An efficient hybrid reliability analysis method based on active learning Kriging model and multimodal‐optimization‐based importance sampling

Abstract

AbstractA novel method is proposed, which aims to solve rare‐event hybrid reliability problems with random and interval variables, where the performance function has various failure zones. It combines the active learning Kriging (ALK) model with importance sampling (IS) and evolutionary multimodal‐based multiobjective optimization (EMO‐MMO). The surrogate limit state surfaces (LSS) for the upper and lower failure probability bounds are respectively defined considering the Kriging variance. Failure candidate solutions located in different failure regions are generated by the EMO‐MMO method. Subsequently, all the most probable failure points (MPPs) are identified from those candidate solutions. The IS samples are simulated around the MPPs using the MPP‐based IS method. The IS samples located in unimportant regions are removed in order to improve the efficiency of approximating the surrogate LSSs. The optimal training points are selected from the truncated IS samples to update the Kriging model. After several training iterations, the surrogate LSSs are convergent. Ultimately, a reliable and unbiased estimation of the upper and lower failure probability bounds is provided. The performance of the ALK‐EMO‐IS‐HRA approach is verified through five application examples.