Simulating Multivariate Multidimensional Homogenous Non-Gaussian Field Based on Unified Hermite Polynomial Model

Abstract

Reasonable simulation of stochastic fields is a key prerequisite for addressing stochastic mechanics problems with Monte Carlo simulation solver. This paper presents a novel method to simulate m-variate and n-dimensional (mV-nD) homogenous non-Gaussian fields according to the prescribed power spectral density matrix (PSDM) and first four moments. In the proposed method, the unified Hermite polynomial model (UHPM) is first extended to mV-nD homogenous non-Gaussian fields. Then, based on the extended UHPM, a complete transformation model from the normalized non-Gaussian correlation function matrix (CFM) into the underlying Gaussian CFM with its applicable range is derived. In addition, two types of potential incompatibility of the transformation arising from the prescribed PSDM and first four moments are defined and neatly solved. Finally, a unified simulation framework for mV-nD homogenous non-Gaussian fields is presented, where the fast Fourier transform technique can be embedded in both spectral representation method and Wiener-Khintchine transformation to speed up the simulation progress. Two numerical examples including the simulations of non-Gaussian wind fields and non-Gaussian fields of material properties are presented to demonstrate the effectiveness of the proposed method.