Maximum Entropy Approach for Stationary Response of Nonlinear Stochastic Oscillators

[+] Author and Article Information
R. J. Chang

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101 Republic of China

J. Appl. Mech 58(1), 266-271 (Mar 01, 1991) (6 pages) doi:10.1115/1.2897162 History: Received January 10, 1989; Revised May 04, 1989; Online March 31, 2008


A new approach based on the maximum entropy method is developed for deriving the stationary probability density function of a stable nonlinear stochastic system. The technique is implemented by employing the density function with undetermined parameters from the entropy method and solving a set of algebraic moment equations from a nonlinear stochastic system for the unknown parameters. For a wide class of stochastic systems with given density functions, an explicit density function of the stochastic system perturbed by a nonlinear function of states and noises can be obtained. Three nonlinear oscillators are selected for illustrating the present scheme and the validity of the derived density functions is further supported by some exact solutions and Monte Carlo simulations.

Copyright © 1991 by The American Society of Mechanical Engineers
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