Sliced inverse regression-based sparse polynomial chaos expansions for reliability analysis in high dimensions

Abstract

Reliability analysis requires a large number of original model evaluations, especially for high-nonlinear and high-dimensional problems. This could be computationally expensive when a single evaluation is time-consuming, finite element models for example. Metamodeling techniques have been developed for reliability assessments in order to enhance computational efficiency. Polynomial chaos expansions are widely used for metamodel buildings, but suffering from the “curse of dimensionality”. This work proposes an efficient reliability method which combines the sliced inverse regression (SIR) with sparse polynomial chaos expansions (SPCE). The SIR technique is firstly adopted to achieve a dimension reduction by finding a new input vector which reduces the dimension of the original input vector without losing the essential information of model responses. Then a SPCE metamodel is built with respect to the reduced dimensionality by means of the stepwise regression technique. An iteration algorithm is employed to select the optimal metamodel for a given size of design of experiments. Three representative examples with random variables ranging from 6 to 300 are provided for validation, which show great effectiveness and efficiency of the proposed approach, particularly for high-dimensional problems.