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In reliability analysis for the practical engineering problems with the time-consuming model, it has become an important challenge that how to obtain accurate reliability assessment with a minimum number of calls. In order to reduce the computational cost, this paper develops a new sequential surrogate method combining adaptive kriging and Markov chain Monte Carlo simulation with a novel learning strategy for reliability analysis. The proposed method is named AK-MCMC, which takes full advantage of the classification feature of reliability analysis based on the surrogate models, and it can efficiently approximate the classification boundary of the performance function. First, the learning strategy is developed to sequentially pick out the informative samples for updating the experimental design samples. Then, a new stopping criterion is adopted to guarantee the classification accuracy of the constructed kriging model. In this way, the proposed method skillfully makes reliability evaluation independent of an adaptive iterative process, which greatly improves the efficiency of model refinement. Finally, the proposed method is applied to several examples, which contain small failure probability problem, non-linearity problem, and engineering problem with an implicit performance function. In particular, the efficiency of the proposed AK-MCMC method is proved for the problems with small failure probability.

A New Sequential Surrogate Method for Reliability Analysis and its Applications in Engineering