A direct probabilistic approach to solve state equations for nonlinear systems under random excitation

摘要

In this paper, a direct probabilistic approach (DPA) is presented to formulate and solve moment equations for nonlinear systems excited by environmental loads that can be either a stationary or nonstationary random process. The proposed method has the advantage of obtaining the response’s moments directly from the initial conditions and statistical characteristics of the corresponding external exci-tations. First, the response’s moment equations are directly derived based on a DPA, which is completely independent of the Itô/filtering approach since no specific assumptions regarding the correlation structure of excitation are made. By solving them under Gaussian closure, the response’s moments can be obtained. Subsequently, a multiscale algo-rithm for the numerical solution of moment equations is exploited to improve computational efficiency and avoid much wall-clock time. Finally, a comparison of the results with Monte Carlo (MC) simulation gives good agreement. Furthermore, the advantage of the multiscale algorithm in terms of efficiency is also demonstrated by an engineering example.