KSME International Journal

, Volume 16, Issue 5, pp 619–632 | Cite as

Kriging interpolation methods in geostatistics and DACE model

  • Je-Seon Ryu
  • Min-Soo Kim
  • Kyung-Joon Cha
  • Tae Hee Lee
  • Dong-Hoon Choi
Materials & Fracture · Solids & Structures · Dynamics & Control · Production & Design


In recent study on design of experiments, the complicate metamodeling has been studied because defining exact model using computer simulation is expensive and time consuming. Thus, some designers often use approximate models, which express the relation between some inputs and outputs. In this paper, we review and compare the complicate metamodels, which are expressed by the interaction of various data through trying many physical experiments and running a computer simulation. The prediction model in this paper employs interpolation schemes known as ordinary kriging developed in the fields of spatial statistics and kriging in Design and Analysis of Computer Experiments (DACE) model. We will focus on describing the definitions, the prediction functions and the algorithms of two kriging methods, and assess the error measures of those by using some validation methods.

Key Words

Kriging Ordinary Kriging DACE Model Semivariogram Correlation Function BLUP 


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  1. Bacchi, B. and Kottegoda, N. T., 1995, “Identification and Calibration of Spatial Correlation Patterns of Rain Fall,”Journal of Hydrology, Vol. 165, pp. 311–348.CrossRefGoogle Scholar
  2. Barendrengt, L. G., 1987, “The Estimation of the Generalized Covariance When it is a Linear Combination of Two Known Generalized Covariances,”Water Resour. Res., Vol. 23, No. 4, pp. 583–590.CrossRefGoogle Scholar
  3. Besag, J. E., 1977, “Efficiency of Pseudo Likelihood Estimation for Simple Gaussian Fields,”Biometrika, Vol. 64, No. 3, pp. 616–618.MATHCrossRefMathSciNetGoogle Scholar
  4. Booker et al., 1995, “Global Modeling for Optimization: Boeing/IBM/Rice Collaborative Project,” 1995 Final Report, ISSTECH-95-032, The Boeing Company, Seattle, WA.Google Scholar
  5. Booker et al., 1996, “Multi-Level Design Optimization: A Boeing/IBM/Rice Collaborative Project,” 1996 Final Report, ISSTECH-96-031, The Boeing Company, Seattle, WA.Google Scholar
  6. Booker, A. J., 1996, “Case Studies in Design and Analysis of Computer Experiments,”Proceedings of the Section on Physical and Engineering Sciences, American Statistical Association.Google Scholar
  7. Chung, H. S. and Alons, J. J., 2000, “Comparison of Approximation Models with Merit Functions for Design Optimization,”American Institute of Aeronautics and Astronautics, 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, September 6–8, 2000, Long Beach, CA, AIAA-2000-4754, pp. 381–391.Google Scholar
  8. Cox, D. D. and John, S., 1995, “SDO: A Statistical Method for Global Optimization,”Proceedings of the ICASE/NAS Langley Workshop on Multidisciplinary Optimization, Hampton, March 13–16, VA, SIAM, pp. 315–329.Google Scholar
  9. Cressie, N., 1986, “Kriging Nonstaionary Data,”Journal of the American Statistical Association, Vol. 81, pp. 625–634.MATHCrossRefGoogle Scholar
  10. Cressie, N., 1991,Statistics for Spatial Data, John Wiley & sons, New York, pp. 1–143.MATHGoogle Scholar
  11. Currin et al., 1988, “A Bayesian Approach to the Design and Analysis of Computer Experiments,” Technical Report ORNL-6498, Oak Ridge National Laboratory.Google Scholar
  12. Deceneiere et al., 1998, “Applications of Kriging to Image Sequence Cooling,”Signal Processing; Image Communication, Vol. 13, pp. 227–249.CrossRefGoogle Scholar
  13. Dubrule, O., 1983, “Two Methods with Different Objections, Splines and Kriging,”Mathematical Geology, Vol. 15, pp. 245–257.CrossRefMathSciNetGoogle Scholar
  14. Gambolati, G. and Galcati, G., 1985, “Modello Efficiente di Interpolazione Basato Sulta Teoria del Kriging,” Rapporto Tecnico Enel. SI-723/85, CRIS-Serv. Idrol. ENEL-CRIS Laboratory, Mestre, Italy.Google Scholar
  15. Gandin, L. S., 1963, “Objective Analysis of Meteorlolgical Ffelds,” Gidrometeorologicheskoe Izdatelstvo (GIMIZ).Google Scholar
  16. Guinta, A. A., 1997,Aircraft Multidisciplinary Design Optimization Using Design of Experiments Theory and Response Surface Modeling, Ph. D Dissertation and MAD Center Report No. 97-05-01, Department of Aerospace and Ocean Engineering, Virginia, Polytechnic Institute and State University, Blacksburg, VA.Google Scholar
