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的求解十分耗时。为此，本文建立了极小失效概率估计的元模型二次重要抽样法。在所建方法中，分层加权聚类策略被设计来二次构造归一化因子估计的重要抽样密度，提高了归一化因子的估计效率。算例结果表明，在精度一致的条件下，本文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，本文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 method (Meta-IS) 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, this paper proposes a meta-model-based double importance sampling method (Meta-IS2) for estimating extremely small failure probabilities. In the proposed method, a hierarchical weighted clustering strategy is designed to construct an IS-PDF for estimating the normalization factor, thereby improving the computational efficiency of the reliability analysis. Under equivalent accuracy, the computational efficiency of the proposed method significantly outperforms that of the existing Meta-IS in the cases with extremely small failure probabilities, as demonstrated through three numerical and one engineering case studies.