Bayesian metamodeling for computer experiments using the gaussian kriging models

Quality and Reliability Engineering International

Volumn 28, Issue 4, 2012, Pages 455-466

  Deng, Haisong ^a   Shao, Wenze ^b   Ma, Yizhong ^b   Wei, Zhuihui ^b  

^a NANJING AUDIT UNIVERSITY   (China)

^b NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

computer experiments; Gaussian Kriging; metamodeling; robust design; sparseness prior

Indexed keywords

COMPUTER EXPERIMENT; KRIGING; METAMODELING; ROBUST DESIGNS; SPARSENESS PRIOR;

BAYESIAN NETWORKS; BENCHMARKING; DESIGN OF EXPERIMENTS; GAUSSIAN DISTRIBUTION; INFERENCE ENGINES; PRODUCT DESIGN; RANDOM PROCESSES;

INTERPOLATION;

EID: 84861405859     PISSN: 07488017     EISSN: 10991638     Source Type: Journal    
DOI: 10.1002/qre.1259     Document Type: Article

References (59)

1. Wheelwright SC, Clark KB,. Revolutionizing Product Development. The Free Press: New York, 1992.
2. Taguchi G,. Introduction to Quality Engineering. Kraus International Publications: White Plains, NY 1986.
3. Bates R, Kenett RS, Steinberg DM, Wynn HP,. Achieving robust design from computer simulations. Quality Technology and Quantitative Management 2006; 3 (2): 161-177.
4. Currin C, Mitchell TJ, Morris MD, Ylvisaker D,. Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments. Journal of the American Statistical Association 1991; 86: 953-963.
5. Thomke S, Holzner M, Gholami T,. The crash in the machine. Scientific American 1999; 280: 72-77.
6. Iman RL, Johnson ME, Watson CC,. Statistical aspects of forecast planning for hurricanes. The American Statistician 2006; 60 (2): 1713-1726.
7. Xiao X, Edwards JR, Hassan HA, Cutler A,. Variable turbulent Schmidt-number formulation for scramjet applications. AIAA Journal 2006; 44 (3): 593-599.
8. Sweetman B,. VentureStar: 21st century space shuttle. Popular Science 1996; 42-47.
9. Gu L,. A comparison of polynomial based regression models in vehicle safety analysis. In ASME Design Engineering Technical Conferences-Design Automation Conference, Diaz A,. Ed., ASME: Pittsburgh, 2001; DAC-21063.
10. Jones B, Johnson RT,. Design and analysis for the Gaussian process model. Quality and Reliability Engineering International 2009; 25: 515-524.
11. Santner TJ, Williams BJ, Notz WI,. The Design and Analysis of Computer Experiments. Springer Series in Statistics. Springer: New York, 2003.
12. Sacks J, Welch WJ, Mitchell TJ, Wynn HP,. Design and analysis of computer experiments. Statistical Science 1989; 4 (4): 409-435.
13. Sacks J, Schiller SB, Welch WJ,. Designs for computer experiments. Technometrics 1989; 31 (1): 41-47.
14. Martin JD, Simpson TW,. On using Kriging models as probabilistic models in design. SAE Transactions Journal of Materials & Manufacturing 2004; 5: 129-139.
15. Kenett RS, Steinberg DM,. New frontiers in the design of experiments. Quality Progress 2006; 39: 61-65. (Pubitemid 44328885)
16. Dellino G, Kleijnen JPC, Meloni C,. Robust optimization in simulation: Taguchi and Krige combined. Submitted for the publication on INFORMS Journal on Computing 2010.
17. Joseph VR, Hung Y, Sudjianto A,. Blind Kriging: a new method for developing metamodels. ASME Journal of Mechanical Design 2008; 130: 031102-1-8.
18. Linkletter CD, Bingham D, Hengartner N, Higdon D, Ye KQ,. Variable selection for Gaussian process models in computer experiments. Technometrics 2006; 48: 478-490. (Pubitemid 44865389)
19. Joseph VR,. Limit Kriging. Technometrics 2006; 48: 458-466. (Pubitemid 44865387)
20. Li R, Sudjianto A,. Analysis of computer experiments using penalized likelihood in Gaussian Kriging models. Technometrics 2005; 47: 111-120. (Pubitemid 40701505)
21. Myers RH, Montgomery D,. Response Surface Methodology: Process and Product Optimization Using Designed Experiments. John Wiley and Sons: Toronto, 1995.
22. McKay MD, Bechman RJ, Conover WJ,. A Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 1979; 21 (2): 239-245. (Pubitemid 9452235)
23. Park JS,. Optimal Latin-hypercube designs for computer experiments. Journal of Statistical Planning Inference 1994; 39: 95-111.
24. Ye KQ, Li W, Sudjianto A,. Algorithmic construction of optimal symmetric Latin hypercube designs. Journal of Statistical Planning and Inferences 2000; 90: 145-159.
25. Fang KT, Lin DKJ, Winker P, Zhang Y,. Uniform design: theory and application. Technometrics 2000; 39 (3): 237-248.
26. Kalagnanam JR, Diwekar UM,. An efficient sampling technique for off-line quality control. Technometrics 1997; 39 (3): 308-319. (Pubitemid 127634028)
27. Meckesheimer M, Booker AJ, Barton RR, Simpson TW,. Computationally inexpensive metamodel assessment strategies. AIAA Journal 2002; 40 (10): 2053-2060. (Pubitemid 35295818)
28. Owen A,. Orthogonal arrays for computer experiments, integration, and visualization. Statistica Sinica 1992; 2: 439-452.
29. Hedayat AS, Sloane NJA, Stufken J,. Orthogonal Arrays: Theory and Applications. Springer: New York, 1999.
