Unconditional and conditional simulation of nonstationary and non-Gaussian vector and field with prescribed marginal and correlation by using iteratively matched correlation

Abstract

In many probabilistic analysis problems, the homogeneous/nonhomogeneous non-Gaussian field is represented as a mapped Gaussian field based on the Nataf translation system. We propose a new sample-based iterative procedure to estimate the underlying Gaussian correlation for homogeneous/nonhomogeneous non-Gaussian vector or field. The numerical procedure takes advantage that the range of feasible correlation coefficients for non-Gaussian random variables is bounded if the translation system is adopted. The estimated underlying Gaussian correlation is then employed for unconditional as well as conditional simulation of the non-Gaussian vector or field according to the theory of the translation process. We then present the steps for augmenting the simulated non-Gaussian field through the Karhunen-Loeve expansion for a refined discretized grid of the field. In addition, the steps to extend the procedure described in the previous section to the multi-dimensional field are highlighted. The application of the proposed algorithms is presented through numerical examples.