Comparing error estimation measures for polynomial and kriging approximation of noise-free functions

Structural and Multidisciplinary Optimization

Volumn 38, Issue 5, 2009, Pages 429-442

  Goel, Tushar ^a   Hafkta, Raphael T ^a,c   Shyy, Wei ^b  

^a UNIVERSITY OF FLORIDA   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

^c LIVERMORE SOFTWARE TECHNOLOGY CORPORATION   (United States)

Author keywords

Ensemble strategy; Error measures; Prediction variance; PRESS; Surrogate models

Indexed keywords

ENSEMBLE STRATEGY; ERROR MEASURES; PREDICTION VARIANCE; PRESS; SURROGATE MODELS;

BLOCK CODES; ERROR ANALYSIS; ESTIMATION; MAGNETIC RESONANCE SPECTROSCOPY; MAXIMUM LIKELIHOOD ESTIMATION; MEAN SQUARE ERROR; PRESSES (MACHINE TOOLS); STATISTICS; SURFACE PROPERTIES; UNCERTAINTY ANALYSIS;

POLYNOMIAL APPROXIMATION;

EID: 67349175273     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-008-0290-z     Document Type: Article

References (23)

1. Congdon CD, Martin JD (2007) On using standard residuals as a metric of kriging model quality. In: Proceedings of the 48th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Honolulu HI, 23 Apr-26 Apr, AIAA-2007-1928
2. Currin C, Mitchell TJ, Morris MD, Ylvisaker D (1998) A Bayesian approach to the design and analysis of computer experiments. Technical report ORNL-6498. Oak Ridge National Laboratory, Oak Ridge, TN
3. D Den Hertog JPC Kleijnen AYD Siem 2006 The correct kriging variance estimated by bootstrapping J Oper Res Soc 57 4 400 409
4. Dixon LCW, Szegö GP (1978) Towards global optimization 2. North-Holland, Amsterdam
5. Goel T (2007) Multiple surrogates and error modeling in optimization of liquid rocket propulsion components. PhD thesis, Dept. of Mechanical and Aerospace Engineering, The University of Florida, Gainesville, FL
6. T Goel RT Haftka W Shyy NV Queipo 2007 Ensemble of surrogates Struct Multidisc Optim 33 199 216 (Pubitemid 46198778)
7. T Goel RT Haftka W Shyy LT Watson 2008 Pitfalls of using a single criterion for selecting experimental designs Int J Numer Methods Eng 75 2 127 155
8. DR Jones M Schonlau WJ Welch 1998 Efficient global optimization of expensive black-box functions J Glob Optim 13 4 455 492 (Pubitemid 128507405)
9. Khuri AI, Cornell JA (1996) Response surfaces: designs and analysis. Marcel Dekker, New York
10. JPC Kleijnen WCM van Beers 2004 Application-driven sequential designs for simulation experiments: kriging metamodeling J Oper Res Soc 55 9 876 883
11. Lophaven SN, Nielsen HB, Sondergaard J (2002a) DACE: a MATLAB kriging toolbox, version 2.0, information and mathematical modeling. Technical University of Denmark, Denmark
12. Lophaven SN, Nielsen HB, Sondergaard J (2002b) DACE: aspects of the MATLAB toolbox DACE, information and mathematical modeling. Technical University of Denmark, Denmark
13. Martin JD (2005) A methodology for evaluating system-level uncertainty in the conceptual design of complex multidisciplinary systems. PhD thesis, Dept. of Mechanical Engineering, The Pennsylvania State University, University Park, PA
14. JD Martin TW Simpson 2005 Use of kriging models to approximate deterministic computer models AIAA Journal 43 4 853 863
15. G Matheron 1963 Principles of geostatistics Econ Geol 58 1246 1266
16. MATLAB (2002) The language of technical computing, version 6.5 release 13. The MathWorks Inc., Natick, MA
17. M McKay W Conover R Beckman 1979 A comparison of three methods for selecting values of input variables in the analysis of output from a computer code Technometrics 21 239 245 (Pubitemid 9452235)
18. M Meckesheimer RR Barton TW Simpson A Booker 2002 Computationally inexpensive metamodel assessment strategies AIAA J 40 10 2053 2060 (Pubitemid 35295818)
19. TJ Mitchell MD Morris 1992 Bayesian design and analysis of computer experiments: two examples Stat Sin 2 2 359 379
20. Myers RH, Montgomery DC (1995) Response surface methodology-process and product optimization using de signed experiments. Wiley, New York
21. NV Queipo RT Haftka W Shyy T Goel R Vaidyanathan PK Tucker 2005 Surrogate-based analysis and optimization Prog Aerosp Sci 41 1 28
22. Ueberhuber CW (1997) Numerical computation 2: methods, software and analysis. Springer, Berlin, p 71
23. Wu YT, Shin Y, Sues R, Cesare M (2001) Safety factor based approach for probability-based design optimization. In: Proceedings of the 42nd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Seattle WA, 2001, AIAA-2001-1522