An efficient reliability analysis strategy for low failure probability problems

For engineering, there are two major challenges in reliability analysis. First, to ensure the accuracy of simulation results, mechanical products are usually defined implicitly by complex numerical models that require time-consuming. Second, the mechanical products are fortunately designed with a large safety margin, which leads to a low failure probability. This paper proposes an efficient and high-precision adaptive active learning algorithm based on the Kriging surrogate model to deal with the problems with low failure probability and time-consuming numerical models. In order to solve the problem with multiple failure regions, the adaptive kernel-density estimation is introduced and improved. Meanwhile, a new criterion for selecting points based on the current Kriging model is proposed to improve the computational efficiency. The criterion for choosing the best sampling points considers not only the probability of misjudging the sign of the response value at a point by the Kriging model but also the distribution information at that point. In order to prevent the distance between the selected training points from too close, the correlation between training points is limited to avoid information redundancy and improve the computation efficiency of the algorithm. Finally, the efficiency and accuracy of the proposed method are verified compared with other algorithms through two academic examples and one engineering application.