Multivariate output global sensitivity analysis using multi-output support vector regression

Models with multivariate outputs are widely used for risk assessment and decision-making in practical applications. In this paper, multi-output support vector regression (M-SVR) is employed for global sensitivity analysis (GSA) with multivariate output models. The orthogonal polynomial kernel is used to build the M-SVR meta-model, and the covariance-based sensitivity indices of multivariate output are obtained analytically by post-processing the coefficients of M-SVR model. In order to improve the performance of the orthogonal polynomial kernel M-SVR model, a kernel function iteration algorithm is introduced further. The proposed method take advantage of the information of all outputs to get robust meta-model. To validate the performance of the proposed method, two high-dimensional analytical functions and a hydrological model (HYMOD) with multiple outputs are examined, and a detailed comparison is made with the sparse polynomial chaos expansion meta-model developed in UQLab Toolbox. Results show that the proposed methods are efficient and accurate for GSA of the complex multivariate output models.