An explicit method for simulating non-Gaussian and non-stationary stochastic processes by Karhunen-Loève and polynomial chaos expansion

Abstract

A new method is developed for explicitly representing and synthesizing non-Gaussian and non-stationary stochastic processes that have been specified by their covariance function and marginal cumulative distribution function. The target process is firstly represented in the Karhunen-Loève (K-L) series form, the random coefficients in the K-L series is subsequently decomposed using one-dimensional polynomial chaos (PC) expansion. In this way, the target process is represented in an explicit form, which is particularly well suited for stochastic finite element analysis of structures as well as for general purpose simulation of realizations of these processes. The key feature of the proposed method is that the covariance of the resulting process automatically matches the target covariance, and one only needs to iterate the marginal distribution to match the target one. Three illustrative examples are used to demonstrate the proposed method.