Novel Hermite Polynomial Model Based on Probability-Weighted Moments for Simulating Non-Gaussian Stochastic Processes

Abstract

The Hermite polynomial model based on the first-four central moments of non-Gaussian distribution is widely applied to simulate non-Gaussian stochastic processes due to its simplicity and efficiency. Although a variety of expressions have been developed to approximate the coefficients of the Hermite polynomial model, unsatisfactory accuracy and limited applicability could still be encountered. Compared to the central moments, probability-weighted moments possess abundant characteristics of probability distribution. In this paper, a new form of Hermite polynomial model is proposed based on probability-weighted moments for simulating non-Gaussian stochastic processes. The coefficients of the Hermite polynomial model can be conveniently determined via a linear system of equations, leading to a wide application range of the model. More importantly, the sample accuracy for simulating non-Gaussian processes can be significantly improved, and the incompatibility problem can be avoided to some extent by using the proposed model. In addition, a fast strategy for determining the Gaussian auto-correlation function is also suggested, which avoids the complicated manipulations of cubic equations of Gaussian and non-Gaussian auto-correlation functions. A classical example is investigated to demonstrate the better accuracy and applicability over conventional Hermite polynomial models for simulating non-Gaussian stochastic processes. Two engineering cases are also investigated to demonstrate practical applications of the proposed model.