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An efficient modularized sample-based method to estimate the first-order Sobol׳ index

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  • Li, Chenzhao
  • Mahadevan, Sankaran

Abstract

Sobol׳ index is a prominent methodology in global sensitivity analysis. This paper aims to directly estimate the Sobol׳ index based only on available input–output samples, even if the underlying model is unavailable. For this purpose, a new method to calculate the first-order Sobol׳ index is proposed. The innovation is that the conditional variance and mean in the formula of the first-order index are calculated at an unknown but existing location of model inputs, instead of an explicit user-defined location. The proposed method is modularized in two aspects: 1) index calculations for different model inputs are separate and use the same set of samples; and 2) model input sampling, model evaluation, and index calculation are separate. Due to this modularization, the proposed method is capable to compute the first-order index if only input–output samples are available but the underlying model is unavailable, and its computational cost is not proportional to the dimension of the model inputs. In addition, the proposed method can also estimate the first-order index with correlated model inputs. Considering that the first-order index is a desired metric to rank model inputs but current methods can only handle independent model inputs, the proposed method contributes to fill this gap.

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  • Li, Chenzhao & Mahadevan, Sankaran, 2016. "An efficient modularized sample-based method to estimate the first-order Sobol׳ index," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 110-121.
    • Handle: RePEc:eee:reensy:v:153:y:2016:i:c:p:110-121
    DOI: 10.1016/j.ress.2016.04.012
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    1. Wu, Qiong-Li & Cournède, Paul-Henry & Mathieu, Amélie, 2012. "An efficient computational method for global sensitivity analysis and its application to tree growth modelling," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 35-43.
    2. Tarantola, S. & Gatelli, D. & Mara, T.A., 2006. "Random balance designs for the estimation of first order global sensitivity indices," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 717-727.
    3. Li, Chenzhao & Mahadevan, Sankaran, 2016. "Role of calibration, validation, and relevance in multi-level uncertainty integration," Reliability Engineering and System Safety, Elsevier, vol. 148(C), pages 32-43.
    4. Weirs, V. Gregory & Kamm, James R. & Swiler, Laura P. & Tarantola, Stefano & Ratto, Marco & Adams, Brian M. & Rider, William J. & Eldred, Michael S., 2012. "Sensitivity analysis techniques applied to a system of hyperbolic conservation laws," Reliability Engineering and System Safety, Elsevier, vol. 107(C), pages 157-170.
    5. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    6. Helton, J.C. & Johnson, J.D. & Sallaberry, C.J. & Storlie, C.B., 2006. "Survey of sampling-based methods for uncertainty and sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1175-1209.
    7. Zhang, Xufang & Pandey, Mahesh D., 2014. "An effective approximation for variance-based global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 164-174.
    8. Sobol’, I.M. & Tarantola, S. & Gatelli, D. & Kucherenko, S.S. & Mauntz, W., 2007. "Estimating the approximation error when fixing unessential factors in global sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 92(7), pages 957-960.
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    Cited by:

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    3. WoongHee Jung & Aikaterini P. Kyprioti & Ehsan Adeli & Alexandros A. Taflanidis, 2023. "Exploring the sensitivity of probabilistic surge estimates to forecast errors," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 115(2), pages 1371-1409, January.
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    6. Ma, Yuan-Zhuo & Jin, Xiang-Xiang & Zhao, Xiang & Li, Hong-Shuang & Zhao, Zhen-Zhou & Xu, Chang, 2024. "Reliability-oriented global sensitivity analysis using subset simulation and space partition," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    7. Xiao, Sinan & Oladyshkin, Sergey & Nowak, Wolfgang, 2020. "Reliability analysis with stratified importance sampling based on adaptive Kriging," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    8. Wei, Daijun & Zhang, Xiaoge & Mahadevan, Sankaran, 2018. "Measuring the vulnerability of community structure in complex networks," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 41-52.

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