Regresyon ve Kriging Meta-Modelleri için Kullanılan Deney Tasarımı Yöntemleri

Abstract

Benzetim modelinden veri üretmenin oldukça zaman alıcı olduğu durumlarda eniyileme, duyarlılık analizi gibi amaçlarla meta-model kullanılır. Deney tasarımı meta-model kurma çalışmalarının en önemli aşamalarından biridir ve benzetim modelinin hangi girdi değişkenleri kombinasyonları için çalıştırılacağı belirlenir. Seçilen meta-modelin yapısına uygun deney tasarımı kullanılması gerekir. Bu çalışmada literatürde regresyon ve kriging meta-modelleri için kullanılan deney tasarımı yöntemleri incelenmiş ve yorumlanmıştır.

Keywords

• Deney tasarımı,Latin hiperküp tasarım,Tam faktöriyel tasarım,Azaltılmış faktöriyel tasarım,Merkezi bileşik tasarım,Kriging meta-modeli

References

1. [1] J.P.C Kleijnen, “Regression metamodels for generalizing simulation results,” IEEE Transactions on systems, man and cybernetics, vol. 9, no. 2, 1979.
2. [2] M. Balaban, “Benzetimde olağan ve genel kriging meta-modelleri,” Abstract Book of EurasianSciEnTech, 1st International Eurasian Conference on Science, Engineering and Technology, Ankara, Türkiye, 2018, pp. 63.
3. [3] V.C.P. Chen, K.L. Tsui, R.R. Barton and J.K. Allen, “A review of design and modeling in computer experiments,” Handbook of Statistics, vol. 22, pp.231–261, 2003.
4. [4] T.W. Simpson, J.D. Peplinski, P.N. Koch and J.K. Allen, “On the use of statistics in design and the implications for deterministic computer experiments,” Proceedings of DETC’97, 1997 ASME Design Engineering Technical Conferences, 1997, pp. 14-17.
5. [5] R.R. Barton, “Simulation metamodels,” Proceedings of the 1998 Winter Simulation Conference, 1998, pp. 167-174.
6. [6] R.R. Barton, “Tutorial: simulation metamodeling,” Proceedings of the 2015 Winter Simulation Conference, 2015, pp. 1765-1771.
7. [7] J. Sacks, W.J. Welch, T.J. Mitchell, and H.P. Wynn, “Design and analysis of computer experiments,” Statistical Science, vol. 4, pp. 409-435, 1989.
8. [8] W. van Beers and J.P.C. Kleijnen, “Kriging for Interpolation in random simulation,” Journal of the Operational Research Society, no. 54, pp. 255-262, 2003.

9. [9] T.W. Simpson, L. Dennis, and W. Chen, “Sampling Strategies for Computer Experiments: Design and Analysis,” International Journal of Reliability and Application, vol.2, pp.209-240, 2002.
10. [10] I. Batmaz and S.Tunali, “Second-Order Experimental Designs for Simulation Metamodeling,” Simulation, vol.78, no.12, pp. 699-715, 2002.
11. [11] A.A. Giunta, S.F. Wojtkiewicz Jr., and M.S. Eldred, “Overview of modern design of experiments methods for computational simulations,” AIAA-2003-0649, 2003.
12. [12] J.P.C Kleijnen, “An overview of the design and analysis of simulation experiments for sensitivity analysis” European Journal of Operational Research, Vol. 164, no. 2, pp.287-300, 2005.
13. [13] J.P.C Kleijnen, S.M. Sanchez, T.W. Lucas, and T.M. Cioppa, “A User’s Guide to the Brave New World of Designing Simulation Experiments,” INFORMS Journal on Computing, vol. 17, no.3, pp. 263–289, 2005.
14. [14] R. T. Johnson, D. C. Montgomery, B. Jones and J. W. Fowler, “Comparing designs for computer simulation experiments,” Proceedings of the 2008 Winter Simulation Conference, 2008, pp. 463-470.
15. [15] S.M. Sanchez and H. Wan, “Work smarter, not harder: a tutorial on designing and conducting simulation experiments,” Proceedings of the 2015 Winter Simulation Conference, 2015, pp. 1795-1809.
16. [16] J.P.C Kleijnen, “Regression and kriging metamodels with their experimental designs in simulation: A review,” European Journal of Operational Research, vol. 256, no.1, pp.1-16, 2017.
17. [17] A.M. Law, Simulation, Modeling and Analysis, 4th ed., McGraw-Hill International Edition, New York, USA, 2007.
18. [18] W.E. Biles, J.P.C. Kleijnen, W.C. Van Beers, and M.I. Van Nieuwenhuyse, “Kriging metamodeling in constrained simulation optimization: an explorative study,” Proceedings of the 2007 Winter Simulation Conference, 2007, pp. 355-362.
19. [19] T.W. Simpson and F. Mistree, “Kriging models for global approximation in simulation-based multidisciplinary design optimization,” AIAA Journal, vol. 39, no. 12, 2001.
20. [20] W.C. Van Beers and J.P.C. Kleijnen, “Kriging interpolation in simulation: a survey,” Proceedings of the 2004 Winter Simulation Conference, 2004, pp. 113-121.
21. [21] D.C. Montgomery, Design and Analysis of Experiments, 5.ed. New York, USA: John Wiley & Sons, Inc, 2001, 680 pages.
22. [22] R.H. Myers, D.C. Montgomery and C.M. Anderson-Cook, Response surface Methodology, 3. ed., New York, USA: John Wiley & Sons, Inc, 2009, 689 pages.
23. [23] M G.D. Mc Kay, R.J. Beckman, and W.J. Conover, “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code,” Technometrics, vol. 21, pp. 239– 245, 1979.
24. [24] T.J. Santner, B.J. Williams and W.İ. Notz, The design and analysis of computer experiments, New York, USA: Springer-Verlag, 2003.
25. [25] K.T. Fang, R. Li, and A. Sudjianto, Design and modeling for computer experiments, Taylor & Francis Group, Boca Raton, 2006.
26. [26] I. Van Nieuwenhuyse, J.P.C. Kleijnen, and W. Van Beers, “Constrained optimization in simulation: a novel approach,” Technical report, Department of Decision Sciences and Information Management, Katholieke Universiteit, Leuven, Belgium, 2008.
27. [27] V.R Joseph and Y. Hung, “Orthogonal-maximin latin hypercube designs,” Statistica Sinica, vol.18, pp.171- 186, 2008.
28. [28] A.B. Owen, “Orthogonal arrays for computer experiments, integration and visualization,” Statistica Sinica, no. 2, pp. 439-452, 1992.
29. [29] B. Tang, Orthogonal array-based Latin hypercubes. Journal of the American Statistical Association, no. 88, pp. 1392-1397, 1993.
30. [30] A.B. Owen, “Controlling correlation in Latin hypercube samples,” Journal of the American Statistical Association, no. 89, pp. 1517-1522, 1994.
31. [31] B. Tang, “Selecting Latin hypercubes using correlation criteria,” Statistica Sinica, vol. 8, pp. 965-977, 1998.
32. [32] K.Q. Ye, “Orthogonal column Latin hypercubes and their application in computer experiments,” Journal of the American Statistical Association, vol.93, pp.1430-1439, 1998.
33. [33] M. Balaban ve B. Dengiz, “Benzetim eniyilemesinde lognormal ordinary kriging meta-modeli”, Yedinci Ulusal Savunma Uygulamaları Modelleme ve Simülasyon Konferansı Bildiri Kitabı, ODTÜ, Ankara, 2017, ss.158-168.