Kernel-based global sensitivity analysis obtained from a single data set

• Published in: Reliability engineering & system safety Vol. 235; no. C; p. 109173
• Main Authors: Barr, John, Rabitz, Herschel
• Format: Journal Article
• Language: English
• Published: United States Elsevier Ltd 01.07.2023; Elsevier
• Subjects: ENGINEERING; Global sensitivity analysis; Kernel methods; Moment-independent; Multivariate outputs; Kernel methods; 46E22; Moment-independent; Multivariate outputs; 62E10; Global sensitivity analysis; 62H10
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2023.109173

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. •A numerical method for kernel-based global sensitivity analysis from a single data set is developed.•The theory is extended to define conditional sensitivity indices.•An uncertainty decomposition is derived that remains valid when input dependencies exist.•The new procedures are applied to benchmark test cases.