Results from global sensitivity analysis (GSA) often guide the understanding of complicated input-output systems. Kernel-based GSA methods have recently been proposed for their capability of treating a broad scope of complex systems. In this paper we develop a new set of kernel GSA tools when only a single set of input-output data is available. Three key advances are made: (1) A new numerical estimator is proposed that demonstrates an empirical improvement over previous procedures. (2) A computational method for generating inner statistical functions from a single data set is presented. (3) A theoretical extension is made to define conditional sensitivity indices, which reveal the degree that the inputs carry shared information about the output when inherent input-input correlations are present. Utilizing these conditional sensitivity indices, a decomposition is derived for the output uncertainty based on what is called the optimal learning sequence of the input variables, which remains consistent when correlations exist between the input variables. While these advances cover a range of GSA subjects, a common single data set numerical solution is provided by a technique known as the conditional mean embedding of distributions. The new methodology is implemented on benchmark systems to demonstrate the provided insights.
翻译:全球敏感性分析(GSA)的结果往往指导对复杂的输入-产出系统的理解。以内核为基础的GSA方法最近为它们处理复杂系统广泛范围的能力提出了建议。在本文件中,当只有单一的一套输入-产出数据时,我们开发了一套新的GSA内核工具。取得了三个关键进展:(1) 提出了一个新的数字估计器,表明比以往程序有经验改进。(2) 提出了一个从单一数据集生成内部统计功能的计算法。(3) 提出了一个理论扩展法,以界定有条件的敏感指数,表明在存在输入-输入内在相互关系时,投入与产出共享信息的程度。利用这些有条件的敏感指数,根据所谓的输入变量的最佳学习顺序,得出产出不确定性的分解。当输入变量之间有联系时,这种差异保持不变。虽然这些进步涉及一系列GSA主题,但一个共同的单一数据集数字解决办法是由一种称为有条件平均嵌入分布法的技术提供的。在基准系统上采用了新的方法,以显示所提供的洞察力。