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Global sensitivity analysis of computer models with functional inputs

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  • Iooss, Bertrand
  • Ribatet, Mathieu

Abstract

Global sensitivity analysis is used to quantify the influence of uncertain model inputs on the response variability of a numerical model. The common quantitative methods are appropriate with computer codes having scalar model inputs. This paper aims at illustrating different variance-based sensitivity analysis techniques, based on the so-called Sobol's indices, when some model inputs are functional, such as stochastic processes or random spatial fields. In this work, we focus on large cpu time computer codes which need a preliminary metamodeling step before performing the sensitivity analysis. We propose the use of the joint modeling approach, i.e., modeling simultaneously the mean and the dispersion of the code outputs using two interlinked generalized linear models (GLMs) or generalized additive models (GAMs). The “mean model†allows to estimate the sensitivity indices of each scalar model inputs, while the “dispersion model†allows to derive the total sensitivity index of the functional model inputs. The proposed approach is compared to some classical sensitivity analysis methodologies on an analytical function. Lastly, the new methodology is applied to an industrial computer code that simulates the nuclear fuel irradiation.

Suggested Citation

  • Iooss, Bertrand & Ribatet, Mathieu, 2009. "Global sensitivity analysis of computer models with functional inputs," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1194-1204.
    • Handle: RePEc:eee:reensy:v:94:y:2009:i:7:p:1194-1204
    DOI: 10.1016/j.ress.2008.09.010
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    References listed on IDEAS

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    1. Iooss, Bertrand & Van Dorpe, François & Devictor, Nicolas, 2006. "Response surfaces and sensitivity analyses for an environmental model of dose calculations," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1241-1251.
    2. Ruffo, Paolo & Bazzana, Livia & Consonni, Alberto & Corradi, Anna & Saltelli, Andrea & Tarantola, Stefano, 2006. "Hydrocarbon exploration risk evaluation through uncertainty and sensitivity analyses techniques," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1155-1162.
    3. 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.
    4. Jacques, Julien & Lavergne, Christian & Devictor, Nicolas, 2006. "Sensitivity analysis in presence of model uncertainty and correlated inputs," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1126-1134.
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    2. Ye, Dongwei & Nikishova, Anna & Veen, Lourens & Zun, Pavel & Hoekstra, Alfons G., 2021. "Non-intrusive and semi-intrusive uncertainty quantification of a multiscale in-stent restenosis model," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
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    5. Fruth, J. & Roustant, O. & Kuhnt, S., 2015. "Sequential designs for sensitivity analysis of functional inputs in computer experiments," Reliability Engineering and System Safety, Elsevier, vol. 134(C), pages 260-267.
    6. Xu, Yanwen & Kohtz, Sara & Boakye, Jessica & Gardoni, Paolo & Wang, Pingfeng, 2023. "Physics-informed machine learning for reliability and systems safety applications: State of the art and challenges," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    7. Emanuele Borgonovo & William Castaings & Stefano Tarantola, 2011. "Moment Independent Importance Measures: New Results and Analytical Test Cases," Risk Analysis, John Wiley & Sons, vol. 31(3), pages 404-428, March.
    8. Bernard Roblès & Manuel Avila & Florent Duculty & Pascal Vrignat & Stephane Bégot & Frédéric Kratz, 2014. "Hidden Markov model framework for industrial maintenance activities," Journal of Risk and Reliability, , vol. 228(3), pages 230-242, June.
    9. Zhu, Xujia & Sudret, Bruno, 2021. "Global sensitivity analysis for stochastic simulators based on generalized lambda surrogate models," Reliability Engineering and System Safety, Elsevier, vol. 214(C).
    10. Pierre Étoré & Clémentine Prieur & Dang Khoi Pham & Long Li, 2020. "Global Sensitivity Analysis for Models Described by Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 803-831, June.
    11. López-Lopera, Andrés F. & Idier, Déborah & Rohmer, Jérémy & Bachoc, François, 2022. "Multioutput Gaussian processes with functional data: A study on coastal flood hazard assessment," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).

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