Profust reliability analysis (RA) is established on probability assumption for the model inputs and fuzzy state assumption, and it is a useful tool to measure the safety degree of the structure with fuzzy failure state. In order to overcome the inefficiency of the existing AK-MCS method in profust RA for the structure with small profust failure probability, a novel dual-stage adaptive Kriging (DS-AK) method is proposed. Firstly, to improve the sampling efficiency, the importance sampling (IS) is used to estimate the profust failure probability where the optimal importance sampling density (OISD) is derived in this paper. As the analytical expression of the OISD cannot be acquired, the Kriging model for the true performance function is employed to build an approximate OISD. Then, the profust failure probability can be expressed as the product of the augmented profust failure probability and the correction factor, which are estimated in two different stages of the proposed DS-AK method. In the first stage of the DS-AK method, a Kriging model is constructed and updated to obtain the approximate OISD and generate the IS samples, and the augmented profust failure probability can be estimated as a byproduct. In the second stage of the DS-AK method, the current Kriging model is continuously updated to accurately predict the membership functions of the fuzzy failure domain at the IS samples generated in the first stage, from which the correction factor can be calculated efficiently. Finally, the fuzzy failure probability can be estimated as the product of augmented failure probability estimate obtained in the first stage and the correction factor estimate acquired in the second stage. Results of the validation cases demonstrate the accuracy, efficiency and robustness of the proposed method in estimating profust failure probability.

率模可靠性分析（RA）被上建立亲bability假设为模型的输入和福ZZY ST建立假设，是衡量具有模糊破坏状态的结构安全度的有用工具。为了克服现有的AK-MCS方法在profust RA中对profust失效概率较小的效率低下的问题，提出了一种新型的双阶段自适应克里格法（DS-AK）。首先，为了提高采样效率，本文采用重要性抽样（IS）估计了最优失效概率，并推导了最优重要性抽样密度（OISD）。由于无法获得OISD的解析表达式，因此采用真实性能函数的Kriging模型来构建近似OISD。然后，可以将profust失败概率表示为增加的profust失败概率与校正因子的乘积，在建议的DS-AK方法的两个不同阶段对它们进行估算。在DS-AK方法的第一阶段，构建和更新Kriging模型以获得近似OISD并生成IS样本，并且可以将增加的Profust失败概率估计为副产品。在DS-AK方法的第二阶段，将不断更新当前的Kriging模型，以准确预测第一阶段生成的IS样本上的模糊失效域的隶属函数，从而可以有效地计算出校正因子。最后，可以将模糊故障概率估计为第一阶段获得的增强故障概率估计值与第二阶段获得的校正因子估计值的乘积。验证案例的结果证明了准确性，