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Derivative-based new upper bound of Sobol’ sensitivity measure

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

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.

Suggested Citation

  • Song, Shufang & Zhou, Tong & Wang, Lu & Kucherenko, Sergei & Lu, Zhenzhou, 2019. "Derivative-based new upper bound of Sobol’ sensitivity measure," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 142-148.
    • Handle: RePEc:eee:reensy:v:187:y:2019:i:c:p:142-148
    DOI: 10.1016/j.ress.2018.04.024
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    References listed on IDEAS

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    1. Sobol´ I.M. & Kucherenko S.S., 2005. "On global sensitivity analysis of quasi-Monte Carlo algorithms," Monte Carlo Methods and Applications, De Gruyter, vol. 11(1), pages 83-92, March.
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    4. Roustant, O. & Fruth, J. & Iooss, B. & Kuhnt, S., 2014. "Crossed-derivative based sensitivity measures for interaction screening," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 105-118.
    5. Lamboni, M. & Iooss, B. & Popelin, A.-L. & Gamboa, F., 2013. "Derivative-based global sensitivity measures: General links with Sobol’ indices and numerical tests," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 87(C), pages 45-54.
    6. Sobol’, I.M. & Kucherenko, S., 2009. "Derivative based global sensitivity measures and their link with global sensitivity indices," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3009-3017.
    7. Andrea Saltelli, 2002. "Sensitivity Analysis for Importance Assessment," Risk Analysis, John Wiley & Sons, vol. 22(3), pages 579-590, June.
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    2. Nogal, M. & Nogal, A., 2021. "Sensitivity method for extreme-based engineering problems," Reliability Engineering and System Safety, Elsevier, vol. 216(C).

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