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A new kind of sensitivity index for multivariate output

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  • Li, Luyi
  • Lu, Zhenzhou
  • Wu, Danqing

Abstract

Mathematical and computational models with correlated multivariate output are commonly used for risk assessment and decision support in engineering. Traditional methods for sensitivity analysis of the model with scalar output fail to provide satisfactory results for this multivariate case. In this work, we introduce a new sensitivity index which looks at the influence of input uncertainty on the entire distribution of the multivariate output without reference to a specific moment of the output. The definition of the new index is based on the multivariate probability integral transformation (PIT), which can take into account both of the uncertainties and the correlations among multivariate output. The mathematical properties of the proposed sensitivity index are discussed and its differences with the sensitivity indices previously introduced in the literature are highlighted. Two numerical examples and a rotating shaft model of an aircraft wing are employed to illustrate the validity and potential benefits of the new sensitivity index.

Suggested Citation

  • Li, Luyi & Lu, Zhenzhou & Wu, Danqing, 2016. "A new kind of sensitivity index for multivariate output," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 123-131.
    • Handle: RePEc:eee:reensy:v:147:y:2016:i:c:p:123-131
    DOI: 10.1016/j.ress.2015.11.006
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    Cited by:

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    2. Ismael Ahrazem Dfuf & José Manuel Mira McWilliams & María Camino González Fernández, 2019. "Multi-Output Conditional Inference Trees Applied to the Electricity Market: Variable Importance Analysis," Energies, MDPI, vol. 12(6), pages 1-24, March.
    3. Guo, Qing & Liu, Yongshou & Chen, Bingqian & Yao, Qin, 2021. "A variable and mode sensitivity analysis method for structural system using a novel active learning Kriging model," Reliability Engineering and System Safety, Elsevier, vol. 206(C).
    4. Daniel W. Gladish & Ross Darnell & Peter J. Thorburn & Bhakti Haldankar, 2019. "Emulated Multivariate Global Sensitivity Analysis for Complex Computer Models Applied to Agricultural Simulators," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(1), pages 130-153, March.
    5. 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.
    6. Yicheng Zhou & Zhenzhou Lu & Yan Shi & Kai Cheng, 2019. "A vine copula–based method for analyzing the moment-independent importance measure of the multivariate output," Journal of Risk and Reliability, , vol. 233(3), pages 338-354, June.
    7. Xiao, Sinan & Lu, Zhenzhou & Wang, Pan, 2018. "Multivariate global sensitivity analysis for dynamic models based on wavelet analysis," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 20-30.
    8. Xiao, Sinan & Lu, Zhenzhou & Xu, Liyang, 2017. "Multivariate sensitivity analysis based on the direction of eigen space through principal component analysis," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 1-10.
    9. Soha Saad & Florence Ossart & Jean Bigeon & Etienne Sourdille & Harold Gance, 2021. "Global Sensitivity Analysis Applied to Train Traffic Rescheduling: A Comparative Study," Energies, MDPI, vol. 14(19), pages 1-29, October.
    10. Liu, Fuchao & Wei, Pengfei & Tang, Chenghu & Wang, Pan & Yue, Zhufeng, 2019. "Global sensitivity analysis for multivariate outputs based on multiple response Gaussian process model," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 287-298.

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