Zhao Jianyu, Zeng Shengkui, Guo Jianbin, Du Shaohua
School of Reliability and Systems Engineering, Beihang University, Beijing 100191, China.
Science and Technology on Reliability and Environmental Engineering Laboratory, Beihang University, Beijing 100191, China.
Entropy (Basel). 2018 Mar 16;20(3):202. doi: 10.3390/e20030202.
To optimize contributions of uncertain input variables on the statistical parameter of given model, e.g., reliability, global reliability sensitivity analysis (GRSA) provides an appropriate tool to quantify the effects. However, it may be difficult to calculate global reliability sensitivity indices compared with the traditional global sensitivity indices of model output, because statistical parameters are more difficult to obtain, Monte Carlo simulation (MCS)-related methods seem to be the only ways for GRSA but they are usually computationally demanding. This paper presents a new non-MCS calculation to evaluate global reliability sensitivity indices. This method proposes: (i) a 2-layer polynomial chaos expansion (PCE) framework to solve the global reliability sensitivity indices; and (ii) an efficient method to build a surrogate model of the statistical parameter using the maximum entropy (ME) method with the moments provided by PCE. This method has a dramatically reduced computational cost compared with traditional approaches. Two examples are introduced to demonstrate the efficiency and accuracy of the proposed method. It also suggests that the important ranking of model output and associated failure probability may be different, which could help improve the understanding of the given model in further optimization design.
为了优化给定模型的不确定输入变量对统计参数（如可靠性）的贡献，全局可靠性灵敏度分析（GRSA）提供了一种合适的工具来量化这些影响。然而，与模型输出的传统全局灵敏度指标相比，计算全局可靠性灵敏度指标可能会很困难，因为统计参数更难获得，与蒙特卡罗模拟（MCS）相关的方法似乎是进行GRSA的唯一途径，但它们通常计算量很大。本文提出了一种新的非MCS计算方法来评估全局可靠性灵敏度指标。该方法提出：（i）一个两层多项式混沌展开（PCE）框架来求解全局可靠性灵敏度指标；（ii）一种有效的方法，利用PCE提供的矩，采用最大熵（ME）方法构建统计参数的代理模型。与传统方法相比，该方法的计算成本大幅降低。通过两个例子来证明所提方法的效率和准确性。研究还表明，模型输出的重要性排序和相关的失效概率可能不同，这有助于在进一步的优化设计中加深对给定模型的理解。
