Epistemic uncertainty quantification techniques including evidence theory for large-scale structures

Computers and Structures

Volumn 82, Issue 13-14, 2004, Pages 1101-1112

  Bae, Ha Rok ^a   Grandhi, Ramana V ^a   Canfield, Robert A ^b  

^a Wright State University   (United States)

^b AIR FORCE INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Belief; Evidence theory; Multi point approximation; Plausibility; Possibility theory

Indexed keywords

AERODYNAMICS; COMPUTATIONAL METHODS; DATA REDUCTION; FINITE ELEMENT METHOD; FUZZY CONTROL; NORMAL DISTRIBUTION; PROBABILITY; PROBABILITY DENSITY FUNCTION; PROBLEM SOLVING; STRUCTURAL ANALYSIS;

BELIEF; EVIDENCE THEORY; MULTI POINT APPROXIMATION; PLAUSIBILITY; POSSIBILITY THEORY;

MECHANICAL ENGINEERING;

EID: 2442496608     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2004.03.014     Document Type: Conference Paper

References (27)

1. Helton J.C. Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty. J Stat. Comput. Simul. 57:1997;3-76.
2. Oberkampf WL, Helton JC. Mathematical representation of uncertainty. Non-deterministic approaches Forum 2001, Seattle, WA, AIAA-2001-1645.
3. Zadeh L. Fuzzy sets. Inf. Control. 8:1965;338-353.
4. Wood L.K., Otto N.K., Antonsson K.E. Engineering design calculations with fuzzy parameters. Fuzzy Sets Syst. 53:1992;1-20.
5. Antonsson E.K., Otto N.K. Improving engineering design with fuzzy sets. Dubois D., Prade H., Yager R.R. Fuzzy information engineering: a guided tour of applications. 1997;John Wiley & Sons, New York.
6. Penmetsa R.C., Grandhi R.V. Efficient estimation of structural reliability for problems with uncertain intervals. Comput. Struct. 80:2002;1103-1112.
7. Shafer G. A mathematical theory of evidence. Princeton, NJ: 1976.
8. Yager R.R., Kacprzyk J., Fedrizzi M. Advances in the Dempster-Shafer theory of evidence. 1994;John Wiley & Sons, New York.
9. Zadeh L. Review of shafer's a mathematical theory of evidence. Artif. Intell. Mag. 5:1984;81-83.
10. Sentz K, Ferson S. Combination of evidence in Dempster-Shafer theory. SAND2002-0835 Report. Sandia National Laboratories. 2002.
11. Cohen P.R. Heuristic reasoning about uncertainty: an artificial intelligence approach. 1985;Morgan Kaufmann, London.
12. Nguyen H.T., Walker E.A. A first course in fuzzy logic. 1997;CRC press, Boca Raton.
13. Tonon F., Bernardini A., Mammino A. Determination of parameters range in rock engineering by means of random set theory. Reliability Eng. Syst. Saf. 70:2000;241-261.
14. Arora J.S. Introduction to optimum design. 1989;McGraw-Hill, New York.
15. Walpole R.E. Probability and statistics for engineers and scientists. 1998;Prentice, New Jersy.
16. Dong W.M., Shah H.C. Vertex method for computing functions of fuzzy variable. Fuzzy Sets Syst. 24:1987;65-78.
17. Xu S., Grandhi R.V. Multi-point approximation development: thermal structural optimization case study. Int. J. Numer. Methods Eng. 48:2000;1151-1164.
18. Wang L.P., Grandhi R.V. Improved two-point function approximations for design optimization. AIAA J. 33(9):1995;1720-1727.
19. Xu S., Grandhi R.V. Structural optimization with thermal and mechanical constraints. J. Aircr. 36(1):1999;29-35.
20. Wang L.P., Grandhi R.V. Multi-point approximations: comparisons using structural size, configuration and shape design. Struct. Optimization. 12:1996;177-185.
21. GENESIS user manual. Colorado: Vanderplaats Research & Development; 2000.
22. Dubois D., Prade H. Random sets and fuzzy interval analysis. Fuzzy Sets Syst. 38:1990;308-312.
23. Dong W.M., Wong F.S. Fuzzy weighted averages and implementation of the extension principle. Fuzzy Sets Syst. 21:1987;183-199.
24. Liou T.S., Wang M.J. Fuzzy weighted average: an improved algorithm. Fuzzy Sets Syst. 49:1992;307-315.
25. Guh Y.Y., Hon C.C., Wang K.M., Lee E.S. Fuzzy weighted average: a max-min paired elimination method. Comput. Math. Appl. 32:1996;115-123.
26. Savage L.J. The foundations of statistics. 1972;Dover Pub, New York.
27. Tonon F. Using random set theory to propagate epistemic uncertainty through a mechanical system. Reliability Eng. Syst. Saf. [in press].