Abstract
A variety of analysis strategies and design methodologies are widely applied to accommodate uncertainties in engineering design. Generally there exist two different types of uncertainties in practice, aleatory uncertainty and epistemic uncertainty. When data and information are very limited, the probabilistic methodology may not be appropriate. Among several alternative tools, possibility theory is proved to be a computationally efficient and stable tool to handle incomplete information. In this paper, we first introduce two issues concerned with possibilistic approaches: reliability analysis and design optimization. Then the type of uncertainties in these issues are explained with emphasis on the epistemic uncertainty. After that, this paper presents both theoretical development and computational improvement of possibility theory in recent years. More details are given to reveal the capability and characteristics of quantified uncertainty from different aspects. In the end, future research directions are summarized.
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References
Klir, G.J.: Principles of Uncertainty: What Are They? Why Do We Need Them? Fuzzy Sets Syst. 74, 15–31 (1995)
Kangas, A.S., Kangas, J.: Probability, Possibility and Evidence: Approaches to Consider Risk and Uncertainty in Forestry Decision Analysis. Forest Policy and Economics 6, 169–188 (2004)
Nikolaidis, E., Haftka, R.T.: Theories of Uncertainty for Risk Assessment When Data Is Scarce. http://www.eng.utoledo.edu/~enikolai/
O’Connor, P.D.T., Newton, D.E., Bromley, R. (eds.): Practical Reliability Engineering. John Wiley and Sons, England (1995)
Papalambros, P.Y., Michelena, N.F.: Trend and Challenges in System Design Optimization. In: Proceedings of the Int. Workshop on Multidisc. Des. Optim. Pretoria, S. Africa (2000)
Padmanabhan, D.: Reliability-Based Optimization for Multidisciplinary System Design. Ph.D Dissertation, Graduate School of the University of Notre Dame, Indiana (2003)
Oberkampf, W.L., Helton, J.C., Joslyn, C.A., et al.: Challenge Problems: Uncertainty in System Response Given Uncertain Parameters. Relia. Eng. Syst. Safety 85, 11–19 (2004)
Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainty and Information. Prentice Hall, Englewood Cliff, New Jersey (1998)
Oberkampf, W.L., DeLand, S.M., Rutherford B.M., et al.: Estimation of Total Uncertainty in Modeling and Simulation. Sandia Report SAND2000-0824, Albuquerque, NM (2000)
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall, New York (1995)
Biondini, F., Bontempi, F., Malerba, P.G.: Fuzzy Reliability Analysis of Concrete Structures. Comp. Struct. 82, 1033–1052 (2004)
Bai, X.G., Asgarpoor, S.: Fuzzy-Based Approaches to Substation Reliability Evaluation. Electric Power Systems Research 69, 197–204 (2004)
Möller, B., Beer, M., Graf, W., et al.: Possibility Theory Based Safety Assessment. Computer-Aided Civil and Infrastructure Engineering 14, 81–91 (1999)
Limbourg, P.: Multi-Objective Optimization of Problems with Epistemic Uncertainty. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 413–427. Springer, Heidelberg (2005)
Agarwal, H.: Reliability Based Design Optimization: Formulations and Methodologies. Ph.D Dissertation, University of Notre Dame (2004)
Zadeh, L.A.: Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets Syst. 1, 3–28 (1978)
Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1988)
de Cooman, G.: Possibility Theory- I, II, III. Int. J. General Syst. 25, 291–371 (1997)
Klir, G.J.: Fuzzy Sets: An Overview of Fundamentals, Applications and Personal Views. Beijing Normal University Press, Beijing (2000)
Nikolaidis, E., Chen, S., Cudney, H.H., et al.: Comparison of Probabilistic and Possibility Theory-Based Methods for Design against Catastrophic Failure under Uncertainty. J. Mech. Des, ASME 126, 386–394 (2004)
Dubois, D., Prade, H.: Possibility Theory and Its Applications: A Retrospective and Prospective View. In: The IEEE Int. Conf. on Fuzzy Systems, pp. 3–11 (2003)
Mourelatos, Z., Zhou, J.: Reliability Estimation and Design with Insufficient Data Based on Possibility Theory. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conf. AIAA-2004-4586, Albany, NewYork (2004)
