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Reliability Analysis of Structures Under Hybrid Uncertainty

  • Subrata Chakraborty
  • Palash Chandra Sam
Chapter
Part of the Springer Series in Reliability Engineering book series (RELIABILITY)

Abstract

In engineering applications it is important to model and adequately treat all the available information during the analysis and design phase. Typically, the information are originated from different sources: field measurements, experts’ judgments, objective and subjective considerations. Over these features, the influences originated from the human errors, imperfections in the construction techniques, influence of the boundary and environmental conditions are added. All these aspects can be brought back to one common denominator: presence of uncertainty. The uncertainty can be viewed as a part or class of imperfection in the information that attempts to model a system behavior in the real world (see Fig. 1). It is the gradual assessment of the truth content of postulation e.g., in relation to the occurrence of a defined event. Normally, the uncertainty is viewed in two categories, namely aleatory and epistemic. The aleatory uncertainty is classified as objective and irreducible uncertainty with sufficient information on the input uncertain data. These are inherently connected to the problem at hand and cannot be influenced by the designer. The epistemic uncertainty is classified as subjective and reducible uncertainty that stems from the lack of knowledge about the input uncertain data. It arises from the cognitive sources involving the definition of certain parameters, human errors, inaccuracies, manufacturing and measurement tolerances, etc.

Keywords

Uncertain Parameter Fuzzy Variable Uncertain Variable Limit State Function Evidence Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The first author gratefully acknowledges the financial support from the Alexander von Humboldt Foundation during the preparation of this manuscript. He is also grateful to Professor R. S. Langley, University of Cambridge, UK for introducing him to the research topic.

