Uncertain reliability index in finite element reliability analysis

International Journal of Reliability and Safety

Volumn 1, Issue 1-2, 2006, Pages 77-101

  Koduru, Smitha D ^a   Haukaas, Terje ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Bayesian methods; epistemic uncertainty; finite element reliability; fuzzy randomness; OpenSees; software development

Indexed keywords

EID: 65649109537     PISSN: 1479389X     EISSN: 14793903     Source Type: Journal    
DOI: 10.1504/ijrs.2006.010691     Document Type: Article

References (44)

1. Ang, A.H-S. (2004) ‘Modeling and analysis of uncertainties for risk-informed decisions in engineering – with application to bridges’, Proceedings of Second International Conference on Bridge Maintenance, Safety and Management, IABMAS’04, Kyoto, Japan.
2. Ang, A.H-S. and Tang, W.H. (1975) Probability Concepts in Engineering Planning and Design, Vol. 1, New York: Wiley.
3. Ayyub, B.M. (2004) ‘From dissecting ignorance to solving algebraic problems’, Reliability Engineering and System Safety, Vol. 85, Nos. 1-3, pp.223–238.
4. Bebamzadeh, A. and Haukaas, T. (2004) ‘Accounting for uncertain model and analysis errors in nonlinear finite element analysis’, Proceedings of Ninth ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability, Albuquerque, New Mexico.
5. Ben-Haim, Y. (2004) ‘Uncertainty, probability and information-gaps’, Reliability Engineering and System Safety, Vol. 85, Nos. 1-3, pp.249–266.
6. Berleant, D. and Zhang, J. (2004) ‘Representation and problem solving with distribution envelope determination (DEnv)’, Reliability Engineering and System Safety, Vol. 85, Nos. 1-3, pp.153–168.
7. Bernardini, A. (1999) ‘What are the random and fuzzy sets and how to use them for uncertainty modelling in engineering systems?’ in I. Elishakoff (Ed). Whys and Hows in Uncertainty Modelling: Probability, Fuzziness and Anti-Optimization, New York: Springer Wien.
8. Bjerager, P. and Krenk, S. (1989) ‘Parameter sensitivity in first order reliability theory’, Journal of Engineering Mechanics, Vol. 115, No. 7, pp.1577–1582.
9. Box, G.E.P. and Tiao, G.C. (1973) Bayesian Inference in Statistical Analysis, New York: Wiley.
10. Chou, K.C. and Yuan, J. (1993) ‘Fuzzy-Bayesian approach to reliability of existing structures’, Journal of Structural Engineering, Vol. 119, No. 11, pp.3276–3290.
11. de Cooman, G. and Troffaes, M.C.M (2004) ‘Coherent lower previsions in systems modeling: products and aggregation rules’, Reliability Engineering and System Safety, Vol. 85, Nos. 1-3, pp.113–134.
12. Der Kiureghian, A. (1989) ‘Measures of structural safety under imperfect states of knowledge’, Journal of Structural Engineering, Vol. 115, No. 5, pp.1119–1140.
13. Der Kiureghian, A. and Taylor, R.L. (1983) ‘Numerical methods in structural reliability’, Proceedings of the Fourth International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP4, Florence, Italy.
14. Der Kiureghian, A. and Zhang, Y. (1999) ‘Space-variant finite element reliability analysis’, Computer Methods in Applied Mechanics and Engineering, Vol. 168, Nos. 1-4, pp.173–183.
15. Ditlevsen, O. (1983) ‘Fundamental postulate in structural safety’, Journal of Engineering Mechanics, Vol. 109, No. 4, pp.1096–1102.
16. Elishakoff, I. (1999) ‘Are probabilistic and anti-optimization approaches compatible?’ in I. Elishakoff (Ed). Whys and Hows in Uncertainty Modelling: Probability, Fuzziness and Anti-Optimization, New York: Springer Wien.
17. Frier, C. and Sorensen, J. (2003) ‘Stochastic finite element analysis of non-linear structures modelled by plasticity theory’, Proceedings of the Ninth International Conference on Applications of Statistics and Probability in Civil Engineering; ICASP9, San Francisco, CA.
18. Gutierrez, M., Carmeliet, J. and de Borst, R. (1994) ‘Finite element reliability methods using Diana’, in G.M.A. Kusters and M.A.N. Hendriks (Eds). Diana Computational Mechanics 1994.
19. Hacking, I. (1975) The Emergence of Probability: A Philosophical Study of Early Ideas About Probability, Induction and Statistical Inference, London, NY: Cambridge University Press.
20. Haldar, A. and Mahadevan, S. (2000) Reliability Assessment Using Stochastic Finite Element Analysis, New York: John Wiley and Sons.
