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A Vine Copula-Based Global Sensitivity Analysis Method for Structures with Multidimensional Dependent Variables

Author

Listed:
  • Zhiwei Bai

    (School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China)

  • Hongkui Wei

    (State Key Laboratory of Intelligent Manufacturing System Technology, Beijing Institute of Electronic System Engineering, Beijing 100854, China)

  • Yingying Xiao

    (State Key Laboratory of Intelligent Manufacturing System Technology, Beijing Institute of Electronic System Engineering, Beijing 100854, China)

  • Shufang Song

    (School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China)

  • Sergei Kucherenko

    (Centre for Process Systems Engineering, Imperial College London, London SW7 2AZ, UK)

Abstract

For multidimensional dependent cases with incomplete probability information of random variables, global sensitivity analysis (GSA) theory is not yet mature. The joint probability density function (PDF) of multidimensional variables is usually unknown, meaning that the samples of multivariate variables cannot be easily obtained. Vine copula can decompose the joint PDF of multidimensional variables into the continuous product of marginal PDF and several bivariate copula functions. Based on Vine copula, multidimensional dependent problems can be transformed into two-dimensional dependent problems. A novel Vine copula-based approach for analyzing variance-based sensitivity measures is proposed, which can estimate the main and total sensitivity indices of dependent input variables. Five considered test cases and engineering examples show that the proposed methods are accurate and applicable.

Suggested Citation

  • Zhiwei Bai & Hongkui Wei & Yingying Xiao & Shufang Song & Sergei Kucherenko, 2021. "A Vine Copula-Based Global Sensitivity Analysis Method for Structures with Multidimensional Dependent Variables," Mathematics, MDPI, vol. 9(19), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2489-:d:649837
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    References listed on IDEAS

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    1. Sarazin, Gabriel & Morio, Jérôme & Lagnoux, Agnès & Balesdent, Mathieu & Brevault, Loïc, 2021. "Reliability-oriented sensitivity analysis in presence of data-driven epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    2. 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.
    3. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    4. Huard, David & Evin, Guillaume & Favre, Anne-Catherine, 2006. "Bayesian copula selection," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 809-822, November.
    5. Zdeněk Kala, 2020. "Sensitivity Analysis in Probabilistic Structural Design: A Comparison of Selected Techniques," Sustainability, MDPI, vol. 12(11), pages 1-19, June.
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    Cited by:

    1. Congcong Zhou & Zhenzhong Shen & Liqun Xu & Yiqing Sun & Wenbing Zhang & Hongwei Zhang & Jiayi Peng, 2023. "Global Sensitivity Analysis Method for Embankment Dam Slope Stability Considering Seepage–Stress Coupling under Changing Reservoir Water Levels," Mathematics, MDPI, vol. 11(13), pages 1-24, June.

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