References

  1. 1.
    Möller B, Beer M, Graf W, Hoffman A (1999) Possibility theory based safety assessment. Comput Aided Civil Infrastruct Eng Special Issue on Fuzzy Model 14:81–91CrossRefGoogle Scholar
  2. 2.
    Box GEP, Draper NR (1987) Empirical model building and response surface. Wiley, New YorkGoogle Scholar
  3. 3.
    Jin R, Chen W, Simpson T (2001) Comparative studies of metamodelling techniques under multiple modeling criteria. Struct Multidis Optim 23:1–13CrossRefGoogle Scholar
  4. 4.
    Ditlevsen O, Madsen HO (1996) Structural reliability methods. Wiley, West SussexGoogle Scholar
  5. 5.
    Melchers RE (1999) Structural reliability analysis and prediction. Wiley, West SussexGoogle Scholar
  6. 6.
    Haldar A, Mahadevan S (2000) Reliability assessment using stochastic finite element analysis. Wiley, USAGoogle Scholar
  7. 7.
    BenHaim Y, Elishakoff I (1990) Convex models of uncertainty in applied mechanics. Elsevier Science, AmsterdamGoogle Scholar
  8. 8.
    BenHaim Y (1995) A non-probabilistic measure of reliability of linear systems based on expansion of convex models. Struct Saf 17:91–109CrossRefGoogle Scholar
  9. 9.
    Penmetsa RC, Grandhi RV (2002) Efficient estimation of structural reliability for problems with uncertain intervals. Comput Struct 80:1103–1112CrossRefGoogle Scholar
  10. 10.
    Qiu Z, Yang D, Elishakoff I (2008) Probabilistic interval reliability of structural systems. Int J Solids Struct 45:2850–2860MATHCrossRefGoogle Scholar
  11. 11.
    Karanki DR, Kushwaha HS, Verma AK, Ajit S (2009) Uncertainty analysis based on probability bounds (p-box) approach in probabilistic safety assessment. Risk Anal 29(5):662–675CrossRefGoogle Scholar
  12. 12.
    Luo Y, Kang Z, Luo Z, Li A (2008) Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model. Struct Multidis Optim 37(2):107–119CrossRefGoogle Scholar
  13. 13.
    Brown CB (1979) A fuzzy safety measure, entropy constructed probabilities. J Eng Mech ASCE 105(5):855–871Google Scholar
  14. 14.
    Shiraishi N, Furuta H (1983) Reliability analysis based on fuzzy probability. J Eng Mech ASCE 109(6):1445–1459CrossRefGoogle Scholar
  15. 15.
    Yao J, Furuta H (1986) Probabilistic treatment of fuzzy events in civil engineering. Prob Eng Mech 1(1):58–61CrossRefGoogle Scholar
  16. 16.
    Furuta H (1995) Reliability and optimization of structural systems. In: Rackwitz R, Augusti G, Borri A (eds) Proceedings of the VI IFIP WG 7.5 working Congress. Chapman and Hall, LondonGoogle Scholar
  17. 17.
    Yubin L, Qiao Z, Wang G (1997) Fuzzy random reliability of structures based on fuzzy random variables. Fuzzy Sets Syst 86:345–355MATHCrossRefGoogle Scholar
  18. 18.
    Cremona C, Gao Y (1997) The possibilistic theory: theoretical aspects and applications. Struct Saf 19(2):173–201CrossRefGoogle Scholar
  19. 19.
    Möller B, Graf W, Beer M (2003) Safety assessment of structures in view of fuzzy randomness. Comput Struct 81:1567–1582CrossRefGoogle Scholar
  20. 20.
    Bing Li, Zhu M, Xu K (2000) A practical method for fuzzy reliability analysis of mechanical structures. Reliab Eng Syst Safety 67:311–315CrossRefGoogle Scholar
  21. 21.
    Jiang Q, Chen CH (2003) A numerical algorithm of fuzzy reliability. Reliab Eng Syst Safety 80:299–307CrossRefGoogle Scholar
  22. 22.
    Möller B, Beer M (2005) Fuzzy randomness uncertainty in civil engineering and computational mechanics. Springer-Verlag, LondonGoogle Scholar
  23. 23.
    Langley RS (2000) Unified approach to probabilistic and possibilistic analysis of uncertain systems. J Eng Mech ASCE 126(11):1163–1172CrossRefGoogle Scholar
  24. 24.
    Chakraborty S (2003) Safety assessment of structures under hybrid uncertainty, Technical Report, CUED/C-MECH/TR-86 (ISSN 0309-7420), Cambridge UniversityGoogle Scholar
  25. 25.
    Sophie QC (2000) Comparing probabilistic and fuzzy set approaches for design in the presence of uncertainty, Ph.D. Thesis, Virginia Polytechnic Institute, State UniversityGoogle Scholar
  26. 26.
    Nikolaidis E, Chen S, Cudney H, Raphael TH, Rosca RT (2004) Comparison of probability and possibility for design against catastrophic failure under uncertainty. J Mech Des ASME 126:386–394CrossRefGoogle Scholar
  27. 27.
    Kam TY, Brown CB (1983) Updating parameters with fuzzy entropies. J Eng Mech ASCE 198(6):1334–1343CrossRefGoogle Scholar
  28. 28.
    Haldar A, Reddy RK (1992) A random fuzzy analysis of existing structures. Fuzzy Sets Syst 48:201–210CrossRefGoogle Scholar
  29. 29.
    Rahman MS, Khalid M, Zahaby El (1997) Probabilistic liquefaction risk analysis using fuzzy variables. Soil Dyn Earthq Eng 16:63–79CrossRefGoogle Scholar
  30. 30.
    Zhenyu L, Chen Q (2002) A new approach to fuzzy finite element analysis. Comput Meth Appl Mech 191:5113–5118MATHCrossRefGoogle Scholar
  31. 31.
    Chakraborty S, Sam PC (2007) Probabilistic safety analysis of structures under hybrid uncertainty. Int J Numer Meth Eng 70(4):405–422MATHCrossRefGoogle Scholar
  32. 32.
    Marano GC, Quaranta G, Mezzina M (2008) Fuzzy time-dependent reliability analysis of RC beams subject to pitting corrosion. J Mater Civil Eng ASCE 20(9):578–587CrossRefGoogle Scholar
  33. 33.
    Rao SS, Chen L, Mulkay E (1998) Unified finite element method for engineering systems with hybrid uncertainties. AIAA J 36(7):1291–1299CrossRefGoogle Scholar
  34. 34.
    Ferrari P, Savoia M (1998) Fuzzy number theory to obtain conservative results with respect to probability. Comput Meth Appl Mech Eng 160:205–222MathSciNetMATHCrossRefGoogle Scholar
  35. 35.
    Savoia M (2002) Structural reliability analysis through fuzzy number approach, with application to stability. Comput Struct 80:1087–1102MathSciNetCrossRefGoogle Scholar
  36. 36.
    Smith SA, Krisnamurthy T, Mason BH (2002) Optimized vertex method and hybrid reliability, 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA-2002-1465Google Scholar
  37. 37.
    Adduri PR, Penmetsa RC (2008) Confidence bounds on component reliability in the presence of mixed uncertain variables. Int J Mech Sci 50:481–489CrossRefGoogle Scholar
  38. 38.
    Du X (2008) Unified uncertainty analysis by the first order reliability method. J Mech Design ASME 130:091401–091410CrossRefGoogle Scholar
  39. 39.
    Luo Y, Zhan Kang, Alex Li(2009) Structural reliability assessment based on probability and convex set mixed model. Comput Struct 87:1408–1415CrossRefGoogle Scholar
  40. 40.
    Du L, Choi KK (2008) An inverse analysis method for design optimization with both statistical and fuzzy uncertainties. Struct Multidis Optim 37:107–119CrossRefGoogle Scholar
  41. 41.
    Huang H-Z, Zhang X (2009) Design optimization with discrete and continuous variables of aleatory and epistemic uncertainties. J Mech Design ASME 131:0310061–0310068Google Scholar
  42. 42.
    DeLuca A, Termini S (1970) A definition of non probabilistic entropy in the setting of fuzzy set theory. Inform Control 20:301–312MathSciNetCrossRefGoogle Scholar
  43. 43.
    Puig B, Akian J (2004) Non-Gaussian simulation using Hermite polynomials expansion and maximum entropy principle. Prob Eng Mech 19:293–305CrossRefGoogle Scholar
  44. 44.
    Dubois D, Prade H (1991) Random sets and fuzzy interval analysis. Fuzzy Sets Syst 42:87–101MathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    Kiureghian AD, Lin HZ, Hwang SJ (1987) Second-order reliability approximations. J Eng Mech ASCE 113(8):1208–1225CrossRefGoogle Scholar
  46. 46.
    Zadeh L (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of Civil EngineeringBengal Engineering and Science UniversityShibpur, HowrahIndia

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