Research Article
Year 2022,
Volume: 37 Issue: 3, 1185 - 1196, 28.02.2022
Abstract
Bu çalışmada, benzetim modeli ile veri üretmenin maliyetli olabileceği karmaşık yapıdaki problemler için benzetim modelinin yerine kullanılabilecek Kriging tabanlı bir meta-model önerilmektedir. Üniversal Kriging (ÜK) meta-modelinin drift fonksiyonu yapısının bilinmediği durumlar için önerilen bu yeni model yapısında, ÜK meta-modelinde drift fonksiyonu olarak kullanılan birinci ve ikinci dereceden regresyon modelleri yerine, kesirli değerler de alabilen değişkenlerin bir güç fonksiyonu kullanılmıştır. Kesirli Üniversal Kriging (KÜK) meta-modeli olarak adlandırılan bu meta modelin kestirim gücü deneysel analizlerle incelenmiştir. Geçerleme analizleri Ortalama Hata Kare (OHK) ve Enbüyük hata Kare (EHK) başarım ölçütlerine göre KÜK meta-modellerinin üstün kestirim gücüne sahip olduğunu ortaya koymuştur. Böylece, benzetim modelinin girdi-çıktı ilişkisinin karesel polinomial durumdan farklı ve daha yüksek dereceden etkilerini de içeren bir güç fonksiyonu ile ifade edilebilir olması durumunda, KÜK meta-modelleri yeni bir meta-model yaklaşımı olarak bu çalışmada önerilmektedir.
Keywords
Meta-model Ordinary Kriging Üniversal Kriging Kesirli Üniversal Kriging Latin hiperküp tasarım
Supporting Institution
yok
Project Number
yok
Thanks
Bu çalışmanın tamamlanması sürecinde yaptıkları değerli katkılar için Prof. Dr. Fulya Altıparmak ve Doç. Dr. Ebru Angun’a teşekkürü borç biliriz.
References
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- Van Beers, W. and Kleijnen, J.P.C., Kriging for interpolation in random simulation, Journal of the Operational Research Society,54, 255-262, 2003.
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- Owen, A.B., Controlling correlation in Latin hypercube samples, Journal of the American Statistical Association, 89, 1517-1522, 1994.
- Tang, B., Selecting Latin hypercubes using correlation criteria, Statistica Sinica, 8, 965-977, 1998.
- Ye, K.Q., Orthogonal column Latin hypercubes and their application in computer experiments, Journal of the American Statistical Association, 93, 1430-1439, 1998.
- Simpson, T., Comparison of response surface and kriging models in the multidisciplinary design of an aerospike nozzle, ICASE Report No. 98-16, NASA/CR-1998-206935, 1998.
- Jamil, M. and Yang, X.S., A literature survey of benchmark functions for global optimization problems, Int. Journal of Mathematical Modeling and Numerical Optimization, 4(2), 150–194, 2013.
- Ishigami, T. and Homma, T., An importance quantification technique in uncertainty analysis for computer models, In Uncertainty Modeling and Analysis, Proceedings., IEEE, 398-403, 1990.
Year 2022,
Volume: 37 Issue: 3, 1185 - 1196, 28.02.2022
Abstract
Project Number
yok
References
- Biles, W.E., Kleijnen, J.P.C., Van Beers, W.C.M. and Van Nieuwenhuyse, I., Kriging metamodeling in constrained simulation optimization: an explorative study, Proceedings of the 2007 Winter Simulation Conference, 355-362, 2007.
- Barton, R.R., Simulation metamodels, Proceedings of the 1998 Winter Simulation Conference, 167-174, 1998. Kleijnen, J.P.C., Regression metamodels for generalizing simulation results, IEEE Transactions on systems, man and cybernetics, SMC-9, 2, 93-96, 1979.
- Barton, R.R., Tutorial: simulation metamodeling, Proceedings of the 2015 Winter Simulation Conference, 1765-177, 2015
- Myers, R.H., Montgomery D.C. and Anderson-Cook, C.M., Response surface Methodology, 3. ed., John Wiley & Sons, Inc, New York, USA, 2009, 689 pages.
- Kleijnen, J.P.C., Kriging metamodeling in simulation: a review, European Journal of Operational Research, 192, 707–716, 2009.
- Simpson T.W., Peplinski J.D., Koch P.N., and Allen J.K., On the use of statistics in design and the implications for deterministic computer experiments, Proceedings of DETC’97, 1997 ASME Design Engineering Technical Conferences, Sacramento, California, September 14-17, 1997.
