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

Zhiwei Bai, Hongkui Wei, Yingying Xiao, Shufang Song and Sergei Kucherenko
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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

Mathematics, 2021, vol. 9, issue 19, 1-20

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.

Keywords: Vine copula; global sensitivity analysis; multivariate correlation analysis; Nataf model; probability density function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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