Design under uncertainty using a combination of evidence theory and a Bayesian approach

SAE International Journal of Materials and Manufacturing

Volumn 1, Issue 1, 2009, Pages 122-135

  Zhou, Jun ^a   Mourelatos, Zissimos P ^a   Ellis, Clifton ^b  

^a OAKLAND UNIVERSITY   (United States)

^b U S ARMY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BASIC PROBABILITY ASSIGNMENT; BAYESIAN APPROACHES; DESIGN DECISIONS; DESIGN METHOD; DESIGN METHODOLOGY; DESIGN OPTIMIZATION; DESIGN UNDER UNCERTAINTY; ENGINEERING DESIGN; EVIDENCE THEORIES; FUZZY INFORMATION; INCOMPLETE INFORMATION; MODEL UNCERTAINTIES; NON-PROBABILISTIC UNCERTAINTY; NUMBER OF SAMPLES; OPTIMAL DESIGN METHODS; POSSIBILITY-BASED DESIGN OPTIMIZATIONS; PRACTICAL ENGINEERING APPLICATIONS; PROBABILITY THEORY; PRODUCT RELIABILITY; RANDOM UNCERTAINTIES; SAMPLE POINT; UNCERTAIN VARIABLES;

BAYESIAN NETWORKS; OPTIMIZATION; UNCERTAINTY ANALYSIS;

DESIGN;

EID: 77953236401     PISSN: 19463979     EISSN: 19463987     Source Type: Journal    
DOI: 10.4271/2008-01-0377     Document Type: Article

References (43)

