Abstract

The probabilistic dependence in a multi-variate random field consists of two parts: the spatial dependence of a random quantity at different positions and the probabilistic dependence between different random variables at the same position. The classical model cannot capture the possible non-Gaussian dependence or nonlinear dependence between different random variables. To this end, in this paper, an approach by synthesizing the spatial correlation function and the multi-variate copula function (SCFVCF) is proposed. In this model, the correlation function model is adopted to quantify the spatial dependence involved in the random field of the prime variable, and the copula function model is adopted to quantify the dependence configuration between subordinate variables. The properties of such multi-variate random fields are then studied. To generate samples of such multi-variate random fields, the spectral representation method is incorporated with the conditional sampling method. As an example, to illustrate the application of SCFVCF, the random field of the constitutive parameters of concrete is adopted. The results demonstrate that the proposed method can capture the spatial dependence of compressive strength, and at the same time the dependence configuration between different parameters is consistent with the test complete compressive stress-strain curves.

摘要

多元随机场中的概率相关性由两部分组成：随机量在不同位置的空间相关性和同一位置不同随机变量之间的概率相关性。经典模型无法捕捉到不同随机变量之间可能存在的非高斯依赖或非线性依赖。为此，本文提出了一种综合空间相关函数和多元copula函数（SCFVCF）的方法。该模型采用相关函数模型量化主变量随机场所涉及的空间依赖关系，采用copula函数模型量化从属变量之间的依赖配置。然后研究这种多元随机场的性质。为了生成此类多变量随机场的样本，将谱表示方法与条件采样方法相结合。作为例子，为了说明SCFVCF的应用，采用混凝土本构参数的随机场。结果表明，所提出的方法可以捕获抗压强度的空间依赖性，同时不同参数之间的依赖配置与测试完整的压缩应力-应变曲线一致。