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

被引：6

作者：

Bai, Zhiwei ^{[1
]}

Wei, Hongkui ^{[2
]}

Xiao, Yingying ^{[2
]}

Song, Shufang ^{[1
]}

Kucherenko, Sergei ^{[3
]}

机构：

[1] Northwestern Polytech Univ, Sch Aeronaut, Xian 710072, Peoples R China

[2] Beijing Inst Elect Syst Engn, State Key Lab Intelligent Mfg Syst Technol, Beijing 100854, Peoples R China

[3] Imperial Coll London, Ctr Proc Syst Engn, London SW7 2AZ, England

来源：

MATHEMATICS | 2021年 / 9卷 / 19期

关键词：

Vine copula; global sensitivity analysis; multivariate correlation analysis; Nataf model; probability density function; RELIABILITY-ANALYSIS; MODELS; INDEXES; INPUTS;

D O I：

10.3390/math9192489

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页数：20

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