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An Efficient Possibility-Based Design Optimization Method for a Combination of Interval and Random Variables
Technical Paper
2007-01-0553
ISSN: 0148-7191, e-ISSN: 2688-3627
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English
Abstract
Reliability-based design optimization accounts for variation. However, it assumes that statistical information is available in the form of fully defined probabilistic distributions. This is not true for a variety of engineering problems where uncertainty is usually given in terms of interval ranges. In this case, interval analysis or possibility theory can be used instead of probability theory. This paper shows how possibility theory can be used in design and presents a computationally efficient sequential optimization algorithm. The algorithm handles problems with only uncertain or a combination of random and uncertain design variables and parameters. It consists of a sequence of cycles composed of a deterministic design optimization followed by a set of worst-case reliability evaluation loops. A crank-slider mechanism example demonstrates the accuracy and efficiency of the proposed sequential algorithm.
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Citation
Zhou, J. and Mourelatos, Z., "An Efficient Possibility-Based Design Optimization Method for a Combination of Interval and Random Variables," SAE Technical Paper 2007-01-0553, 2007, https://doi.org/10.4271/2007-01-0553.Also In
Reliability and Robust Design in Automotive Engineering, 2007
Number: SP-2119; Published: 2007-04-16
Number: SP-2119; Published: 2007-04-16
SAE 2007 Transactions Journal of Passenger Cars: Mechanical Systems
Number: V116-6; Published: 2008-08-15
Number: V116-6; Published: 2008-08-15
References
- Tu, J. Choi, K. K. Park, Y. H. “A New Study on Reliability-Based Design Optimization” ASME Journal of Mechanical Design 121 4 557 564 1999
- Wu, Y.-T. Shin, Y. Sues, R. Cesare, M. “Safety - Factor Based Approach for Probabilistic - Based Design Optimization,” 42 nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference Seattle, WA 2001
- Choi, K. K. Youn, B. D. “Hybrid Analysis Method for Reliability-Based Design Optimization,” ASME Journal of Mechanical Design 125 2 221 232 2001
- Lee, J. O. Yang, Y. O. Ruy, W. S. “A Comparative Study on Reliability Index and Target Performance Based Probabilistic Structural Design Optimization,” Computers and Structures 80 257 269 2002
- Liang, J. Mourelatos, Z. P. Tu, J. “A Single Loop Method for Reliability-Based Design Optimization,” Proceedings of ASME Design Engineering Technical Conferences , Paper# DETC2004/DAC-57255 2004
- Oberkampf, W. Helton, J. Sentz, K. “Mathematical Representations of Uncertainty,” AIAA Non-Deterministic Approaches Forum, AIAA 2001-1645 Seattle, WA April 16-19 2001
- Klir, G. J. Yuan, B. Fuzzy Sets and Fuzzy Logic: Theory and Applications Prentice Hall 1995
- Klir, G. J. Filger, T. A. Fuzzy Sets, Uncertainty, and Information Prentice Hall 1988
- Dubois, D. Prade, H. Possibility Theory Plenum Press New York 1988
- Moore, R. E. Interval Analysis Prentice-Hall 1966
- Zadeh, L. A. “Fuzzy Sets,” Information and Control 8 338 353 1965
- Muhanna, R. L. Mullen, R. L. “Uncertainty in Mechanics Problems - Interval-Based Approach,” Journal of Engineering Mechanics 127 6 557 566 2001
- Penmetsa, R. C. Grandhi, R. V. “Efficient Estimation of Structural Reliability for Problems with Uncertain Intervals,” Computers and Structures 80 1103 1112 2002
- Du, X. Sudjianto, A. Huang, B. “Reliability Based Design with a Mixture of Random and Interval Variables,” ASME Journal of Mechanical Design 127 1068 1076 2005
- Rao, S. S. Cao, L. “Optimum Design of Mechanical Systems Involving Interval Parameters,” ASME Journal of Mechanical Design 124 465 472 2002
- Gu, X. Renaud, J. E. Batill, S. M. “An Investigation of Multidisciplinary Design Subject to Uncertainties,” 7 th AIAA/USAF/NASA/ISSMO Multidisciplinary Analysis & Optimization Symposium St. Louis, Missouri 1998
- Elishakoff, I. E. Haftka, R. T. Fang, J. “Structural Design under Bounded Uncertainty - Optimization with Anti-Optimization,” Computers and Structures 53 1401 1405 1994
- Lombardi, M. Haftka, R. T. “Anti-Optimization Technique for Structural Design under Load Uncertainties,” Computer Methods in Applied Mechanics and Engineering 157 19 31 1998
- Du, X. Chen, W. “An Integrated Methodology for Uncertainty Propagation and Management in Simulation-Based Systems Design,” AIAA Journal 38 8 1471 1478 2000
- Mourelatos, Z. P. Zhou, J “Reliability Estimation with Insufficient Data Based on Possibility theory” AIAA Journal 43 8 1696 1705 2005
- Choi, K. K. Du, L. Youn, B. D. “A New Fuzzy Analysis Method for Possibility-Based Design Optimization,” 10 th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA 2004-4585 Albany, NY 2004
- Nikolaidis, E. Chen, S. Cudney, H. Haftka, R. T. Rosca, R. “Comparison of Probability and Possibility for Design Against Catastrophic Failure Under Uncertainty,” ASME Journal of Mechanical Design 126 3 386 394 2004
- Du, X. Chen, W. “Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design,” ASME Journal of Mechanical Design 126 225 233 2004
- Ross, T. J. Fuzzy Logic with Engineering Applications McGraw Hill 1995
- Zadeh, L. A. “Fuzzy Sets as a Basis for a Theory of Possibility,” Fuzzy Sets and Systems 1 3 28 1978
- Akpan, U. O. Rushton, P. A. Koko, T. S. “Fuzzy Probabilistic Assessment of the Impact of Corrosion on Fatigue of Aircraft Structures,” Paper AIAA-2002-1640 2002
- Dong, W. Shah, H. C “Vertex Method for Computing Functions of Fuzzy Variables,” Fuzzy Sets and Systems 24 65 78 1987
- Rao, S. S. Sawyer, J. P. “A Fuzzy Finite Element Approach for the Analysis of Imprecisely Defined Systems,” AIAA Journal 33 2264 2370 1995