Constructing adaptive generalized polynomial chaos method to measure the uncertainty in continuous models: A computational approach

Abstract

Due to errors in measurements and inherent variability in the quantities of interest, models based on random differential equations give more realistic results than their deterministic counterpart. The generalized polynomial chaos (gPC) is a powerful technique used to approximate the solution of these equations when the random inputs follow standard probability distributions. But in many cases these random inputs do not have a standard probability distribution. In this paper, we present a step-by-step constructive methodology to implement directly a useful version of adaptive gPC for arbitrary distributions, extending the applicability of the gPC. The paper mainly focuses on the computational aspects, on the implementation of the method and on the creation of a useful software tool. This tool allows the user to easily change the types of distributions and the order of the expansions, and to study their effects on the convergence and on the results. Several examples illustrating the usefulness of the method are included.