Kozine, I.O., Filimonov, Y.V.: Imprecise Reliabilities: Experiences and Advances. Relia. Eng. Syst. Safety 67, 75–83 (2000)
Choi, K.K., Du, L., Youn, B.D.: A New Fuzzy Analysis Method for Possibility-Based Design Optimization. In: 10th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA-2004-4585, Albany, NewYork (2004)
Youn, B.D., Choi, K.K., Du, L.: Integration of Reliability- and Possibility-Based Design Optimizations Using Performance Measure Approach. SAE Int. (2004)
Youn, B.D.: Integrated Framework for Design Optimization under Aleatory and/or Epistemic Uncertainties Using Adaptive-loop Method. ASME 2005-85253. In: Des. Eng. Tech.Conf. and Comp. Information in Eng. Conf. Long Beach, California (2005)
Youn, B.D., Choi, K. K., Du, L., et al.: Integration of Possibility-Based Optimization to Robust Design for Epistemic Uncertainty. In: 6th World Congresses of Struct. Multidisc. Optim. Brazil (2005)
Langley, R.S.: Unified Approach to Probabilistic and Possibilistic Analysis of Uncertain Systems. J. Eng. Mech. 126, 1163–1172 (2000)
Cai, K.Y., Wen, C.Y., Zhang, M.L.: Fuzzy Variables as a Basis for a Theory of Fuzzy Reliability in the Possibility Context. Fuzzy Sets Syst. 42, 145–172 (1991)
Huang, H.Z., Tong, X., Zuo, M.J.: Posbist Fault Tree Analysis of Coherent Systems. Relia. Eng. Syst. Safety 84, 141–148 (2004)
Huang, H.Z., Zuo, M.J., Sun, Z.Q.: Bayesian Reliability Analysis for Fuzzy Lifetime Data. Fuzzy Sets Syst. 157, 1674–1686 (2006)
Utkin, L.V., Gurov, S.V.: A General Formal Approach for Fuzzy Reliability Analysis in the Possibility Context. Fuzzy Sets Syst. 83, 203–213 (1996)
Onisawa, T.: An Approach of System Reliability Analysis Using Failure Possibility and Success Possibility. Fuzzy Sets Syst. 27, 87–103 (1988)
Cappelle, B., Kerre, E.E.: On a Possibilistic Approach to Reliability Theory. In: Proceedings of the 2nd Int. Symposium on Uncertainty Analysis, Maryland, MD, pp. 415–418 (1993)
Cai, K.Y.: System Failure Engineering and Fuzzy Methodology: An Introductory Overview. Fuzzy Sets Syst. 83, 113–133 (1996)
Cappelle, B., Kerre, E.E.: Computer Assisted Reliability Analysis: An Application of Possibilistic Reliability Theory to a Subsystem of a Nuclear Power Plant. Fuzzy Sets Syst. 74, 103–113 (1995)
Utkin, L.V., Coolen, F.P.A.: Imprecise Reliability: An Introductory Overview, http://maths.dur.ac.uk/stats
Hall, J., Lawry, J.: Imprecise Probabilities of Engineering System Failure from Random and Fuzzy Set Reliability Analysis. In: 2nd Int. Symposium on Imprecise Probabilities and Their Applications, Ithaca, New York (2001)
Coolen, F.P.A.: On the Use of Imprecise Probabilities in Reliability. Quality and Relia. Eng. Int. 20, 193–202 (2004)
Coolen, F.P.A., Coolen-Schrijner, P., Yan, K.J.: Nonparametric Predictive Inference in Reliability. Relia. Eng. Syst. Safety 78, 185–193 (2002)
Aughenbaugh, J.M., Paredis, C.J.J.: The Value of Using Imprecise Probabilities in Engineering Design. J. Mech. Des. 128, 969–979 (2006)
Youn, B.D., Choi, K.K.: Selecting Probabilistic Approaches for Reliability-Based Design Optimization. AIAA Journal 42, 124–131 (2004)
Tu, J., Choi, K.K.: A New Study on Reliability-Based design Optimization. ASME J. Mech. Des. 121, 557–564 (1999)
Youn, B.D., Choi, K.K.: Enriched Performance Measure Approach for Reliability-Based Design Optimization. AIAA Journal 43, 874–884 (2005)
Hall, D.L., Llinas, J.: An Introduction to Multisensor Data Fusion. Proceeding of the IEEE 85, 6–23 (1997)
Zhuang, Z.W., Yu, W.X., Wang, H., et al.: Information Fusion and Application in Reliability Assessment (in Chinese). Systems Engineering and Electronics 22, 75–80 (2000)
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He, LP., Huang, HZ., Du, L., Zhang, XD., Miao, Q. (2007). A Review of Possibilistic Approaches to Reliability Analysis and Optimization in Engineering Design. In: Jacko, J.A. (eds) Human-Computer Interaction. HCI Applications and Services. HCI 2007. Lecture Notes in Computer Science, vol 4553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73111-5_118
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DOI: https://doi.org/10.1007/978-3-540-73111-5_118
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