Adaptive relevance vector machine combined with Markov-chain-based importance sampling for reliability analysis

Many engineering systems involve complex implicit performance functions, and evaluating the failure probability of these systems usually requires time-consuming finite element simulations. In this research, a new reliability method is proposed by combining relevance vector machine and Markov-chain-based importance sampling (RVM-MIS), which improves computational efficiency by decreasing the number of expensive model simulations. Relevance vector machine (RVM) is a machine learning method based on the concept of probabilistic Bayesian learning framework. It is worth noting that RVM provides predicted value of the sample and corresponding variance. Due to this important feature, various active learning functions can be applied to improve the accuracy of RVM to approximate real performance functions. In addition, Markov-chain-based importance sampling (MIS) is utilized to generate important samples covering areas that significantly contribute to failure probability. The important samples are then predicted by a well-constructed RVM to obtain failure probability, rather than being evaluated using real performance functions, so the computation time is drastically decreased. RVM-MIS reduces the number of calls to real performance function while ensuring the accuracy of results. Four academic examples and a bearing statics problem with an implicit performance function are performed to verify the accuracy and efficiency of the proposed method.