Non-linear Dynamical Systems (non-linear + dynamical_system)

Distribution by Scientific Domains


Selected Abstracts


Non-parametric,parametric model for random uncertainties in non-linear structural dynamics: application to earthquake engineering

EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 3 2004
Christophe Desceliers
Abstract This paper deals with the transient response of a non-linear dynamical system with random uncertainties. The non-parametric probabilistic model of random uncertainties recently published and extended to non-linear dynamical system analysis is used in order to model random uncertainties related to the linear part of the finite element model. The non-linearities are due to restoring forces whose parameters are uncertain and are modeled by the parametric approach. Jayne's maximum entropy principle with the constraints defined by the available information allows the probabilistic model of such random variables to be constructed. Therefore, a non-parametric,parametric formulation is developed in order to model all the sources of uncertainties in such a non-linear dynamical system. Finally, a numerical application for earthquake engineering analysis is proposed concerning a reactor cooling system under seismic loads. Copyright 2003 John Wiley & Sons, Ltd. [source]


Performance characterization of a non-linear system as both an adaptive notch filter and a phase-locked loop

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 1 2004
M. Karimi-Ghartemani
Abstract The behaviour of a non-linear dynamical system is described. The system may be characterized as an adaptive notch filter, or alternatively, as a phase-locked loop. Either way, the system has the inherent capability of directly providing estimates of the parameters of the extracted sinusoidal component of its input signal, namely its amplitude, phase and frequency. The structure and mathematical properties of the system are presented for two cases of fixed-frequency and varying-frequency operation. The effects of parameter setting of the system on its performance are studied in detail using computer simulations. Transient and steady-state behaviour of the system are studied in the presence of noise. Simplicity of structure, high noise immunity and robustness and the capability of direct estimation of amplitude, phase and frequency are the salient features of the system when envisaged as an adaptive notch filter or a phase-locked loop. Copyright 2004 John Wiley & Sons, Ltd. [source]


Nonparametric probabilistic approach of uncertainties for elliptic boundary value problem

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6-7 2009
Christian SoizeArticle first published online: 2 FEB 200
Abstract The paper is devoted to elliptic boundary value problems with uncertainties. Such a problem has already been analyzed in the context of the parametric probabilistic approach of system parameters uncertainties or for random media. Model uncertainties are induced by the mathematical,physical process, which allows the boundary value problem to be constructed from the design system. If experiments are not available, the Bayesian approach cannot be used to take into account model uncertainties. Recently, a nonparametric probabilistic approach of both the model uncertainties and system parameters uncertainties has been proposed by the author to analyze uncertain linear and non-linear dynamical systems. Nevertheless, the use of this concept that has to be developed for dynamical systems cannot directly be applied for elliptic boundary value problem, for instance, for a linear elastostatic problem relative to an elastic bounded domain. We then propose an extension of the nonparametric probabilistic approach in order to take into account model uncertainties for strictly elliptic boundary value problems. The theory and its validation are presented. Copyright 2009 John Wiley & Sons, Ltd. [source]


A procedure for the computation of accurate PWL approximations of non-linear dynamical systems

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 2 2006
Lorenzo Repetto
Abstract In this paper we propose a variational method to find out piecewise-linear (PWL) approximations of non-linear dynamical systems in view of their circuit implementations. The method is based on some significant trajectories of the dynamical system and provides reasonably accurate PWL approximations with a relatively low number of parameters. The effectiveness of the method is validated by applying it to the approximation of limit cycles (both stable and unstable) in the Bautin system. Copyright 2006 John Wiley & Sons, Ltd. [source]