poly-quadratically stable control law and to guarantee the feasibility and stability of the original nonlinear system. This approach can greatly reduce computational burden in traditional nonlinear predictive control strategy. Finally a simulation example illustrating the strategy is presented.
Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles
Kononova, Olga; Marx, Kenneth A; Wuite, Gijs J L; Roos, Wouter H; Barsegov, Valeri
2015-01-01
We present a new theory for modeling forced indentation spectral lineshapes of biological particles, which considers non-linear Hertzian deformation due to an indenter-particle physical contact and bending deformations of curved beams modeling the particle structure. The bending of beams beyond the critical point triggers the particle dynamic transition to the collapsed state, an extreme event leading to the catastrophic force drop as observed in the force (F)-deformation (X) spectra. The theory interprets fine features of the spectra: the slope of the FX curves and the position of force-peak signal, in terms of mechanical characteristics --- the Young's moduli for Hertzian and bending deformations E_H and E_b, and the probability distribution of the maximum strength with the strength of the strongest beam F_b^* and the beams' failure rate m. The theory is applied to successfully characterize the $FX$ curves for spherical virus particles --- CCMV, TrV, and AdV.
Nonlinear Model Predictive Control for Oil Reservoirs Management
DEFF Research Database (Denmark)
Capolei, Andrea
. With this objective function we link the optimization problem in production optimization to the Markowitz portfolio optimization problem in finance or to the the robust design problem in topology optimization. In this study we focus on open-loop configuration, i.e. without measurement feedback. We demonstrate......, the research community is working on improving current feedback model-based optimal control technologies. The topic of this thesis is production optimization for water flooding in the secondary phase of oil recovery. We developed numerical methods for nonlinear model predictive control (NMPC) of an oil field....... Further, we studied the use of robust control strategies in both open-loop, i.e. without measurement feedback, and closed-loop, i.e. with measurement feedback, configurations. This thesis has three main original contributions: The first contribution in this thesis is to improve the computationally...
Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation
Petráš, Ivo
2011-01-01
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...
MODELING NONLINEAR DYNAMICS OF CIRCULATING FLUIDIZED BEDS USING NEURAL NETWORKS
Institute of Scientific and Technical Information of China (English)
Wei; Chen; Atsushi; Tsutsumi; Haiyan; Lin; Kentaro; Otawara
2005-01-01
In the present work, artificial neural networks (ANNs) were proposed to model nonlinear dynamic behaviors of local voidage fluctuations induced by highly turbulent interactions between the gas and solid phases in circulating fluidized beds. The fluctuations of local voidage were measured by using an optical transmittance probe at various axial and radial positions in a circulating fluidized bed with a riser of 0.10 m in inner diameter and 10 m in height. The ANNs trained with experimental time series were applied to make short-term and long-term predictions of dynamic characteristics in the circulating fluidized bed. An early stop approach was adopted to enhance the long-term prediction capability of ANNs. The performance of the trained ANN was evaluated in terms of time-averaged characteristics, power spectra, cycle number and short-term predictability analysis of time series measured and predicted by the model.
The rigid-flexible nonlinear robotic manipulator: Modeling and control
Fenili, André; Balthazar, José Manoel
2011-05-01
The State-Dependent Riccati Equation (SDRE) control of a nonlinear rigid-flexible two link robotic manipulator is investigated. Different cases are considered assuming small deviations and large deviations from the desired final states. The nonlinear governing equations of motion are coupled, providing considerable excitation of all the nonlinear terms. The results present satisfactory final states but also undesirable overshoot.
Nonlinear inverse modeling of sensor based on back-propagation fuzzy logical system
Institute of Scientific and Technical Information of China (English)
Li Jun; Liu Junhua
2007-01-01
Objective To correct the nonlinear error of sensor output, a new approach to sensor inverse modeling based on Back-Propagation Fuzzy Logical System (BP FS) is presented. Methods The BP FS is a computationally efficient nonlinear universal approximator, which is capable of implementing complex nonlinear mapping from its input pattern space to the output with fast convergence speed. Results The neuro-fuzzy hybrid system, i.e. BP FS, is then applied to construct nonlinear inverse model of pressure sensor. The experimental results show that the proposed inverse modeling method automatically compensates the associated nonlinear error in pressure estimation, and thus the performance of pressure sensor is significantly improved. Conclusion The proposed method can be widely used in nonlinearity correction of various kinds of sensors to compensate the effects of nonlinearity and temperature on sensor output.
Study of unsteady cavitation on NACA66 hydrofoil using dynamic cubic nonlinear subgrid-scale model
Directory of Open Access Journals (Sweden)
Xianbei Huang
2015-11-01
Full Text Available In this article, we describe the use of a new dynamic cubic nonlinear model, a new nonlinear subgrid-scale model, for simulating the cavitating flow around an NACA66 series hydrofoil. For comparison, the dynamic Smagorinsky model is also used. It is found that the dynamic cubic nonlinear model can capture the turbulence spectrum, while the dynamic Smagorinsky model fails. Both models reproduce the cavity growth/destabilization cycle, but the results of the dynamic cubic nonlinear model are much smoother. The re-entrant jet is clearly captured by the models, and it is shown that the re-entrant jet cuts the cavity into two parts. In general, the dynamic cubic nonlinear model provides improvement over the dynamic Smagorinsky model for the calculation of cavitating flow.
Nonlinear system modeling with random matrices: echo state networks revisited.
Zhang, Bai; Miller, David J; Wang, Yue
2012-01-01
Echo state networks (ESNs) are a novel form of recurrent neural networks (RNNs) that provide an efficient and powerful computational model approximating nonlinear dynamical systems. A unique feature of an ESN is that a large number of neurons (the "reservoir") are used, whose synaptic connections are generated randomly, with only the connections from the reservoir to the output modified by learning. Why a large randomly generated fixed RNN gives such excellent performance in approximating nonlinear systems is still not well understood. In this brief, we apply random matrix theory to examine the properties of random reservoirs in ESNs under different topologies (sparse or fully connected) and connection weights (Bernoulli or Gaussian). We quantify the asymptotic gap between the scaling factor bounds for the necessary and sufficient conditions previously proposed for the echo state property. We then show that the state transition mapping is contractive with high probability when only the necessary condition is satisfied, which corroborates and thus analytically explains the observation that in practice one obtains echo states when the spectral radius of the reservoir weight matrix is smaller than 1.
Nonlinear damping calculation in cylindrical gear dynamic modeling
Guilbault, Raynald; Lalonde, Sébastien; Thomas, Marc
2012-04-01
The nonlinear dynamic problem posed by cylindrical gear systems has been extensively covered in the literature. Nonetheless, a significant proportion of the mechanisms involved in damping generation remains to be investigated and described. The main objective of this study is to contribute to this task. Overall, damping is assumed to consist of three sources: surrounding element contribution, hysteresis of the teeth, and oil squeeze damping. The first two contributions are considered to be commensurate with the supported load; for its part however, squeeze damping is formulated using expressions developed from the Reynolds equation. A lubricated impact analysis between the teeth is introduced in this study for the minimum film thickness calculation during contact losses. The dynamic transmission error (DTE) obtained from the final model showed close agreement with experimental measurements available in the literature. The nonlinear damping ratio calculated at different mesh frequencies and torque amplitudes presented average values between 5.3 percent and 8 percent, which is comparable to the constant 8 percent ratio used in published numerical simulations of an equivalent gear pair. A close analysis of the oil squeeze damping evidenced the inverse relationship between this damping effect and the applied load.
Nonlinear sigma models with compact hyperbolic target spaces
Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James
2016-06-01
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1, 2]. Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Saturable Lorentz model for fully explicit three-dimensional modeling of nonlinear optics
Varin, Charles; Emms, Rhys; Brabec, Thomas
2014-01-01
Inclusion of the instantaneous Kerr nonlinearity in the FDTD framework leads to implicit equations that have to be solved iteratively. In principle, explicit integration can be achieved with the use of anharmonic oscillator equations, but it tends to be unstable and inappropriate for studying strong-field phenomena like laser filamentation. In this paper, we show that nonlinear susceptibility can be provided instead by an harmonic oscillator driven by a nonlinear force. When the nonlinear force is tailored to mimic atomic transition saturation, the model agree quantitatively with the quantum mechanical solutions of a two-level system, up to the 9th harmonic. Moreover, we demonstrate that fully explicit leapfrog integration of the saturable harmonic oscillator is stable, even for the intense laser fields that characterize laser filamentation and high harmonic generation.
Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.
2015-10-01
An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit
Pakarzadeh, H.; Rezaei, S. M.
2016-01-01
In this article, we investigate for the first time the dispersion and the nonlinear characteristics of the tapered photonic crystal fibers (PCFs) as a function of length z, via solving the eigenvalue equation of the guided mode using the finite-difference frequency-domain method. Since the structural parameters such as the air-hole diameter and the pitch of the microstructured cladding change along the tapered PCFs, dispersion and nonlinear properties change with the length as well. Therefore, it is important to know the exact behavior of such fiber parameters along z which is necessary for nonlinear optics applications. We simulate the z dependency of the zero-dispersion wavelength, dispersion slope, effective mode area, nonlinear parameter, and the confinement loss along the tapered PCFs and propose useful relations for describing dispersion and nonlinear parameters. The results of this article, which are in a very good agreement with the available experimental data, are important for simulating pulse propagation as well as investigating nonlinear effects such as supercontinuum generation and parametric amplification in tapered PCFs.
Modeling of the nonlinear resonant response in sedimentary rocks
Energy Technology Data Exchange (ETDEWEB)
Ten Cate, James A [Los Alamos National Laboratory; Shankland, Thomas J [Los Alamos National Laboratory; Vakhnenko, Vyacheslav O [NON LANL; Vakhnenko, Oleksiy [NON LANL
2009-04-03
We suggest a model for describing a wide class of nonlinear and hysteretic effects in sedimentary rocks at longitudinal bar resonance. In particular, we explain: hysteretic behaviour of a resonance curve on both its upward and downward slopes; linear softening of resonant frequency with increase of driving level; gradual (almost logarithmic) recovery of resonant frequency after large dynamical strains; and temporal relaxation of response amplitude at fixed frequency. Starting with a suggested model, we predict the dynamical realization of end-point memory in resonating bar experiments with a cyclic frequency protocol. These theoretical findings were confirmed experimentally at Los Alamos National Laboratory. Sedimentary rocks, particularly sandstones, are distinguished by their grain structure in which each grain is much harder than the intergrain cementation material. The peculiarities of grain and pore structures give rise to a variety of remarkable nonlinear mechanical properties demonstrated by rocks, both at quasistatic and alternating dynamic loading. Thus, the hysteresis earlier established for the stress-strain relation in samples subjected to quasistatic loading-unloading cycles has also been discovered for the relation between acceleration amplitude and driving frequency in bar-shaped samples subjected to an alternating external drive that is frequency-swept through resonance. At strong drive levels there is an unusual, almost linear decrease of resonant frequency with strain amplitude, and there are long-term relaxation phenomena such as nearly logarithmic recovery (increase) of resonant frequency after the large conditioning drive has been removed. In this report we present a short sketch of a model for explaining numerous experimental observations seen in forced longitudinal oscillations of sandstone bars. According to our theory a broad set of experimental data can be understood as various aspects of the same internally consistent pattern. Furthermore
Extended nonlinear feedback model for describing episodes of high inflation
Szybisz, Martín A.; Szybisz, Leszek
2017-01-01
An extension of the nonlinear feedback (NLF) formalism to describe regimes of hyper- and high-inflation in economy is proposed in the present work. In the NLF model the consumer price index (CPI) exhibits a finite time singularity of the type 1 /(tc - t) (1 - β) / β, with β > 0, predicting a blow up of the economy at a critical time tc. However, this model fails in determining tc in the case of weak hyperinflation regimes like, e.g., that occurred in Israel. To overcome this trouble, the NLF model is extended by introducing a parameter γ, which multiplies all terms with past growth rate index (GRI). In this novel approach the solution for CPI is also analytic being proportional to the Gaussian hypergeometric function 2F1(1 / β , 1 / β , 1 + 1 / β ; z) , where z is a function of β, γ, and tc. For z → 1 this hypergeometric function diverges leading to a finite time singularity, from which a value of tc can be determined. This singularity is also present in GRI. It is shown that the interplay between parameters β and γ may produce phenomena of multiple equilibria. An analysis of the severe hyperinflation occurred in Hungary proves that the novel model is robust. When this model is used for examining data of Israel a reasonable tc is got. High-inflation regimes in Mexico and Iceland, which exhibit weaker inflations than that of Israel, are also successfully described.
The Mathematics of Psychotherapy: A Nonlinear Model of Change Dynamics.
