Structural Engineering and Mechanics

  • 제62권4호
  • /
  • Pages.507-517
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  • 2017
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A novel evidence theory model and combination rule for reliability estimation of structures

  • Tao, Y.R. (College of Mechanical Engineering, Hebei University of Technology) ;
  • Wang, Q. (Department of Mechanical Engineering, Hunan Institute of Engineering) ;
  • Cao, L. (Department of Mechanical Engineering, Hunan Institute of Engineering) ;
  • Duan, S.Y. (College of Mechanical Engineering, Hebei University of Technology) ;
  • Huang, Z.H.H. (Department of Mechanical Engineering, Hunan Institute of Engineering) ;
  • Cheng, G.Q. (Department of Mechanical Engineering, Hunan Institute of Engineering)
  • 투고 : 2016.06.12
  • 심사 : 2017.01.26
  • 발행 : 2017.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

Due to the discontinuous nature of uncertainty quantification in conventional evidence theory(ET), the computational cost of reliability analysis based on ET model is very high. A novel ET model based on fuzzy distribution and the corresponding combination rule to synthesize the judgments of experts are put forward in this paper. The intersection and union of membership functions are defined as belief and plausible membership function respectively, and the Murfhy's average combination rule is adopted to combine the basic probability assignment for focal elements. Then the combined membership functions are transformed to the equivalent probability density function by a normalizing factor. Finally, a reliability analysis procedure for structures with the mixture of epistemic and aleatory uncertainties is presented, in which the equivalent normalization method is adopted to solve the upper and lower bound of reliability. The effectiveness of the procedure is demonstrated by a numerical example and an engineering example. The results also show that the reliability interval calculated by the suggested method is almost identical to that solved by conventional method. Moreover, the results indicate that the computational cost of the suggested procedure is much less than that of conventional method. The suggested ET model provides a new way to flexibly represent epistemic uncertainty, and provides an efficiency method to estimate the reliability of structures with the mixture of epistemic and aleatory uncertainties.

