An adaptive polynomial chaos expansion for high-dimensional reliability analysis

Abstract

Efficiency is greatly concerned in reliability analysis community, especially for the problems with high-dimensional input random variables, because the computation cost of common reliability analysis methods may increase sharply with respect to the dimension of the problem. This paper proposes a novel meta-model based on the concepts of polynomial chaos expansion (PCE), dimension-reduction method (DRM), and information-theoretic entropy. Firstly, a PCE method based on DRM is developed to approximate the original function by a series of PCEs of univariate components. Compared with the PCE of the original function, the DRM-based PCE can reduce the computational cost. Before constructing the meta-model, a prior of the degree of the PCE is required, which determines the accuracy and efficiency of the PCE. However, the prior is usually determined by experience. According to the maximum entropy principle, this paper proposes an adaptive method for the selection of the polynomial chaos basis efficiently. With the adaptive PCE method based on DRM, a novel meta-model method is proposed, with which the reliability analysis can be achieved by Monte Carlo simulation efficiently. In order to verify the performance of the proposed method, three numerical examples and one structural dynamics engineering example are tested, with good accuracy and efficiency.