Direct Generation of Non-Gaussian Weighted Integrals

A simple numerical algorithm is proposed for directly generating realizations of weighted integrals (or, similarly, local averages) of non-Gaussian random fields for use in simulation-based stochastic finite-element analyses. The method uses a Gaussian quadrature integration rule to numerically evaluate an individual weighted integral (or local average), thus reducing the computation of the integral to a summation of a small number of properly weighted non-Gaussian random variables. Consequently, the need to generate actual realizations of the non-Gaussian random field is eliminated. The vector of non-Gaussian random variables is obtained from a nonlinear mapping of a vector of properly correlated Gaussian random variables, which in turn is obtained from a vector of uncorrelated Gaussian random variables using modal decomposition. The "proper" correlation structure of the Gaussian random variables is established a priori from the correlation structure of the non-Gaussian random variables, which itself is established a priori from the known or desired correlation structure of the non-Gaussian random field. Numerical results are provided to demonstrate the statistical equivalence of weighted integrals (or local averages) generated using the proposed approach to those computed using conventional numerical integration of actual realizations of the nonGaussian random field.