Model validation via uncertainty propagation and data transformations

AIAA Journal

Volumn 42, Issue 7, 2004, Pages 1406-1415

  Chen, Wei ^a,c   Baghdasaryan, Lusine ^b,d   Buranathiti, Thaweepat ^a,e   Cao, Jian ^a,e  

^a NORTHWESTERN UNIVERSITY   (United States)

^b UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

^c Intgd Design Automation Laboratory   (United States)

^d Department of Mechanical Engineering ^*

^e Department of Mechanical Engineering   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; CORRELATION METHODS; DATA TRANSFER; MATHEMATICAL MODELS; UNCERTAIN SYSTEMS;

DATA TRANSFORMATIONS; MODEL VALIDATION; SIMULATION MODELS; UNCERTAINTY PROPAGATION;

COMPUTATIONAL METHODS;

EID: 3343008964     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.491     Document Type: Article

References (43)

1. Hills, G. R., and Trucano, T. G., "Statistical Validation of Engineering and Scientific Models; Background," Sandia National Labs., Rept. SAND99-1256, Albuquerque, NM, May 1999.
2. Oberkampf, W. L., and Trucano, T. G., "Validation Methodology in Computational Fluid Dynamics," AIAA Paper 2000-2549, June 2000.
3. Guide for the Verification and Validation of Computational Fluid Dynamics Simulations, AIAA-G-077-1998, AIAA, Reston, VA, 1998.
4. Sargent, R. G., "Validation and 'Verification of Simulation Models," Proceedings of the 1999 Winter Simulation Conference, ACM Press, New York, 1999, pp. 39-48.
5. Gregoire, T. G., and Reynolds, M. R., "Accuracy Testing and Estimation Alternatives," Forest Science, Vol. 34, No. 2, 1988, pp. 302-320.
6. Helton, J. C., "Uncertainty and Sensitivity Analysis in the Presence of Stochastic and Subjective Uncertainty," Journal Statistical Computation and Simulation, Vol. 57, 1997, pp. 3-76.
7. Apostolakis, G., "Model Uncertainty: Its Characterization and Quantification," A Commentary on Model Uncertainty, edited by A. Mosleh, N. Siu, C. Smidts, and C. Lui, NUREG/CP-0138, U.S. Nuclear Regulatory Commission, 1994.
8. Trucano, T. G., "Prediction and Uncertainty in Computational Modeling of Complex Phenomena: A Whitepaper," Sandia National Labs., Rept. SAND98-2776, Albuquerque, NM, Dec. 1998.
9. Hazelrigg, G. A., "On the Role and Use of Mathematical Models in Engineering Design," Journal of Mechanical Design, Vol. 121, No. 3, 1999, pp. 336-341.
10. Halton, J. H., "On the Efficiency of Certain Quasi-Random Sequences of Points in Evaluating Multi-Dimensional Integrals," Numerische Mathematik, Vol. 2, 1960, pp. 84-90.
11. Hammersley, J. M., "Monte Carlo Methods for Solving Multivariate Problems," Annals of the New York Academy of Sciences, Vol. 86, 1960, pp. 844-874.
12. Owen, A. B., "Latin Supercube Sampling for Very High Dimensional Simulation," ACM Transactions on Modeling and Computer Simulation, Vol. 8, No. 1, 1998, pp. 71-102.
13. Myers, R. H., and Montgomery, D. C., Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 2nd ed., Wiley, New York, 2002.
14. Kleijnen, J. P. C., Statistical Tools for Simulation Practitioners, Marcel Dekker, New York, 1986.
15. Chen, W., Allen, J. K., Mavris, D., and Mistree, F., "A Concept Exploration Method for Determining Robust Top-Level Specifications," Engineering Optimization, Vol. 26, 1996. pp. 137-158.
16. Simpson, T. W., Peplinski, J., Koch, P. N., and Allen, J. K., "Metamodels for Computer-Based Engineering Design: Survey and Recommendations," Engineering with Computers, Vol. 17, No. 2, 2001, pp. 129-150.
17. Barton, R. R., "Metamodels for Simulation Input-Output Relations," Proceedings of the 1992 Winter Simulation Conference, edited by J. J. Swain, D. Goldsman, and R. C. Grain, Inst. of Electrical and Electronics Engineers, New York, 1992, pp. 289-299.
18. Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P., "Design and Analysis of Computer Experiments," Statistical Science, Vol. 4, No. 4, 1989, pp. 409-435.
19. Simpson, T. W., Mauery, T. M., Korte, J. J., and Mistree, F., "Kriging Metamodels for Global Approximation in Simulation-Based Multidisciplinary Design Optimization," AIAA Journal, Vol. 39, No. 12, 2001, pp. 2233-2241.
