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 non-stationary response PDFs estimated by the improved WPI approach agree well with the Monte Carlo simulation results.