论文标题
Shapley效应效果估计以可靠性为导向的灵敏度分析，并通过重要性抽样进行相关输入
Shapley effect estimation in reliability-oriented sensitivity analysis with correlated inputs by importance sampling
论文作者
论文摘要
面向可靠性的灵敏度分析旨在通过量化数值模型的每个输入变量对与其失败相关的兴趣量的影响来结合可靠性和灵敏度分析。特别是，目标灵敏度分析的重点是发生故障的发生，并且更精确地旨在确定哪些输入更有可能导致系统故障。沙普利效应是能够处理相关输入变量的定量全局灵敏度指数。它们最近已适应目标灵敏度分析框架。在本文中，我们研究了这些指标的两个基于重要性抽样的估计方案，这些索引比现有概率较小时更有效。此外，只有I.I.D.提出了根据重要性采样辅助分布分布的输入/输出n样本。此扩展只能根据可靠性分析的重要性采样辅助分布来估算Shapley效应，而没有对数值模型进行其他调用。此外，从理论上讲，我们研究了某些估计器的偏差以及重要性采样的好处。我们还提供了数值准则，最后，现实的测试案例显示了所提出方法的实际兴趣。
Reliability-oriented sensitivity analysis aims at combining both reliability and sensitivity analyses by quantifying the influence of each input variable of a numerical model on a quantity of interest related to its failure. In particular, target sensitivity analysis focuses on the occurrence of the failure, and more precisely aims to determine which inputs are more likely to lead to the failure of the system. The Shapley effects are quantitative global sensitivity indices which are able to deal with correlated input variables. They have been recently adapted to the target sensitivity analysis framework. In this article, we investigate two importance-sampling-based estimation schemes of these indices which are more efficient than the existing ones when the failure probability is small. Moreover, an extension to the case where only an i.i.d. input/output N-sample distributed according to the importance sampling auxiliary distribution is proposed. This extension allows to estimate the Shapley effects only with a data set distributed according to the importance sampling auxiliary distribution stemming from a reliability analysis without additional calls to the numerical model. In addition, we study theoretically the absence of bias of some estimators as well as the benefit of importance sampling. We also provide numerical guidelines and finally, realistic test cases show the practical interest of the proposed methods.