20. Meckesheimer, M., Barton, R. R., Limayem, F., and Yannou, B., "Meta-modeling of Combined Discrete/Continuous Responses," Design Theory and Methodology-DTM'00, edited by J. K. Allen, American Society of Mechanical Engineers, Fairfield, NJ, 2000.
21. Jin, R., Chen, W., and Simpson, T., "Comparative Studies of Metamodeling Techniques Under Multiple Modeling Criteria," Journal of Structural and Multidisciplinary Optimization, Vol. 23, No. 1, 2001, pp. 1-13.
22. Jin, R., Du, X., and Chen, W., "The Use of Metamodeling Techniques for Optimization Under Uncertainty," Journal of Structural and Multidisciplinary Optimization, Vol. 25, No. 2, 2003, pp. 99-116; also American Society of Mechanical Engineers, ASME Paper DAC21039, 2001.
23. Bartlet, M. S., "The Use of Transformations," Biometrics, Vol. 3, No. 1, 1947, pp. 39-52.
24. Tukey, J. W., "On the Comparative Anatomy of Transformations," Annals of Mathematical Statistics, Vol. 28, No. 3, 1957, pp. 602-632.
25. Box, G. E. P., and Cox, D. R., "An Analysis of Transformations, " Journal of the Royal Statistical Society B, Vol. 26, No. 2, 1964, pp. 211-252.
26. Hinkley, D., "On Quick Choice of Power Transformation," Applied Statistics, Vol. 26, No. 1, 1977, pp. 67-69.
27. Manly, B. F. J., "Exponential Data Transformations," Statistician, Vol. 25, No. 1, 1976, pp. 37-42.
28. John, J. A., and Draper, N. R., "An Alternative Family of Transformations," Applied Statistics, Vol. 29, No. 2, 1980, pp. 190-197.
29. Yeo, I.-K., and Johnson, R., "A New Family of Power Transformations to Improve Normality or Symmetry," Biometrika, Vol. 87, 2000, pp. 954-959.
30. Atkinson, A. C., "Testing Transformations to Normality," Journal of the Royal Statistical Society B, Vol. 35. No. 3, 1973, pp. 473-479.
31. Carroll, R. J., "A Robust Method for Testing Transformations to Achieve Approximate Normality," Journal of the Royal Statistical Society B, Vol. 42, No. 1, 1980, pp. 71-78.
32. Atkinson, A. C., and Riani, M., "Bivariate Boxplots, Multiple Outliers, Multivariate Transformations and Discriminant Analysis: The 1997 Hunter Lecture," Environmetrics. Vol. 8, 1997, pp. 583-602.
33. Krzanowski, W. J., Principles of Multivariate Analysis: A User's Perspective, paperback ed., Clarendon, Oxford, 1990.
34. Box. G. E. P., and Tidwell, P. W., "Transformation of the Independent Variables," Technometrica, Vol. 4, No. 4, 1962, pp. 531-550.
35. Koehler, J. R., and Owen, A. B., "Computer Experiments," Handbook of Statistics, edited by S. Ghosh and C. R. Rao, Vol. 13, Elsevier Science. New York, 1996, pp. 261-308.
36. Kleinbaum, D.G., Kupper, L. L., Muller, K. E., and Nizam, A., Applied Regression Analysis and Other Multivariate Methods, 3rd ed., Duxbury, Pacific Grove, CA, 1998.
37. Mardia, K. V., "Applications of Some Measures of Multivariate Skewness and Kurtosis for Testing Normality and Robustness Studies," Sankhya B, Vol. 36, 1974, pp. 115-128.
38. Song, N., Qian, D., Cao, J., Liu, W. K., and Li, S., "Effective Prediction of Springback in Straight Flanging," Journal of Engineering Materials and Technology, Vol. 123, No. 4, 2001, pp. 456-461.
39. Hu, Y., and Walters, G. N., "A Few Issues On Accuracy of Springback Simulation of Automobile Parts," Society of Automotive Engineers, SAE Paper 1999-01-1000, March 1999.
40. Esche, S., and Kinzel, G., "The Effect of Modeling Parameters and Bending on Two-dimensional Sheet Metal Forming Simulation," SAE Transactions, Vol. 107, No. 7, 1998, pp. 74-85.
41. "ABAQUS™: User's Manual," Hibbit, Karison, and Sorensen, Inc., Pawtucket, RI, 1998.
42. Birnbaum, Z. W., "Numerical Tabulation of the Distribution of Kolmogorov's Statistic for Finite Sample Size," Journal of the American Statistical Association, Vol. 47, No. 259, 1952, pp. 425-441.
43. Sudjianto, A., Juneja, L., Agrawal, H. V., and Vora, M., "Computer Aided Reliability and Robustness Assessment," International Journal of Reliability, Quality and Safety Engineering, Vol. 5, No. 2, 1998, pp. 181-193.