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

Abstract

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.