A data-driven polynomial chaos method considering correlated random variables

Abstract

Variable correlation commonly exists in practical engineering applications. However, most of the existing polynomial chaos (PC) approaches for uncertainty propagation (UP) assume that the input random variables are independent. To address variable correlation, an intrusive PC method has been developed for dynamic system, which however is not applicable to problems with black-box-type functions. Therefore, based on the existing data-driven PC method, a new non-intrusive data-driven polynomial chaos approach that can directly consider variable correlation for UP of black-box computationally expensive problems is developed in this paper. With the proposed method, the multivariate orthogonal polynomial basis corresponding to the correlated input random variables is conveniently constructed by solving the moment-matching equations based on the correlation statistical moments to consider the variable correlation. A comprehensive comparative study on several numerical examples of UP and design optimization under uncertainty with correlated input random variables is conducted to verify the effectiveness and advantage of the proposed method. The results show that the proposed method is more accurate than the existing data-driven PC method with Nataf transformation when the variable distribution is known, and it can produce accurate results with unknown variable distribution, demonstrating its effectiveness.