Non-Gaussian linearization method for stochastic parametrically and externally excited nonlinear systems

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Abstract

A new practical non-Gaussian linearization method is developed for the problem of the dynamic response of a stable nonlinear system under both stochastic parametric and external excitations. The non-Gaussian linearization system is derived through a non-Gaussian density that is constructed as the weighted sum of undetermined Gaussian densities. The undetermined Gaussian parameters are then derived through solving a set of nonlinear algebraic moment relations. The method is illustrated by a Duffing-type stochastic system with/without parametric noise excited term. The accuracy in predicting the stationary and nonstationary variances by the present approach is compared with some exact solutions and Monte Carlo simulations.

Original languageEnglish
Pages (from-to)20-26
Number of pages7
JournalJournal of Dynamic Systems, Measurement and Control, Transactions of the ASME
Volume114
Issue number1
DOIs
Publication statusPublished - 1992 Jan 1

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linearization
nonlinear systems
Linearization
Nonlinear systems
Stochastic systems
dynamic response
Dynamic response
moments
excitation
simulation
Monte Carlo simulation

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Information Systems
  • Instrumentation
  • Mechanical Engineering
  • Computer Science Applications

Cite this

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AB - A new practical non-Gaussian linearization method is developed for the problem of the dynamic response of a stable nonlinear system under both stochastic parametric and external excitations. The non-Gaussian linearization system is derived through a non-Gaussian density that is constructed as the weighted sum of undetermined Gaussian densities. The undetermined Gaussian parameters are then derived through solving a set of nonlinear algebraic moment relations. The method is illustrated by a Duffing-type stochastic system with/without parametric noise excited term. The accuracy in predicting the stationary and nonstationary variances by the present approach is compared with some exact solutions and Monte Carlo simulations.

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