21. Hall, J.W. and Lawry, J. (2003) ‘Fuzzy label methods for constructing imprecise limit state functions’, Structural Safety, Vol. 25, No. 4, pp.317–341.
22. Haukaas, T. and Der Kiureghian, A. (2004) Finite Element Reliability and Sensitivity Methods for Performance-Based Engineering, Report No. PEER 2003/14, Pacific Earthquake Engineering Research Center, University of California, Berkeley.
23. Haukaas, T. and Der Kiureghian, A. (2005) ‘Parameter sensitivity and importance measures in nonlinear finite element reliability analysis’, Journal of Engineering Mechanics, Vol. 131, No. 10, pp.1013–1026.
24. Hohenbichler, M. and Rackwitz, R. (1986) ‘Sensitivity and importance measures in structural reliability’, Civil Engineering Systems, Vol. 3, No. 4, pp.203–209.
25. Hora, S.C. (1996) ‘Aleatory and epistemic uncertainty in probability elicitation with an example from hazardous waste management’, Reliability Engineering and System Safety, Vol. 54, Nos. 2-3, pp.217–223.
26. Imai, K. and Frangopol, D.M. (2000) ‘Geometrically nonlinear finite element reliability analysis of structural systems, i: theory ii: applications’, Computers and Structures, Vol. 7, No. 6, pp.677–709.
27. Körner, R. (1997) ‘On the variance of fuzzy random variables’, Fuzzy Sets and Systems, Vol. 92, No. 1, pp.83–93.
28. Kozine, I.O. and Utkin, L.V. (2004) ‘An approach to combining unreliable pieces of evidence and their propagation in system response analysis’, Reliability Engineering and System Safety, Vol. 85, Nos. 1-3, pp.103–112.
29. Krätschmer, V. (2001) ‘A unified approach to fuzzy random variables’, Fuzzy Sets and Systems, Vol. 123, No. 1, pp.1–9.
30. Langley, R.S. (2000) ‘Unified approach to probabilistic and possibilistic analysis of uncertain systems’, Journal of Engineering Mechanics, Vol. 126, Nos. 11, pp.1163–1172.
31. Lee, C-B. and Park, J-W. (1997) ‘Reliability analysis based on fuzzy-Bayesian approach’, Seventh International Conference on Computing in Civil and Building Engineering, Seoul, South Korea.
32. Liu, P-L. and Der Kiureghian, A. (1986) ‘Multivariate distribution models with prescribed marginals and covariances’, Probabilistic Engineering Mechanics, Vol. 1, No. 2, pp.105–112.
33. Liu, P-L. and Der Kiureghian, A. (1991) ‘Finite element reliability of geometrically nonlinear uncertain structures’, Journal of Engineering Mechanics, Vol. 17, No. 8, pp.1806–1825.
34. McWilliam, S. (2001) ‘Anti-optimization of uncertain structures using interval analysis’, Computers and Structures, Vol. 79, No. 4, pp.421–430.
35. Möller, B. and Beer, M. (2004) Fuzzy Randomness: Uncertainty in Civil Engineering and Computational Mechanics, Berlin, NY: Springer.
36. O’Hagan, A. and Oakley, J.E. (2004) ‘Probability is perfect, but we can’t elicit it perfectly’, Reliability Engineering and System Safety, Vol. 85, Nos. 1-3, pp.239–248.
37. Parry, G.W. (1996) ‘The characterization of uncertainty in probabilistic risk assessments of complex systems’, Reliability Engineering and System Safety, Vol. 54, Nos. 2-3, pp.119–126.
38. Rao, S.S. and Berke, L. (1996) ‘Analysis of uncertain structural systems using interval analysis’, 37th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference: A Collection of Technical Papers, Utah: Salt Lake City.
39. Sudret, B. and Der Kiureghian, A. (2000) Stochastic Finite Element Methods and Reliability: A State-of-the-Art Report, Report No. UCB/SEMM-2000/08, Department of Civil and Environmental Engineering, University of California, Berkeley.
40. Taheri, S.M. and Behboodian, J. (2001) ‘A Bayesian approach to fuzzy hypothesis testing’, Fuzzy Sets and Systems, Vol. 123, No. 1, pp.39–48.
41. Thacker, B.H., Riha, D.S., Millwater, H.R. and Enright, M.P. (2001) ‘Errors and uncertainties in probabilistic engineering analysis’, American Institute of Aeronautics and Astronautics, AIAA 123.
42. Vick, S.G. (2002) Degrees of Belief: Subjective Probability and Engineering Judgment, Virginia: ASCE Press.
43. Winkler, S.C. (1996) ‘Uncertainty in probabilistic risk assessment’, Reliability Engineering and System Safety, Vol. 54, Nos. 2-3, pp.127–132.
44. Zhang, Y. and Der Kiureghian, A. (1997) Finite Element Reliability Methods for Inelastic Structures, Report No. UCB/SEMM-97/05, Department of Civil and Environmental Engineering, University of California, Berkeley.