Abstract Random excitations, such as wind velocity, always exhibit non-Gaussian features. Sample realisations of stochastic processes satisfying given features should be generated, in order to perform the dynamical analysis of structures under stochastic loads based on the Monte Carlo simulation. In this paper, an efficient method is proposed to generate stationary non-Gaussian stochastic processes. It involves an iterative scheme that produces a class of sample processes satisfying the following conditions. (1) The marginal cumulative distribution function of each sample process is perfectly identical to the prescribed one. (2) The ensemble-averaged power spectral density function of these non-Gaussian sample processes is as close to the prescribed target as possible. In this iterative scheme, the underlying processes are generated by means of the spectral representation method that recombines the upgraded power spectral density function with the phase contents of the new non-Gaussian processes in the latest iteration. Numerical examples are provided to demonstrate the capabilities of the proposed approach for four typical non-Gaussian distributions, some of which deviate significantly from the Gaussian distribution. It is found that the estimated power spectral density functions of non-Gaussian processes are close to the target ones, even for the extremely non-Gaussian case. Furthermore, the capability of the proposed method is compared to two other methods. The results show that the proposed method performs well with convergence speed, accuracy, and random errors of power spectral density functions.

中文翻译：

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通过迭代方案升级相位和幅度内容生成强非高斯随机过程

摘要 随机激励，如风速，总是表现出非高斯特征。应生成满足给定特征的随机过程的样本实现，以便基于蒙特卡罗模拟对随机载荷下的结构进行动力学分析。在本文中，提出了一种生成平稳非高斯随机过程的有效方法。它涉及一个迭代方案，该方案产生一类满足以下条件的样本过程。(1)每个样本过程的边际累积分布函数与规定的完全一致。(2)这些非高斯采样过程的集合平均功率谱密度函数尽可能接近规定的目标。在这个迭代方案中，底层过程是通过谱表示方法生成的，该方法将升级后的功率谱密度函数与最新迭代中新的非高斯过程的相位内容重新组合。提供了数值例子来证明所提出的方法对于四种典型的非高斯分布的能力，其中一些分布显着偏离高斯分布。发现非高斯过程的估计功率谱密度函数接近目标值，即使对于极端非高斯情况也是如此。此外，将所提出方法的能力与其他两种方法进行了比较。结果表明，该方法在收敛速度、精度和功率谱密度函数随机误差方面表现良好。