Mixed kernel function support vector regression for global sensitivity analysis

Abstract 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.

[1]  Ilya M. Sobol,et al.  Theorems and examples on high dimensional model representation , 2003, Reliab. Eng. Syst. Saf..

[2]  Wenrui Hao,et al.  A new interpretation and validation of variance based importance measures for models with correlated inputs , 2013, Comput. Phys. Commun..

[3]  Bo Liu,et al.  Improved particle swarm optimization combined with chaos , 2005 .

[4]  Bruno Sudret,et al.  Global sensitivity analysis using polynomial chaos expansions , 2008, Reliab. Eng. Syst. Saf..

[5]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[6]  Zhenzhou Lu,et al.  Importance analysis for models with correlated input variables using state dependent parameters approach , 2013 .

[7]  Guido Smits,et al.  Improved SVM regression using mixtures of kernels , 2002, Proceedings of the 2002 International Joint Conference on Neural Networks. IJCNN'02 (Cat. No.02CH37290).

[8]  A. Saltelli,et al.  Non-parametric statistics in sensitivity analysis for model output: A comparison of selected techniques , 1990 .

[9]  Vladimir Vapnik,et al.  Statistical learning theory , 1998 .

[10]  Wei-Chiang Hong,et al.  Chaotic particle swarm optimization algorithm in a support vector regression electric load forecasting model , 2009 .

[11]  Ronald L. Iman,et al.  Assessing hurricane effects. Part 2. Uncertainty analysis , 2002, Reliab. Eng. Syst. Saf..

[12]  Emanuele Borgonovo,et al.  A new uncertainty importance measure , 2007, Reliab. Eng. Syst. Saf..

[13]  Seymour Geisser,et al.  The Predictive Sample Reuse Method with Applications , 1975 .

[14]  T. Ishigami,et al.  An importance quantification technique in uncertainty analysis for computer models , 1990, [1990] Proceedings. First International Symposium on Uncertainty Modeling and Analysis.

[15]  I. Sobol,et al.  Global sensitivity indices for nonlinear mathematical models. Review , 2005 .

[16]  Bruno Sudret,et al.  Global sensitivity analysis using low-rank tensor approximations , 2016, Reliab. Eng. Syst. Saf..

[17]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[18]  Bruno Sudret,et al.  Adaptive sparse polynomial chaos expansion based on least angle regression , 2011, J. Comput. Phys..

[19]  Chih-Jen Lin,et al.  A Practical Guide to Support Vector Classication , 2008 .

[20]  Ilya M. Sobol,et al.  Sensitivity Estimates for Nonlinear Mathematical Models , 1993 .

[21]  Paola Annoni,et al.  Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index , 2010, Comput. Phys. Commun..

[22]  Bernhard Schölkopf,et al.  Learning with kernels , 2001 .

[23]  Z. Zhong,et al.  Application of mixed kernels function (MKF) based support vector regression model (SVR) for CO2 - Reservoir oil minimum miscibility pressure prediction , 2016 .

[24]  Zhe Li,et al.  Research on Combination Kernel Function of Support Vector Machine , 2008, 2008 International Conference on Computer Science and Software Engineering.

[25]  Ping-Feng Pai,et al.  System reliability forecasting by support vector machines with genetic algorithms , 2006, Math. Comput. Model..

[26]  Jin Fengxiang,et al.  A Novel Granular Support Vector Machine Based on Mixed Kernel Function , 2012 .

[27]  Javad Hamidzadeh,et al.  New Hermite orthogonal polynomial kernel and combined kernels in Support Vector Machine classifier , 2016, Pattern Recognit..

[28]  Shih-Wei Lin,et al.  Particle swarm optimization for parameter determination and feature selection of support vector machines , 2008, Expert Syst. Appl..

[29]  Saltelli Andrea,et al.  Global Sensitivity Analysis: The Primer , 2008 .

[30]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[31]  J.-M. Bourinet,et al.  Rare-event probability estimation with adaptive support vector regression surrogates , 2016, Reliab. Eng. Syst. Saf..

[32]  Chih-Jen Lin,et al.  Asymptotic Behaviors of Support Vector Machines with Gaussian Kernel , 2003, Neural Computation.

[33]  I. D. Gates,et al.  Support vector regression for porosity prediction in a heterogeneous reservoir: A comparative study , 2010, Comput. Geosci..

[34]  Ian D. Gates,et al.  Support vector machines for petrophysical modelling and lithoclassification , 2011 .

[35]  Ping-Feng Pai,et al.  Software reliability forecasting by support vector machines with simulated annealing algorithms , 2006, J. Syst. Softw..

[36]  Z. Zeng,et al.  Displacement prediction of landslide based on PSOGSA-ELM with mixed kernel , 2013, 2013 Sixth International Conference on Advanced Computational Intelligence (ICACI).

[37]  S. Sathiya Keerthi,et al.  Improvements to Platt's SMO Algorithm for SVM Classifier Design , 2001, Neural Computation.

[38]  B. Sudret,et al.  An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis , 2010 .

[39]  Ronald L. Iman,et al.  Assessing hurricane effects. Part 1. Sensitivity analysis , 2002, Reliab. Eng. Syst. Saf..

[40]  Nilay Shah,et al.  The identification of model effective dimensions using global sensitivity analysis , 2011, Reliab. Eng. Syst. Saf..

[41]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[42]  Bruno Sudret,et al.  Efficient computation of global sensitivity indices using sparse polynomial chaos expansions , 2010, Reliab. Eng. Syst. Saf..