A novel reliability analysis method combining adaptive relevance vector machine and subset simulation for small failure probability

In this paper, a novel reliability analysis method is proposed by combining relevance vector machine and subset simulation (RVM-SS). It not only improves the computational efficiency of reliability analysis that requires expensive finite element simulations, but also ensures the accuracy of the evaluated failure probability. In this method, relevance vector machine (RVM) is first utilized to approach relatively rough limit states. Subsequently, subset simulation (SS) is performed based on the constructed RVM. Simultaneously, in order to improve the prediction accuracy of RVM, samples in the first and last level of SS are used for the sequential refinement of RVM. In addition, a learning function considering the current design of experiment position and a stopping condition for reliability prediction error estimation are applied to avoid redundant iterations in RVM update process. The updated RVM proves to have a high prediction accuracy for sample symbols, so the obtained failure probability is accurate. Furthermore, the samples are predicted by the carefully constructed RVM instead of being assessed with the time-consuming performance function, resulting in a significant reduction in computational effort. The efficiency and accuracy of the proposed method are verified by five examples involving small failure probability, nonlinearity, high-dimensional and implicit problems.