Quantification of multiple-variate random field by synthesizing the spatial correlation function of prime variable and copula function

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.