30. Wang GG, Shan S,. Review of metamodeling techniques in support of engineering design optimization. ASME Transactions. Journal of Mechanical Design 2007; 45 (6): 1208-1221.
31. Jin R, Chen W, Simpson TW,. Comparative studies of metamodeling techniques under multiple modeling criteria. Structural and Multidisciplinary Optimization 2001; 23 (1): 1-13. (Pubitemid 34271934)
32. Jin R, Chen W, Sudjianto A,. On sequential sampling for global metamodeling for in engineering design. In ASME 2002 Design Engineering Technical Conferences and Computer and Information in Engineering Conference, ASME: Montreal, Canada, 2002; DETC2002/DAC-34092.
33. Papadrakakis M, Lagaros M, Tsompanakis Y,. Structural optimization using evolution strategies and neural networks. Computer Methods in Applied Mechanics and Engineering 1998: 156 (1-4): 309-333. (Pubitemid 128396491)
34. Varadarajan S, Chen W, Pelka CJ,. Robust concept exploration of propulsion systems with enhanced model approximation capabilities. Engineering Optimization 2000; 32 (3): 309-334. (Pubitemid 30577376)
35. Friedman JH,. Multivariate adaptive regressive splines. The Annals of Statistics 1991; 19 (1): 1-67.
36. Mullur AA, Messac A,. Extended radial basis functions: more flexible and effective metamodeling. AIAA Journal 2005; 43 (6): 1306-1315. (Pubitemid 40818963)
37. Fang H, Horstemeyer MF,. Global response approximation with radial basis functions. Journal of Engineering Optimization 2006; 38 (4): 407-424.
38. Simpson TW, Mauery TM, Korte JJ, Mistree F,. Kriging metamodels for global approximation in simulation-based multidisciplinary design optimization. AIAA Journal 2001; 39 (12): 2233-2241. (Pubitemid 34023417)
39. Martin JD, Simpson TW,. On the use of Kriging models to approximate deterministic computer models. AIAA Journal 2005; 43 (4): 853-863. (Pubitemid 40611902)
40. Kleijnen JPC, van Beers W,. Kriging for interpolation in random simulation. Journal of the Operational Research Society 2003; 54: 255-262.
41. Smola AJ, Scholkopf B,. A tutorial on support vector regression. Statistics and Computing 2004; 14: 199-222. (Pubitemid 39063488)
42. Clarke SM, Griebsch JH, Simpson TW,. Analysis of support vector regression for approximation of complex engineering analyses. Transactions of ASME, Journal of Mechanical design 2005; 127 (6): 1077-1087. (Pubitemid 41709565)
43. Koehler JR, Owen AB,. Computer Experiments. In Handbook of Statistics, Ghosh S, Rao CR, Eds., Elsevier Science: New York, 1996.
44. Wipf DP,. Bayesian methods for finding sparse representations. PhD Dissertation, University of California, San Diego, 2006.
45. Figueiredo M,. Adaptive sparseness for supervised learning. IEEE Transactions on Pattern Analysis and Machine Intelligence 2003; 25 (9): 1150-1159.
46. Park T, Casella G,. The Bayesian Lasso. Journal of the American Statistical Association 2008; 103 (482): 681-686.
47. Varona L, Mekkawy W, Gianola D, Blasco A,. A whole genome analysis using robust asymmetric distributions. Genetical Research 2005; 88: 143-151.
48. Yi NJ, Xu SZ,. Bayesian LASSO for quantitative trait loci mapping. Genetics 2008; 179: 1045-1055.
49. Babacan SD, Molina R, Katsaggelos AK,. Bayesian compressive sensing using Laplace priors. IEEE Transactions on Image Processing 2010; 19 (1): 53-63.
50. Welch WJ, Buck RJ, Sacks J, Wynn HP, Mitchell T, Morris MD,. Screening, predicting, and computer experiments. Technometrics 1992; 34: 15-25.
51. Gano SE, Renaud JE, Martin JD, Simpson TW,. Update strategies for Kriging models for use in variable fidelity optimization. In 1st AIAA Multidisciplinary Design Optimization Specialist Conference, AIAA: Austin, Texas, 2005.
52. Lophaven SN, Nielsen HB, Sndergaard J,. DACE: a Matlab Kriging toolbox. Technical Report, IMM-REP-2002-12, Technical University of Denmark, 2002.
53. Tipping M, Faul A,. Fast marginal likelihood maximization for sparse Bayesian models. In Proceedings of the 9th Int. Workshop Artificial Intelligence and Statistics, Bishop CM, Frey BJ, Eds., Society for Artificial Intelligence and Statistics (SAIS): Key West, Florida, 2003.
54. Hoffman RM, Sudjianto A, Du X, Stout J,. Robust piston design and optimization using piston secondary motion analysis. SAE Transactions 2003; SAE Paper 2003-01-0148.
55. Fan J, Li R,. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 2001; 96 (456): 1348-1360. (Pubitemid 33695585)
56. Fang KT, Li R, Sudjianto A,. Design and Modeling for Computer Experiments. New York: CRC Press, 2006.
57. Fang KT, Lin DKJ,. Uniform designs and their application in industry. Handbook on Statistics in Industry 2003; 22: 131-170.
58. Fang KT, Ho WM, Xu ZQ,. Case studies of computer experiments with uniform design. Technical Report, Hong Kong Baptist University, 2000.
59. Li R,. Model selection for analysis of uniform design and computer experiment. International Journal of Reliability, Quality and Safety Engineering 2002; 9 (4): 367-382.