1. Tu, J., Choi, K. K. and Park, Y. H., "A New Study on Reliability-Based Design Optimization", ASME Journal of Mechanical Design, 121, 557-564, 1999.
2. Liang, J., Mourelatos, Z. P., and Tu, J., "A Single-Loop Method for Reliability-Based Design Optimization," Proceedings of ASME Design Engineering Technical Conferences, Paper# DETC2004/ DAC-57255, 2004.
3. nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Seattle, WA, 2001.
4. Lee, J. O., Yang, Y. O. and Ruy, W. S., "A Comparative Study on Reliability Index and Target Performance Based Probabilistic Structural Design Optimization," Computers and Structures, 80, 257-269, 2002.
5. Youn, B. D., Choi, K. K. and Park, Y. H. "Hybrid Analysis Method for Reliability-Based Design Optimization," ASME Journal of Mechanical Design, 125(2), 221-232, 2001.
6. Oberkampf, W., Helton, J. and Sentz, K., "Mathematical Representations of Uncertainty," AIAA Non-Deterministic Approaches Forum, AIAA 2001-1645, Seattle, WA, April 16-19, 2001.
7. Sentz, K. and Ferson, S., "Combination of Evidence in Dempster - Shafer Theory," Sandia National Laboratories Report SAND2002-0835, April 2002.
8. Klir, G. J. and Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, 1995.
9. Klir, G. J. and Filger, T. A., Fuzzy Sets, Uncertainty, and Information, Prentice Hall, 1988.
10. Yager, R. R., Fedrizzi, M. and Kacprzyk, J. (Editors), Advances in the Dempster - Shafer Theory of Evidence, John Wiley & Sons, Inc., 1994.
11. Dubois, D. and Prade, H., Possibility Theory, Plenum Press, New York, 1988.
12. Moore, R. E., Interval Analysis, Prentice-Hall, 1966.
13. Zadeh, L. A., "Fuzzy Sets," Information and Control, 8, 338-353, 1965.
14. Muhanna, R. L. and Mullen, R. L., "Uncertainty in Mechanics Problems - Interval-Based Approach," Journal of Engineering Mechanics, 127(6), 557-566, 2001.
15. Mullen, R. L. and Muhanna, R. L., "Bounds of Structural Response for all Possible Loadings," ASCE Journal of Structural Engineering, 125(1), 98-106, 1999.
16. Penmetsa, R. C. and Grandhi, R. V., "Efficient Estimation of Structural Reliability for Problems with Uncertain Intervals," Computers and Structures, 80, 1103-1112, 2002.
17. Du, X. and Sudjianto, A., "Reliability-Based Design with a Mixture of Random and Interval Variables," Proceedings of ASME Design Engineering Technical Conferences, Paper# DETC2003/ DAC- 48709, 2003.
18. Rao, S. S. and Cao, L., "Optimum Design of Mechanical Systems Involving Interval Parameters," ASME Journal of Mechanical Design, 124, 465-472, 2002.
19. Gu, X., Renaud, J. E. and Batill, S. M., "An Investigation of Multidisciplinary Design Subject to Uncertainties," 7th AIAA/USAF/NASA/ISSMO Multidisciplinary Analysis & Optimization Symposium, St. Louis, Missouri, 1998.
20. Elishakoff, I. E., Haftka, R. T. and Fang, J. "Structural Design under Bounded Uncertainty -Optimization with Anti-Optimization," Computers and Structures, 53, 1401-1405, 1994.
21. Lombardi, M. and Haftka, R. T., "Anti-Optimization Technique for Structural Design under Load Uncertainties," Computer Methods in Applied Mechanics and Engineering, 157, 19-31, 1998.
22. Du, X. and Chen, W., "An Integrated Methodology for Uncertainty Propagation and Management in Simulation-Based Systems Design," AIAA Journal, 38(8), 1471-1478, 2000.
23. Mourelatos, Z. P. and Zhou, J., "Reliability Estimation with Insufficient Data Based on Possibility theory", AIAA Journal, 43(8), 1696-1705, 2005.
24. Zhou, J. and Mourelatos, Z. P., "A Sequential Algorithm for Possibility-Based Design Optimization," ASME Journal of Mechanical Design, 130(1), 2008.
25. Choi, K. K., Du, L. and Youn, B. D., "A New Fuzzy Analysis Method for Possibility-Based Design Optimization," 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA 2004- 4585, Albany, NY, 2004.
26. Nikolaidis, E., Chen, S., Cudney, H., Haftka, R. T. and Rosca, R., "Comparison of Probability and Possibility for Design Against Catastrophic Failure Under Uncertainty," ASME Journal of Mechanical Design, 126, 2004.
27. Oberkampf, W. L. and Helton, J. C., "Investigation of Evidence Theory for Engineering Applications," AIAA Non-Deterministic Approaches Forum, AIAA 2002-1569, Denver, CO, April, 2002.
28. Bae, H-R, Grandhi, R. V. and Canfield, R. A., "An Approximation Approach for Uncertainty Quantification Using Evidence Theory," Reliability Engineering and System Safety, 86, 215-225, 2004.
29. Bae, H-R, Grandhi, R. V. and Canfield, R. A., "Epistemic Uncertainty Quantification Techniques Including Evidence Theory for Large-Scale Structures," Computers and Structures, 82, 1101-1112, 2004.
30. Agarwal, H., Renaud, J. E., Preston, E. L. and Padmanabhan, D., "Uncertainty Quantification Using Evidence Theory in Multidisciplinary Design Optimization," Reliability Engineering and System Safety, 85, 281-294, 2004.
31. Mourelatos, Z. P. and Zhou, J., "A Design Optimization Method using Evidence Theory," ASME Journal of Mechanical Design, 128(4), 901-908, 2006.
32. Box, G. and Tiao, G., Bayesian Inference in Statistical Analysis, John Wiley & Sons, New York, 1992.
33. Dempster, A. P., "A Generalization of Bayesian Inferences based on a Sample from a Finite Univariate Population," Biometrics, 54(2-3), 515-528, 1967.
34. Siu, N. O. and Kelly, D. L., "Bayesian Parameter Estimation in Probabilistic Risk Assessment," Reliability Engineering System Safety, 62(1-2), 89- 116, 1998.
35. Ross, T. J., Fuzzy Logic with Engineering Applications, McGraw Hill, 1995.
36. Sentz, K. and Ferson, S., "Combination of Evidence in Dempster - Shafer Theory," Sandia National Laboratories Report SAND2002-0835, April 2002.
37. Dong, W. M. and Shah, H. C., "Vertex Method for Computing Functions of Fuzzy Variables," Fuzzy Sets and Systems, 24, 65-78, 1987.
38. th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA 2004- 4585, Albany, NY, 2004.
39. th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA-2003- 1669, Norfolk, VA, April 7-10, 2003.
40. Ye, K. Q., Li, W. and A. Sudjianto, Algorithmic Construction of Optimal Symmetric Latin Hypercube Designs, Journal of Statistical Planning and Inference, 90, 145-159, 2000.
41. Jones, D. R., Perttunen, C. D. and Stuckman, B. E., "Lipschitzian Optimization without the Lipschitz Constant," Journal of Optimization Theory and Applications, 73(1), 157-181, 1993.
42. Subroto, G. and Papalambros, P.Y., "A Bayesian Approach to Reliability-Based Optimization with Incomplete Information," ASME Journal of Mechanical Design, 128(4), 909-918, 2006.
43. Lewis, K. and Mistree, F., "Collaborative, Sequential and Isolated Decisions in Design," Proceedings of ASME Design Engineering Technical Conferences, Paper# DETC1997/ DTM-3883, 1997.