Simulation of a non-Gaussian stochastic process based on a combined distribution of the UHPM and the GBD

Abstract

To simulate non-Gaussian stochastic processes based on the first four moments, various simulation methods are presented, in which the determination of the transformation model and the calculation of the correlation coefficients between non-Gaussian stochastic processes and Gaussian stochastic processes are the critical procedures in these simulation methods. However, some existing simulation methods are limited to specific ranges. Furthermore, their practical applications are affected negatively due to the expensive cost of determining the transformation model and the correlation coefficients between non-Gaussian and Gaussian stochastic processes. Therefore, an accurate and efficient simulation method of a non-Gaussian stochastic process with a broader range is proposed in this article. Since the simulation of non-Gaussian processes and the Nataf transformation of non-Gaussian variables have some similar characteristics, a new combined distribution is proposed based on the unified Hermite polynomial model (UHPM) and the generalized beta distribution (GBD). Then, the combined distribution is employed in the simulation of non-Gaussian stochastic processes, in which the transformation model is deduced by the combined distribution. The correlation coefficient transformation function (CCTF) between the Gaussian and non-Gaussian stochastic processes can be evaluated through the interpolation method. Furthermore, numerical examples are presented to show the accuracy and effectiveness of the proposed simulation method for non-Gaussian stochastic processes.