Schiepek, Gunter; Aas, Benjamin; Viol, Kathrin
2016-07-01
Psychotherapy is a dynamic process produced by a complex system of interacting variables. Even though there are qualitative models of such systems the link between structure and function, between network and network dynamics is still missing. The aim of this study is to realize these links. The proposed model is composed of five state variables (P: problem severity, S: success and therapeutic progress, M: motivation to change, E: emotions, I: insight and new perspectives) interconnected by 16 functions. The shape of each function is modified by four parameters (a: capability to form a trustful working alliance, c: mentalization and emotion regulation, r: behavioral resources and skills, m: self-efficacy and reward expectation). Psychologically, the parameters play the role of competencies or traits, which translate into the concept of control parameters in synergetics. The qualitative model was transferred into five coupled, deterministic, nonlinear difference equations generating the dynamics of each variable as a function of other variables. The mathematical model is able to reproduce important features of psychotherapy processes. Examples of parameter-dependent bifurcation diagrams are given. Beyond the illustrated similarities between simulated and empirical dynamics, the model has to be further developed, systematically tested by simulated experiments, and compared to empirical data.
Non-linear model for compression tests on articular cartilage.
Grillo, Alfio; Guaily, Amr; Giverso, Chiara; Federico, Salvatore
2015-07-01
Hydrated soft tissues, such as articular cartilage, are often modeled as biphasic systems with individually incompressible solid and fluid phases, and biphasic models are employed to fit experimental data in order to determine the mechanical and hydraulic properties of the tissues. Two of the most common experimental setups are confined and unconfined compression. Analytical solutions exist for the unconfined case with the linear, isotropic, homogeneous model of articular cartilage, and for the confined case with the non-linear, isotropic, homogeneous model. The aim of this contribution is to provide an easily implementable numerical tool to determine a solution to the governing differential equations of (homogeneous and isotropic) unconfined and (inhomogeneous and isotropic) confined compression under large deformations. The large-deformation governing equations are reduced to equivalent diffusive equations, which are then solved by means of finite difference (FD) methods. The solution strategy proposed here could be used to generate benchmark tests for validating complex user-defined material models within finite element (FE) implementations, and for determining the tissue's mechanical and hydraulic properties from experimental data.
Nonlinear dynamics approach of modeling the bifurcation for aircraft wing flutter in transonic speed
DEFF Research Database (Denmark)
Matsushita, Hiroshi; Miyata, T.; Christiansen, Lasse Engbo
2002-01-01
The procedure of obtaining the two-degrees-of-freedom, finite dimensional. nonlinear mathematical model. which models the nonlinear features of aircraft flutter in transonic speed is reported. The model enables to explain every feature of the transonic flutter data of the wind tunnel tests...
Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS
DEFF Research Database (Denmark)
Bolker, B.M.; Gardner, B.; Maunder, M.
2013-01-01
) to specific suggestions about how to change the mathematical description of models to make them more amenable to parameter estimation. A companion web site (https://groups.nceas.ucsb.edu/nonlinear-modeling/projects) presents detailed examples of application of the three tools to a variety of typical...
Sensorless position estimator applied to nonlinear IPMC model
Bernat, Jakub; Kolota, Jakub
2016-11-01
This paper addresses the issue of estimating position for an ionic polymer metal composite (IPMC) known as electro active polymer (EAP). The key step is the construction of a sensorless mode considering only current feedback. This work takes into account nonlinearities caused by electrochemical effects in the material. Owing to the recent observer design technique, the authors obtained both Lyapunov function based estimation law as well as sliding mode observer. To accomplish the observer design, the IPMC model was identified through a series of experiments. The research comprises time domain measurements. The identification process was completed by means of geometric scaling of three test samples. In the proposed design, the estimated position accurately tracks the polymer position, which is illustrated by the experiments.
Nonlinear model predictive control based on collective neurodynamic optimization.
Yan, Zheng; Wang, Jun
2015-04-01
In general, nonlinear model predictive control (NMPC) entails solving a sequential global optimization problem with a nonconvex cost function or constraints. This paper presents a novel collective neurodynamic optimization approach to NMPC without linearization. Utilizing a group of recurrent neural networks (RNNs), the proposed collective neurodynamic optimization approach searches for optimal solutions to global optimization problems by emulating brainstorming. Each RNN is guaranteed to converge to a candidate solution by performing constrained local search. By exchanging information and iteratively improving the starting and restarting points of each RNN using the information of local and global best known solutions in a framework of particle swarm optimization, the group of RNNs is able to reach global optimal solutions to global optimization problems. The essence of the proposed collective neurodynamic optimization approach lies in the integration of capabilities of global search and precise local search. The simulation results of many cases are discussed to substantiate the effectiveness and the characteristics of the proposed approach.
Nonlinear Dynamics of Dipoles in Microtubules: Pseudo-Spin Model
Nesterov, Alexander I; Berman, Gennady P; Mavromatos, Nick E
2016-01-01
We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frames of the classical pseudo-spin model. We derive the system of nonlinear dynamical ordinary differential equations of motion for interacting dipoles, and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.
Nonlinear dynamics of dipoles in microtubules: Pseudospin model.
Nesterov, Alexander I; Ramírez, Mónica F; Berman, Gennady P; Mavromatos, Nick E
2016-06-01
We perform a theoretical study of the dynamics of the electric field excitations in a microtubule by taking into consideration the realistic cylindrical geometry, dipole-dipole interactions of the tubulin-based protein heterodimers, the radial electric field produced by the solvent, and a possible degeneracy of energy states of individual heterodimers. The consideration is done in the frame of the classical pseudospin model. We derive the system of nonlinear dynamical partial differential equations of motion for interacting dipoles and the continuum version of these equations. We obtain the solutions of these equations in the form of snoidal waves, solitons, kinks, and localized spikes. Our results will help to achieve a better understanding of the functional properties of microtubules including the motor protein dynamics and the information transfer processes. Our considerations are based on classical dynamics. Some speculations on the role of possible quantum effects are also made.
Non-linear rheology in a model biological tissue
Matoz-Fernandez, D A; Barrat, Jean-Louis; Bertin, Eric; Martens, Kirsten
2016-01-01
Mechanical signaling plays a key role in biological processes like embryo development and cancer growth. One prominent way to probe mechanical properties of tissues is to study their response to externally applied forces. Using a particle-based model featuring random apoptosis and environment-dependent division rates, we evidence a crossover from linear flow to a shear-thinning regime with increasing shear rate. To rationalize this non-linear flow we derive a theoretical mean-field scenario that accounts for the interplay of mechanical and active noise in local stresses. These noises are respectively generated by the elastic response of the cell matrix to cell rearrangements and by the internal activity.
Stabilizing model predictive control for constrained nonlinear distributed delay systems.
Mahboobi Esfanjani, R; Nikravesh, S K Y
2011-04-01
In this paper, a model predictive control scheme with guaranteed closed-loop asymptotic stability is proposed for a class of constrained nonlinear time-delay systems with discrete and distributed delays. A suitable terminal cost functional and also an appropriate terminal region are utilized to achieve asymptotic stability. To determine the terminal cost, a locally asymptotically stabilizing controller is designed and an appropriate Lyapunov-Krasoskii functional of the locally stabilized system is employed as the terminal cost. Furthermore, an invariant set for locally stabilized system which is established by using the Razumikhin Theorem is used as the terminal region. Simple conditions are derived to obtain terminal cost and terminal region in terms of Bilinear Matrix Inequalities. The method is illustrated by a numerical example.
Effective action and vacuum expectations in nonlinear $\\sigma$ model
Fayzullaev, B A
2015-01-01
The equations for effective action for nonlinear $\\sigma$ model are derived using DeWitt method in two forms - for generator of vertex parts $\\Gamma$ and for generator of weakly connected parts $W$. Loop-expansion solutions to these equations are found. It is shown that vacuum expectation values for various quantities including divergence of a N\\"{o}ther current, trace of the energy-momentum tensor and so on, can be calculated by this method. Also it is shown that vacuum expectation to the sigma-field is determined by an explicit combination of tree Green function and classical solution. It is shown that the limit when coupling constant tends to zero is singular one.
Nonlinear model predictive control of managed pressure drilling.
Nandan, Anirudh; Imtiaz, Syed
2017-07-01
A new design of nonlinear model predictive controller (NMPC) is proposed for managed pressure drilling (MPD) system. The NMPC is based on output feedback control architecture and employs offset-free formulation proposed in [1]. NMPC uses active set method for computing control inputs. The controller implements an automatic switching from constant bottom hole pressure (CBHP) regulation to flow control mode in the event of a reservoir kick. In the flow control mode the controller automatically raises the bottom hole pressure setpoint, and thereby keeps the reservoir fluid flow to the surface within a tunable threshold. This is achieved by exploiting constraint handling capability of NMPC. In addition to kick mitigation the controller demonstrated good performance in containing the bottom hole pressure (BHP) during the pipe connection sequence. The controller also delivered satisfactory performance in the presence of measurement noise and uncertainty in the system. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
A nonlinear model for rotationally constrained convection with Ekman pumping
Julien, Keith; Calkins, Michael A; Knobloch, Edgar; Marti, Philippe; Stellmach, Stephan; Vasil, Geoffrey M
2016-01-01
It is a well established result of linear theory that the influence of differing mechanical boundary conditions, i.e., stress-free or no-slip, on the primary instability in rotating convection becomes asymptotically small in the limit of rapid rotation. This is accounted for by the diminishing impact of the viscous stresses exerted within Ekman boundary layers and the associated vertical momentum transport by Ekman pumping. By contrast, in the nonlinear regime recent experiments and supporting simulations are now providing evidence that the efficiency of heat transport remains strongly influenced by Ekman pumping in the rapidly rotating limit. In this paper, a reduced model is developed for the case of low Rossby number convection in a plane layer geometry with no-slip upper and lower boundaries held at fixed temperatures. A complete description of the dynamics requires the existence of three distinct regions within the fluid layer: a geostrophically balanced interior where fluid motions are predominately ali...
Nonlinear model predictive control for chemical looping process
Energy Technology Data Exchange (ETDEWEB)
Joshi, Abhinaya; Lei, Hao; Lou, Xinsheng
2017-08-22
A control system for optimizing a chemical looping ("CL") plant includes a reduced order mathematical model ("ROM") that is designed by eliminating mathematical terms that have minimal effect on the outcome. A non-linear optimizer provides various inputs to the ROM and monitors the outputs to determine the optimum inputs that are then provided to the CL plant. An estimator estimates the values of various internal state variables of the CL plant. The system has one structure adapted to control a CL plant that only provides pressure measurements in the CL loops A and B, a second structure adapted to a CL plant that provides pressure measurements and solid levels in both loops A, and B, and a third structure adapted to control a CL plant that provides full information on internal state variables. A final structure provides a neural network NMPC controller to control operation of loops A and B.
Modeling and compensation of transmitter nonlinearity in coherent optical OFDM.
Amiralizadeh, Siamak; Nguyen, An T; Rusch, Leslie A
2015-10-05
We present a comprehensive study of nonlinear distortions from an optical OFDM transmitter. Nonlinearities are introduced by the combination of effects from the digital-to-analog converter (DAC), electrical power amplifier (PA) and optical modulator in the presence of high peak-to-average power ratio (PAPR). We introduce parameters to quantify the transmitter nonlinearity. High input backoff avoids OFDM signal compression from the PA, but incurs high penalties in power efficiency. At low input backoff, common PAPR reduction techniques are not effective in suppressing the PA nonlinear distortion. A bit error distribution investigation shows a technique combining nonlinear predistortion with PAPR mitigation could achieve good power efficiency by allowing low input backoff. We use training symbols to extract the transmitter nonlinear function. We show that piecewise linear interpolation (PLI) leads to an accurate transmitter nonlinearity characterization. We derive a semi-analytical solution for bit error rate (BER) that validates the PLI approximation accurately captures transmitter nonlinearity. The inverse of the PLI estimate of the nonlinear function is used as a predistorter to suppress transmitter nonlinearity. We investigate performance of the proposed scheme by Monte Carlo simulations. Our simulations show that when DAC resolution is more than 4 bits, BER below forward error correction limit of 3.8 × 10(-3) can be achieved by using predistortion with very low input power backoff for electrical PA and optical modulator.
Lukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models
Baianu, I C
2004-01-01
A categorical and Lukasiewicz-Topos framework for Lukasiewicz Algebraic Logic models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes is proposed. Lukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Lukasiewicz Topos with an n-valued Lukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis.
Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles.
Directory of Open Access Journals (Sweden)
Olga Kononova
2016-01-01
Full Text Available The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams modeling the particle structure. The beams' deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F-deformation (X spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young's moduli for Hertzian and bending deformations, and the structural damage dependent beams' survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications.
Modelling female fertility traits in beef cattle using linear and non-linear models.
