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Comparison study on the accuracy of metamodeling technique for non-convex functions

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Abstract

In order to increase the efficiency of design optimization, many efforts have been made on studying the metamodel techniques for effectively representing expensive and complex models. In this study, a comparison is conducted on the accuracy of several widely used meta-model techniques — moving least squares (MLS), Kriging, support vector regression (SVR) and radial basis functions (RBF) — which are able to approximate non-convex functions well. RMSE (root mean squared error) value is identified as a measure of the accuracy for this comparison. Each metamodel technique is used to approximate the six well-known mathematical functions and a resign of experiment (DOE) is generated by using the Latin hypercube design (LHD), which is also performed for each resulting metamodel. The results show that Kriging and MLS can create a more accurate metamodel than SVR and RBF with the mathematical functions tested.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Hanyang University Graduate school, Seoul, 133-791, Korea

    Byeong-Soo Kim & Yong-Bin Lee

  2. The Center of Innovative Design Optimization Technology (iDOT), Hanyang University, Seoul, 133-791, Korea

    Dong-Hoon Choi

Authors
  1. Byeong-Soo Kim
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  2. Yong-Bin Lee
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  3. Dong-Hoon Choi
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Corresponding author

Correspondence to Dong-Hoon Choi.

Additional information

This paper was recommended for publication in revised form by Associate Editor Dae-Eun Kim

Byeong-Soo Kim received B.S and M.S. degree in Mechanical Engineering from Hanyang University in 2006 and 2008, respectively. Mr. Kim is currently a Research Engineer at LG Electronics.

Yong-Bin Lee received a B.S. and M.S. degree in Mechanical Engineering from Hanyang University in 2002 and 2004, respectively. He is currently a Ph.D. student in Hanyang University. Mr. Lee’s research interests are in the area of optimization, approximation, and design of experiments.

Dong-Hoon Choi received a B.S. degree in Mechanical Engineering from Seoul National University in 1975. He then went on to receive his M.S. from KAIST in 1977 and Ph. D. degree from University of Wisconsin-Madison in 1986, respectively. Dr. Choi is currently a Professor at the School of Mechanical Engineering at Hanyang University in Seoul, Korea. He is currently the director of iDOT(the center of innovative design optimization technology). Prof. Choi’s research interests are in the area of optimization techniques: developing MDO methodology, developing optimization techniques to ensure a reliability of optimum solution, and developing approximation optimization technique, etc.

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Kim, BS., Lee, YB. & Choi, DH. Comparison study on the accuracy of metamodeling technique for non-convex functions. J Mech Sci Technol 23, 1175–1181 (2009). https://doi.org/10.1007/s12206-008-1201-3

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  • DOI: https://doi.org/10.1007/s12206-008-1201-3

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