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.
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March 1991
Research Papers
Maximum Entropy Approach for Stationary Response of Nonlinear Stochastic Oscillators
R. J. Chang
R. J. Chang
Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101 Republic of China
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R. J. Chang
Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 70101 Republic of China
J. Appl. Mech. Mar 1991, 58(1): 266-271 (6 pages)
Published Online: March 1, 1991
Article history
Received:
January 10, 1989
Revised:
May 4, 1989
Online:
March 31, 2008
Citation
Chang, R. J. (March 1, 1991). "Maximum Entropy Approach for Stationary Response of Nonlinear Stochastic Oscillators." ASME. J. Appl. Mech. March 1991; 58(1): 266–271. https://doi.org/10.1115/1.2897162
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