{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T11:22:12Z","timestamp":1762341732191,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2021,10,4]],"date-time":"2021-10-04T00:00:00Z","timestamp":1633305600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Numerical Wind-tunnel Project","award":["NNW 2019ZT2-A05"],"award-info":[{"award-number":["NNW 2019ZT2-A05"]}]},{"name":"Nature Science Foundation of China","award":["NSFC 11902254"],"award-info":[{"award-number":["NSFC 11902254"]}]},{"name":"AECC Project","award":["GJCZ-1007-19"],"award-info":[{"award-number":["GJCZ-1007-19"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/math9192489","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T01:57:54Z","timestamp":1633917474000},"page":"2489","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Vine Copula-Based Global Sensitivity Analysis Method for Structures with Multidimensional Dependent Variables"],"prefix":"10.3390","volume":"9","author":[{"given":"Zhiwei","family":"Bai","sequence":"first","affiliation":[{"name":"School of Aeronautics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongkui","family":"Wei","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Intelligent Manufacturing System Technology, Beijing Institute of Electronic System Engineering, Beijing 100854, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingying","family":"Xiao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Intelligent Manufacturing System Technology, Beijing Institute of Electronic System Engineering, Beijing 100854, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shufang","family":"Song","sequence":"additional","affiliation":[{"name":"School of Aeronautics, Northwestern Polytechnical University, Xi\u2019an 710072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sergei","family":"Kucherenko","sequence":"additional","affiliation":[{"name":"Centre for Process Systems Engineering, Imperial College London, London SW7 2AZ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1002\/wilm.42820050114","article-title":"Global sensitivity indices for nonlinear mathematical models. 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