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

참고문헌

  1. Acar Erdem and Raphael T. Haftka (2005), "Reliability based aircraft structural design optimization with uncertainty about probability distributions", 6th World Congresses of Structural and Multidisciplinary Optimization.
  2. Aghili Sayed Javad and Hamze Hajian-Hoseinabadi (2014), "The reliability investigation considering data uncertainty; an application of Fuzzy Transformation Method in substation protection", Int. J. Electrical Pow. Energy Syst., 63, 988-999. https://doi.org/10.1016/j.ijepes.2014.06.067
  3. Alyanak Edward, Ramana Grandhi and Ha-Rok Bae (2008), "Gradient projection for reliability-based design optimization using evidence theory", Eng. Optimiz., 40(10), 923-935. https://doi.org/10.1080/03052150802168942
  4. Bae, H., Grandhi, R.V. and Canfield, R.A. (2004), "Epistemic uncertainty quantification techniques including evidence theory for large-scale structures", Int. J. Comput. Struct., 82(13), 1101-1112. https://doi.org/10.1016/j.compstruc.2004.03.014
  5. Bai, Y.C, X. Han and C. Jiang (2012), "Comparative study of metamodeling techniques for reliability analysis using evidence theory", Adv. Eng. Softw., 53, 61-71. https://doi.org/10.1016/j.advengsoft.2012.07.007
  6. Bi, R.G., Han, X., Jiang, C., Bai, Y.C. and Liu, J. (2014), "Uncertain buckling and reliability analysis of the piezoelectric functionally graded cylindrical shells based on the nonprobabilistic convex model", Int. J. Comput. Method., 11(06), 1350080. https://doi.org/10.1142/S0219876213500801
  7. Canizes Bruno, Joao Soares and Zita Vale (2012), "Hybrid fuzzy Monte Carlo technique for reliability assessment in transmission power systems", Energy, 45(1), 1007-01017. https://doi.org/10.1016/j.energy.2012.06.049
  8. Catherine K. Murphy (2000), "Combining belief functions when evidence conflicts", Decision Support Syst., 29(1), 1-9. https://doi.org/10.1016/S0167-9236(99)00084-6
  9. Chakraborty, S. and Sam, P.C. (2007), "Probabilistic safety analysis of structures under hybrid uncertainty", Int. J. Numer. Meth. Eng., 70(4), 405-422. https://doi.org/10.1002/nme.1883
  10. Chakraborty, S. and Sam, P.C. (2007), "Probabilistic safety analysis of structures under hybrid uncertainty", Int. J. Numer. Meth. Eng., 70(4), 405-422. https://doi.org/10.1002/nme.1883
  11. Cornell, C.A. (1969), "A probability-based structural code", J. Am. Concrete Inst., 66(12), 974-985.
  12. Du Xiaoping (2006), "Uncertainty analysis with probability and evidence theories", ASME 2006 International Design Technical Conferences & Computers and Information in Engineering Conference.
  13. Fang, Y.F., Xiong, J.B. and Tee, K.F. (2015), "Time-variant structural fuzzy reliability analysis under stochastic loads applied several times", Struct. Eng. Mech., 55(3), 525-534. https://doi.org/10.12989/sem.2015.55.3.525
  14. Fuh Ching Fen, Rong Jea and Jin-Shieh Su (2014), "Fuzzy system reliability analysis based on level ($\lambda$, 1) interval-valued fuzzy numbers", Inform. Sci., 272, 185-197. https://doi.org/10.1016/j.ins.2014.02.106
  15. Hurtado, J.E., Alvarez, D.A. and Ramirez, J. (2012), "Fuzzy structural analysis based on fundamental reliability concepts", Comput. Struct., 112, 183-192.
  16. Jiang, C., Zheng, J., Ni, B.Y. and Han, X. (2015), "A probabilistic and interval hybrid reliability analysis method for structures with correlated uncertain parameters", Int. J. Comput. Method., 12(04), 1540006. https://doi.org/10.1142/S021987621540006X
  17. Jiang. C., Z. Zhang, X. Han and J. Liu (2013), "A novel evidencetheory-based reliability analysis method for structures with epistemic uncertainty", Comput. Struct., 129, 1-12. https://doi.org/10.1016/j.compstruc.2013.08.007
  18. Kumar, M. and Yadav, S.P. (2012), "A novel approach for analyzing fuzzy system reliability using different types of intuitionistic fuzzy failure rates of components", ISA transactions, 51(2), 288-297. https://doi.org/10.1016/j.isatra.2011.10.002
  19. Li pingke (2005), "The entropy of fuzzy variables[D]", Beijing, Qinghua University. (in Chinese)
  20. Li, D., Jiang, C., Han, X. and Zhang, Z. (2011), "An efficient optimization method for uncertain problems based on nonprobabilistic interval model", Int. J. Comput. Method., 8(04), 837-850. https://doi.org/10.1142/S021987621100285X
  21. Li, G., Lu, Z. and Xu, J. (2015), "A fuzzy reliability approach for structures based on the probability perspective", Struct. Safe., 54, 10-18. https://doi.org/10.1016/j.strusafe.2014.09.008
  22. Li, L. and Lu, Z. (2014), "Interval optimization based line sampling method for fuzzy and random reliability analysis", Appl. Math. Model., 38(13), 3124-3135. https://doi.org/10.1016/j.apm.2013.11.027
  23. Lu, Z.Z. and Song, Shufang (2009), "Structural reliability and reliability sensitivity analysis[M]", Beijing, Science Press.
  24. Lu, Zhenzhou and Yue, Zhufeng (2004), "Unified reliability model for fuzziness and randomness of the basic variables and state variables in structure", Chinese J. Theo. Appl. Mech., 36(5), 533-539.
  25. Melchers, R.E. (1989), "Importance sampling in structural systems", Struct. Safe., 6(1), 3-10. https://doi.org/10.1016/0167-4730(89)90003-9
  26. Ni, Z. and Qiu, Z. (2010), "Hybrid probabilistic fuzzy and nonprobabilistic model of structural reliability", Comput. Indust. Eng., 58(3), 463-467. https://doi.org/10.1016/j.cie.2009.11.005
  27. Oberkampf, W.L. and Helton, J.C. (2001), "Mathematical representation of uncertainty", 3rd Non-Deterministic Approaches Forum, Paper No.AIAA-2001-1645.
  28. Purba Julwan Hendry, Jie Lu and Guangquan Zhang (2014), "A fuzzy-based reliability approach to evaluate basic events of fault tree analysis for nuclear power plant probabilistic safety assessment", Fuzzy Set. Syst., 243, 50-69. https://doi.org/10.1016/j.fss.2013.06.009
  29. Purba, J.H., Tjahyani, D.S., Ekariansyah, A.S. and Tjahjono, H. (2015), "Fuzzy probability based fault tree analysis to propagate and quantify epistemic uncertainty", Ann. Nuclear Energy, 85, 1189-1199. https://doi.org/10.1016/j.anucene.2015.08.002
  30. Singiresu S. Rao and Kiran K. Annamdas (2009), "An evidencebased fuzzy approach for the safety analysis of uncertain systems", 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Palm Springs, California.
  31. Suo Bin and Yongsheng Cheng (2013), "Computational intelligence approach for uncertainty quantification using evidence theory", J. Syst. Eng. Electron., 24(2), 121-124.
  32. Tao. Y.R., X. Han and S.Y. Duan (2014), "Reliability analysis for multidisciplinary systems with the mixture of epistemic and aleatory uncertainties", Int. J. Numer. Meth. Eng., 97(1), 68-78. https://doi.org/10.1002/nme.4587
  33. Xiao, N.C., Huang, H.Z., Li, Y. and Zuo, M.J. (2012), "Unified uncertainty analysis using the maximum entropy approach and simulation", Reliability and Maintainability Symposium (RAMS), 2012 Proceedings-Annual (pp. 1-8). IEEE.
  34. Zadeh L.A. (1965), "Fuzzy sets", Inform. Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  35. Zhang, Y. (2015), "A fuzzy residual strength based fatigue life prediction method", Struct. Eng. Mech., 56(23), 201-221. https://doi.org/10.12989/sem.2015.56.2.201

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