Derivative-based new upper bound of Sobol’ sensitivity measure

Shufang Song, Tong Zhou, Lu Wang, Sergei Kucherenko and Zhenzhou Lu

Reliability Engineering and System Safety, 2019, vol. 187, issue C, 142-148

Abstract: Global sensitivity (also called “uncertainty importance measure†) can reflect the effect of input variables on output response. The variance-based importance measure proposed by Sobol’ has highly general applicability. The Sobol’ total sensitivity index Sitotcan estimate the total contribution of input variables to the model output, including the self-influence of variable and the intercross influence of variable vectors. However, the computational load of Sitot is extremely heavy for double-loop simulation. The main sensitivity index Si is the lower bound of Sitot, and new upper bounds of Sitot based derivative are derived and proposed. New upper bounds of Sitot for different variable distribution types (such as uniform, normal, exponential, triangular, beta and gamma) are analyzed, and the process and formulas are presented comprehensively according to functional analysis and the Euler–Lagrange equation. Derivative-based upper bounds are easy to implement and evaluate numerically. Several numerical and engineering examples are adopted to verify the efficiency and applicability of the presented upper bounds, which can effectively estimate the Sitot value.

Keywords: Global sensitivity; Uncertainty importance measure; Total sensitivity index; Main sensitivity index; Euler–Lagrange equation; Functional analysis; Derivative-based important measure (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:reensy:v:187:y:2019:i:c:p:142-148

DOI: 10.1016/j.ress.2018.04.024

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