Maximum entropy method for estimation of response distribution of nonlinear systems subjected to non-white random excitation

Abstract

The approximate analytical method using the maximum entropy method (MEM) is proposed to estimate the stationary probability density function of nonlinear systems subjected to non-white random excitation. The MEM is often used to estimate the response distribution of nonlinear systems subjected to Gaussian white noise. In order to obtain the response distribution, the moment equations are used as the constraint conditions on the MEM. However, in the case of nonlinear systems under non-white random excitation, the term of the cross-correlation between the excitation and the response in the moment equations is generally not able to be calculated. In the proposed method, the equivalent linearization technique is applied to calculate the cross-correlation approximately. Using the method, we estimate the stationary response probability density functions of a Duffing oscillator and an asymmetric nonlinear system subjected to non-white excitation with the exponentially decaying correlation function. In the analysis, a wide range of the excitation bandwidth is considered. To demonstrate the effectiveness of the method, the results are compared with those of Monte Carlo simulation.