Simultaneous model building and validation with uniform designs of experiments

Engineering Optimization

Volumn 39, Issue 5, 2007, Pages 497-512

  Narayanan, A ^a   Toropov, V V ^b   Wood, A S ^c   Campean, I F ^c  

^a ALTAIR ENGINEERING   (United States)

^b UNIVERSITY OF LEEDS   (United Kingdom)

^c UNIVERSITY OF BRADFORD   (United Kingdom)

Author keywords

Design of experiments; Latin hypercube; Simultaneous model build and validation

Indexed keywords

COMPUTATIONAL GEOMETRY; GENETIC ALGORITHMS; ITERATIVE METHODS; MATHEMATICAL MODELS; OPTIMIZATION; PARALLEL PROCESSING SYSTEMS; POTENTIAL ENERGY FUNCTIONS;

GENETIC OPERATORS; HYPERCUBES;

DESIGN OF EXPERIMENTS;

EID: 34347224412     PISSN: 0305215X     EISSN: 10290273     Source Type: Journal    
DOI: 10.1080/03052150701399978     Document Type: Conference Paper

References (27)

1. Audze, P. and Eglais, V., New approach to planning out of experiments. Prob. Dynam. & Strength, Zinatne, 1977, 35, 104-107 (in Russian).
2. Bates, S.J., Sienz, J. and Langley, D.S., Formulation of the Audze-Eglais uniform Latin hypercube design of experiments. Adv. Eng. Software, 2003, 34, 493-506.
3. Bates, S.J., Sienz, J. and Toropov V.V., Formulation of the optimal Latin hypercube design of experiments using a permutation genetic algorithm, in Proceedings of the 45th AIAA Structures, Structural Dynamics & Materials Conference, 2004.
4. Beachkofski, B.K. and Grandhi, R.V., Improved distributed hypercube sampling, in Proceedings of the 43rd Structures, Structural Dynamics & Materials Conference, Article AIAA-2002-1274, 2002.
5. Cary, M., A model based engine calibration methodology for a port fuel injection spark ignition engine. PhD thesis, University of Bradford, 2003.
6. 2-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs. Maths. Comp., 2000, 71, 275-296.
7. Husslage, B., van Dam, E. and den Hertog, D., Nested maximin Latin hypercube designs in two dimensions. Center Discussion Article 2005-79, 11 pp, 2005.
8. Jin, R., Chen, W. and Sudjianto, A., An efficient algorithm for constructing optimal design of computer experiments, in Proceedings of the ASME Design Automation Conference, Article DETCDAC48760, 2003.
9. Johnson, M.E., Moore, L.M. and Ylvisaker, D., Minimax and maximin distance designs. J. Stat. Plan. Inf., 1990, 26, 131-148.
10. Leary, S., Bhaskar, A. and Keane, A.J., Optimal orthogonal-array-based Latin hypercubes. J. Appl. Stat., 2003, 30, 585-598.
11. Manteufel, R.D., Distributed hypercube sampling algorithm, in Proceedings of the 42nd Structures, Structural Dynamics & Materials Conference, Article AIAA-2001-1673, 2001.
12. McKay, M., Beckman, R. and Conover, W., A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technomet., 1979, 21, 239-246.
13. Michaelewicz, Z. Genetic Algorithms + Data Structures = Evolution Programs, 3rd edition, 1996 (Springer-Verlag: Berlin).
14. Morris, M.D. and Mitchell, T.J., Exploratory designs for computer experiments. J. Stat. Plan. Inf., 1995, 43, 381-402.
15. Myers, R.H. and Montgomery, D.C., Response Surface Methodology: Process and Product Optimization using Designed Experiments, 1995 (Wiley: New York, NY).
16. Narayanan, A., Development of optimal model building and validation design of experiments. MSc thesis, University of Bradford, 2006.
17. Park, J.S., Optimal Latin hypercube designs for computer experiments. J. Stat. Plan. Inf., 1994, 39, 95-111.
18. Romero, V.J., Burkardt, J.V., Gunzburger, M.D. and Peterson, J.S., Initial evaluation of pure and Latinized centroidal Voronoi tessellation for non-uniform statistical sampling, in Proceedings of the Fourth International Conference on Sensitivity Analysis of Model Output, 2004.
19. Sacks, J., Schiller, S.B. and Welch, W.J., Designs for computer experiments. Technomet., 1989, 34, 15-25.
20. Sacks, J., Welch, W.J., Mitchell, T.J. and Wynn, H.P., Design and analysis of computer experiments (with discussion). Stat. Sci., 1989, 4, 409-435.
21. Santner, Th.J., Williams, B.J. and Notz, W.I., Design and Analysis of Computer Experiments, Series in Statistics, 2003 (Springer-Verlag: New York, NY).
22. Shewry, M.C. and Wynn, H.P., Maximum entropy sampling. J. Appl. Stat., 1987, 14, 165-170.
23. Stinstra, E.D., den Hertog, D., Stehouwer, H.P. and Vestjens, A., Constrained maximin designs for computer experiments. Technomet., 2003, 45, 340-346.
24. Tang, B., Orthogonal array-based Latin hypercubes. J. Amer. Stat. Assoc., Theory and Methods, 1993, 88, 1392-1397.
25. van Dam, E.R., Husslage, B.G.M., den Hertog, D. and Melissen, J.B.M., Maximin Latin hypercube designs in two dimensions. Center Discussion Article 2005-08, 16 pp, 2005.
26. Wang, L., Shan, S. and Wang, G.G., Mode-pursuing sampling method for global optimization on expensive black-box functions. Eng. Optim., 2004, 36, 419-438.
27. Ye, K.Q., Li, W. and Sudianto, A., Algorithmic construction of optimal symmetric Latin hypercube designs. J. Stat. Plan. Inf., 2000, 90, 145-159.