Conservative surrogate model using weighted kriging variance for sampling-based RBDO

Journal of Mechanical Design, Transactions of the ASME

Volumn 135, Issue 9, 2013, Pages

  Zhao, Liang ^a   Choi, K K ^b   Lee, Ikjin ^c   Gorsich, David ^d  

^a SCHLUMBERGER   (United States)

^b University of Iowa   (United States)

^c UNIVERSITY OF CONNECTICUT   (United States)

^d US Army Research Development and Engineering Command   (United States)

Author keywords

Conservative surrogate model; Corrected Akaike Information Criterion (AICc); Dynamic Kriging method; Limited number of samplings; Reliability based design optimization (RBDO); Weighted Kriging variance

Indexed keywords

COMPUTER AIDED DESIGN; FORECASTING; FUEL ADDITIVES; INTELLIGENT SYSTEMS; MACHINE DESIGN; MONTE CARLO METHODS; RELIABILITY ANALYSIS; SAFETY ENGINEERING; SENSITIVITY ANALYSIS;

CONSERVATIVE SURROGATE MODEL; CORRECTED AKAIKE INFORMATION CRITERIA (AICC); CORRECTED AKAIKE INFORMATION CRITERIONS; DYNAMIC KRIGING METHOD; KRIGING; KRIGING METHODS; LIMITED NUMBER OF SAMPLING; RELIABILITY-BASED DESIGN OPTIMIZATION; SURROGATE MODELING; WEIGHTED KRIGING VARIANCE;

KRIGING;

EID: 84903633368     PISSN: 10500472     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.4024731     Document Type: Article

References (38)

