A new reliability method for small failure probability problems by combining the adaptive importance sampling and surrogate models

Reliability analysis for structural systems with multiple failure modes and expensive-to-evaluate simulations is challenging. In this paper, a new and efficient system reliability method is proposed based on the adaptive importance sampling and kriging models. The Metropolis–Hastings (M–H) algorithm is used to construct several Markov chains to fully explore complex failure regions. A number of Markov chain states are selected as the center of the component importance sampling functions to generate samples for reliability analysis. Based on the component importance sampling function of each selected chain state, the system importance sampling function is constructed with the weighting index. The system importance sampling function can be constructed effectively because it does not involve time-consuming simulations and the most probable point (MPP) search. The new learning function, which is directly linked to the system failure probability, is developed to adaptively select the best added samples for refining the kriging models at each iteration. The adaptive importance sampling method and kriging models are well-combined for system reliability analysis in the proposed method. Compared with existing methods, the proposed method, generally, offers the following advantages: (1) The learning function and stopping criterion are directly linked to system failure probability; (2)the adaptive importance sampling and kriging models are well-combined to yield accurate results based on a small sample size for small failure probability problems; (3) the weights of sampling centers are considered, and the MPP search is not required at each iteration; (4) it is applicable for complex systems regardless of the structure and system failure probability level. Three numerical examples are analyzed, which demonstrate that the proposed method is effective for complex system reliability analysis. •A new learning function by combining adaptive importance sampling and kriging models is proposed.•The MPP search is not required to construct the system importance sampling function at each iteration.•The learning function and stopping criterion are directly linked to system failure probability.•The proposed method requires a small sample size and is effective for small failure probability problems.•The proposed method can be used for complex structural systems with implicit performance functions.