为减小传统子集模拟法求解失效概率及可靠性灵敏度估计值的方差，提出了一种基于条件期望的子集模拟方法，其理论基础是全方差公式，即多维变量条件期望的方差不大于变量自身的方差。所提方法将传统子集模拟法中计算失效概率和可靠性灵敏度的多维综合变量均值的估计转换为条件期望均值的估计，并将条件期望均值的两重概率估计进一步转换成可采用核密度进行计算的积分形式，从而可以在不增加传统子集模拟法计算量的条件下减小估计值的方差。最后通过算例计算进一步验证了理论分析的正确性：基于条件期望的子集模拟方法有效地减小了失效概率和灵敏度计算结果的方差，提高了计算的收敛性和稳定性。%In order to reduce the variance in estimating the probability failure and reliability sensitivity , an im-proved subset simulation method is put forward .The proposed method is based on total variance formula in which the variance of the multidimensional variables with conditional expectation is not greater than that of the variables themselves.So that the mean of multidimensional variables to estimate the probability failure and reliability sensitiv -ity is transformed into the mean of conditional expectation in this paper .The latter contains twofold probability esti-mation and then is converted into an integral form that can be estimated with kernel density to reduce the variance without calculation increasing .Finally, some examples demonstrate that the theoretical analysis is correct and the proposed method reduces the variance and improves the convergence and stability in calculating the probability fail -ure and reliability effectively .
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