Analysis of Support Vector Regression for Approximation of Complex Engineering Analyses

[+] Author and Article Information
Stella M. Clarke

Department of Industrial & Manufacturing Engineering,  The Pennsylvania State University, University Park, PA 16802

Jan H. Griebsch

Lehrstuhl für Effiziente Algorithmen, The Technical University of Munich, Munich, Germany

Timothy W. Simpson1

Departments of Mechanical & Nuclear and Industrial & Manufacturing Engineering, The Pennsylvania State University, University Park, PA 16802tws8@psu.edu


Corresponding author.

J. Mech. Des 127(6), 1077-1087 (Aug 13, 2004) (11 pages) doi:10.1115/1.1897403 History: Received October 07, 2003; Revised August 13, 2004

A variety of metamodeling techniques have been developed in the past decade to reduce the computational expense of computer-based analysis and simulation codes. Metamodeling is the process of building a “model of a model” to provide a fast surrogate for a computationally expensive computer code. Common metamodeling techniques include response surface methodology, kriging, radial basis functions, and multivariate adaptive regression splines. In this paper, we investigate support vector regression (SVR) as an alternative technique for approximating complex engineering analyses. The computationally efficient theory behind SVR is reviewed, and SVR approximations are compared against the aforementioned four metamodeling techniques using a test bed of 26 engineering analysis functions. SVR achieves more accurate and more robust function approximations than the four metamodeling techniques, and shows great potential for metamodeling applications, adding to the growing body of promising empirical performance of SVR.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Accounting for slack variables

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Figure 2

Eighth-order one-dimensional function

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Figure 3

Flowchart of the SVR algorithm

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Figure 4

Fit of one-dimensional function using SVR

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Figure 5

Comparison of errors between metamodeling techniques relative to SVR

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Figure 6

Comparison of errors for linear functions relative to SVR

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Figure 7

Comparison of errors for nonlinear functions relative to SVR

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Figure 8

Comparison of normalized standard deviations of errors between metamodels relative to SVR



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