Meta-model-based double importance sampling method for extremely small failure probability estimation

Based on a surrogate model of the performance function with an adaptive learning strategy, the metamodel-based importance sampling (Meta-IS) method can approximate the optimal importance sampling probability density function (IS-PDF) for estimating failure probabilities, making it an efficient approach for reliability analysis. However, when dealing with extremely small failure probabilities, estimating the normalization factor in the IS-PDF becomes computationally expensive for Meta-IS. To mitigate the computational burden, a meta-model-based double importance sampling (Meta-IS₂) method for estimating extremely small failure probabilities is proposed. The hierarchical weighted clustering strategy is designed to construct an IS-PDF for estimating the normalization factor. The feasibility of the proposed method is verified with instants. The results show that, under equivalent accuracy, the computational efficiency of the proposed method is no less than that of the existing Meta-IS method. Furthermore, for the cases with extremely small failure probabilities, the proposed method significantly outperforms that of the existing Meta-IS method.