Simulating Stationary Non-Gaussian Processes Based on Unified Hermite Polynomial Model

Abstract

In determining structural responses under random excitation using the Monte Carlo method, simulation of non-Gaussian processes is always a challenge. Various methods have been developed to simulate non-Gaussian processes but literature suggests that the complete expression of the Gaussian correlation function matrix (CFM) and the corresponding applicable range of the target non-Gaussian CFM have not been attempted in the transformation based on the Hermite polynomial model (HPM) to date. The intention of this paper is to derive a complete transformation model of CFM from non-Gaussian to Gaussian processes with the applicable range of the target non-Gaussian CFM based on the unified Hermite polynomial model (UHPM). An efficient procedure for simulating stationary non-Gaussian processes is also presented for easy application. It is found in the paper that the complete transformation model of Gaussian CFM is necessary because HPMs are not always monotonic and that the proposed method can simulate stationary non-Gaussian processes efficiently and accurately. The proposed method can equip researchers and engineers with a more efficient and accurate tool to handle non-Gaussian processes frequently encountered in engineering practices.