Abstract

This paper presents an adaptive-sparse polynomial chaos expansion (adaptive-sparse PCE) method for performing engineering reliability analysis and design. The proposed method leverages three ideas: (i) an adaptive scheme to build sparse PCE with the minimum number of bivariate basis functions, (ii) a new projection method using dimension reduction techniques to effectively compute the expansion coefficients of system responses, and (iii) an integration of copula to handle nonlinear correlation of input random variables. The proposed method thus has three distinct features for reliability analysis and design: (a) no need of response sensitivities, (b) no extra cost to evaluate probabilistic sensitivity for design, and (c) capability to handle a nonlinear correlation. Besides, an error decomposition scheme of the proposed method is presented to help analyze error sources in probability analysis. Several engineering problems are used to demonstrate the effectiveness of the adaptive-sparse PCE method.