Maximum Entropy Approach for Stationary Response of Nonlinear Stochastic Oscillators

1991 ◽  
Vol 58 (1) ◽  
pp. 266-271 ◽  
Author(s):  
R. J. Chang
Keyword(s):  
Maximum Entropy ◽  
Density Function ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Nonlinear Function ◽  
Entropy Method ◽  
Nonlinear Stochastic System ◽  
Density Functions ◽  
Unknown Parameters ◽  
Stochastic Oscillators

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.

Statistical Linearization Model for the Response Prediction of Nonlinear Stochastic Systems Through Information Closure Method

2004 ◽  
Vol 126 (3) ◽  
pp. 438-448 ◽  
Author(s):  
R. J. Chang ◽  
S. J. Lin
Keyword(s):  
Maximum Entropy ◽  
Density Function ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Stability Boundary ◽  
Response Prediction ◽  
Linearization Method ◽  
System Response ◽  
Statistical Linearization ◽  
Nonlinear Stochastic System

A new linearization model with density response based on information closure scheme is proposed for the prediction of dynamic response of a stochastic nonlinear system. Firstly, both probability density function and maximum entropy of a nonlinear stochastic system are estimated under the available information about the moment response of the system. With the estimated entropy and property of entropy stability, a robust stability boundary of the nonlinear stochastic system is predicted. Next, for the prediction of response statistics, a statistical linearization model is constructed with the estimated density function through a priori information of moments from statistical data. For the accurate prediction of the system response, the excitation intensity of the linearization model is adjusted such that the response of maximum entropy is invariant in the linearization model. Finally, the performance of the present linearization model is compared and supported by employing two examples with exact solutions, Monte Carlo simulations, and Gaussian linearization method.

Reliability Analysis for Stiffened Plate on the Maximum Entropy Method

2012 ◽  
Vol 525-526 ◽  
pp. 361-364
Author(s):  
Jian He ◽  
Xiao Yan Chen
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Maximum Entropy ◽  
Density Function ◽  
Failure Probability ◽  
Maximum Entropy Method ◽  
Random Variables ◽  
Entropy Method ◽  
Stiffened Plate ◽  
Performance Function

Stiffened plate is widely used in vessel structure because of its high bearing capacity and low weight so the research of failure probability for stiffened plate under explosion load has important engineering meaning. Stiffened plate under near-field explosion is taken as research subject, dynamite density and yield stress of plate are selected as random variables, the original values of one hundred groups of random variables are gotten through the random number generation program, and the moments of random variables are obtained. Based on failure criterion of displacement ductility, the performance function of structure is established, probability density function of performance function is fitted using maximum entropy method then the failure probability of stiffened plate structure is obtained. So as to solve the problem of calculate failure probability when the sample size is small and the probability density function is unknown.

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