Naya, H; Peñagaricano, F; Urioste, J I
2017-06-01
Female fertility traits are key components of the profitability of beef cattle production. However, these traits are difficult and expensive to measure, particularly under extensive pastoral conditions, and consequently, fertility records are in general scarce and somehow incomplete. Moreover, fertility traits are usually dominated by the effects of herd-year environment, and it is generally assumed that relatively small margins are kept for genetic improvement. New ways of modelling genetic variation in these traits are needed. Inspired in the methodological developments made by Prof. Daniel Gianola and co-workers, we assayed linear (Gaussian), Poisson, probit (threshold), censored Poisson and censored Gaussian models to three different kinds of endpoints, namely calving success (CS), number of days from first calving (CD) and number of failed oestrus (FE). For models involving FE and CS, non-linear models overperformed their linear counterparts. For models derived from CD, linear versions displayed better adjustment than the non-linear counterparts. Non-linear models showed consistently higher estimates of heritability and repeatability in all cases (h(2 ) 0.23 and r > 0.24, for non-linear models). While additive and permanent environment effects showed highly favourable correlations between all models (>0.789), consistency in selecting the 10% best sires showed important differences, mainly amongst the considered endpoints (FE, CS and CD). In consequence, endpoints should be considered as modelling different underlying genetic effects, with linear models more appropriate to describe CD and non-linear models better for FE and CS. © 2017 Blackwell Verlag GmbH.
Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS
Bolker, Benjamin M.; Gardner, Beth; Maunder, Mark; Berg, Casper W.; Brooks, Mollie; Comita, Liza; Crone, Elizabeth; Cubaynes, Sarah; Davies, Trevor; de Valpine, Perry; Ford, Jessica; Gimenez, Olivier; Kéry, Marc; Kim, Eun Jung; Lennert-Cody, Cleridy; Magunsson, Arni; Martell, Steve; Nash, John; Nielson, Anders; Regentz, Jim; Skaug, Hans; Zipkin, Elise
2013-01-01
1. Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open-source model fitting tools and discusses general strategies for defining and fitting models. 2. R is convenient and (relatively) easy to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. 3. Our model-fitting suggestions range from general cultural advice (where possible, use the tools and models that are most common in your subfield) to specific suggestions about how to change the mathematical description of models to make them more amenable to parameter estimation. 4. A companion web site (https://groups.nceas.ucsb.edu/nonlinear-modeling/projects) presents detailed examples of application of the three tools to a variety of typical ecological estimation problems; each example links both to a detailed project report and to full source code and data.
Simple models for quorum sensing: Nonlinear dynamical analysis
Chiang, Wei-Yin; Li, Yue-Xian; Lai, Pik-Yin
2011-10-01
Quorum sensing refers to the change in the cooperative behavior of a collection of elements in response to the change in their population size or density. This behavior can be observed in chemical and biological systems. These elements or cells are coupled via chemicals in the surrounding environment. Here we focus on the change of dynamical behavior, in particular from quiescent to oscillatory, as the cell population changes. For instance, the silent behavior of the elements can become oscillatory as the system concentration or population increases. In this work, two simple models are constructed that can produce the essential representative properties in quorum sensing. The first is an excitable or oscillatory phase model, which is probably the simplest model one can construct to describe quorum sensing. Using the mean-field approximation, the parameter regime for quorum sensing behavior can be identified, and analytical results for the detailed dynamical properties, including the phase diagrams, are obtained and verified numerically. The second model consists of FitzHugh-Nagumo elements coupled to the signaling chemicals in the environment. Nonlinear dynamical analysis of this mean-field model exhibits rich dynamical behaviors, such as infinite period bifurcation, supercritical Hopf, fold bifurcation, and subcritical Hopf bifurcations as the population parameter changes for different coupling strengths. Analytical result is obtained for the Hopf bifurcation phase boundary. Furthermore, two elements coupled via the environment and their synchronization behavior for these two models are also investigated. For both models, it is found that the onset of oscillations is accompanied by the synchronized dynamics of the two elements. Possible applications and extension of these models are also discussed.
Intelligent modeling and identification of aircraft nonlinear flight
Institute of Scientific and Technical Information of China (English)
Alireza Roudbari; Fariborz Saghafi
2014-01-01
In this paper, a new approach has been proposed to identify and model the dynamics of a highly maneuverable fighter aircraft through artificial neural networks (ANNs). In general, air-craft flight dynamics is considered as a nonlinear and coupled system whose modeling through ANNs, unlike classical approaches, does not require any aerodynamic or propulsion information and a few flight test data seem sufficient. In this study, for identification and modeling of the aircraft dynamics, two known structures of internal and external recurrent neural networks (RNNs) and a proposed structure called hybrid combined recurrent neural network have been used and compared. In order to improve the training process, an appropriate evolutionary method has been applied to simultaneously train and optimize the parameters of ANNs. In this research, it has been shown that six ANNs each with three inputs and one output, trained by flight test data, can model the dynamic behavior of the highly maneuverable aircraft with acceptable accuracy and without any priori knowledge about the system.
Nonlinear FOPDT Model Identification for the Superheat Dynamic in a Refrigeration System
DEFF Research Database (Denmark)
Yang, Zhenyu; Sun, Zhen; Andersen, Casper
2011-01-01
the considered system is discretized, the nonlinear FOPDT identification problem is formulated as a Mixed Integer Non-Linear Programming problem, and then an identification algorithm is proposed by combining the Branch-and-Bound method and Least Square technique, in order to on-line identify these time......An on-line nonlinear FOPDT system identification method is proposed and applied to model the superheat dynamic in a supermarket refrigeration system. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its parameters are time dependent. After...
Institute of Scientific and Technical Information of China (English)
AN Zhi-Wu; WANG Xiao-Min; LI Ming-Xuan; DENG Ming-Xi; MAO Jie
2009-01-01
Based on the exact solutions for the second-harmonic generations of the fundamental longitudinal and transverse waves propagating normally through a thin elastic layer between two solids, the approximate representations termed as 'nonlinear spring models' relating the stresses and displacements on both sides of the interface are rigorously developed by asymptotic expansions of the wave fields for an elastic layer in the limit of small thickness to wavelength ratio. The applicability for the so-called nonlinear spring models is numerically analyzed by comparison with exact solutions for the second harmonic wave reflections. The present nonlinear spring models lay a theoretical foundation to evaluate the interracial properties by nonlinear acoustic waves.
An Improved Nonlinear Circuit Model for GaAs Gunn Diode in W-Band Oscillator
Zhang, Bo; Fan, Yong; Zhang, Yonghong
An improved nonlinear circuit model for a GaAs Gunn diode in an oscillator is proposed based on the physical mechanism of the diode. This model interprets the nonlinear harmonic character on the Gunn diode. Its equivalent nonlinear circuit of which can assist in the design of the Gunn oscillator and help in the analysis of the fundamental and harmonic characteristics of the GaAs Gunn diode. The simulation prediction and the experiment of the Gunn oscillator show the feasibility of the nonlinear circuit model for the GaAs Gunn oscillator.
Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin
2016-08-01
This paper proposes a new nonlinear joint model updating method for shear type structures based on the instantaneous characteristics of the decomposed structural dynamic responses. To obtain an accurate representation of a nonlinear system's dynamics, the nonlinear joint model is described as the nonlinear spring element with bilinear stiffness. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by the analytical mode decomposition (AMD) method. Then, an objective function based on the residuals of the instantaneous frequencies and amplitudes between the experimental structure and the nonlinear model is created for the nonlinear joint model updating. The optimal values of the nonlinear joint model parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a single-story shear type structure subjected to earthquake and harmonic excitations is simulated as a numerical example. Then, a beam structure with multiple local nonlinear elements subjected to earthquake excitation is also simulated. The nonlinear beam structure is updated based on the global and local model using the proposed method. The results show that the proposed local nonlinear model updating method is more effective for structures with multiple local nonlinear elements. Finally, the proposed method is verified by the shake table test of a real high voltage switch structure. The accuracy of the proposed method is quantified both in numerical and experimental applications using the defined error indices. Both the numerical and experimental results have shown that the proposed method can effectively update the nonlinear joint model.
Using nonlinear models in fMRI data analysis: model selection and activation detection.
Deneux, Thomas; Faugeras, Olivier
2006-10-01
There is an increasing interest in using physiologically plausible models in fMRI analysis. These models do raise new mathematical problems in terms of parameter estimation and interpretation of the measured data. In this paper, we show how to use physiological models to map and analyze brain activity from fMRI data. We describe a maximum likelihood parameter estimation algorithm and a statistical test that allow the following two actions: selecting the most statistically significant hemodynamic model for the measured data and deriving activation maps based on such model. Furthermore, as parameter estimation may leave much incertitude on the exact values of parameters, model identifiability characterization is a particular focus of our work. We applied these methods to different variations of the Balloon Model (Buxton, R.B., Wang, E.C., and Frank, L.R. 1998. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn. Reson. Med. 39: 855-864; Buxton, R.B., Uludağ, K., Dubowitz, D.J., and Liu, T.T. 2004. Modelling the hemodynamic response to brain activation. NeuroImage 23: 220-233; Friston, K. J., Mechelli, A., Turner, R., and Price, C. J. 2000. Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics. NeuroImage 12: 466-477) in a visual perception checkerboard experiment. Our model selection proved that hemodynamic models better explain the BOLD response than linear convolution, in particular because they are able to capture some features like poststimulus undershoot or nonlinear effects. On the other hand, nonlinear and linear models are comparable when signals get noisier, which explains that activation maps obtained in both frameworks are comparable. The tools we have developed prove that statistical inference methods used in the framework of the General Linear Model might be generalized to nonlinear models.
Computational Modeling of Ultrafast Pulse Propagation in Nonlinear Optical Materials
Goorjian, Peter M.; Agrawal, Govind P.; Kwak, Dochan (Technical Monitor)
1996-01-01
There is an emerging technology of photonic (or optoelectronic) integrated circuits (PICs or OEICs). In PICs, optical and electronic components are grown together on the same chip. rib build such devices and subsystems, one needs to model the entire chip. Accurate computer modeling of electromagnetic wave propagation in semiconductors is necessary for the successful development of PICs. More specifically, these computer codes would enable the modeling of such devices, including their subsystems, such as semiconductor lasers and semiconductor amplifiers in which there is femtosecond pulse propagation. Here, the computer simulations are made by solving the full vector, nonlinear, Maxwell's equations, coupled with the semiconductor Bloch equations, without any approximations. The carrier is retained in the description of the optical pulse, (i.e. the envelope approximation is not made in the Maxwell's equations), and the rotating wave approximation is not made in the Bloch equations. These coupled equations are solved to simulate the propagation of femtosecond optical pulses in semiconductor materials. The simulations describe the dynamics of the optical pulses, as well as the interband and intraband.
Charge quantization in the CP(1) nonlinear σ-model
Energy Technology Data Exchange (ETDEWEB)
Hellerman, Simeon, E-mail: simeon.hellerman.1@gmail.com; Kehayias, John, E-mail: john.kehayias@ipmu.jp; Yanagida, Tsutomu T., E-mail: tsutomu.tyanagida@ipmu.jp
2014-01-20
We investigate the consistency conditions for matter fields coupled to the four-dimensional (N=1 supersymmetric) CP(1) nonlinear sigma model (the coset space SU(2){sub G}/U(1){sub H}). We find that consistency requires that the U(1){sub H} charge of the matter be quantized, in units of half of the U(1){sub H} charge of the Nambu–Goldstone (NG) boson, if the matter has a nonsingular kinetic term and the dynamics respect the full group SU(2){sub G}. We can then take the linearly realized group U(1){sub H} to comprise the weak hypercharge group U(1){sub Y} of the Standard Model. Thus we have charge quantization without a Grand Unified Theory (GUT), completely avoiding problems like proton decay, doublet–triplet splitting, and magnetic monopoles. We briefly investigate the phenomenological implications of this model-building framework. The NG boson is fractionally charged and completely stable. It can be naturally light, avoiding constraints while being a component of dark matter or having applications in nuclear physics. We also comment on the extension to other NLSMs on coset spaces, which will be explored more fully in a followup paper.
Charge Quantization in the CP(1) Nonlinear Sigma-Model
Hellerman, Simeon; Yanagida, Tsutomu T
2013-01-01
We investigate the consistency conditions for matter fields coupled to the four-dimensional (N = 1 supersymmetric) CP(1) nonlinear sigma model (the coset space SU(2)_G/U(1)_H). We find that consistency requires that the U(1)_H charge of the matter be quantized, in units of half of the U(1)_H charge of the Nambu-Goldstone (NG) boson, if the matter has a nonsingular kinetic term and the dynamics respect the full group SU(2)_G. We can then take the linearly realized group U(1)_H to comprise the weak hypercharge group U(1)_Y of the Standard Model. Thus we have charge quantization without a Grand Unified Theory (GUT), completely avoiding problems like proton decay, doublet-triplet splitting, and magnetic monopoles. We briefly investigate the phenomenological implications of this model-building framework. The NG boson is fractionally charged and completely stable. It can be naturally light, avoiding constraints while being a component of dark matter or having applications in nuclear physics. We also comment on the ...
On two transverse nonlinear models of axially moving beams
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit- ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av- eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif- ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte- gro-partial-differential equation gives better results for large amplitude vibration.
