Simulating strongly non-Gaussian and non-stationary processes using Karhunen–Loève expansion and L-moments-based Hermite polynomial model

Abstract

A novel and efficient method is proposed for simulating strongly non-Gaussian and non-stationary processes by combining Karhunen–Loève expansion with Linear-moments-based (L-moments-based) Hermite polynomial model (HPM). In this method, the complete transformation from non-stationary non-Gaussian auto-correlation function (ACF) to non-stationary Gaussian ACF is realized using L-moments-based HPM. Then, the underlying Gaussian processes is represented by Karhunen–Loève expansion and further transformed into target non-stationary non-Gaussian processes by L-moments-based HPM. Moreover, a novel approach is proposed to deal with the two kinds of incompatibilities that may occur in strongly non-Gaussian processes, including that non-stationary non-Gaussian ACF falls outside of its applicable range and non-stationary Gaussian ACF is non-positive semi-definite. It can be found from some representative numerical examples that the precision and efficiency of the proposed method are considerable.