  17. Giunta et al., 1998, “A Comparison of Approximation Modeling technique: Polynomial Versus Interpolating Models,” 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis & Optimization, September 2–4, St, Louis, MI, AIAA, AIAA-98-4758.Google Scholar
  18. Goldberger, A. S., 1962, “Best Linear Unbiased Prediction in the Generalized Linear Regression Model,”Journal of the American Association, Vol. 57, pp. 369–375.MATHCrossRefMathSciNetGoogle Scholar
  19. Kitanidis, P. K., 1983, “Statistical Estimation of Polynomial Generalized Covariance Functions and Hydrologic Method,”Journal of Hydrology Science, Vol. 36, No. 3, pp. 223–240.Google Scholar
  20. Krige, D. G., 1951, “A Statistical Approach to Some Basic Mine Valuation Problems on the Witwatersrand,”Journal of the Chemical, Metallurgical and Mining Society of South Africa, Vol. 52, pp. 119–139.Google Scholar
  21. Mardia et al., 1996, “Kriging and Splines with Derivative Information,” Biometrica, Vol. 83, pp. 207–221.MATHCrossRefMathSciNetGoogle Scholar
  22. Matheron, G., 1962, “Traite de Geotatistique Appliquee,”Tome I. Memoires du Burean de Recherches Geologigues et Minieres, No. 14.Google Scholar
  23. Matheron, G., 1963, “Principles of Geostatistics,”Economic Geology, Vol. 58, pp. 1246–1266.CrossRefGoogle Scholar
  24. Matheron, G., 1969, “Le Krigeage Universel,”Les Cahiers du Centre de Morpholgie, Mathematique, Vol. 1, Ecole de Mines, Fonteinbleu, Fronce.Google Scholar
  25. Mitchell, T. J. and Morris, M. D., 1992, “The Spatially Correlation Function Approach to Response Surface Estimation,”Proceedings of the 1992 Winter Simulation Conference, December 13–16, Arlington, VA, IEEE, pp. 565–571.Google Scholar
  26. Myers, R. H. and Montgomery, D. C., 1995,Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons, NY.MATHGoogle Scholar
  27. Osio, I. G., and Amon, C. H., 1996, “An Engineering Design Methodology with Multistage Bayesian Surrogates and Optimal Sampling,”Research in Engineering Design, Vol. 8, No. 4, pp. 189–206.CrossRefGoogle Scholar
  28. Piazza, et al., 1983, “The Making and Testing of Geographic Gene-Frequency Maps,”Biometrics, Vol. 37, pp. 635–659.CrossRefMathSciNetGoogle Scholar
  29. Ripley, B. D., 1988,Statistical Inference for Spatial Processes, Cambridge: Cambridge University Press.Google Scholar
  30. Sacks, et al., 1989, “Design and Analysis of Computer Experiments”,Statistical Science, Vol. 4, No. 4, pp. 409–435.MATHCrossRefMathSciNetGoogle Scholar
  31. Sasena, M. J., 1998,Optimization of Computer Simulations via Smoothing Splines and Kriging Metamodels, M. S. Thesis, Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI.Google Scholar
  32. Simpson, T. W., 1998,A Concept Exploration Method for Product Family Design, Ph. D. Dissertation, Department of Mechanical Engineering, Georgia Institute of Technology.Google Scholar
  33. Simpson, et al., 1998, “Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization,”American Institute of Aeronautics and Astronautics, AIAA-98-4755, pp. 381–391.Google Scholar
  34. Stephen, et al., 1996, “S+SPATIALSTATS User’s Manual,” MathSoft, Inc., Seattle, Washington, pp. 73–120.Google Scholar
  35. Torczon, V., 1993,On the Convergence of Pattern Search Methods, Technical Report 93-10, Department of Computational and Applied Mathematics, Rice University, Houston, TX 77251-1892.Google Scholar
  36. Trosset, M. W. and Torczon, V., 1997,Numerical Optimization Using Computer Experiments, Report No. TR97-02, Department of Computational and Applied Mathematics, Rice University, Houston, TX.Google Scholar
  37. Volpi, G. and Gambolati, G., 1978, “On the Use of a Main Trend for the Kriging Technique in Hydrology,”Adv. Water Resourvoir. Vol. 1, No. 6, pp. 345–349.CrossRefGoogle Scholar
  38. Webster, R., 1985,Quantitative Spatial Analysis of Soil in the Field, Advances in Soil science 3, B. A. Stewart (ed.), New York, Springer-Verlag, pp. 1–70.Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2002

Authors and Affiliations

  • Je-Seon Ryu
    • 2
  • Min-Soo Kim
    • 1
  • Kyung-Joon Cha
    • 2
  • Tae Hee Lee
    • 3
  • Dong-Hoon Choi
    • 1
  1. 1.Center of Innovative Design Optimization TechnologyHanyang UniversitySeoulKorea
  2. 2.Department of MathematicsHanyang UniversitySeoulKorea
  3. 3.School of Mechanical EngineeringHanyang UniversitySeoulKorea

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