Efficient reliability analysis with a CDA-based dimension-reduction model and polynomial chaos expansion

Abstract

Polynomial chaos expansion (PCE) is a versatile tool for building a meta-model in various engineering fields. Unfortunately, it is largely affected by the curse of dimensionality and its application for reliability analysis is usually hindered unless high truncated degrees are used. To alleviate this problem, this paper presents a new method based on contribution-degree analysis (CDA), an exact dimension-reduction model (DRM) and polynomial chaos expansion for efficient reliability analysis. First, the original performance function is decomposed as a summation of several component functions including one lower-dimensional interacting component function and several one-dimensional non-interacting component functions via a CDA-based DRM. Then, the full PCE or sparse PCE is employed to reconstruct the lower-dimensional interacting component function instead of the original complicated multi-dimensional performance function, whereas one-dimensional full PCEs are utilized for approximating the non-interacting component functions. In this way, we avoid building a PCE meta-model for the original multivariate performance function, thus the number of unknown coefficients is significantly reduced and the computational burden for reliability analysis is eased accordingly. Pertinent examples including both analytical performance functions and finite-element models are investigated, which demonstrates that the proposed method achieves a good trade-off of efficiency and accuracy for reliability analysis.