Nonlinear stochastic systems

Date Issued:: 1992
Summary:: This thesis is concerned with nonlinear dynamical systems subject to random or combined random and deterministic excitations. To this end, a systematic procedure is first developed to obtain the exact stationary probability density for the response of a nonlinear system under both additive and multiplicative excitations of Gaussian white noises. This procedure is applicable to a class of systems called the class of generalized stationary potential. The basic idea is to separate the circulatory probability flow from the noncirculatory flow, thus obtaining two sets of equations for the probability potential. It is shown that previously published exact solutions are special cases of this class. For those nonlinear systems not belonging to the class of generalized stationary potential, an approximate solution technique is developed on the basis of weighted residuals. The original system is replaced by the closest system belonging to the class of generalized stationary potential, in the sense that the statistically weighted residuals are zero for some suitably selected weighting functions. The consistency of the approximation technique is proved in terms of certain statistical moments. The above exact and approximate solution techniques are extended to two types of nonlinear systems: one subjected to non-Gaussian impulsive noise excitations and another subjected to combined harmonic and broad-band random excitations. Approximation procedures are devised to obtain stationary probabilistic solutions for these two types of problems. Monte Carlo simulations are performed to substantiate the accuracy of the approximate solution procedures.

Title:	Nonlinear stochastic systems.	66 views 38 downloads
Name(s):	Cai, Guo-Qiang Florida Atlantic University, Degree grantor Lin, Y. K., Thesis advisor College of Engineering and Computer Science Department of Ocean and Mechanical Engineering
Type of Resource:	text
Genre:	Electronic Thesis Or Dissertation
Issuance:	monographic
Date Issued:	1992
Publisher:	Florida Atlantic University
Place of Publication:	Boca Raton, Fla.
Physical Form:	application/pdf
Extent:	171 p.
Language(s):	English
Summary:	This thesis is concerned with nonlinear dynamical systems subject to random or combined random and deterministic excitations. To this end, a systematic procedure is first developed to obtain the exact stationary probability density for the response of a nonlinear system under both additive and multiplicative excitations of Gaussian white noises. This procedure is applicable to a class of systems called the class of generalized stationary potential. The basic idea is to separate the circulatory probability flow from the noncirculatory flow, thus obtaining two sets of equations for the probability potential. It is shown that previously published exact solutions are special cases of this class. For those nonlinear systems not belonging to the class of generalized stationary potential, an approximate solution technique is developed on the basis of weighted residuals. The original system is replaced by the closest system belonging to the class of generalized stationary potential, in the sense that the statistically weighted residuals are zero for some suitably selected weighting functions. The consistency of the approximation technique is proved in terms of certain statistical moments. The above exact and approximate solution techniques are extended to two types of nonlinear systems: one subjected to non-Gaussian impulsive noise excitations and another subjected to combined harmonic and broad-band random excitations. Approximation procedures are devised to obtain stationary probabilistic solutions for these two types of problems. Monte Carlo simulations are performed to substantiate the accuracy of the approximate solution procedures.
Identifier:	12293 (digitool), FADT12293 (IID), fau:9196 (fedora)
Collection:	FAU Electronic Theses and Dissertations Collection
Note(s):	College of Engineering and Computer Science Thesis (Ph.D.)--Florida Atlantic University, 1992.
Subject(s):	Nonlinear theories Stochastic systems Stochastic processes
Held by:	Florida Atlantic University Libraries
Persistent Link to This Record:	http://purl.flvc.org/fcla/dt/12293
Sublocation:	Digital Library
Use and Reproduction:	Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Use and Reproduction:	http://rightsstatements.org/vocab/InC/1.0/
Host Institution:	FAU
Is Part of Series:	Florida Atlantic University Digital Library Collections.

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