Robust design concept in possibility theory and optimization for system with both random and fuzzy input variables

2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007

Volumn 6 PART B, Issue , 2008, Pages 1183-1193

  Du, Liu ^a   Choi, Kyung K ^a   Lee, Ikjin ^a  

^a University of Iowa   (United States)

Author keywords

Mixed variable robust design optimization; Possibility theory; Robustness analysis; Robustness measure

Indexed keywords

CUMULATIVE DISTRIBUTION FUNCTION (CDF); DESIGN AUTOMATION CONFERENCE (DAC); FUZZY INPUTS; FUZZY VARIABLES; IN ORDER; INPUT DATA; INTEGRATION POINTS; INTERNATIONAL DESIGNS; MAXIMAL POSSIBILITY SEARCH (MPS); MIXED ANALYSIS; NUMERICAL EXAMPLES; OUTPUT PERFORMANCE; PERFORMANCE MEASURE (PF); POSSIBILITY THEORY; PROBABILITY THEORY; ROBUST DESIGN OPTIMIZATION (RDO); ROBUST DESIGNS; SEARCH METHODS; STATISTICAL INFORMATION; TECHNICAL CONFERENCES;

AEROSPACE APPLICATIONS; ARCHITECTURAL DESIGN; AUTOMATION; CLUSTER ANALYSIS; COMPUTATIONAL METHODS; COMPUTER AIDED DESIGN; COMPUTER NETWORKS; COMPUTERS; DISTRIBUTION FUNCTIONS; ENGINEERING; FAILURE ANALYSIS; FUZZY SETS; INDUSTRIAL ENGINEERING; INVERSE PROBLEMS; MECHANIZATION; MEMBERSHIP FUNCTIONS; MULTITASKING; NUMBER THEORY; NUMERICAL ANALYSIS; NUMERICAL METHODS; OPTIMIZATION; PAPER; PLASMA SPRAYING; PROBABILITY; PROBABILITY DISTRIBUTIONS; QUALITY ASSURANCE; RANDOM PROCESSES; RANDOM VARIABLES; RELIABILITY; RISK ASSESSMENT; ROBOTICS; SET THEORY; TECHNOLOGY; VARIATIONAL TECHNIQUES;

FUZZY LOGIC;

EID: 44949212884     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC2007-35106     Document Type: Conference Paper

References (22)

1. Nikolaidis, E., Cudney, H. H., Chen, S., Haftka, R. T., and Rosea, R., "Comparison of Probability and Possibility for Design Against Catastrophic Failure Under Uncertainty," Journal of Mechanical Design, Vol. 126, No. 3, 2004, pp. 386-394.
2. Mourelatos Z. P., and Zhou, J., "Reliability Estimation and Design with Insufficient Data Based on Possibility Theory," AIAA Journal, Vol. 43, No. 8, 2005, pp. 1696-1705.
3. Du L., Choi K. K., Youn B. D., and Gorsich D., "Possibility-Based Design Optimization Method For Design Problems With Both Statistical And Fuzzy Input Data," Journal of Mechanical Design, Vol. 128, No. 4, 928-935, 2006.
4. Du L., Choi K. K., and Youn B. D., "Inverse Possibility Analysis Method for Possibility-Based Design Optimization," AIAAJ, Vol. 44, No. 11, 2682-2690, 2006.
5. Du, L., Choi, K.K., "An Inverse Analysis Method for Design Optimization with Both Statistical and Fuzzy Uncertainties," ASME DETC2006-99731, Philadelphia, Pennsylvania, September 10-13, 2006.
6. Kalsi, M., Hacker, K., and Lewis, K., "A Comprehensive Robust Design Approach for Decision Trade-Offs in Complex Systems Design," ASME Journal of Mechanical Design, Vol. 123, No. 1, pp. 1-10, 2001.
7. Su, J., and Renaud, J. E., "Automatic Differentiation in Robust Optimization," AIAA Journal, Vol. 35, No. 6, pp. 1072-1079, 1997.
8. Youn, B. D., Choi, K. K., and Yi, K., "Performance Moment Integration (PMI) Method for Quality Assessment in Reliability-Based Robust Optimization," Mechanics Based Design of Structures and Machines, Vol. 33, No. 2, pp. 185-213, 2005.
9. Du, X., Sudjianto, A., and Chen, W., "An Integrated Framework for Optimization Under Uncertainty Using Inverse Reliability Strategy," ASME Journal of Mechanical Design, Vol. 126, No. 4, pp. 562-570, 2004.
10. Mourelatos, Z. P. and Liang, J., "A Methodology for Trading-off Performance and Robustness under Uncertainty," Journal Of Mechanical Design Vol.128 No. 4 pp. 856-863, 2006.
11. Lee, I., Choi, K.K., Du, L., and Gorsich, D., "Dimension Reduction Method for Reliability-Based Robust Design Optimization," Computers & Structures, to appear, 2007.
12. Jung, D. H., and Lee, B. C., "Development of a simple and efficient method for robust optimization," International Journal for Numerical Methods in Engineering, Vol. 53, pp. 2201-2215, 2002.
13. Xu, H., and Rahman, S., "Generalized Dimension-Reduction Method for Multi-dimensional Integration in Stochastic Mechanics," International Journal for Numerical Methods in Engineering, Vol. 61, No. 12, pp. 1992-2019, 2004.
14. Xu, H., and Rahman, S., "Univariate Dimension-Reduction Method for Multi-dimensional Integration in Stochastic Mechanics," Probabilistic Engineering Mechanics, Vol. 19, No. 4, pp. 393-408, 2004.
15. Youn, B. D., Du, L., Choi, K.K., Gorsich, D., "Integration of Possibility-Based Optimization to Robust Design for Epistemic Uncertainty," ASME, Journal of Mechanical Design, to appear, 2007.
16. DeCooman, G., "Possibility theory .1. The measure- and integral-theoretic groundwork," International Journal Of General Systems Vol. 25 No. 4 pp. 291-323 1997.
17. DeCooman, G., "Possibility theory .2. Conditional possibility," International Journal Of General Systems Vol. 25 No. 4 pp. 325-351 1997.
18. DeCooman, G., "Possibility theory .3. Possibilistic independence," International Journal Of General Systems Vol. 25 No. 4 pp. 353-371 1997.
19. DeCooman, G., "Possibility and necessity integrals," Fuzzy Sets And Systems, Vol. 77 No. 2, pp. 207-227, 1996.
20. Zadeh, L. A., "Fuzzy Sets," Information and Control, Vol. 8, No. 12, pp. 338-353, 1965.
21. Youn, B. D., Choi, K. K., Yang, R. -J., and Gu, L., "Reliability- Based Design Optimization for Crashworthiness of Vehicle Side Impact," Structural Multidisciplinary Optimization, Vol. 26, No. 3-4, pp. 272-283, 2004.
22. Vanderplaats, G. M., DOT User's Manual, VR&D, Cororado Springs, 1997.