利用多项式混沌展开计算基于导数的全局灵敏度测度
Computing derivative-based global sensitivity measures using polynomial chaos expansions
摘要：
在计算机实验领域，敏感性分析旨在量化计算模型的每个输入参数（或其组合）相对于模型输出不确定性的相对重要性。方差分解方法导致众所周知的Sobol'指数被认为是准确的技术，在一个相当高的计算成本，虽然。使用多项式混沌展开（PCE）来计算Sobol指数，可以减轻计算负担。然而，在处理大维度输入向量时，首先使用筛选方法以丢弃不重要的变量是一种良好的做法。在这方面，最近开发了{ \em基于导数的全球敏感性度量}（DGSM）。在本文中，我们将展示如何多项式混沌展开可用于计算分析DGSMs作为一个纯粹的后处理。这需要分析推导的正交多项式的衍生物进入PC的扩展。在敏感性分析中的两个著名的基准问题上说明了该方法的有效性。
英文摘要：
In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol' indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to alleviate the computational burden though. However, when dealing with large dimensional input vectors, it is good practice to first use screening methods in order to discard unimportant variables. The {\em derivative-based global sensitivity measures} (DGSM) have been developed recently in this respect. In this paper we show how polynomial chaos expansions may be used to compute analytically DGSMs as a mere post-processing. This requires the analytical derivation of derivatives of the orthonormal polynomials which enter PC expansions. The efficiency of the approach is illustrated on two well-known benchmark problems in sensitivity analysis.
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