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http://dx.doi.org/10.3795/KSME-A.2005.29.2.277

Generalized Kriging Model for Interpolation and Regression  

Jung Jae Jun (한양대학교 대학원 기계설계학과)
Lee Tae Hee (한양대학교 기계공학부)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.29, no.2, 2005 , pp. 277-283 More about this Journal
Abstract
Kriging model is widely used as design analysis and computer experiment (DACE) model in the field of engineering design to accomplish computationally feasible design optimization. In general, kriging model has been applied to many engineering applications as an interpolation model because it is usually constructed from deterministic simulation responses. However, when the responses include not only global nonlinearity but also numerical error, it is not suitable to use Kriging model that can distort global behavior. In this research, generalized kriging model that can represent both interpolation and regression is proposed. The performances of generalized kriging model are compared with those of interpolating kriging model for numerical function with error of normal distribution type and trigonometric function type. As an application of the proposed approach, the response of a simple dynamic model with numerical integration error is predicted based on sampling data. It is verified that the generalized kriging model can predict a noisy response without distortion of its global behavior. In addition, the influences of maximum likelihood estimation to prediction performance are discussed for the dynamic model.
Keywords
Generailzed Kriging Model; Interpolating Kriging Model; Maximum Liklihood Estmiation;
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1 Stulajter, F., 1997, 'Predictions in Nonlinear Regression Models,' Acta Mathematica Universitatis Comenianae, Vol. LXVI, No.1, pp. 71-81
2 Cox, D.D., Park, J.J. and Singer, C.E., 2001, 'A Statistical Method for Tuning a Computer Code to a Data Base,' Computational Statistics & Data Analysis, Vol. 37,pp. 77-92   DOI   ScienceOn
3 Simpson, T'W. Mauery, TM., Korte, U. and Mistree, F., 2001, 'Kriging Models for Global Approximation in Simulation-Based Multidisciplinary Design Optimization,' AIAA Journal, Vol. 39, No. 12, pp.2234-2241
4 Lee, T.H., Lee, C.J. and Lee, K.K, 2003, 'Shape Optimization of a CRT based on Response Surface and Kriging Metamodels,' Trans. of KSME (A), Vol. 27, No. 30, pp. 381-386
5 Mitchell, T.J. and Morris, M.D., 1992, 'The Spatial Correlation Function Approach to Response Surface Estimation,' Proceedings of the i992 Winter Simulation Conference, pp. 565-571   DOI
6 Sasena, M., Parkinson, M., Goovaerts, P., Papalambros and P., Reed, M., 2002, 'Adaptive Experimental Design Applied to An Ergonomics Testing Procedure,' Proceedings of DETC`02 ASME 2002 Design Engineering Technical Conferences and Computers and information in Engineering Conference, Montreal
7 Koehler, J.R. and Owen, A.B., 1996, 'Cornpter Experiments,' in Ghosh, S. and Rao, C.R., eds, Handbook of Statistics, 13, pp. 261-308, Elsevier Science, New York.
8 Lee, T.H., Lee, C.S., Jung, J.J., Kim, H.W., Hong, S., and Choi, J.S., 2003, 'Prediction of the Motion of Tracked Vehicle on Soft Soil Using Kriging Metamodel,' Proceedings of The Fifth Ocean Mining Symposium, ISOPE, pp. 144-149
9 Matheron, G., 1963, 'Principles of Geostatistics,' Economic Geology, Vol. 58, pp. 1246-1266   DOI
10 Sacks, J., Schiller, S.B. and Welch, ws., 1989, 'Designs for Computer Experiment,' Technometrics, Vol. 31, No.1, pp. 41-47   DOI
11 Sacks, J., Welch, W.J., Mitchell, T.J. and Wynn, H.P., 1989, 'Design and Analysis of Computer Experiments,' Statistical Science, Vol. 4, No.4, pp. 409-435   DOI   ScienceOn