失效概率矩独立全局灵敏度分析的高效算法

失效概率矩独立全局灵敏度分析对指导可靠性优化至关重要，本文从乘法降维及Edgeworth级数展开的角度提出一种失效概率矩独立全局灵敏度指标分析的高效算法。所提算法通过Edgeworth级数展开将失效概率矩独立全局灵敏度指标的求解转化为输出无条件及条件前四阶整数矩的求解。对于输出的无条件及条件四阶矩的计算，基于乘法降维的思想，本文推导了重复利用计算输出的无条件矩的输入输出样本来计算条件矩以及外层关于输入变量一维积分的计算公式，使得仅需重复利用输出无条件前四阶矩求解产生的积分网格内的数据即可同时求得输出的前四阶条件矩以及外层关于输入变量的一维积分。所提算法大大提高了失效概率矩独立全局灵敏度的分析效率。航空发动机涡轮盘以及汽车前轴的分析结果验证了所提算法的高效性及准确性。

Efficient algorithm for analyzing moment-independent global reliability sensitivity

The moment-independent global reliability sensitivity analysis can provide useful information for guiding the reliability-based design optimization. This paper proposes an efficient algorithm for moment-independent global reliability sensitivity analysis based on the multiplicative dimensional reduction technique and the Edgeworth expansion. By adopting Edgeworth expansion, the estimation of the moment-independent global reliability sensitivity index is approximately converted into the estimations of the unconditional and the conditional first four-order moments of the model output and is efficiently estimated by employing the multiplicative dimensional reduction technique. Based on this technique, this paper derives the algorithms of the conditional first four-order moments and the outer expectation of the sensitivity index by repeatedly assembling the information in the integration grid obtained from the estimation process of the unconditional first four-order moments of model output. The proposed algorithm improves the efficiency for analyzing the moment-independent global reliability sensitivity. The analyses of an aeroengine turbine disk and an automobile front axle demonstrate the efficiency and accuracy of the proposed method in estimating the moment-independent global reliability sensitivity index.