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

Mathematics

Sergei Kucherenko¹  Shufang Song²  Zhiwei Bai²  Yingying Xiao³  Hongkui Wei³ 

[1] Centre for Process Systems Engineering, Imperial College London, London SW7 2AZ, UK;School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China;State Key Laboratory of Intelligent Manufacturing System Technology, Beijing Institute of Electronic System Engineering, Beijing 100854, China;

关键词: Vine copula;    global sensitivity analysis;    multivariate correlation analysis;    Nataf model;    probability density function;   

DOI  :  10.3390/math9192489

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown