CAJ | 학술논문

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。
위감소전통자집모의법구해실효개솔급가고성령민도고계치적방차，제출료일충기우조건기망적자집모의방법，기이론기출시전방차공식，즉다유변량조건기망적방차불대우변량자신적방차。소제방법장전통자집모의법중계산실효개솔화가고성령민도적다유종합변량균치적고계전환위조건기망균치적고계，병장조건기망균치적량중개솔고계진일보전환성가채용핵밀도진행계산적적분형식，종이가이재불증가전통자집모의법계산량적조건하감소고계치적방차。최후통과산례계산진일보험증료이론분석적정학성：기우조건기망적자집모의방법유효지감소료실효개솔화령민도계산결과적방차，제고료계산적수렴성화은정성。
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 .