在自适应训练功能函数代理模型的基础上，元模型重要抽样方法可以逼近求解失效概率的最优重要抽样密度，因此其可以高效解决可靠性分析问题。然而，在面对极小失效概率时，元模型重要抽样密度中包含的归一化因子求解十分耗时。为此，提出极小失效概率估计的元模型二次重要抽样方法，设计分层加权聚类策略来二次构造归一化因子估计的重要抽样密度，并通过算例对所提方法的有效性进行验证。结果表明：在精度一致的条件下，所提方法的效率不低于已有的元模型重要抽样方法，且对于极小失效概率估计问题，所提方法的效率远高于已有的元模型重要抽样方法。

Based on a surrogate model of the performance function with an adaptive learning strategy， the meta-model-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.