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Global Sensitivity Analysis for multivariate output using Polynomial Chaos Expansion

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  • Garcia-Cabrejo, Oscar
  • Valocchi, Albert

Abstract

Many mathematical and computational models used in engineering produce multivariate output that shows some degree of correlation. However, conventional approaches to Global Sensitivity Analysis (GSA) assume that the output variable is scalar. These approaches are applied on each output variable leading to a large number of sensitivity indices that shows a high degree of redundancy making the interpretation of the results difficult. Two approaches have been proposed for GSA in the case of multivariate output: output decomposition approach [9] and covariance decomposition approach [14] but they are computationally intensive for most practical problems. In this paper, Polynomial Chaos Expansion (PCE) is used for an efficient GSA with multivariate output. The results indicate that PCE allows efficient estimation of the covariance matrix and GSA on the coefficients in the approach defined by Campbell et al. [9], and the development of analytical expressions for the multivariate sensitivity indices defined by Gamboa et al. [14].

Suggested Citation

  • Garcia-Cabrejo, Oscar & Valocchi, Albert, 2014. "Global Sensitivity Analysis for multivariate output using Polynomial Chaos Expansion," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 25-36.
  • Handle: RePEc:eee:reensy:v:126:y:2014:i:c:p:25-36
    DOI: 10.1016/j.ress.2014.01.005
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    Cited by:

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    13. 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.
    14. 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.
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    16. Wu, Zeping & Wang, Donghui & Okolo N, Patrick & Hu, Fan & Zhang, Weihua, 2016. "Global sensitivity analysis using a Gaussian Radial Basis Function metamodel," Reliability Engineering and System Safety, Elsevier, vol. 154(C), pages 171-179.
    17. Oladyshkin, Sergey & Nowak, Wolfgang, 2018. "Incomplete statistical information limits the utility of high-order polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 137-148.
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    21. 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.
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    23. 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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