A sequential experimental design for multivariate sensitivity analysis using polynomial chaos expansion

Multivariate output sensitivity analysis has gained much attention when the output of the computational model is a vector. A preferable strategy to deal with the multivariate output issue is the covariance decomposition approach based on the polynomial chaos expansion (PCE) metamodel. However, since the PCE construction depends on the quality of experimental design to some extent, the selection of design points is significant in determining the accuracy of the sensitivity estimator. In this article, a PCE-based sequential experimental design is proposed to estimate the multivariate output sensitivity index. In this method, the optimal design point is sequentially selected to minimize the determinant of covariance matrix of the sensitivity estimator. To validate the performance of the proposed method, several numerical examples are presented, which show that the sequential design approach performs better than other prevalent methods in terms of accuracy and robustness.