Finite dimensional models for random functions

Abstract

Truncated Karhunen–Loève (KL) representations are used to construct finite dimensional (FD) models for non-Gaussian functions with finite variances. The second moment specification of the random coefficients of these representations are enhanced to full probabilistic characterization by using translation, polynomial chaos, and translated polynomial chaos models, referred to as T, PC, and PCT models. Following theoretical considerations on KL representations and T, PC, and PCT models, three numerical examples are presented to illustrate the implementation and performance of these models. The PCT models inherit the desirable features of both T and PC models. It approximates accurately all quantities of interest considered in these examples.