A transformation-based framework for modeling and simulation of multivariate non-Gaussian random fields

Résumé fourni par la source

Accurate modeling of multivariate non-Gaussian random fields remains a fundamental challenge in reliable engineering computation, particularly when nonlinear dependencies coexist with spatial correlation. This study introduces a new framework in which the probabilistic model is defined by the original marginal distributions together with linear correlations of Gaussianized transformed variables. This leads to a transformed correlation function that preserves non-Gaussian marginals while consistently characterizing spatial variability. The bridge function, originally developed for Gaussian fields, is extended to reconcile spatial correlation with nonlinear dependencies such as those captured by vine copulas. Based on this model, an efficient non-iterative simulation algorithm is developed. Numerical results show that the method accurately reproduces marginal distributions, nonlinear dependence, and spatial correlation in complex engineering fields.

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