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

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.

Automated summary

By using Vine copula, the joint probability density function of multidimensional variables can be decomposed into the product of marginal PDF and bivariate copula functions, transforming multidimensional dependent problems into two-dimensional dependent problems. A novel Vine copula-based approach is proposed for analyzing variance-based sensitivity measures, accurately estimating the main and total sensitivity indices of dependent input variables. Test cases and engineering examples demonstrate the accuracy and applicability of the proposed methods.