1. Haldar, A., and Mahadevan, S., 2000, Probability, Reliability and Statistical Methods in Engineering Design, John Wiley & Sons, New York.
2. Yi, K., Choi, K. K., Kim, N. H., and Botkin, M. E., 2007, "Design Sensitivity Analysis and Optimization for Minimizing Springback of Sheet-Formed Part," Int. J. Numer. Methods Eng., 71, pp. 1483-1511. (Pubitemid 47412463)
3. Yu, X., and Du, X., 2006, "Reliability-Based Multidisciplinary Optimization for Aircraft Wing Design," Struct. Infrastruct. Eng., 2(3-4), pp. 277-289.
4. Lee, I., Choi, K. K., Noh., Y., Zhao., L., and Gorsich., D., 2011, "Sampling-Based Stochastic Sensitivity Analysis Using Score Functions for RBDO Problems With Correlated Random Variables," ASME J. Mech. Des., 133(2), p. 021003.
5. Lee, I., Choi, K. K., and Zhao, L., 2011, "Sampling-Based RBDO Using the Dynamic Kriging (D-Kriging) Method and Stochastic Sensitivity Analysis," J. Struct. Multidiscip. Optim., 44(3), pp. 299-317.
6. Rubinstein, R. Y., and Kroese, D. P., 2008, Simulation and the Monte Carlo Method, Wiley-Interscience, New York.
7. Krige, D. G., 1951, "A Statistical Approach to Some Basic Mine Valuation Problems on the Witwatersrand," J. Chem., Metall. Min. Eng. Soc. S Afr., 52(6), pp. 119-139.
8. Martin, J. D., and Simpson, T. W., 2005, "Use of Kriging Models to Approximate Deterministic Computer Models," AIAA J., 43(4), pp. 853-863. (Pubitemid 40611902)
9. Forrester, A., Sobester, A., and Keane, A. J., 2008, Engineering Design Via Surrogate Modeling: A Practical Guide, Wiley, Hoboken, NJ.
10. Chiles, J. P., and Delfiner, P., 1999, Geostatistics: Modeling Spatial Uncertainty, Wiley, New York.
11. Suykens, J. A. K., and Vandewalle, J., 1999, "Least Square Support Vector Machine Classifiers," Neural Process. Lett., 9(3), pp. 293-300.
12. Smola, A. J., and Scholkopf, B., 2004, "A Tutorial on Support Vector Regression," Stat. Comput., 14(3), pp. 199-222.
13. Xie, L., Gu, N., Li, D., Cao, Z., Tan, M., and Nahavandi, S., 2013, "Concurrent Control Chart Patterns RecognitionWith Singular Spectrum Analysis and Support Vector Machine," Comput. Ind. Eng., 64(1), pp. 280-289.
14. Song, H., Choi, K. K., Lee, I., Zhao, L., and Lamb, D., 2011, "Adaptive Virtual Support Vector Machine for the Reliability Analysis of High-Dimensional Problems," 37th ASME Design Automation Conference, Aug. 28-31, Washington, DC.
15. Zhao, L., Choi, K. K., and Lee, I., 2011, "Metamodeling Method Using Dynamic Kriging for Design Optimization," AIAA J., 49(9), pp. 2034-2046.
16. Zhao, L., Choi, K. K., and Lee, I., 2009, "Response Surface Method Using Sequential Sampling for Reliability-Based Design Optimization," Proceedings of the ASME IDETC/CIE 2009, Aug. 30th-Sept 2nd, San Diego, Paper No. DETC2009-87084.
17. Chan, K. Y., Skerlos, S. J., Papalambros, P., 2007, "An Adaptive Sequential Linear Programming Algorithm for Optimal Design Problems With Probabilistic Constraints," ASME J. Mech. Des., 129(2), pp. 140-149. (Pubitemid 46736245)
18. Elishakoff, I., 2004, Safety Factors and Reliability: Friends or Foes? Kluwer Academic, Norwell, MA.
19. Acar, E., Kale, A., and Haftka, R. T., 2007, "Comparing Effectiveness of Measures That Improve Aircraft Structural Safety," J. Aerosp. Eng., 20(3), pp. 186-199. (Pubitemid 46934855)
20. Picheny, V., Kim, N. H., and Haftka, R. T., 2008, "Conservative Predictions Using Surrogate Modeling," 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials, April 7-10, Schaumburg, IL.
21. Picheny, V., 2009, "Improving Accuracy and Compensating for Uncertainty in Surrogate Modeling," Ph.D. dissertation, University of Florida, Gainesville, FL.
22. Picheny, V., Ginsbourger, D., Roustant, O., Haftka, R. T., and Kim, N. H., 2010, "Adaptive Designs of Experiments for Accurate Approximation of a Target Region," ASME J. Mech. Des., 132(7), p. 071008.
23. Hertog, D., Kleijnen, J., and Siem, A., 2006, "The Correct Kriging Variance Estimated by Bootstrapping," J. Oper. Res. Soc., 57, pp. 400-409.
24. Luna, S. D., and Young, A., 2003, "The Bootstrap and Kriging Prediction Intervals," Scand. J. Stat., 30, pp. 175-192.
25. Picheny, V., Kim, N. H., and Haftka, R. T., 2010, "Application of Bootstrap Method in Conservative Estimation of Reliability With Limited Samples," Struct. Multidiscip. Optim., 41 (2), pp. 205-217.
26. Viana, F. A. C., and Haftka, R. T., 2009, "Cross Validation Can Estimate How Well Prediction Variance Correlates With Error," AIAA J., 47(9), pp. 2266-2270.
27. Viana, F. A. C., Haftka, R. T., and Steffen, V., 2009, "Multiple Surrogates: How Cross-Validation Errors Can Help Us to Obtain the Best Predictor," Struct. Multidiscip. Optim., 39(4), pp. 439-457.
28. Viana, F. A. C., Picheny, V., and Haftka, R. T., 2010, "Using Cross Validation to Design Conservative Surrogates," AIAA J., 48(10), pp. 2286-2298.
29. Xiong, F., Chen, W., Xiong, Y., and Yang, S. X., 2011, "Weighted Stochastic Response Surface Method Considering Sample Weights," J. Struct. Multidiscip. Optim., 44, pp. 837-849.
30. Akaike, H., 1974, "A New Look at the Statistical Model Identification," IEEE Trans. Autom. Control, 19(6), pp. 716-723.
31. Hoeting, J. A., Davis, R. A., Merton, A. A., and Thompson, S. E., 2006, "Model Selection for Geostatistical Models," Ecol. Appl., 16 (1), pp. 87-98.
32. Hurvich, C. M., and Tsai, C. L., 1989, "Regression and Time Series Model Selection in Small Samples," Biometrika, 76, pp. 297-307.
33. McDonald, M., and Mahadevan, S., 2008, "Design Optimization With System-Level Reliability Constraints," ASME J. Mech. Des., 130(2), p. 021403.
34. Lee, I., Choi, K. K., and Gorsich, D., 2010, "System Reliability-Based Design Optimization Using the MPP-Based Dimension Reduction Method," Struct. Multidiscip. Optim., 41(6), pp. 823-839.
35. Burnham, K. P., and Anderson, D. R., 2002, Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, Springer, New York.
36. Goel, T., Haftka, R., and Shyy, W., 2008, "Comparing Error Estimation Measures for Polynomial and Kriging Approximation of Noise-Free Functions," Struct. Multidiscip. Optim., 38 (5), pp. 429-442.
37. Xiong, F., Xiong, Y., Chen, W., and Yang, S., 2009, "Optimizing Latin Hypercube Design for Sequential Sampling of Computer Experiments," Eng. Optim., 41(8), pp. 793-810.
38. Guo, J., and Du, X., 2009, "Reliability Sensitivity Analysis With Random and Interval Variables," Int. J. Numer. Methods Eng., 78, pp. 1585-1617.