An efficient and robust Kriging-based method for system reliability analysis

Abstract System reliability analysis involving multiple failure modes is challenging when performance functions are associated with time-consuming codes. This paper aims to enhance the efficiency of system reliability analysis by reducing the number of evaluations of time-consuming models. To achieve that, an adaptive Kriging-based method is proposed. In order to develop the method, a quantificational error measure of Kriging models (i.e. surrogate models of performance functions associated with each failure mode) is first derived. The stepwise accuracy-improvement strategy (SAIS) is then modified to solve system reliability problems, and the modified SAIS is called SAIS-SYS. The method for system reliability analysis is finally developed based on the derived error measure and SAIS-SYS. In the proposed method, Kriging models, i.e. the surrogate models of original performance functions, are adaptively refreshed according to SAIS-SYS until the associated error measure is smaller than a prescribed threshold. After Kriging models meet with accuracy requirement, the system failure probability can be obtained through a random simulation method and no additional evaluations of original performance functions is needed. The accuracy, efficiency and robustness of the proposed method are validated by four examples.