Kriging-based analytical technique for global sensitivity analysis of systems with multivariate output

Global sensitivity analysis is of great significance for risk assessment of structural systems. In order to efficiently perform sensitivity analysis for systems with multivariate output, this paper adopts Kriging-based analytical (KBA) technique to estimate multivariate sensitivity indices (MSI). Two MSI are studied in this paper, namely, MSI based on principal component analysis (MSI-PCA) and MSI based on covariance decomposition (MSI-CD). For MSI-PCA, Kriging models of inputs and each retained output principal component (PC) are firstly established, and then KBA technique is used to derive the sensitivities associated with each retained PC and the generalized MSI-PCA. For MSI-CD, Kriging model is constructed to map input variables and each time output variable, based on which subset variances and the corresponding MSI-CD are derived by KBA technique. In addition, to avoid constructing Kriging model at each time instant when calculating MSI-CD, a new double-loop Kriging (D-Kriging) method is developed to further improve the efficiency. The accuracy and efficiency of KBA and D-Kriging methods for MSI estimation are tested and discussed by four examples in Sect. 4.