- Matheron, G., Principles of geostatistics, Economic Geology, 58:1246-1266, 1963.
- Cressie, N.A.C., Statistics for Spatial Data, A Wiley-Interscience publication, New York, 1993.
- Sacks, J., Welch, W.J., Mitchell, T.J. and Wynn, H.P., Design and analysis of computer experiments, Statistical Science, 4, 409-435, 1989.
- Van Beers, W. and Kleijnen, J.P.C., Kriging for interpolation in random simulation, Journal of the Operational Research Society,54, 255-262, 2003.
- Van Beers W. and Kleijnen, J.P.C., Kriging interpolation in simulation: a survey, Technical report, Department of Information Management, Tilburg University, 2004.
- Simpson, T., Mauery, T.M., Korte, J.J. and Mistree, F., Kriging models for global approximation in simulation-based multidisciplinary design optimization. AIAA Journal, 39(12), 2233-2241, 2001.
- Martin, J.D., and Simpson, T., On the use of kriging models to approximate deterministic computer models, Proceedings of DETC’04, 1-12, 2004.
- Mehdad, E. and Kleijnen, J.P.C., Efficient global optimisation for black-box simulation via sequential intrinsic Kriging, Journal of the Operational Research Society, 1-13, 2018.
- Balaban, M and Dengiz, B., Lognormal ordinary kriging metamodel in simulation optimization, Operations Research and Applications: An International Journal (ORAJ), 5 (1), 1-12, 2018.
- Chen, V.C.P., Tsui, K.L., Barton, R.R. and Allen, J.K., A review of design and modeling in computer experiments, Handbook of Statistics, 22, 231–261, 2003.
- Myers, D.E., On variogram estimation, The frontiers of statistical scientific theory & industrial applications, 2, 261-266, 1991.
- Mitchell, T.J. and Morris, M.D., Bayesian design and analysis of computer experiments: two examples. Statistica Sinica, 2, 359–379, 1992.
- Journel, A.G. and Huıjbregts C.J., Mining Geostatistics Academic Press, London, UK, 1978.
- Jin, R., Chen, W. and Sudjianto A., On Sequential Sampling for Global Metamodeling in Engineering Design, ASME 2002 Design Engineering Technical Conferences and Computers and Information in Engineering Conference Montreal, Canada, September 29th October, 1-11, 2002.
- Simpson, T., Mauery, T.M., Korte, J.J. and Mistree, F., Kriging models for global approximation in simulation-based multidisciplinary design optimization, AIAA Journal, 39(12), 2233-2241, 2001.
- Zakerifar, M., Biles, W.E. and Evans, G.W., Kriging metamodeling in multiple-objective simulation optimization, Simulation, 87(10), 843-856, 2011.
- Mc Kay, M G.D., Beckman, R. J. and Conover, W.J., A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21, 239–245, 1979.
- Joseph, V.R. and Hung, Y., Orthogonal-maximin Latin hypercube designs, Statistica Sinica, 18, 171- 186, 2008.
- Owen, A.B., Orthogonal arrays for computer experiments, integration and visualization, Statistica Sinica, 2, 439-452, 1992.
- Tang, B., Orthogonal array-based Latin hypercubes. Journal of the American Statistical Association, 88, 1392-1397, 1993.
- Owen, A.B., Controlling correlation in Latin hypercube samples, Journal of the American Statistical Association, 89, 1517-1522, 1994.
- Tang, B., Selecting Latin hypercubes using correlation criteria, Statistica Sinica, 8, 965-977, 1998.
- Ye, K.Q., Orthogonal column Latin hypercubes and their application in computer experiments, Journal of the American Statistical Association, 93, 1430-1439, 1998.
- Simpson, T., Comparison of response surface and kriging models in the multidisciplinary design of an aerospike nozzle, ICASE Report No. 98-16, NASA/CR-1998-206935, 1998.
- Jamil, M. and Yang, X.S., A literature survey of benchmark functions for global optimization problems, Int. Journal of Mathematical Modeling and Numerical Optimization, 4(2), 150–194, 2013.
- Ishigami, T. and Homma, T., An importance quantification technique in uncertainty analysis for computer models, In Uncertainty Modeling and Analysis, Proceedings., IEEE, 398-403, 1990.
There are 32 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Project Number | yok |
| Publication Date | February 28, 2022 |
| Submission Date | May 12, 2021 |
| Acceptance Date | September 12, 2021 |
| Published in Issue | Year 2022 Volume: 37 Issue: 3 |