On two transverse nonlinear models of axially moving beams
Institute of Scientific and Technical Information of China (English)
DING Hu; CHEN LiQun
2009-01-01
Nonlinear models of transverse vibration of axially moving beams are computationally investigated. A partial-differential equation is derived from the governing equation of coupled planar motion by omit-ting its longitudinal terms. The model can be reduced to an integro-partial-differential equation by av-eraging the beam disturbed tension. Numerical schemes are respectively presented for the governing equations of coupled planar and the two governing equations of transverse motion via the finite dif-ference method and differential quadrature method under the fixed boundary and the simple support boundary. A steel beam and a copper beam are treated as examples to demonstrate the deviations of the solutions to the two transverse equations from the solution to the coupled equation. The numerical results indicate that the differences increase with the amplitude of vibration and the axial speed. Both models yield almost the same precision results for small amplitude vibration and the inte-gro-partial-differential equation gives better results for large amplitude vibration.
Nonlinear dynamic model for magnetically-tunable Galfenol vibration absorbers
Scheidler, Justin J.; Dapino, Marcelo J.
2013-03-01
This paper presents a single degree of freedom model for the nonlinear vibration of a metal-matrix composite manufactured by ultrasonic additive manufacturing that contains seamlessly embedded magnetostrictive Galfenol alloys (FeGa). The model is valid under arbitrary stress and magnetic field. Changes in the composite's natural frequency are quantified to assess its performance as a semi-active vibration absorber. The effects of Galfenol volume fraction and location within the composite on natural frequency are quantified. The bandwidth over which the composite's natural frequency can be tuned with a bias magnetic field is studied for varying displacement excitation amplitudes. The natural frequency is tunable for all excitation amplitudes considered, but the maximum tunability occurs below an excitation amplitude threshold of 1 × 10-6 m for the composite geometry considered. Natural frequency shifts between 6% and 50% are found as the Galfenol volume fraction varies from 25% to 100% when Galfenol is located at the composite neutral axis. At a modest 25% Galfenol by volume, the model shows that up to 15% shifts in composite resonance are possible through magnetic bias field modulation if Galfenol is embedded away from the composite midplane. As the Galfenol volume fraction and distance between Galfenol and composite midplane are increased, linear and quadratic increases in tunability result, respectively.
Non-linear Constitutive Model for the Oligocarbonate Polyurethane Material
Institute of Scientific and Technical Information of China (English)
Marek Pawlikowski
2014-01-01
The polyurethane,which was the subject of the constitutive research presented in the paper,was based on oligocarbonate diols Desmophen C2100 produced by Bayer@.The constitutive modelling was performed with a view to applying the material as the inlay of intervertebral disc prostheses.The polyurethane was assumed to be non-linearly viscohyperelastic,isotropic and incompressible.The constitutive equation was derived from the postulated strain energy function.The elastic and rheological constants were identified on the basis of experimental tests,i.e.relaxation tests and monotonic uniaxial tests at two different strain rates,i.e.λ =0.1 min-1 and λ =1.0 min-1.The stiffness tensor was derived and introduced to Abaqus@finite element (FE) software in order to numerically validate the constitutive model.The results of the constants identification and numerical implementation show that the derived constitutive equation is fully adequate to model stress-strain behavior of the polyurethane material.
Measurements and Modeling of the Nonlinear Behavior of a Guitar Pickup at Low Frequencies †
Directory of Open Access Journals (Sweden)
Antonin Novak
2017-01-01
Full Text Available Description of the physical behavior of electric guitars is still not very widespread in the scientific literature. In particular, the physical models describing a nonlinear behavior of pickups still requires some refinements. The study presented in this paper is focused on nonlinear modeling of the pickups. Two main issues are raised. First, is the currently most used nonlinear model (a Hammerstein model sufficient for the complex nonlinear behavior of the pickup? In other words, would a more complex model, such as a Generalized Hammerstein that can deal better with the nonlinear memory, yield better results? The second troublesome issue is how to measure the nonlinear behavior of a pickup correctly. A specific experimental set-up allowing for driving the pickup in a controlled way (string displacement perpendicular to the pickup and to separate the nonlinear model of the pickup from other nonlinearities in the measurement chain is proposed. Thanks to this experimental set-up, a Generalized Hammerstein model of the pickup is estimated for frequency range 15–500 Hz and the results are compared with a simple Hammerstein model. A comparison with experimental results shows that both models succeed in describing the pickup when used in realistic conditions.
Nonlinear sigma models with compact hyperbolic target spaces
Energy Technology Data Exchange (ETDEWEB)
Gubser, Steven [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Saleem, Zain H. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); National Center for Physics, Quaid-e-Azam University Campus,Islamabad 4400 (Pakistan); Schoenholz, Samuel S. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Stokes, James [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States)
2016-06-23
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models.
Nolte, Daniel; Tsang, Chui Kit; Zhang, Kai Yu; Ding, Ziyun; Kedgley, Angela E; Bull, Anthony M J
2016-10-03
Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank - up to 26mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods.
A Model Predictive Algorithm for Active Control of Nonlinear Noise Processes
Directory of Open Access Journals (Sweden)
Qi-Zhi Zhang
2005-01-01
Full Text Available In this paper, an improved nonlinear Active Noise Control (ANC system is achieved by introducing an appropriate secondary source. For ANC system to be successfully implemented, the nonlinearity of the primary path and time delay of the secondary path must be overcome. A nonlinear Model Predictive Control (MPC strategy is introduced to deal with the time delay in the secondary path and the nonlinearity in the primary path of the ANC system. An overall online modeling technique is utilized for online secondary path and primary path estimation. The secondary path is estimated using an adaptive FIR filter, and the primary path is estimated using a Neural Network (NN. The two models are connected in parallel with the two paths. In this system, the mutual disturbances between the operation of the nonlinear ANC controller and modeling of the secondary can be greatly reduced. The coefficients of the adaptive FIR filter and weight vector of NN are adjusted online. Computer simulations are carried out to compare the proposed nonlinear MPC method with the nonlinear Filter-x Least Mean Square (FXLMS algorithm. The results showed that the convergence speed of the proposed nonlinear MPC algorithm is faster than that of nonlinear FXLMS algorithm. For testing the robust performance of the proposed nonlinear ANC system, the sudden changes in the secondary path and primary path of the ANC system are considered. Results indicated that the proposed nonlinear ANC system can rapidly track the sudden changes in the acoustic paths of the nonlinear ANC system, and ensure the adaptive algorithm stable when the nonlinear ANC system is time variable.
Lorenz, HW; Nusse, HE
Goodwin's nonlinear accelerator model with periodic investment outlays is reconsidered and used as an economic example of the emergence of complex motion in nonlinear dynamical systems. In addition to chaotic attractors, the model can possess coexisting attracting periodic orbits or simple
DEFF Research Database (Denmark)
Péguin-Feissolle, Anne; Strikholm, Birgit; Teräsvirta, Timo
In this paper we propose a general method for testing the Granger noncausality hypothesis in stationary nonlinear models of unknown functional form. These tests are based on a Taylor expansion of the nonlinear model around a given point in the sample space. We study the performance of our tests...
An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models
Chow, Sy-Miin; Ferrer, Emilio; Nesselroade, John R.
2007-01-01
In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways:…
Maximum Likelihood Analysis of Nonlinear Structural Equation Models with Dichotomous Variables
Song, Xin-Yuan; Lee, Sik-Yum
2005-01-01
In this article, a maximum likelihood approach is developed to analyze structural equation models with dichotomous variables that are common in behavioral, psychological and social research. To assess nonlinear causal effects among the latent variables, the structural equation in the model is defined by a nonlinear function. The basic idea of the…
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)
Curvature-induced symmetry breaking in nonlinear Schrodinger models
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Mingaleev, S. F.; Christiansen, Peter Leth
2000-01-01
We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. We show that the energy of localized states decrea...
Nonlinear time-domain modeling of balanced-armature receivers
DEFF Research Database (Denmark)
Jensen, Joe; Agerkvist, Finn T.; Harte, James
2011-01-01
Nonlinear distortion added by the loudspeaker in a hearing aid lowers the signal-to-noise ratio and may degrade the hearing aid user's ability to understand speech. The balancedarmature- type loudspeakers, predominantly used in hearing aids, are inherently nonlinear devices, as any displacement o...
DEFF Research Database (Denmark)
Tornøe, Christoffer Wenzel; Agersø, Henrik; Madsen, Henrik
2004-01-01
The standard software for non-linear mixed-effect analysis of pharmacokinetic/phar-macodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as tong as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential...... equation (ODE) solver package odesolve and the non-Linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlme...
System Identification for Nonlinear FOPDT Model with Input-Dependent Dead-Time
DEFF Research Database (Denmark)
Sun, Zhen; Yang, Zhenyu
2011-01-01
. In order to identify these parameters in an online manner, the considered system is discretized at first. Then, the nonlinear FOPDT identification problem is formulated as a stochastic Mixed Integer Non-Linear Programming problem, and an identification algorithm is proposed by combining the Branch......An on-line iterative method of system identification for a kind of nonlinear FOPDT system is proposed in the paper. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its dead time depends on the input signal and the other parameters are time dependent...
Wei, Xile; Lu, Meili; Wang, Jiang; Tsang, K. M.; Deng, Bin; Che, Yanqiu
2010-05-01
We consider the assumption of existence of the general nonlinear internal model that is introduced in the design of robust output regulators for a class of minimum-phase nonlinear systems with rth degree (r ≥ 2). The robust output regulation problem can be converted into a robust stabilisation problem of an augmented system consisting of the given plant and a high-gain nonlinear internal model, perfectly reproducing the bounded including not only periodic but also nonperiodic exogenous signal from a nonlinear system, which satisfies some general immersion assumption. The state feedback controller is designed to guarantee the asymptotic convergence of system errors to zero manifold. Furthermore, the proposed scheme makes use of output feedback dynamic controller that only processes information from the regulated output error by using high-gain observer to robustly estimate the derivatives of the regulated output error. The stabilisation analysis of the resulting closed-loop systems leads to regional as well as semi-global robust output regulation achieved for some appointed initial condition in the state space, for all possible values of the uncertain parameter vector and the exogenous signal, ranging over an arbitrary compact set.
The numerical modelling of a driven nonlinear oscillator
Energy Technology Data Exchange (ETDEWEB)
Shew, C.
1995-11-01
The torsional oscillator in the Earth Sciences Division was developed at Lawrence Livermore National Laboratory and is the only one of its kind. It was developed to study the way rocks damp vibrations. Small rock samples are tested to determine the seismic properties of rocks, but unlike other traditional methods that propagate high frequency waves through small samples, this machine forces the sample to vibrate at low frequencies, which better models real-life properties of large masses. In this particular case, the rock sample is tested with a small crack in its middle. This forces the rock to twist against itself, causing a {open_quotes}stick-slip{close_quotes} friction, known as stiction. A numerical model that simulates the forced torsional osillations of the machine is currently being developed. The computer simulation implements the graphical language LabVIEW, and is looking at the nonlinear spring effects, the frictional forces, and the changes in amplitude and frequency of the forced vibration. Using LabVIEW allows for quick prototyping and greatly reduces the {open_quotes}time to product{close_quotes} factor. LabVIEW`s graphical environment allows scientists and engineers to use familiar terminology and icons (e.g. knobs, switches, graphs, etc.). Unlike other programming systems that use text-based languages, such as C and Basic, LabVIEW uses a graphical programming language to create programs in block diagram form.
Nonlinear dynamic modeling and resonance tuning of Galfenol vibration absorbers
Scheidler, Justin J.; Dapino, Marcelo J.
2013-08-01
This paper investigates the semi-active control of a magnetically-tunable vibration absorber’s resonance frequency. The vibration absorber that is considered is a metal-matrix composite containing the magnetostrictive material Galfenol (FeGa). A single degree of freedom model for the nonlinear vibration of the absorber is presented. The model is valid under arbitrary stress and magnetic field, and incorporates the variation in Galfenol’s elastic modulus throughout the composite as well as Galfenol’s asymmetric tension-compression behavior. Two boundary conditions—cantilevered and clamped-clamped—are imposed on the composite. The frequency response of the absorber to harmonic base excitation is calculated as a function of the operating conditions to determine the composite’s capacity for resonance tuning. The results show that nearly uniform controllability of the vibration absorber’s resonance frequency is possible below a threshold of the input power amplitude using weak magnetic fields of 0-8 kA m-1. Parametric studies are presented to characterize the effect on resonance tunability of Galfenol volume fraction and Galfenol location within the composite. The applicability of the results to composites of varying geometry and containing different Galfenol materials is discussed.
POD/DEIM Nonlinear model order reduction of an ADI implicit shallow water equations model
Stefanescu, Razvan
2012-01-01
In the present paper we consider a 2-D shallow-water equations (SWE) model on a $\\beta$-plane solved using an alternating direction fully implicit (ADI) finite-difference scheme on a rectangular domain. The scheme was shown to be unconditionally stable for the linearized equations. The discretization yields a number of nonlinear systems of algebraic equations. We then use a proper orthogonal decomposition (POD) to reduce the dimension of the SWE model. Due to the model nonlinearities, the computational complexity of the reduced model still depends on the number of variables of the full shallow - water equations model. By employing the discrete empirical interpolation method (DEIM) we reduce the computational complexity of the reduced order model due to its depending on the nonlinear full dimension model and regain the full model reduction expected from the POD model. To emphasize the CPU gain in performance due to use of POD/DEIM, we also propose testing an explicit Euler finite difference scheme (EE) as an a...
Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties
Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon
2014-01-01
Purpose The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency during anterior-posterior stretching. Method Three materially linear and three materially nonlinear models were created and stretched up to 10 mm in 1 mm increments. Phonation onset pressure (Pon) and fundamental frequency (F0) at Pon were recorded for each length. Measurements were repeated as the models were relaxed in 1 mm increments back to their resting lengths, and tensile tests were conducted to determine the stress-strain responses of linear versus nonlinear models. Results Nonlinear models demonstrated a more substantial frequency response than did linear models and a more predictable pattern of F0 increase with respect to increasing length (although range was inconsistent across models). Pon generally increased with increasing vocal fold length for nonlinear models, whereas for linear models, Pon decreased with increasing length. Conclusions Nonlinear synthetic models appear to more accurately represent the human vocal folds than linear models, especially with respect to F0 response. PMID:22271874
A Modal Model to Simulate Typical Structural Dynamic Nonlinearity [PowerPoint
Energy Technology Data Exchange (ETDEWEB)
Mayes, Randall L.; Pacini, Benjamin Robert; Roettgen, Dan
2016-01-01
Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
Directory of Open Access Journals (Sweden)
Zhenhua Hu
2013-01-01
Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.
MCMC for non-linear state space models using ensembles of latent sequences
2013-01-01
Non-linear state space models are a widely-used class of models for biological, economic, and physical processes. Fitting these models to observed data is a difficult inference problem that has no straightforward solution. We take a Bayesian approach to the inference of unknown parameters of a non-linear state model; this, in turn, requires the availability of efficient Markov Chain Monte Carlo (MCMC) sampling methods for the latent (hidden) variables and model parameters. Using the ensemble ...
A Weakly Nonlinear Model for Kelvin-Helmholtz Instability in Incompressible Fluids
Institute of Scientific and Technical Information of China (English)
WANG Li-Feng; YE Wen-Hua; FAN Zheng-Feng; XUE Chuang; LI Ying-Jun
2009-01-01
A weakly nonlinear model is proposed for the Kelvin-Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling.
Yan, Jun; Li, Bo; Guo, Gang; Zeng, Yonghua; Zhang, Meijun
2013-11-01
Electro-hydraulic control systems are nonlinear in nature and their mathematic models have unknown parameters. Existing research of modeling and identification of the electro-hydraulic control system is mainly based on theoretical state space model, and the parameters identification is hard due to its demand on internal states measurement. Moreover, there are also some hard-to-model nonlinearities in theoretical model, which needs to be overcome. Modeling and identification of the electro-hydraulic control system of an excavator arm based on block-oriented nonlinear(BONL) models is investigated. The nonlinear state space model of the system is built first, and field tests are carried out to reveal the nonlinear characteristics of the system. Based on the physic insight into the system, three BONL models are adopted to describe the highly nonlinear system. The Hammerstein model is composed of a two-segment polynomial nonlinearity followed by a linear dynamic subsystem. The Hammerstein-Wiener(H-W) model is represented by the Hammerstein model in cascade with another single polynomial nonlinearity. A novel Pseudo-Hammerstein-Wiener(P-H-W) model is developed by replacing the single polynomial of the H-W model by a non-smooth backlash function. The key term separation principle is applied to simplify the BONL models into linear-in-parameters structures. Then, a modified recursive least square algorithm(MRLSA) with iterative estimation of internal variables is developed to identify the all the parameters simultaneously. The identification results demonstrate that the BONL models with two-segment polynomial nonlinearities are able to capture the system behavior, and the P-H-W model has the best prediction accuracy. Comparison experiments show that the velocity prediction error of the P-H-W model is reduced by 14%, 30% and 75% to the H-W model, Hammerstein model, and extended auto-regressive (ARX) model, respectively. This research is helpful in controller design, system
Nonlinear dynamical model and response of avian cranial kinesis.
Meekangvan, Preeda; A Barhorst, Alan; Burton, Thomas D; Chatterjee, Sankar; Schovanec, Lawrence
2006-05-01
All modern birds have kinetic skulls in which the upper bill can move relative to the braincase, but the biomechanics and motion dynamics of cranial kinesis in birds are poorly understood. In this paper, we model the dynamics of avian cranial kinesis, such as prokinesis and proximal rhynchokinesis in which the upper jaw pivots around the nasal-frontal (N-F) hinge. The purpose of this paper is to present to the biological community an approach that demonstrates the application of sophisticated predictive mathematical modeling tools to avian kinesis. The generality of the method, however, is applicable to the advanced study of the biomechanics of other skeletal systems. The paper begins with a review of the relevant biological literature as well as the essential morphology of avian kinesis, especially the mechanical coupling of the upper and lower jaw by the postorbital ligament. A planar model of the described bird jaw morphology is then developed that maintains the closed kinematic topology of the avian jaw mechanism. We then develop the full nonlinear equations of motion with the assumption that the M. protractor pterygoideus and M. depressor mandibulae act on the quadrate as a pure torque, and the nasal frontal hinge is elastic with damping. The mechanism is shown to be a single degree of freedom device due to the holonomic constraints present in the quadrate-jugal bar-upper jaw-braincase-quadrate kinematic chain as well as the quadrate-lower jaw-postorbital ligament-braincase-quadrate kinematic chain. The full equations are verified via simulation and animation using the parameters of a Grey Heron (Ardea cinerea). Next we develop a simplified analytical model of the equations by power series expansion. We demonstrate that this model reproduces the dynamics of the full model to a high degree of fidelity. We proceed to use the harmonic balance technique to develop the frequency response characteristics of the jaw mechanism. It is shown that this avian cranial
Research on modeling of nonlinear vibration isolation system based on BouceWen model
Institute of Scientific and Technical Information of China (English)
Zhi-ling PENG; Chun-gui ZHOU
2014-01-01
A feedforword neural network of multi-layer topologies for systems with hysteretic nonlinearity is constructed based on BouceWen dif-ferential model. It not only reflects the hysteresis force characteristics of the BouceWen model, but also determines its corresponding pa-rameters. The simulation results show that restoring forceedisplacement curve hysteresis loop is very close to the real curve. The model trained can accurately predict the time response of system. The model is checked under the noise level. The result shows that the model has higher modeling precision, good generalization capability and a certain anti-interference ability.
Model algorithm control using neural networks for input delayed nonlinear control system
Institute of Scientific and Technical Information of China (English)
Yuanliang Zhang; Kil To Chong
2015-01-01
The performance of the model algorithm control method is partial y based on the accuracy of the system’s model. It is diffi-cult to obtain a good model of a nonlinear system, especial y when the nonlinearity is high. Neural networks have the ability to“learn”the characteristics of a system through nonlinear mapping to rep-resent nonlinear functions as wel as their inverse functions. This paper presents a model algorithm control method using neural net-works for nonlinear time delay systems. Two neural networks are used in the control scheme. One neural network is trained as the model of the nonlinear time delay system, and the other one pro-duces the control inputs. The neural networks are combined with the model algorithm control method to control the nonlinear time delay systems. Three examples are used to il ustrate the proposed control method. The simulation results show that the proposed control method has a good control performance for nonlinear time delay systems.
Directory of Open Access Journals (Sweden)
Yacouba Simporé
2016-01-01
Full Text Available We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. In order to tackle the controllability problem we use an adapted Carleman inequality. Next we consider the nonlinear population dynamics model with a source term called the pollution term. In order to obtain information on the pollution term we use the method of sentinel.
Nonlinear Kalman Filtering in Affine Term Structure Models
DEFF Research Database (Denmark)
Christoffersen, Peter; Dorion, Christian; Jacobs, Kris;
2014-01-01
The extended Kalman filter, which linearizes the relationship between security prices and state variables, is widely used in fixed-income applications. We investigate whether the unscented Kalman filter should be used to capture nonlinearities and compare the performance of the Kalman filter...... with that of the particle filter. We analyze the cross section of swap rates, which are mildly nonlinear in the states, and cap prices, which are highly nonlinear. When caps are used to filter the states, the unscented Kalman filter significantly outperforms its extended counterpart. The unscented Kalman filter also...
Nonlinear Decoupling PID Control Using Neural Networks and Multiple Models
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
For a class of complex industrial processes with strong nonlinearity, serious coupling and uncertainty, a nonlinear decoupling proportional-integral-differential (PID) controller is proposed, which consists of a traditional PID controller, a decoupling compensator and a feedforward compensator for the unmodeled dynamics. The parameters of such controller is selected based on the generalized minimum variance control law. The unmodeled dynamics is estimated and compensated by neural networks, a switching mechanism is introduced to improve tracking performance, then a nonlinear decoupling PID control algorithm is proposed. All signals in such switching system are globally bounded and the tracking error is convergent. Simulations show effectiveness of the algorithm.
Nonlinear Models of Development: An Example from the Socialization of Competence.
Roberts, William L.
1986-01-01
Discusses both the advantages and difficulties of using nonlinear modeling in the context of a model used to study the relations between parental warmth and control and preschool children's competence. (HOD)
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.
Asymptotic solution for EI Nino-southern oscillation of nonlinear model
Institute of Scientific and Technical Information of China (English)
MO Jia-qi; LIN Wan-tao
2008-01-01
A class of nonlinear coupled system for E1 Nino-Southern Oscillation (ENSO) model is considered. Using the asymptotic theory and method of variational iteration, the asymptotic expansion of the solution for ENSO models is obtained.
Sampled-data models for linear and nonlinear systems
Yuz, Juan I
2014-01-01
Sampled-data Models for Linear and Nonlinear Systems provides a fresh new look at a subject with which many researchers may think themselves familiar. Rather than emphasising the differences between sampled-data and continuous-time systems, the authors proceed from the premise that, with modern sampling rates being as high as they are, it is becoming more appropriate to emphasise connections and similarities. The text is driven by three motives: · the ubiquity of computers in modern control and signal-processing equipment means that sampling of systems that really evolve continuously is unavoidable; · although superficially straightforward, sampling can easily produce erroneous results when not treated properly; and · the need for a thorough understanding of many aspects of sampling among researchers and engineers dealing with applications to which they are central. The authors tackle many misconceptions which, although appearing reasonable at first sight, are in fact either p...
Multimodal nonlinear optical imaging of cartilage development in mouse model
He, Sicong; Xue, Wenqian; Sun, Qiqi; Li, Xuesong; Huang, Jiandong; Qu, Jianan Y.
2017-02-01
Kinesin-1 is a kind of motor protein responsible for intracellular transportation and has been studied in a variety of tissues. However, its roles in cartilage development are not clear. In this study, a kinesin-1 heavy chain (Kif5b) knockout mouse model is used to study the functions of kinesin-1 in the cartilage development. We developed a multimodal nonlinear optical (NLO) microscope system integrating stimulated Raman scattering (SRS), second harmonic generation (SHG) and two-photon excited fluorescence (TPEF) to investigate the morphological and biomedical characteristics of fresh tibial cartilage from normal and mutant mice at different developmental stages. The combined forward and backward SHG imaging resolved the fine structure of collagen fibrils in the extracellular matrix of cartilage. Meanwhile, the chondrocyte morphology in different zones of cartilage was visualized by label-free SRS and TPEF images. The results show that the fibrillar collagen in the superficial zone of cartilage in postnatal day 10 and 15 (P10 and P15) knockout mice was significantly less than that of control mice. Moreover, we observed distorted morphology and disorganization of columnar arrangement of chondrocytes in the growth plate cartilage of mutant mice. This study reveals the significant roles of kinesin-1 in collagen formation and chondrocyte morphogenesis.
Nonlinear effects in a conceptual multilayer cloud model
Directory of Open Access Journals (Sweden)
U. Wacker
2006-01-01
Full Text Available As conceptual model for a cloud a system is considered which is open for condensate mass transport and subject to internal processes such as cloud microphysical transformation and vertical condensate transport. The effects of microphysical processes are represented in parameterized form and the system is divided into two layers to account for the vertical structure. The evolution is mathematically described in terms of four coupled nonlinear ODEs; the prognostic variables are the mass concentrations of cloud water as well as precipitation condensate in each of the layers. In the absence of vertical velocity the evolution in the lower layer is triggered by the evolution in the upper layer. In the presence of an upwind, the dynamics in both layers is mutually coupled. Depending on the chosen parameter values up to four steady states are found. When varying the parameter upwind velocity, three regimes are distinguished: For week upwind the long-term evolution is steered by the external sources; for stronger upwind the cloud condensate is blown out of the cloud in the final state and does not contribute to formation of precipitation; for intermediate upwind multiple steady state solution branches arise which characterize the transition between those two regimes.
