An Improved Wiener Path Integral Approach for Stochastic Response Estimation of Nonlinear Systems Under Non-White Excitation

Abstract

An improved Wiener path integral (WPI) approach is developed for predicting the stochastic response probability density functions (PDFs) of nonlinear systems under non-white excitation. Specifically, the excitation process is modeled as the output of a filter whose input is Gaussian white noise, the joint response PDF of the nonlinear system is expressed as a functional integral of the stochastic action over the space of all possible trajectories between the initial and final states, and the second-order variation of the stochastic action is recast to a quadratic form and taken into account in the estimation of the joint response PDF. Compared to the standard WPI approach where the second-order variation of the stochastic action is regarded as a constant, the improved WPI approach developed herein considers the fluctuations of the second-order variation of the stochastic action in the computational domain, thus improving the accuracy of the stochastic response estimation. Two numerical examples are illustrated, and the nonstationary response PDFs estimated by the improved WPI approach agree well with the Monte Carlo simulation results.