Simulation of Multi-Dimensional Gaussian Stochastic Fields by Spectral Representation
Simulation of Multi-Dimensional Gaussian Stochastic Fields by Spectral Representation
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DOI：
10.1115/1.3101883
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发表时间：
1996
影响因子：
14.3
通讯作者：
M. Shinozuka;G. Deodatis
中科院分区：
文献类型：
--
作者：
M. Shinozuka;G. Deodatis
本文的主题是用谱表示法模拟多维均匀高斯随机场。按照这种方法，可以使用余弦级数公式生成随机场的样本函数。当余弦级数中的项数较大时，这些样本函数准确地反映了随机场的规定概率特性。随着样本容量的增加，总体平均功率谱密度或自相关函数接近相应的目标函数。此外，当在与余弦序列基本周期相关的多维域上进行平均时，生成的样本函数具有遍历特性，即空间平均均值、自相关函数和功率谱密度函数与相应的目标相同。模拟随机场的另一个性质是，当余弦级数中的项数接近无穷大时，它是渐近高斯的。该方法的最重要的特点是，余弦级数公式可以非常有效地使用快速傅立叶变换技术进行数值计算。该方法的主要应用领域是结构工程、工程力学和物理学中随机问题的蒙特卡罗解。具体而言，该方法已被应用到涉及随机加载（随机振动理论）和随机材料和几何特性（由于系统随机性的响应变异性）的问题。
The subject of this paper is the simulation of multi-dimensional, homogeneous, Gaussian stochastic fields using the spectral representation method. Following this methodology, sample functions of the stochastic field can be generated using a cosine series formula. These sample functions accurately reflect the prescribed probabilistic characteristics of the stochastic field when the number of terms in the cosine series is large. The ensemble-averaged power spectral density or autocorrelation function approaches the corresponding target function as the sample size increases. In addition, the generated sample functions possess ergodic characteristics in the sense that the spatially-averaged mean value, autocorrelation function and power spectral density function are identical with the corresponding targets, when the averaging takes place over the multi-dimensional domain associated with the fundamental period of the cosine series. Another property of the simulated stochastic field is that it is asymptotically Gaussian as the number of terms in the cosine series approaches infinity. The most important feature of the method is that the cosine series formula can be numerically computed very efficiently using the Fast Fourier Transform technique. The main area of application of this method is the Monte Carlo solution of stochastic problems in structural engineering, engineering mechanics and physics. Specifically, the method has been applied to problems involving random loading (random vibration theory) and random material and geometric properties (response variability due to system stochasticity).