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Sobol' indices for problems defined in non-rectangular domains

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  • Kucherenko, S.
  • Klymenko, O.V.
  • Shah, N.

Abstract

A novel theoretical and numerical framework for the estimation of Sobol’ sensitivity indices for models in which inputs are confined to a non-rectangular domain (e.g., in presence of inequality constraints) is developed. Two numerical methods, namely the quadrature integration method which may be very efficient for problems of low dimensionality and the MC/QMC estimators based on the acceptance-rejection sampling method are proposed for the numerical estimation of Sobol’ sensitivity indices. Several model test functions with constraints are considered for which analytical solutions for Sobol’ sensitivity indices were found. These solutions were used as benchmarks for verifying numerical estimates. The method is shown to be general and efficient.

Suggested Citation

  • Kucherenko, S. & Klymenko, O.V. & Shah, N., 2017. "Sobol' indices for problems defined in non-rectangular domains," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 218-231.
    • Handle: RePEc:eee:reensy:v:167:y:2017:i:c:p:218-231
    DOI: 10.1016/j.ress.2017.06.001
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    References listed on IDEAS

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    1. Plischke, Elmar, 2012. "An adaptive correlation ratio method using the cumulative sum of the reordered output," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 149-156.
    2. Mara, Thierry A. & Tarantola, Stefano, 2012. "Variance-based sensitivity indices for models with dependent inputs," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 115-121.
    3. Kucherenko, Sergei & Feil, Balazs & Shah, Nilay & Mauntz, Wolfgang, 2011. "The identification of model effective dimensions using global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 440-449.
    4. Xu, Chonggang & Gertner, George Zdzislaw, 2008. "Uncertainty and sensitivity analysis for models with correlated parameters," Reliability Engineering and System Safety, Elsevier, vol. 93(10), pages 1563-1573.
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    Cited by:

    1. Zhang, Zheng & Wang, Pan & Hu, Huanhuan & Li, Lei & Li, Haihe & Yue, Zhufeng, 2022. "Efficient reliability-based design optimization for hydraulic pipeline with adaptive sampling region," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    2. Chen, Xin & Molina-Cristóbal, Arturo & Guenov, Marin D. & Riaz, Atif, 2019. "Efficient method for variance-based sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 181(C), pages 97-115.

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