A recursive dimension-reduction method for high-dimensional reliability analysis with rare failure event

Abstract

A new dimension-reduction method (DRM), called ’subset active subspace method (SASM)’, is proposed to compute small failure probabilities encountered in high-dimensional reliability analysis of engineering systems. The basic idea is to introduce a recursive procedure to improve the efficiency, accuracy and applicability of the conventional active subspace method (ASM). For the reliability problems with a rare event, SASM firstly transfers the original high-dimensional reliability problem into a low-dimensional reliability problem in a proper failure domain. Then, a simplified low-dimensional surrogate model is built in order to improve the result of reliability analysis by increasing significantly the samples with a minimum additional computational effort. The proposed method is verified by three nonlinear numerical examples, including theoretical and industrial, explicit and implicit performance functions. Besides, some other existing methods are also investigated and compared to the proposed method. It is found that the proposed method can keep the trade-off between accuracy and efficiency.