Comparative Study of Kriging and Support Vector Regression for Structural Engineering Applications

AbstractMetamodeling techniques have been widely used as substitutes for high-fidelity and time-consuming models in various engineering applications. Examples include polynomial chaos expansions, n...

[1]  D. Krige.  A statistical approach to some basic mine valuation problems on the Witwatersrand, by D.G. Krige, published in the Journal, December 1951 : introduction by the author , 1951 .

[2]  Maurice Lemaire,et al.  Assessing small failure probabilities by combined subset simulation and Support Vector Machines , 2011 .

[3]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[4]  Masoud Rais-Rohani,et al.  A comparative study of metamodeling methods for multiobjective crashworthiness optimization , 2005 .

[5]  Sharif Rahman,et al.  Structural reliability analysis by univariate decomposition and numerical integration , 2007 .

[6]  J. Franco.  Planification d'expériences numériques en phase exploratoire pour la simulation des phénomènes complexes , 2008 .

[7]  W. Pitts,et al.  A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.

[8]  Yves Deville,et al.  DiceKriging, DiceOptim: Two R Packages for the Analysis of Computer Experiments by Kriging-Based Metamodeling and Optimization , 2012 .

[9]  A. Kiureghian,et al.  Optimization algorithms for structural reliability , 1991 .

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

[11]  Søren Nymand Lophaven,et al.  DACE - A Matlab Kriging Toolbox, Version 2.0 , 2002 .

[12]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[13]  Peter W. Glynn,et al.  Stochastic Simulation: Algorithms and Analysis , 2007 .

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

[15]  David S. Broomhead,et al.  Multivariable Functional Interpolation and Adaptive Networks , 1988, Complex Syst..

[16]  Michael James Sasena,et al.  Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations. , 2002 .

[17]  Olivier Chapelle,et al.  Support Vector Machines : principes d'induction, Réglage automatique et connaissances à priori , 2004 .

[18]  Nikolaus Hansen,et al.  The CMA Evolution Strategy: A Tutorial , 2016, ArXiv.

[19]  Christopher K. I. Williams,et al.  Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning) , 2005 .

[20]  Min Xie,et al.  A systematic comparison of metamodeling techniques for simulation optimization in Decision Support Systems , 2010, Appl. Soft Comput..

[21]  P. C. Gehlen,et al.  Computer Experiments , 1996 .

[22]  A. OHagan,et al.  Bayesian analysis of computer code outputs: A tutorial , 2006, Reliab. Eng. Syst. Saf..

[23]  James A. Anderson,et al.  Neurocomputing: Foundations of Research , 1988 .

[24]  François Bachoc,et al.  Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification , 2013, Comput. Stat. Data Anal..

[25]  R. Brereton,et al.  Support vector machines for classification and regression. , 2010, The Analyst.

[26]  Donald R. Jones,et al.  A Taxonomy of Global Optimization Methods Based on Response Surfaces , 2001, J. Glob. Optim..

[27]  David Ginsbourger,et al.  Multiples métamodèles pour l'approximation et l'optimisation de fonctions numériques multivariables , 2009 .

[28]  J. Beck,et al.  Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation , 2001 .

[29]  Jorge E. Hurtado,et al.  Filtered importance sampling with support vector margin: A powerful method for structural reliability analysis , 2007 .

[30]  Achille Messac,et al.  Metamodeling using extended radial basis functions: a comparative approach , 2006, Engineering with Computers.

[31]  Etienne de Rocquigny,et al.  Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods , 2012 .

[32]  T. Simpson,et al.  Comparative studies of metamodeling techniques under multiple modeling criteria , 2000 .

[33]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[34]  Nielen Stander,et al.  Stochastic analysis of highly non‐linear structures , 2006 .

[35]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

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

[37]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[38]  V. Vapnik,et al.  Bounds on Error Expectation for Support Vector Machines , 2000, Neural Computation.

[39]  G. Blatman B. Sudret,et al.  Reliability analysis of a pressurized water reactor vessel using sparse polynomial chaos expansions , 2010 .

[40]  Søren Nymand Lophaven,et al.  Aspects of the Matlab toolbox DACE , 2002 .

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

[42]  V. Dubourg.  Adaptive surrogate models for reliability analysis and reliability-based design optimization , 2011 .

[43]  Jean-Marc Bourinet,et al.  RELIABILITY ASSESSMENT WITH ADAPTIVE SURROGATES BASED ON SUPPORT VECTOR MACHINE REGRESSION , 2015 .

[44]  Victor Picheny,et al.  Adaptive Designs of Experiments for Accurate Approximation of a Target Region , 2010 .

[45]  Nikolaus Hansen,et al.  Evaluating the CMA Evolution Strategy on Multimodal Test Functions , 2004, PPSN.

[46]  Stefano Marelli,et al.  UQLab: a framework for uncertainty quantification in MATLAB , 2014 .

[47]  Shie-Jue Lee,et al.  A multiple-kernel support vector regression approach for stock market price forecasting , 2011, Expert Syst. Appl..

[48]  Bertrand Iooss,et al.  An efficient methodology for modeling complex computer codes with Gaussian processes , 2008, Comput. Stat. Data Anal..

[49]  Liquan Mei,et al.  Reasons for Scatter in Crash Simulation Results , 2003 .

[50]  M. Bompard.  MODÈLES DE SUBSTITUTION POUR L'OPTIMISATION GLOBALE DE FORME EN AÉRODYNAMIQUE ET MÉTHODE LOCALE SANS PARAMÉTRISATION , 2011 .

[51]  Dong Zhao,et al.  A comparative study of metamodeling methods considering sample quality merits , 2010 .

[52]  I. Sobol.  On the distribution of points in a cube and the approximate evaluation of integrals , 1967 .

[53]  Damiano Pasini,et al.  A comparative study of metamodeling methods for the design optimization of variable stiffness composites , 2014 .

[54]  Sayan Mukherjee,et al.  Choosing Multiple Parameters for Support Vector Machines , 2002, Machine Learning.

[55]  G. Box,et al.  Empirical Model-Building and Response Surfaces. , 1990 .

[56]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[57]  Robert E. Shannon,et al.  Design and analysis of simulation experiments , 1978, WSC '78.

[58]  Qiang Du,et al.  Centroidal Voronoi Tessellations: Applications and Algorithms , 1999, SIAM Rev..

[59]  M. Aizerman,et al.  Theoretical Foundations of the Potential Function Method in Pattern Recognition Learning , 1964 .

[60]  Ming-Wei Chang,et al.  Leave-One-Out Bounds for Support Vector Regression Model Selection , 2005, Neural Computation.

[61]  Emmanuel Vazquez,et al.  Modélisation comportementale de systèmes non-linéaires multivariables par méthodes à noyaux et applications , 2005 .

[62]  Robert A. Lordo,et al.  Learning from Data: Concepts, Theory, and Methods , 2001, Technometrics.

[63]  M. Balesdent,et al.  Kriging-based adaptive Importance Sampling algorithms for rare event estimation , 2013 .