NSLS-II: Nonlinear Model Calibration for Synchrotrons
Energy Technology Data Exchange (ETDEWEB)
Bengtsson, J.
2010-10-08
This tech note is essentially a summary of a lecture we delivered to the Acc. Phys. Journal Club Apr, 2010. However, since the estimated accuracy of these methods has been naive and misleading in the field of particle accelerators, i.e., ignores the impact of noise, we will elaborate on this in some detail. A prerequisite for a calibration of the nonlinear Hamiltonian is that the quadratic part has been understood, i.e., that the linear optics for the real accelerator has been calibrated. For synchrotron light source operations, this problem has been solved by the interactive LOCO technique/tool (Linear Optics from Closed Orbits). Before that, in the context of hadron accelerators, it has been done by signal processing of turn-by-turn BPM data. We have outlined how to make a basic calibration of the nonlinear model for synchrotrons. In particular, we have shown how this was done for LEAR, CERN (antiprotons) in the mid-80s. Specifically, our accuracy for frequency estimation was {approx} 1 x 10{sup -5} for 1024 turns (to calibrate the linear optics) and {approx} 1 x 10{sup -4} for 256 turns for tune footprint and betatron spectrum. For a comparison, the estimated tune footprint for stable beam for NSLS-II is {approx}0.1. Since the transverse damping time is {approx}20 msec, i.e., {approx}4,000 turns. There is no fundamental difference for: antiprotons, protons, and electrons in this case. Because the estimated accuracy for these methods in the field of particle accelerators has been naive, i.e., ignoring the impact of noise, we have also derived explicit formula, from first principles, for a quantitative statement. For e.g. N = 256 and 5% noise we obtain {delta}{nu} {approx} 1 x 10{sup -5}. A comparison with the state-of-the-arts in e.g. telecomm and electrical engineering since the 60s is quite revealing. For example, Kalman filter (1960), crucial for the: Ranger, Mariner, and Apollo (including the Lunar Module) missions during the 60s. Or Claude Shannon et al
A Non-linear Stochastic Model for an Office Building with Air Infiltration
DEFF Research Database (Denmark)
Thavlov, Anders; Madsen, Henrik
2015-01-01
This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model param...... heat load reduction during peak load hours, control of indoor air temperature and for generating forecasts of power consumption from space heating....
Prandtl-Ishlinskii hysteresis models for complex time dependent hysteresis nonlinearities
Al Janaideh, M.; Krejčí, P
2012-01-01
We introduce a new class of time dependent hysteresis models by combining the time dependent Prandtl–Ishlinskii model with functional nonlinearities. This combination improves the capability of the time dependent Prandtl–Ishlinskii model to characterize a class of complex time dependent hysteresis nonlinearities in smart actuators. The analytical inversion for the proposed time dependent hysteresis model is also presented in order to extend the inversion algorithm of the inverse time dependen...
Stabilization and Control Models of Systems With Hysteresis Nonlinearities
Directory of Open Access Journals (Sweden)
Mihail E. Semenov
2012-05-01
Full Text Available Mechanical and economic systems with hysteresis nonlinearities are studied in article. Dissipativity condition of inverted pendulum under the hysteresis control is obtained. The solution of the optimal production strategy problem was found where price has hysteresis behaviour.
2013-01-01
This book consists of twenty seven chapters, which can be divided into three large categories: articles with the focus on the mathematical treatment of non-linear problems, including the methodologies, algorithms and properties of analytical and numerical solutions to particular non-linear problems; theoretical and computational studies dedicated to the physics and chemistry of non-linear micro-and nano-scale systems, including molecular clusters, nano-particles and nano-composites; and, papers focused on non-linear processes in medico-biological systems, including mathematical models of ferments, amino acids, blood fluids and polynucleic chains.
Identification of a class of nonlinear state-space models using RPE techniques
DEFF Research Database (Denmark)
Zhou, W. W.; Blanke, Mogens
1986-01-01
The recursive prediction error methods in state-space form have been efficiently used as parameter identifiers for linear systems, and especially Ljung's innovations filter using a Newton search direction has proved to be quite ideal. In this paper, the RPE method in state-space form is developed...... to the nonlinear case and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows...... a quite convincing performance of the filter as combined parameter and state estimator....
Modeling and Non-Linear Self-Tuning Robust Trajectory Control of an Autonomous Underwater Vehicle
Directory of Open Access Journals (Sweden)
Thor Inge Fossen
1988-10-01
Full Text Available A non-linear self-tuning algorithm is demonstrated for an autonomous underwater vehicle. Tighter control is achieved by a non-linear parameter identification algorithm which reduces the parameter uncertainty bounds. Expensive hydrodynamic tests for parameter determination can thus be avoided. Excellent tracking performance and robustness to parameter uncertainty are guaranteed through a robust control strategy based on the estimated parameters. The nonlinear control law is highly robust for imprecise models and the neglected dynamics. The non-linear self-tuning control strategy is simulated for the horizontal positioning of an underwater vehicle.
Institute of Scientific and Technical Information of China (English)
LIN Xiangguo; LIANG Yong
2005-01-01
The processing of nonlinear data was one of hot topics in surveying and mapping field in recent years.As a result, many linear methods and nonlinear methods have been developed.But the methods for processing generalized nonlinear surveying and mapping data, especially for different data types and including unknown parameters with random or nonrandom, are seldom noticed.A new algorithm model is presented in this paper for processing nonlinear dynamic multiple-period and multiple-accuracy data derived from deformation monitoring network.
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.
Nonlinear Model Algorithmic Control of a pH Neutralization Process
Institute of Scientific and Technical Information of China (English)
ZOU Zhiyun; YU Meng; WANG Zhizhen; LIU Xinghong; GUO Yuqing; ZHANG Fengbo; GUO Ning
2013-01-01
Control of pH neutralization processes is challenging in the chemical process industry because of their inherent strong nonlinearity.In this paper,the model algorithmic control (MAC) strategy is extended to nonlinear processes using Hammerstein model that consists of a static nonlinear polynomial function followed in series by a linear impulse response dynamic element.A new nonlinear Hammerstein MAC algorithm (named NLH-MAC) is presented in detail.The simulation control results of a pH neutralization process show that NLH-MAC gives better control performance than linear MAC and the commonly used industrial nonlinear propotional plus integral plus derivative (PID) controller.Further simulation experiment demonstrates that NLH-MAC not only gives good control response,but also possesses good stability and robustness even with large modeling errors.
USTIFICATION OF A TWO-DIMENSIONAL NONLINEAR SHELL MODEL OF KOITER'S TYPE
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A two-dimensional nonlinear shell model"of Koiter's type"has recently been proposed by the first author. It is shown here that, according to two mutually exclusive sets of assumptions bearing on the associated manifold of admissible inextensional displacements, the leading term of a formal asymptotic expansion of the solution of this two-dimensional model, with the thickness as the"small" parameter, satisfies either the two-dimensional equations of a nonlinearly elastic "membrane" shell or those of a nonlinearly elastic "flexural" shell. These conclusions being identical to those recently drawn by B. Miara, then by V. Lods and B. Miara, for the leading term of a formal asymptotic expansion of the solution of the equations of three-dimensional nonlinear elasticity, again with the thickness as the "small" parameter, the nonlinear shell model of Koiter's type considered here is thus justified, at least formally.
A nonlinear model reference adaptive inverse control algorithm with pre-compensator
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In this paper, the reduced-order modeling (ROM)technology and its corresponding linear theory are expanded from the linear dynamic system to the nonlinear one, and H∞ control theory is employed in the frequency domain to design some nonlinear system' s pre-compensator in some special way. The adaptive model inverse control (AMIC)theory coping with nonlinear system is improved as well. Such is the model reference adaptive inverse control with pre-compensator (PCMRAIC). The aim of that algorithm is to construct a strategy of control as a whole. As a practical example of the application, the numerical simulation has been given on matlab software packages. The numerical result is given. The proposed strategy realizes the linearization control of nonlinear dynamic system. And it carries out a good performance to deal with the nonlinear system.
Linear and nonlinear modeling of light propagation in hollow-core photonic crystal fiber
DEFF Research Database (Denmark)
Roberts, John; Lægsgaard, Jesper
2009-01-01
Hollow core photonic crystal fibers (HC-PCFs) find applications which include quantum and non-linear optics, gas detection and short high-intensity laser pulse delivery. Central to most applications is an understanding of the linear and nonlinear optical properties. These require careful modeling...
Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable
du Toit, Stephen H. C.; Cudeck, Robert
2009-01-01
A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution…
The influence of storms on finite amplitude sand wave dynamics: an idealized nonlinear model
Campmans, G.H.P.; Roos, P.C.; de Vriend, H.J.; Hulscher, S.J.M.H.
2017-01-01
We investigate the effects of storms on finite amplitude sand wave growth using a new idealized nonlinear morphodynamic model. We find that the growth speed initially linearly increases with sand wave amplitude, after which nonlinear effects cause the growth to decrease. This finally leads to an
Fujimoto, Kenji; Scherpen, Jacquelien M. A.
2010-01-01
This paper discusses balanced realization and model order reduction for both continuous-time and discrete-time general nonlinear systems based on singular value analysis of the corresponding Hankel operators. Singular value analysis clarifies the gain structure of a given nonlinear operator. Here it
Similarity Reduction and Integrability for the Nonlinear Wave Equations from EPM Model
Institute of Scientific and Technical Information of China (English)
YAN ZhenYa
2001-01-01
Four types of similarity reductions are obtained for the nonlinear wave equation arising in the elasto-plasticmicrostructure model by using both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou. As a result, the nonlinear wave equation is not integrable.``
Provable first-order transitions for nonlinear vector and gauge models with continuous symmetries
Enter, Aernout C.D. van; Shlosman, Senya B.
2005-01-01
We consider various sufficiently nonlinear vector models of ferromagnets, of nematic liquid crystals and of nonlinear lattice gauge theories with continuous symmetries. We show, employing the method of Reflection Positivity and Chessboard Estimates, that they all exhibit first-order transitions in t
The finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model
Balog, Janos(Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, MTA Lendület Holographic QFT Group, 1525, Budapest 114, P.O.B. 49, Hungary); Hegedus, Arpad
2009-01-01
Nonlinear integral equations are proposed for the description of the full finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model in a periodic box. Numerical results for the energy eigenvalues are compared to the rotator spectrum and perturbation theory for small volumes and with the recently proposed generalized Luscher formulas at large volumes.
Energy Technology Data Exchange (ETDEWEB)
Sayyar-Rodsari, Bijan; Schweiger, Carl; Hartman, Eric
2007-10-07
The difficult problems being tackled in the accelerator community are those that are nonlinear, substantially unmodeled, and vary over time. Such problems are ideal candidates for model-based optimization and control if representative models of the problem can be developed that capture the necessary mathematical relations and remain valid throughout the operation region of the system, and through variations in system dynamics. The goal of this proposal is to develop the methodology and the algorithms for building high-fidelity mathematical representations of complex nonlinear systems via constrained training of combined first-principles and neural network models.
Real-Time Onboard Global Nonlinear Aerodynamic Modeling from Flight Data
Brandon, Jay M.; Morelli, Eugene A.
2014-01-01
Flight test and modeling techniques were developed to accurately identify global nonlinear aerodynamic models onboard an aircraft. The techniques were developed and demonstrated during piloted flight testing of an Aermacchi MB-326M Impala jet aircraft. Advanced piloting techniques and nonlinear modeling techniques based on fuzzy logic and multivariate orthogonal function methods were implemented with efficient onboard calculations and flight operations to achieve real-time maneuver monitoring and analysis, and near-real-time global nonlinear aerodynamic modeling and prediction validation testing in flight. Results demonstrated that global nonlinear aerodynamic models for a large portion of the flight envelope were identified rapidly and accurately using piloted flight test maneuvers during a single flight, with the final identified and validated models available before the aircraft landed.
Directory of Open Access Journals (Sweden)
Lavrov Kirill
2016-01-01
Full Text Available The hyperelastic orthotropic material model is proposed to describe the nonlinear behavior of concrete under monotonic multiaxial loading with taking into account the tension-compression anisotropy. The orthotropy is introduced for the correct description of concrete cracking. The hyperelasticity provides unconditional thermodynamical consistency and advantages in numerical solving of boundary value problems. Identification of model parameters is based on four experimental deformation diagrams of concrete: axial stress - axial strain and axial stress - transverse strain under uniaxial tension and compression. The results of the hyperelastic orthotropic model are compared with Karpenko’s orthotropic model and experimental data for multiaxial loading.
Directory of Open Access Journals (Sweden)
Jingjing Wu
2015-01-01
Full Text Available A robust particle filter (PF and its application to fault/defect detection of nonlinear system are investigated in this paper. First, an adaptive parametric model is exploited as the observation model for a nonlinear system. Second, by incorporating the parametric model, particle filter is employed to estimate more accurate hidden states for the nonlinear stochastic system. Third, by formulating the problem of defect detection within the hypothesis testing framework, the statistical properties of the proposed testing are established. Finally, experimental results demonstrate the effectiveness and robustness of the proposed detector on real defect detection and localization in images.
