A new model is proposed to represent and simulate Gaussian/non-Gaussian stochastic processes. In the proposed model, stochastic harmonic function (SHF) is extended to represent multivariate Gaussian process firstly. Compared with the conventional spectral representation method (SRM), the SHF based model requires much fewer variables and Cholesky decompositions. Then, SHF based model is further extended to univariate/multivariate non-Gaussian stochastic process simulation. The target non-Gaussian process can be obtained from the corresponding underlying Gaussian processes by memoryless nonlinear transformation. For arbitrarily given marginal probability distribution function (PDF), the covariance function of the underlying multivariate Gaussian process can be determined easily by introducing the Mehler’s formula. And when the incompatibility between the target non-Gaussian power spectral density (PSD) or PSD matrix and marginal PDF exists, the calibration of the target non-Gaussian spectrum will be required. Hence, the proposed model can be regarded as SRM to efficiently generate Gaussian/non-Gaussian processes. Finally, several numerical examples are addressed to show the effectiveness of the proposed method.

提出了一种新模型来表示和模拟高斯/非高斯随机过程。在所提出的模型中，首先扩展了随机调和函数（SHF）来表示多元高斯过程。与传统的频谱表示方法 (SRM) 相比，基于 SHF 的模型需要更少的变量和 Cholesky 分解。然后，基于 SHF 的模型进一步扩展到单变量/多变量非高斯随机过程模拟。目标非高斯过程可以通过无记忆非线性变换从相应的底层高斯过程中获得。对于任意给定的边际概率分布函数 (PDF)，可以通过引入 Mehler 公式轻松确定底层多元高斯过程的协方差函数。当目标非高斯功率谱密度（PSD）或PSD矩阵与边际PDF不兼容时，需要对目标非高斯谱进行校准。因此，所提出的模型可以被视为有效生成高斯/非高斯过程的 SRM。最后，通过几个数值例子来说明所提出方法的有效性。