Mixed kernel function support vector regression for global sensitivity analysis

• Published in: Mechanical systems and signal processing Vol. 96; pp. 201 - 214
• Main Authors: Cheng, Kai, Lu, Zhenzhou, Wei, Yuhao, Shi, Yan, Zhou, Yicheng
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 01.11.2017; Elsevier BV
• Subjects: Functions (mathematics); Global sensitivity analysis; Kernel functions; Mixed kernel function; Polynomials; Post-processing; Regression analysis; Sensitivity analysis; Support vector machines; Support vector regression; Global sensitivity analysis; Support vector regression; Mixed kernel function
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2017.04.014

•Mixed kernel support vector regression is employed for sensitivity analysis.•Sobol indices are obtained by post-processing the coefficients of the meta-model.•The proposed method is efficient for high-dimensional non-linear problems. Global sensitivity analysis (GSA) plays an important role in exploring the respective effects of input variables on an assigned output response. Amongst the wide sensitivity analyses in literature, the Sobol indices have attracted much attention since they can provide accurate information for most models. In this paper, a mixed kernel function (MKF) based support vector regression (SVR) model is employed to evaluate the Sobol indices at low computational cost. By the proposed derivation, the estimation of the Sobol indices can be obtained by post-processing the coefficients of the SVR meta-model. The MKF is constituted by the orthogonal polynomials kernel function and Gaussian radial basis kernel function, thus the MKF possesses both the global characteristic advantage of the polynomials kernel function and the local characteristic advantage of the Gaussian radial basis kernel function. The proposed approach is suitable for high-dimensional and non-linear problems. Performance of the proposed approach is validated by various analytical functions and compared with the popular polynomial chaos expansion (PCE). Results demonstrate that the proposed approach is an efficient method for global sensitivity analysis.