On using standard residuals as a metric of kriging model quality

Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference

Volumn 3, Issue , 2007, Pages 2801-2814

  Congdon, Christopher D ^a,c   Martin, Jay D ^a,b,d  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b State College   (United States)

^c The Pennsylvania State University   (United States)

^d AIAA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADIABATIC FLAME TEMPERATURE; BRANIN TEST FUNCTION; GAUSSIAN SPATIAL PROCESS; KRIGING MODEL; LEAVE-ONE-OUT CROSS-VALIDATION;

COMPUTER SIMULATION; DECISION MAKING; INTERPOLATION; PARAMETER ESTIMATION;

MATHEMATICAL MODELS;

EID: 34547547977     PISSN: 02734508     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (30)

1. Martin, J. D., Simpson, T. W., "On Using Kriging Models as Probabilistic Models in Design," SAE Transactions Journal of Materials and Manufacturing, Vol. 5, No. 2005, pp. 129-139.
2. Sacks, J., Welch, W. J., Mitchell, T. J., Wynn, H. P., "Design and Analysis of Computer Experiments," Statistical Science, Vol. 4, No. 4, 1989, pp. 409-435.
3. Martin, J. D., "A Methodology for Evaluating System-Level Uncertainty in the Conceptual Design of Complex Multidisciplinary Systems," Ph.D. Thesis, Mechanical Engineering, The Pennsylvania State University, University Park, PA, 2005.
4. Goovaerts, P., Geostatistics for Natural Resources Evaluation, Oxford University Press, New York, 1997.
5. Currin, C., Mitchell, T. J., Morris, M. D., Ylvisaker, D., "A Bayesian Approach to the Design and Analysis of Computer Experiments," Oak Ridge National Laboratory ORNL-6498, 1988.
6. Wackernagel, H., Multivariate Geostatistcs, Springer-Verlag Berlin Heidelberg, New York, 2003.
7. Ripley, B. D., Spatial Statistics, John Wiley & Sons, New York, 1981.
8. Goldberger, "Best Linear Unbiassed Prediction in the Generalized Linear Regression Model," Journal of the Americal Statistical Association, Vol. 57, No. 298, 1962, pp. 369.
9. Martin, J. D., Simpson, T. W., "Use of Kriging Models to Approximate Deterministic Computer Models," AIAA Journal, Vol. 43, No. 4, 2005, pp. 853-863.
10. Booker, A. J., Conn, A. R., Dennis, J. E. J., Frank, M., Trosset, M., Torczonm, V., "Global Modeling for Optimization," The Boeing Company 1995.
11. Currin, C., Mitchell, T. J., Morris, M. D., Ylvisaker, D., "Bayesian Prediction of Deterministic Functions, with Applications to the Design and Analysis of Computer Experiments," Journal of the American Statistical Association, Vol. 86, No. 416, 1991, pp. 953-963.
12. Koehler, J. R., Owen, A. B., "Computer Experiments," Handbook of Statistics, edited by Ghosh, S., Rao, C. R., Elsevier, New York, 1996, pp. 261-308.
13. Myers, R. H., Montgomery, D. C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 2nd ed., John Wiley & Sons, Inc., New York, 2002.
14. Kutner, M. H., Nachtsheim, C., Neter, J., Li, W., Applied Linear Statistical Models, McGraw Hill, Homewood, Ill, 2005.
15. Cook, R. D., "Exploring Partial Residual Plots," Technometrics, Vol. 35, No. 4, 1993, pp. 351-362.
16. Shapiro, S. S., Wilk, M. B., "An Analysis of Variance Test for Normality (Complete Samples)," Biometrika, Vol. 52, No. 3/4, 1965, pp. 591-611.
17. Cliff, A. D., Ord, J. K., Spatial Autocorrelation, Pion, London, 1973.
18. Cook, R. D., Weisberg, S., "Diagnostics for Heteroscedasticity in Regression," Biometrika, Vol. 70, No. 1, 1983, pp. 1-10.
19. Jones, D. R., Schonlau, M., Welch, W. J., "Efficient Global Optimization of Expensive Black-Box Functions," Journal of Global Optimization, Vol. 13, No. 4, 1998, pp. 455-492.
20. Booker, A. J., Dennis, J. E., Jr., Frank, P. D., Serafini, D. B., Torczon, V., Trosset, M., "A Rigorous Framework for Optimization of Expensive Functions by Surrogates," Structural Optimization, Vol. 17, No. 1, 1999, pp. 1-13.
21. Martin, J. D., Simpson, T. W., "A Study on the Use of Kriging Models to Approximate Deterministic Computer Models," 2003 ASME Design Engineering Technical Conference, Chicago, IL.
22. Schonlau, M., "Computer Experiments and Global Optimization," Dissertation, Department of Statistics, University of Waterloo, Waterloo, Ontario, Canada, 1997.
23. Turns, S., An Introduction to Combustion- Concepts and Applications, McGraw Hill, 2001.
24. Martin, J. D., Simpson, T. W., "A Methodology to Manage System-Level Uncertainty During Conceptual Design," ASME Journal of Mechanical Design, Vol. 128, No. 4, 2006, pp. 959-968.
25. Lin, Y., "An Efficient Robust Concept Exploration Method and Sequential Exploratory Experimental Design," Dissertation, Department of Mechanical Engineering, Georgia Institute of Technology, Atlanta, 2004.
26. Jin, R., Chen, W., Sudjianto, A., "On Sequential Sampling for Global Meta-Modeling in Engineering Design," 2002 ASME Design Technical Conference, Montreal, Canada, DETC2002/DAC-34092.
27. van Beers, W. C. M., Kleijnen, J. P. C., "Kriging Interpolation in Simulation: A Survey," Proceedings of the 2004 Winter Simulation Conference, Washington, DC.
28. Dixon, L. C. W., Szego, G. P., "The Global Optimization Problem; an Introduction," Towards Global Optimization, edited by Dixon, L. C. W., Szego, G. P., North Holland, Amsterdam, 1978, pp. 1-15.
29. Booker, A. J., "Well-Conditioned Kriging Models for Optimization of Computer Simulations," The Boeing Company M&CT-TECH-00-002, 2000.
30. Higdon, D., Swall, J., Kern, J., "Non-Stationary Spatial Modeling," Bayesian Statistics, Vol. 6, No. 1999, pp. 761-768.