Probabilistic safety analysis of structures under hybrid uncertainty

International Journal for Numerical Methods in Engineering

Volumn 70, Issue 4, 2007, Pages 405-422

  Chakraborty, Subrata ^a   Sam, Palash Chandra ^a  

^a INDIAN INSTITUTE OF ENGINEERING SCIENCE AND TECHNOLOGY   (India)

Author keywords

Equivalent transformation; Fuzzy; Hybrid uncertainty; Random; Reliability

Indexed keywords

FUZZY SETS; MEMBERSHIP FUNCTIONS; RANDOM VARIABLES; RELIABILITY ANALYSIS; RISK ANALYSIS; SAFETY FACTOR; UNCERTAINTY ANALYSIS;

EQUIVALENT TRANSFORMATION; EVIDENCE THEORY; HYBRID UNCERTAINTY; SECOND MOMENT FORMAT;

STRUCTURAL ANALYSIS;

FUZZY SETS; MEMBERSHIP FUNCTIONS; RANDOM VARIABLES; RELIABILITY ANALYSIS; RISK ANALYSIS; SAFETY FACTOR; STRUCTURAL ANALYSIS; UNCERTAINTY ANALYSIS;

EID: 34247373452     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1883     Document Type: Article

References (35)

1. Qiu Z, Wang Z. Comparison of dynamic response of structures with uncertain but bounded parameters using nonprobabilistic interval analysis method and probabilistic approach. International Journal of Solids and Structures 2003; 40:5423-5439.
2. Ben Haim Y, Elishakoff I. Convex Models of Uncertainty in Applied Mechanics. Elsevier: Amsterdam, 1990.
3. Elishakoff I, Lin YK, Zhu LP. Probabilistic and Convex Models of Uncertainty in Acoustically Excited Structures. Elsevier: Amsterdam, 1994.
4. Mullen RL, Muhanna RL. Bounds of structural response for all possible loading combinations. Journal of Structural Engineering (ASCE) 1999; 125:98-106.
5. Ganzerli S, Pantelides CP. Optimum structural design via convex models for optimum design. Computers and Structures 2000; 74(6):639-647.
6. Cremona C, Gao Y. The possibilistic reliability theory: theoretical aspects and applications. Structural Safety 1997; 19(2):173-201.
7. Móoller B, Beer M, Graph W, Hoffman A. Possibility theory based safety assessment. Computer-Aided Civil and Infrastructure Engineering 1999; 14:81-91.
8. Móoller B, Graf W, Beer M. Safety assessment of structures in view of fuzzy randomness. Computers and Structures 2003; 81:1567-1582.
9. Bing Li, Zhu M, Xu K. A practical method for fuzzy reliability analysis of mechanical structures. Reliability Engineering and System Safety 2000; 67:311-315.
10. Wu C, Hao H, Zhou Y. Distinctive and fuzzy failure probability analysis of an anisotropic rock mass to explosion load. International Journal for Numerical Methods in Engineering 2003; 56:767-786.
11. Langley RS. Unified approach to probabilistic and possibilistic analysis of uncertain systems. Journal of Engineering Mechanics (ASCE) 2000; 126(11): 1163-1172.
12. Chakraborty S. Safety assessment of structures under hybrid uncertainty. Cambridge University Engineering Department Technical Report, CUED/C-MECH/TR-86 (ISSN 0309-7420), 2003.
13. Nikolaidis E, Chen S, Cudney H, Raphael TH, Rosca RT. Comparison of probability and possibility for design against catastrophic failure under uncertainty. Transactions of the ASME, Journal of Mechanical Design 2004; 126:386-394.
14. Sophie QC. Comparing probabilistic and fuzzy set approaches for design in the presence of uncertainty. Ph.D. Thesis, Virginia Polytechnic Institute and State University, 2000.
15. Brown CB. Entropy constructed probabilities. Journal of Engineering Mechanics (ASCE) 1980; 106(4):663-669.
16. Kam TY, Brown CB. Updating parameters with fuzzy entropies. Journal of Engineering Mechanics (ASCE) 1983; 198(6):1334-1343.
17. Haldar A, Reddy RK. A random fuzzy analysis of existing structures. Fuzzy Sets and Systems 1992; 48:201-210.
18. Rahman MS, Zahaby KMEI. Probabilistic liquefaction risk analysis using fuzzy variables. Soil Dynamics and Earthquake Engineering 1997; 16:63-79.
19. Zhenyu L, Chen Q. A new approach to fuzzy finite element analysis. Computer Methods in Applied Mechanics 202; 191:5113-5118.
20. Ferrari P, Savoia M. Fuzzy number theory to obtain conservative results with respect to probability. Computer Methods in Applied Mechanics and Engineering 1998; 160:205-222.
21. Savoia M. Structural reliability analysis through fuzzy number approach with application to stability. Computers and Structures 2002; 80:1087-1102.
22. Smith SA, Krishnamurthy T, Mason BH. Optimized vertex method and hybrid reliability. 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 2002; 1465.
23. Penmetsa RC, Grandhi RC. Efficient estimation of structural reliability for problems with uncertain intervals. Computers and Structures 2002; 80:1103-1112.
24. Thoft-Christensen P, Baker MJ. Structural Reliability Theory and its Applications. Springer: Berlin, Germany, 1982.
25. Tichy M. Applied Methods of Structural Reliability. Kluwer Academic Publishers: Dordrecht, Netherlands, 1993.
26. Ditlevsen O, Madsen HO. Structural Reliability Methods. Wiley: West Sussex, England, 1996.
27. Melchers RE. Structural Reliability Analysis and Prediction. Wiley: Chichester, West Sussex, England, 1999.
28. Haldar A, Mahadevan S. Reliability Assessment Using Stochastic Finite Element Analysis. Wiley: New York, U.S.A., 2000.
29. DeLuca A, Termini S. A definition of nonprobabilistic entropy in the setting of fuzzy set theory. Information and Control1970; 20:301-312.
30. Puig B, Akian J. Non-Gaussian simulation using Hermite polynomials expansion and maximum entropy principle. Probabilistic Engineering Mechanics 2004; 19:293-305.
31. Dubois D, Prade H. Random sets and fuzzy interval analysis. Fuzzy Sets System 1991; 42:87-101.
32. Zadeh LA. Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems. Fuzzy Sets and Applications: Selected Papers 1978; 1:3-28.
33. Myers RH, Montogmery DC. Response Surface Methodology: Process and Product Optimization using Designed Experiments. Wiley: New York, 1995.
34. Bucher GC, Bourgund U. A fast and efficient response surface approach for structural reliability problems. Structural Safety 1990; 7:57-66.
35. Rajashekhar MR, Ellingwood BR. A new look at the response surface approach for reliability analysis. Structural Safety 1993; 12:205-220.