Calibration of the Nonlinear Accelerator Model at the Diamond Storage Ring
Bartolini, Riccardo; Rowland, James; Martin, Ian; Schmidt, Frank
2010-01-01
The correct implementation of the nonlinear ring model is crucial to achieve the top performance of a synchrotron light source. Several dynamics quantities can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these methods are based on the analysis of turn-by-turn data of excited betatron oscillations. We present the experimental results of the campaign of measurements carried out at the Diamond. A combination of Frequency Map Analysis (FMA) and detuning with momentum measurements has allowed a precise calibration of the nonlinear model capable of reproducing the nonlinear beam dynamics in the storage ring
Weissel, Florian; Huber, Marco F.; Hanebeck, Uwe D.
2007-01-01
Model identification and measurement acquisition is always to some degree uncertain. Therefore, a framework for Nonlinear Model Predictive Control (NMPC) is proposed that explicitly considers the noise influence on nonlinear dynamic systems with continuous state spaces and a finite set of control inputs in order to significantly increase the control quality. Integral parts of NMPC are the prediction of system states over a finite horizon as well as the problem specific modeling of reward func...
Identification of non-linear models of neural activity in bold fmri
DEFF Research Database (Denmark)
Jacobsen, Daniel Jakup; Madsen, Kristoffer Hougaard; Hansen, Lars Kai
2006-01-01
Non-linear hemodynamic models express the BOLD signal as a nonlinear, parametric functional of the temporal sequence of local neural activity. Several models have been proposed for this neural activity. We identify one such parametric model by estimating the distribution of its parameters. These ....... These distributions are themselves stochastic, therefore we estimate their variance by epoch based leave-one-out cross validation, using a Metropolis-Hastings algorithm for sampling of the posterior parameter distribution....
Modeling of the wave transmission properties of large arteries using nonlinear elastic tubes.
Pythoud, F; Stergiopulos, N; Meister, J J
1994-11-01
We propose a new, simple way of constructing elastic tubes which can be used to model the nonlinear elastic properties of large arteries. The tube models are constructed from a silicon elastomer (Sylgard 184, Dow Corning), which exhibits a nonlinear behavior with increased stiffness at high strains. Tests conducted on different tube models showed that, with the proper choice of geometric parameters, the elastic properties, in terms of area-pressure relation and compliance, can be similar to that of real arteries.
Nguyen, Thu Thuy; Bazzoli, Caroline; Mentré, France
2012-01-01
International audience; Bioequivalence or interaction trials are commonly studied in crossover design and can be analysed by nonlinear mixed effects models as an alternative to noncompartmental approach. We propose an extension of the population Fisher information matrix in nonlinear mixed effects models to design crossover pharmacokinetic trials, using a linearisation of the model around the random effect expectation, including within-subject variability and discrete covariates fixed or chan...
Efficent Estimation of the Non-linear Volatility and Growth Model
2009-01-01
Ramey and Ramey (1995) introduced a non-linear model relating volatility to growth. The solution of this model by generalised computer algorithms for non-linear maximum likelihood estimation encounters the usual difficulties and is, at best, tedious. We propose an algebraic solution for the model that provides fully efficient estimators and is elementary to implement as a standard ordinary least squares procedure. This eliminates issues such as the ‘guesstimation’ of initial values and mul...
CONFIDENCE REGIONS IN TERMS OF STATISTICAL CURVATURE FOR AR(q) NONLINEAR REGRESSION MODELS
Institute of Scientific and Technical Information of China (English)
刘应安; 韦博成
2004-01-01
This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence regions for parameters and parameter subsets in terms of statistical curvatures are given based on the likelihood ratio statistics and score statistics. Several previous results, such as [1] and [2] are extended to AR(q)nonlinear regression models.
Modeling and Backstepping-based Nonlinear Control Strategy for a 6 DOF Quadrotor Helicopter
Institute of Scientific and Technical Information of China (English)
Ashfaq Ahmad Mian; Wang Daobo
2008-01-01
In this article,a nonlinear model of an underactuated six degrees of freedom (6 DOF) quadrotor helicopter is derived on the basis of the Newton-Euler formalism.The derivation comprises determining equations of the motion of the quadrotor in three dimensions andapproximating the actuation forces through the modeling of aerodynamic coefficients and electric motor dynamics.The derived modelcomposed of translatioual and rotational subsystems is dynamically unstable,so a sequential nonlinear control strategy is used.The con-trol strategy includes feedback linearization coupled with a PD controller for the translational subsystem and a backstepping-based PID nonlinear controller for the rotational subsystem of the quadrotor.The performances of the nonlinear control method are evaluated by nonlinear simulation and the results demonstrate the effectiveness of the proposed control strategy for the quadrotor helicopter inquasi-stationary flights.
Institute of Scientific and Technical Information of China (English)
ZHANG Ying-Yue; YANG Qiu-Ying; CHEN Tian-Lun
2007-01-01
We introduce a modified small-world network adding new links with nonlinearly preferential connection instead of adding randomly, then we apply Bak-Sneppen (BS) evolution model on this network. We study several important structural properties of our network such as the distribution of link-degree, the maximum link-degree, and the length of the shortest path. We further argue several dynamical characteristics of the model such as the important critical value fc, the f0 avalanche, and the mutating condition, and find that those characteristics show particular behaviors.
Institute of Scientific and Technical Information of China (English)
Yun Li; Hiroshi Kashiwagi
2005-01-01
Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. Results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order.
On the Nonlinear Structural Analysis of Wind Turbine Blades using Reduced Degree-of-Freedom Models
DEFF Research Database (Denmark)
Holm-Jørgensen, Kristian; Larsen, Jesper Winther; Nielsen, Søren R.K.
2008-01-01
, modelling geometrical and inertial nonlinear couplings in the fundamental flap and edge direction. The purpose of this article is to examine the applicability of such a reduced-degree-of-freedom model in predicting the nonlinear response and stability of a blade by comparison to a full model based...... on a nonlinear co-rotating FE formulation. By use of the reduced-degree-of-freedom model it is shown that under strong resonance excitation of the fundamental flap or edge modes, significant energy is transferred to higher modes due to parametric or nonlinear coupling terms, which influence the response...... representing the case of infinitely many included modes, is shown to predict stable and ordered response for all considered parameters. Further, the analysis shows that the reduced-degree-of-freedom model of relatively low order overestimates the response near resonance peaks, which is a consequence...
Synthesis of nonlinear discrete control systems via time-delay affine Takagi-Sugeno fuzzy models.
Chang, Wen-Jer; Chang, Wei
2005-04-01
The affine Takagi-Sugeno (TS) fuzzy model played a more important role in nonlinear control because it can be used to approximate the nonlinear systems more than the homogeneous TS fuzzy models. Besides, it is known that the time delays exist in physical systems and the previous works did not consider the time delay effects in the analysis of affine TS fuzzy models. Hence a parallel distributed compensation based fuzzy controller design issue for discrete time-delay affine TS fuzzy models is considered in this paper. The time-delay effect is considered in the discrete affine TS fuzzy models and the stabilization issue is developed for the nonlinear time-delay systems. Finally, a numerical simulation for a time-delayed nonlinear truck-trailer system is given to show the applications of the present approach.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.
MODELING OF NONLINEAR DEFORMATION AND BUCKLING OF ELASTIC INHOMOGENEOUS SHELLS
Directory of Open Access Journals (Sweden)
Bazhenov V.A.
2014-06-01
Full Text Available The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped mid-surface, geometrical features throughout the thickness, and multilayer structure under complex thermomechanical loading. The method is based on the geometrically nonlinear equations of three-dimensional thermoelasticity and the moment finiteelement scheme. The method is justified numerically. Comparing solutions with those obtained by other authors and by software LIRA and SCAD is conducted.
Wei, Song; Chen, Wen; Hon, Y. C.
2016-11-01
This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.
Unified model and reverse recovery nonlinearities of the driven diode resonator.
de Moraes, Renato Mariz; Anlage, Steven M
2003-08-01
We study the origins of period doubling and chaos in the driven series resistor-inductor-varactor diode (RLD) nonlinear resonant circuit. We find that resonators driven at frequencies much higher than the diode reverse recovery rate do not show period doubling. Models of chaos based on the nonlinear capacitance of the varactor diode display a reverse-recovery-like effect, and this effect strongly resembles reverse recovery of real diodes. We find for the first time that in addition to the known dependence of the reverse recovery time on past current maxima, there are also important nonlinear dependencies on pulse frequency, duty cycle, and dc voltage bias. Similar nonlinearities are present in the nonlinear capacitance models of these diodes. We conclude that a history-dependent and nonlinear reverse-recovery time is an essential ingredient for chaotic behavior of this circuit, and demonstrate for the first time that all major competing models have this effect, either explicitly or implicitly. Besides unifying the two major models of RLD chaos, our work reveals that the nonlinearities of the reverse-recovery time must be included for a complete understanding of period doubling and chaos in this circuit.
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.
WIEDEMANN, A; MULLERKIRSTEN, HJW
1993-01-01
Considering the N = 1 supersymmetry transformations of supersymmetric nonlinear sigma models in 1 + 1 dimensions we construct explicitly conserved Noether currents associated with supersymmetry transformations and derive the associated conserved charges in terms of the basic fields. We compare this
Novel Reduced Order in Time Models for Problems in Nonlinear Aeroelasticity Project
National Aeronautics and Space Administration — Research is proposed for the development and implementation of state of the art, reduced order models for problems in nonlinear aeroelasticity. Highly efficient and...
Chortis, Dimitris I
2013-01-01
This book concerns the development of novel finite elements for the structural analysis of composite beams and blades. The introduction of material damping is also an important aspect of composite structures and it is presented here in terms of their static and dynamic behavior. The book thoroughly presents a new shear beam finite element, which entails new blade section mechanics, capable of predicting structural blade coupling due to composite coupling and/or internal section geometry. Theoretical background is further expanded towards the inclusion of nonlinear structural blade models and damping mechanics for composite structures. The models effectively include geometrically nonlinear terms due to large displacements and rotations, improve the modeling accuracy of very large flexible blades, and enable the modeling of rotational stiffening and buckling, as well as, nonlinear structural coupling. Validation simulations on specimen level study the geometric nonlinearities effect on the modal frequencies and...
Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model
Barghouty, A. F.; El-Nemr, K. W.; Baird, J. K.
2009-01-01
Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.
Nonlinear FOPDT Model Identification for the Superheat Dynamic in a Refrigeration System
DEFF Research Database (Denmark)
Yang, Zhenyu; Sun, Zhen; Andersen, Casper
2011-01-01
An on-line nonlinear FOPDT system identification method is proposed and applied to model the superheat dynamic in a supermarket refrigeration system. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its parameters are time dependent. After......-dependent parameters. The proposed method is firstly tested through a number of numerical examples, and then applied to model the superheat dynamic in a supermarket refrigeration system based on experimental data. As shown in these studies, the proposed method is quite promising in terms of reasonable accuracy, large...... the considered system is discretized, the nonlinear FOPDT identification problem is formulated as a Mixed Integer Non-Linear Programming problem, and then an identification algorithm is proposed by combining the Branch-and-Bound method and Least Square technique, in order to on-line identify these time...
On Calculating the Hougaard Measure of Skewness in a Nonlinear Regression Model with Two Parameters
Directory of Open Access Journals (Sweden)
S. A. EL-Shehawy
2009-01-01
Full Text Available Problem statement: This study presented an alternative computational algorithm for determining the values of the Hougaard measure of skewness as a nonlinearity measure in a Nonlinear Regression model (NLR-model with two parameters. Approach: These values indicated a degree of a nonlinear behavior in the estimator of the parameter in a NLR-model. Results: We applied the suggested algorithm on an example of a NLR-model in which there is a conditionally linear parameter. The algorithm is mainly based on many earlier studies in measures of nonlinearity. The algorithm was suited for implementation using computer algebra systems such as MAPLE, MATLAB and MATHEMATICA. Conclusion/Recommendations: The results with the corresponding output the same considering example will be compared with the results in some earlier studies.
National Research Council Canada - National Science Library
Aoki, Yasunori; Nordgren, Rikard; Hooker, Andrew C
2016-01-01
... a bottleneck in the analysis. We propose a preconditioning method for non-linear mixed effects models used in pharmacometric analyses to stabilise the computation of the variance-covariance matrix...
Walker, Christoph
2010-01-01
A parameter-dependent model involving nonlinear diffusion for an age-structured population is studied. The parameter measures the intensity of the mortality. A bifurcation approach is used to establish existence of positive equilibrium solutions.
Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbæk, Anders
for linearity is of particular interest as parameters of non-linear components vanish under the null. To solve the latter type of testing, we use the so-called sup tests, which here requires development of new (uniform) weak convergence results. These results are potentially useful in general for analysis...
