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

  • Kai Cheng
  • Zhenzhou LuEmail author
  • Kaichao Zhang
Research Paper


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.


Multivariate output sensitivity analysis Multi-output support vector regression Orthogonal polynomial kernel function Polynomial chaos expansion 


Funding information

This work was supported by the National Natural Science Foundation of China (Grant No. NSFC 51475370 and NSFC 51775439).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of AeronauticsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China

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