Combined relevance vector machine technique and subset simulation importance sampling for structural reliability

Abstract

Evaluating the failure probability of engineering structures involving implicit performance functions generally requires time-consuming finite element simulations. The computational effort is usually unbearable, especially for small failure probability. This paper proposes a new reliability analysis method combining relevance vector machine and subset simulation importance sampling, which guarantees the accuracy of results and improves the computational efficiency. In this method, relevance vector machine is first applied to approximate relatively coarse limit states. Then, subset simulation importance sampling is executed based on the constructed relevance vector machine. To improve the prediction accuracy, samples from first and last level are used to refine relevance vector machine. Since only the samples of last level are involved in the calculation of the failure probability, and the updated relevance vector machine has a very high prediction accuracy for the samples of last level, the obtained failure probability is extremely accurate. In addition, the samples are predicted by the well-constructed relevance vector machine rather than evaluated with real performance functions, which drastically decreases the calculation time. To reduce redundant iterations in the update process, a novel learning function based on the current design of experiment position and a stopping condition based on error estimation of reliability prediction are employed. Furthermore, the K-means clustering algorithm is utilized to implement the ability of surrogate model-based subset simulation importance sampling to handle multiple failure mode problems. The efficiency and accuracy of the proposed method are verified by four examples involving different types of features.