Testing and inference in nonlinear cointegrating vector error correction models
DEFF Research Database (Denmark)
Kristensen, D.; Rahbek, A.
2013-01-01
the null of linearity, parameters of nonlinear components vanish, leading to a nonstandard testing problem. We apply so-called sup-tests to resolve this issue, which requires development of new(uniform) functional central limit theory and results for convergence of stochastic integrals. We provide a full...
Reduced-size kernel models for nonlinear hybrid system identification.
Le, Van Luong; Bloch, Grard; Lauer, Fabien
2011-12-01
This brief paper focuses on the identification of nonlinear hybrid dynamical systems, i.e., systems switching between multiple nonlinear dynamical behaviors. Thus the aim is to learn an ensemble of submodels from a single set of input-output data in a regression setting with no prior knowledge on the grouping of the data points into similar behaviors. To be able to approximate arbitrary nonlinearities, kernel submodels are considered. However, in order to maintain efficiency when applying the method to large data sets, a preprocessing step is required in order to fix the submodel sizes and limit the number of optimization variables. This brief paper proposes four approaches, respectively inspired by the fixed-size least-squares support vector machines, the feature vector selection method, the kernel principal component regression and a modification of the latter, in order to deal with this issue and build sparse kernel submodels. These are compared in numerical experiments, which show that the proposed approach achieves the simultaneous classification of data points and approximation of the nonlinear behaviors in an efficient and accurate manner.
Collapse arresting in an inhomogeneous quintic nonlinear Schrodinger model
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Schjødt-Eriksen, Jens; Christiansen, Peter Leth
1999-01-01
Collapse of (1 + 1)-dimensional beams in the inhomogeneous one-dimensional quintic nonlinear Schrodinger equation is analyzed both numerically and analytically. It is shown that in the vicinity of a narrow attractive inhomogeneity, the collapse of beams in which the homogeneous medium would blow up...
Nonlinear wave propagation studies, dispersion modeling, and signal parameters correction
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk
..: ..., 2004, 00. [European Workshop on FP6-AERONEWS /1./. Naples (IT), 13.09.2004-16.09.2004] EU Projects: European Commission(XE) 502927 - AERO-NEWS Institutional research plan: CEZ:AV0Z2076919 Keywords : nodestructive testing * nonlinear elastic wave spectroscopy Subject RIV: BI - Acoustics
Modelling lava flows by Cellular Nonlinear Networks (CNN: preliminary results
Directory of Open Access Journals (Sweden)
C. Del Negro
2005-01-01
Full Text Available The forecasting of lava flow paths is a complex problem in which temperature, rheology and flux-rate all vary with space and time. The problem is more difficult to solve when lava runs down a real topography, considering that the relations between characteristic parameters of flow are typically nonlinear. An alternative approach to this problem that does not use standard differential equation methods is Cellular Nonlinear Networks (CNNs. The CNN paradigm is a natural and flexible framework for describing locally interconnected, simple, dynamic systems that have a lattice-like structure. They consist of arrays of essentially simple, nonlinearly coupled dynamic circuits containing linear and non-linear elements able to process large amounts of information in real time. Two different approaches have been implemented in simulating some lava flows. Firstly, a typical technique of the CNNs to analyze spatio-temporal phenomena (as Autowaves in 2-D and in 3-D has been utilized. Secondly, the CNNs have been used as solvers of partial differential equations of the Navier-Stokes treatment of Newtonian flow.
A Note on a Nonlocal Nonlinear Reaction-Diffusion Model
Walker, Christoph
2011-01-01
We give an application of the Crandall-Rabinowitz theorem on local bifurcation to a system of nonlinear parabolic equations with nonlocal reaction and cross-diffusion terms as well as nonlocal initial conditions. The system arises as steady-state equations of two interacting age-structured populations.
A nonlinear long memory model for US unemployment
D.J.C. van Dijk (Dick); Ph.H.B.F. Franses (Philip Hans); R. Paap (Richard)
2000-01-01
textabstractTwo important empirical features of monthly US unemployment are that shocks to the series seem rather persistent and that unemployment seems to rise faster in recessions than that it falls during expansions. To jointly capture these features of long memory and nonlinearity, respectively,
A multilevel nonlinear mixed-effects approach to model growth in pigs
DEFF Research Database (Denmark)
Strathe, Anders Bjerring; Danfær, Allan Christian; Sørensen, H
2009-01-01
Growth functions have been used to predict market weight of pigs and maximize return over feed costs. This study was undertaken to compare 4 growth functions and methods of analyzing data, particularly one that considers nonlinear repeated measures. Data were collected from an experiment with 40...... pigs maintained from birth to maturity and their BW measured weekly or every 2 wk up to 1,007 d. Gompertz, logistic, Bridges, and Lopez functions were fitted to the data and compared using information criteria. For each function, a multilevel nonlinear mixed effects model was employed because....... Furthermore, studies should consider adding continuous autoregressive process when analyzing nonlinear mixed models with repeated measures....
Model Predictive Control of a Nonlinear System with Known Scheduling Variable
DEFF Research Database (Denmark)
Mirzaei, Mahmood; Poulsen, Niels Kjølstad; Niemann, Hans Henrik
2012-01-01
the control problem of the nonlinear system is simplied into a quadratic programming. Wind turbine is chosen as the case study and we choose wind speed as the scheduling variable. Wind speed is measurable ahead of the turbine, therefore the scheduling variable is known for the entire prediction horizon.......Model predictive control (MPC) of a class of nonlinear systems is considered in this paper. We will use Linear Parameter Varying (LPV) model of the nonlinear system. By taking the advantage of having future values of the scheduling variable, we will simplify state prediction. Consequently...
Grey Box Non-Linearities Modeling and Characterization of a BandPass BAW Filter
Directory of Open Access Journals (Sweden)
M. Mabrouk
2016-06-01
Full Text Available In this work, the non-linearities of a 3G/UMTS geared BandPass Bulk Acoustic Wave ladder filter composed of five resonators were modeled using non-linear modified Butterworth-Van Dyke model. The non-linear characteristics were measured and simulated, and they were compared and found to be fairly identical. The filter's central frequency is 2.12 GHz, the corresponding bandwidth is 61.55 MHz, and the quality factor is 34.55.
Cross-talk induces bifurcations in nonlinear models of synaptic plasticity.
Elliott, Terry
2012-02-01
Linear models of synaptic plasticity provide a useful starting-point for examining the dynamics of neuronal development and learning, but their inherent problems are well known. Models of synaptic plasticity that embrace the demands of biological realism are therefore typically nonlinear. Viewed from a more abstract perspective, nonlinear models of synaptic plasticity are a subset of nonlinear dynamical systems. As such, they may therefore exhibit bifurcations under the variation of control parameters, including noise and errors in synaptic updates. One source of noise or error is the cross-talk that occurs during otherwise Hebbian plasticity. Under cross-talk, stimulation of a set of synapses can induce or modify plasticity in adjacent, unstimulated synapses. Here, we analyze two nonlinear models of developmental synaptic plasticity and a model of independent component analysis in the presence of a simple model of cross-talk. We show that cross-talk does indeed induce bifurcations in these models, entirely destroying their ability to acquire either developmentally or learning-related patterns of fixed points. Importantly, the critical level of cross-talk required to induce bifurcations in these models is very sensitive to the statistics of the afferents' activities and the number of afferents synapsing on a postsynaptic cell. In particular, the critical level can be made arbitrarily small. Because bifurcations are inevitable in nonlinear models, our results likely apply to many nonlinear models of synaptic plasticity, although the precise details vary by model. Hence, many nonlinear models of synaptic plasticity are potentially fatally compromised by the toxic influence of cross-talk and other sources of noise and errors more generally. We conclude by arguing that biologically realistic models of synaptic plasticity must be robust against noise-induced bifurcations and that biological systems may have evolved strategies to circumvent their possible dangers.
Nonlinear dynamics of planetary gears using analytical and finite element models
Ambarisha, Vijaya Kumar; Parker, Robert G.
2007-05-01
Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.
Transform-both-sides nonlinear models for in vitro pharmacokinetic experiments.
Latif, A H M Mahbub; Gilmour, Steven G
2015-06-01
Transform-both-sides nonlinear models have proved useful in many experimental applications including those in pharmaceutical sciences and biochemistry. The maximum likelihood method is commonly used to fit transform-both-sides nonlinear models, where the regression and transformation parameters are estimated simultaneously. In this paper, an analysis of variance-based method is described in detail for estimating transform-both-sides nonlinear models from randomized experiments. It estimates the transformation parameter from the full treatment model and then the regression parameters are estimated conditionally on this estimate of the transformation parameter. The analysis of variance method is computationally simpler compared with the maximum likelihood method of estimation and allows a more natural separation of different sources of lack of fit. Simulation studies show that the analysis of variance method can provide unbiased estimators of complex transform-both-sides nonlinear models, such as transform-both-sides random coefficient nonlinear regression models and transform-both-sides fixed coefficient nonlinear regression models with random block effects.
Sliding Mode Control for Nonlinear System Based on T-S Model
Institute of Scientific and Technical Information of China (English)
WU Zhong-qiang
2002-01-01
Using T-S model as an approximation for nonlinear system, the nonlinear system has been fuzzy into local linear model. The variable structure controller designed by using Lyapunov theory insures the stability of system. The sliding mode controller is designed by using unit vector style, and it suit the uncertain elements satisfying matching condition or do not satisfy matching condition. The effect of the scheme has been tasted with a simulation of an inverted pendulum.
A Model for Estimating Nonlinear Deformation and Damage in Ceramic Matrix Composites (Preprint)
2011-07-01
AFRL-RX-WP-TP-2011-4232 A MODEL FOR ESTIMATING NONLINEAR DEFORMATION AND DAMAGE IN CERAMIC MATRIX COMPOSITES (PREPRINT) Unni Santhosh and...5a. CONTRACT NUMBER In-house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62102F 6. AUTHOR(S) Unni Santhosh and Jalees Ahmad 5d. PROJECT...Composite Materials, 2010 A Model for Estimating Nonlinear Deformation and Damage in Ceramic Matrix Composites Unni Santhosh and Jalees Ahmad Research
Estimation in continuous-time stochastic| volatility models using nonlinear filters
DEFF Research Database (Denmark)
Nielsen, Jan Nygaard; Vestergaard, M.; Madsen, Henrik
2000-01-01
Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308.......Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308....
A unified lattice Boltzmann model for some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Chai Zhenhua [State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074 (China); Shi Baochang [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)], E-mail: sbchust@126.com; Zheng Lin [Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074 (China)
2008-05-15
In this paper, a unified and novel lattice Boltzmann model is proposed for solving nonlinear partial differential equation that has the form DU{sub t} + {alpha}UU{sub x} + {beta}U{sup n}U{sub x} - {gamma}U{sub xx} + {delta} U{sub xxx} = F(x,t). Numerical results agree well with the analytical solutions and results derived by existing literature, which indicates the present model is satisfactory and efficient on solving nonlinear partial differential equations.
A WEAKLY NONLINEAR WATER WAVE MODEL TAKING INTO ACCOUNT DISPERSION OF WAVE PHASE VELOCITY
Institute of Scientific and Technical Information of China (English)
李瑞杰; 李东永
2002-01-01
This paper presents a weakly nonlinear water wave model using a mild slope equation and a new explicit formulation which takes into account dispersion of wave phase velocity, approximates Hedges' (1987) nonlinear dispersion relationship, and accords well with the original empirical formula. Comparison of the calculating results with those obtained from the experimental data and those obtained from linear wave theory showed that the present water wave model considering the dispersion of phase velocity is rational and in good agreement with experiment data.
On the geometry of classically integrable two-dimensional non-linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Mohammedi, N., E-mail: nouri@lmpt.univ-tours.f [Laboratoire de Mathematiques et Physique Theorique (CNRS - UMR 6083), Universite Francois Rabelais de Tours, Faculte des Sciences et Techniques, Parc de Grandmont, F-37200 Tours (France)
2010-11-11
A master equation expressing the zero curvature representation of the equations of motion of a two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. Special attention is paid to those representations possessing a spectral parameter. Furthermore, a closer connection between integrability and T-duality transformations is emphasised. Finally, new integrable non-linear sigma models are found and all their corresponding Lax pairs depend on a spectral parameter.
Nonlinear Stability of a SIRS Epidemic Model with Convex Incidence Rate
Buonomo, B.; Rionero, S.
2010-09-01
We study an epidemic model for infections with non permanent acquired immunity (SIRS). The incidence rate is assumed to be convex respect to the infective class. By using a peculiar Lyapunov function, we obtain necessary and sufficient conditions for the local nonlinear stability of equilibria. Conditions ensuring the global stability of the endemic equilibrium are also obtained. Our procedure allows to enlarge the class of incidence rates ensuring the Lyapunov nonlinear stability of the endemic equilibrium for SIRS models.
Forecasting RMB Exchange Rate Based on a Nonlinear Combination Model of ARFIMA, SVM, and BPNN
Directory of Open Access Journals (Sweden)
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.