Reliability analysis method with small failure probability incorporated adaptive RBF model and multimodal optimization importance sampling

The purpose of structural reliability analysis is to estimate the failure probability of a structure under the action of multiple uncertainties, and traditional methods such as finite element analysis are very time-consuming in performing reliability analysis. To address this problem a new active learning (AL) method for structural reliability analysis that combines a radial basis function (RBF) model and an important sampling (IS) technique based on multimodal optimization is proposed, aiming at estimating small failure probabilities efficiently and accurately. The method uses the RBF model to build a metamodel of the true performance function based on the design of experiments (DoE), obtains the surrogate limit state surface (LSS), and then adopts the evolutionary multi-objective optimization-based multimodal optimization (EMO-MMO) method to acquire the most probable point (MPP) on the surrogate LSS, and builds an instrumental probability density functions (iPDF) based on the weight of each MPP. Finally, new training points are continuously added according to the convergence criterion to make the RBF model sufficiently accurate, and the structural failure probability is solved using the last trained RBF model. The verification results compared with classical reliability analysis and a complex engineering example show that the AL-RBF-IS method can significantly reduce the number of required training points and computing time while guaranteeing the accuracy, especially performing well when dealing with small failure probability problems.