An uncertainty model of structural reliability with imprecise parameters of probability distributions

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 84, Issue 10-11, 2004, Pages 688-699

  Utkin, Lev V ^a  

^a SAINT PETERSBURG STATE FOREST TECHNICAL UNIVERSITY   (Russian Federation)

Author keywords

Expert judgements; Imprecise probabilities; Linear programming; Natural extension; Previsions; Structural reliability

Indexed keywords

EID: 9544223177     PISSN: 00442267     EISSN: None     Source Type: Journal    
DOI: 10.1002/zamm.200410150     Document Type: Conference Paper

References (36)

1. G. Alefeld and J. Herzberger, Introduction to Interval Computations (Academic Press, New York, 1983).
2. B. Ayyub, Elicitation of Expert Opinions for Uncertainty and Risks (CRC Press, 2001).
3. H.-R. Bae, R. Grandhi, and R. Canfield, Sensitivity analysis of structural response uncertainty propagation using evidence theory, in: Proceedings of the 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA, Atlanta, Georgia, USA, 2002, AIAA, pp. 1-11.
4. A. Bardossy and I. Bogardi, Fuzzy fatigue life prediction, Struct. Saf. 6, 25-38 (1989).
5. J. Berger, Statistical Decision Theory and Bayesian Analysis (Springer-Verlag, New York, 1985).
6. V. Bolotin, Statistical Method in Structural Mechanics (Holden Press, San Francisco, 1969).
7. R. Cook, Experts in Uncertainty. Opinion and Subjective Probability in Science (Oxford University Press, New York, 1991).
8. G. deCooman, Precision-imprecision equivalence in a broad class of imprecise hierarchical uncertainty models, J. Stat. Plan. Inf. 105(1), 175-198 (2002).
9. G. de Cooman and P. Walley, A possibilistic hierarchical model for behaviour under uncertainty, Theory Decis. 52(4), 327-374 (2002).
10. D. Dubois and H. Prade, Possibility Theory: An Approach to Computerized Processing of Uncertainty (Plenum Press, New York, 1988).
11. S. Ferson, L. Ginzburg, V. Kreinovich, H. Nguyen, and S. Starks, Uncertainty in risk analysis: Towards a general second-order approach combining interval, probabilistic, and fuzzy techniques, in: Proceedings of FUZZ-IEEE 2002, Honolulu, Hawaii, 2002, IEEE, pp. 1342-1347.
12. A. Freudenthal, Safety and the probability of structural failure, Trans. ASCE 121, 1337-1397 (1956).
13. M. Goldstein, The prevision of a prevision, J. Am. Stat. Soc. 87, 817-819 (1983).
14. I. Good, Some history of the hierarchical Bayesian methodology, in: Bayesian Statistics, edited by J. Bernardo, M. DeGroot, D. Lindley, and A. Smith (Valencia University Press, Valencia, 1980), pp. 489-519.
15. I. R. Goodman and H. T. Nguyen, Probability updating using second order probabilities and conditional event algebra, Inf. Sci. (USA) 121, 3-4, 295-347 (1999).
16. J. Goutsias, R. Mahler, and H. Nguyen, Random Sets - Theory and Applications (Springer, New York, 1997).
17. S. Gurov and L. Utkin, Reliability of Systems under Incomplete Information (Lubavich Publ., Saint Petersburg, 1999), in Russian.
18. J. Hall and J. Lawry, Imprecise probabilities of engineering system failure from random and fuzzy set reliability analysis, in: Imprecise Probabilities and Their Applications, Proceedings of the 1st Int. Symposium ISIPTA'01, 2001, edited by G. deCooman, T. Fine, and T. Seidenfeld (Shaker Publishing, Ithaca, USA, 2001), pp. 195-204.
19. V. P. Kuznetsov, Interval Statistical Models (Radio and Communication, Moscow, 1991), in Russian.
20. H. Kwakernaak, Fuzzy random variables: definitions and theorems, Inf. Sci. (USA) 15, 1-29 (1978).
21. B. Möller, M. Beer, W. Graf, and A. Hoffmann, Possibility theory based safety assessment, Comput.-Aided Civil Infrastruct. Eng. 14, 81-91 (1999).
22. S. Nahmias, Fuzzy variable, Fuzzy Sets Syst. 1, 97-110 (1978).
23. R. Penmetsa and R. Grandhi, Uncertainty propagation using possibility theory and function approximation, Int. J. Mech. Struct. Mach., submitted for publication (2001).
24. R. Penmetsa and R. Grandhi, Efficient estimation of structural reliability for problems with uncertain intervals, Int. J. Mech. Struct. Mach. 80, 1103-1112 (2002).
25. R. V. Grandhi and L. Wang, Reliability-based structural optimization using improved two-point adaptive non-linear approximations, Finite Elem. Anal. Des. 29, 35-48 (1998).
26. F. Tonon and A. Bernardini, A random set approach to optimisation of uncertain structures, Comput. Struct. 68, 583-600 (1998).
27. F. Tonon, A. Bernardini, and I. Elishakoff, Concept of random sets as applied to the design of structures and analysis of expert opinions for aircraft crash, Chaos Solitons Fractals 10(11), 1855-1868 (1999).
28. F. Tonon, A. Bernardini, and A. Mammino, Determination of parameters range in rock engineering by means of random set theory, Reliab. Eng. Syst. Saf. 70(3), 241-261 (2000).
29. F. Tonon, A. Bernardini, and A. Mammino, Reliability analysis of rock mass response by means of random set theory, Reliab. Eng. Syst. Saf. 70(3), 263-282 (2000).
30. L. Utkin and I. Kozine, Different faces of the natural extension, in: Imprecise Probabilities and Their Applications, Proceedings of the 2nd Int. Symposium ISIPTA'01, 2001, edited by G. deCooman, T. Fine, and T. Seidenfeld (Shaker Publishing, Ithaca, USA, 2001), pp. 316-323.
31. L. Utkin and I. Kozine, Stress-strength reliability models under incomplete information, Int. J. Gen. Syst. 31(6), 549-568 (2002).
32. L. Utkin and I. Kozine, Structural reliability modelling under partial source information, in: Proceedings of the Third Int. Conf. on Mathematical Methods in Reliability (Methodology and Practice), NTNU, Trondheim, Norway, 2002, edited by H. Langseth and B. Lindqvist, Norges Teknisk-Naturvitenskapelige Universitet, pp. 647-650.
33. P. Walley, Statistical Reasoning with Imprecise Probabilities (Chapman and Hall, London, 1991).
34. K. Weichselberger, Elementare Grundbegriffe einer allgemeineren Wahrscheinlichkeitsrechnung (Physika, Heidelberg, 2001).
35. L. Yubin, Q. Zhong, and W. Guangyuan, Fuzzy random reliability of structures based on fuzzy random variables, Fuzzy Sets Syst. 86, 345-355 (1997).
36. A. Zellner, An Introduction to Bayesian Inference in Econometrics (Wiley, New York, 1971).