Uncertainty analysis using evidence theory - confronting level-1 and level-2 approaches with data availability and computational constraints

Reliability Engineering and System Safety

Volumn 95, Issue 5, 2010, Pages 550-564

  Limbourg, Philipp ^a   de Rocquigny, Etienne ^b  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b EDF R AND D   (France)

Author keywords

Aleatory uncertainty; Dempster Shafer; Epistemic uncertainty; Flood protection; Imprecise probability

Indexed keywords

ALEATORY UNCERTAINTY; DEMPSTER-SHAFER; EPISTEMIC UNCERTAINTIES; FLOOD PROTECTION; IMPRECISE PROBABILITIES;

COMPUTATIONAL COMPLEXITY; DATA HANDLING; FLOOD CONTROL; FORMAL LOGIC; OCEAN STRUCTURES; RISK ANALYSIS; RISK ASSESSMENT; SAFETY FACTOR; SENSITIVITY ANALYSIS; SYSTEM THEORY;

UNCERTAINTY ANALYSIS;

EID: 77649189592     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2010.01.005     Document Type: Article

References (56)

1. Dempster A.P. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38 (1967) 325-339
2. Shafer G. A mathematical theory of evidence (1976), Princeton University Press, Princeton, USA
3. Helton J.C., and Oberkampf W.L. Special issue on alternative representations of epistemic uncertainty. Reliability Engineering and System Safety 85 (2004) 1-369
4. Aughenbaugh JM. Managing Uncertainty in Engineering Design Using Imprecise Probabilities and Principles of Information Economics. PhD Thesis, Georgia Institute of Technology, 2006.
5. Tonon F., Bae H.-R., Grandhi R., and Pettit C. Using random set theory to calculate reliability bounds for a wing structure. Structure and Infrastructure Engineering 2 (2006) 191-200
6. Agarwal H., Renaud J.E., Preston E.L., and Padmanabhan D. Uncertainty quantification using evidence theory in multidisciplinary design optimization. Reliability Engineering and System Safety 85 (2004) 281-294
7. In: de Rocquigny E., Devictor N., and Tarantola S. (Eds). Uncertainty in industrial practice - a guide to quantitative uncertainty management (2008), Wiley, Chichester, United Kingdom
8. Apostolakis G. The concept of probability in safety assessments of technological systems. Science 250 (1990) 1359-1364
9. Parry G.W. On the meaning of probability in probabilistic safety assessment. Reliability Engineering and System Safety 23 (1988) 309-314
10. Parry G.W. The characterization of uncertainty in probabilistic risk assessments of complex systems. Reliability Engineering and System Safety 54 (1996) 119-126
11. Parry G.W., and Winter P.W. Characterization and evaluation of uncertainty in probabilistic risk analysis. Nuclear Safety 22 (1981) 28-42
12. Hoffman F.O., and Hammonds J.S. Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability. Risk Analysis 14 (1994) 707-712
13. Helton J.C. Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty. Journal of Statistical Computation and Simulation 57 (1997) 3-76
14. Hájek A. Interpretations of Probability. In 'Stanford Encyclopedia of Philosophy', 2007, vol. (http://plato.stanford.edu).
15. Klir G.J. Uncertainty and information: foundations of generalized information theory (2005), Wiley, New York, USA
16. Ferson S., Kreinovich V., Ginzburg L., Myers D.S., and Sentz K. Constructing probability boxes and Dempster-Shafer structures (2003), Sandia National Laboratories, SAND2002-4015, Albuquerque, USA
17. Helton J.C., Johnson J.D., and Oberkampf W.L. An exploration of alternative approaches to the representation of uncertainty in model predictions. Reliability Engineering and System Safety 85 (2004) 39-71
18. Shafer G., and Logan R. Implementing Dempster's rule for hierarchial evidence. Artificial Intelligence 33 (1987) 271-298
19. Guo L. Software quality and reliability prediction using Dempster-Shafer theory (2004), West Virginia University
20. Górski J., and Zagórski M. Reasoning about trust in IT infrastructures. In: Kolowrocki K. (Ed). Advances in Safety and Reliability Vol. 1 (2005), Balkema, Leiden 689-695
21. Sun L., Srivastava R., and Mock T. An information systems security risk assessment model under the Dempster-Shafer theory of belief functions. Journal of Management Information Systems 22 (2006) 109-142
22. Rakowsky U.K., and Gocht U. Modelling of uncertainties in reliability centred maintenance - a Dempster-Shafer approach. In: Aven T., and Vinnem J.E. (Eds). Risk, Reliability and Societal Safety vol. 1 (2007), Taylor and Francis, London 739-745
23. Soundappan P., Nikolaidis E., Haftka R.T., Grandhi R., and Canfield R. Comparison of evidence theory and Bayesian theory for uncertainty modeling. Reliability Engineering and System Safety 85 (2004) 295-311
24. Nilsen T., and Aven T. Models and model uncertainty in the context of risk analysis. Reliability Engineering and System Safety 79 (2003) 309-317
25. Helton J.C. Treatment of uncertainty in performance assessments for complex systems. Risk Analysis 14 (1994) 483-511
26. Paté-Cornell M.E. Uncertainties in risk analysis; six levels of treatment. Reliability Engineering & System Safety 54 (1996) 95-111
27. Winkler R.L. Uncertainty in probabilistic risk assessment. Reliability Engineering & System Safety 54 (1996) 127-132
28. Aven T. Foundations of risk analysis (2003), John Wiley & Sons, Ltd.
29. Apostolakis G. The distinction between aleatory and epistemic uncertainties is important; an example from the inclusion of aging effects in the PSA. In: 'Proceedings of PSA'99'. Washington DC, USA, 1999.
30. In: Helton J.C., and Burmaster D.E. (Eds). Guest editorial: treatment of aleatory and epistemic uncertainty in performance assessments for complex systems. Reliability Engineering & System Safety 54 (1996) 91-94
31. Ferson S., Joslyn C.A., Helton J.C., Oberkampf W.L., and Sentz K. Summary from the epistemic uncertainty workshop: consensus amid diversity. Reliability Engineering and System Safety 85 (2004) 355-369
32. Helton JC, Johnson JD, Oberkampf WL, Sallaberry CJ. (accepted) Representation of Analysis Results Involving Aleatory and Epistemic Uncertainty. Int. J. of General Systems.
33. McGill W.L., and Ayyub B.M. Estimating parameter distributions in structural reliability assessment using the Transferable Belief Model. Computers and Structures 86 (2008) 1052-1060
34. Bae H.-R., Grandhi R.V., and Canfield R.A. An approximation approach for uncertainty quantification using evidence theory. Reliability Engineering and System Safety 86 (2004) 215-225
35. Limbourg P. Dependability modelling under uncertainty (2008), Springer, Berlin, Heidelberg
36. Agarwal H. Reliability based design optimization: formulations and methodologies. PhD Thesis, University of Notre Dame, 2004.
37. Baudrit C, Hélias A, Perrot N. Uncertainty analysis in food engineering involving imprecision and randomness. In: Cooman Gd, Vejnarova J, Zaffalon M, editors. 'ISIPTA'07 - Fifth International Symposium on Imprecise Probability: Theories and Applications'. Prague, Czech Republic, 2007.
38. Tonon F. Using random set theory to propagate epistemic uncertainty through a mechanical system. Reliability Engineering and System Safety 85 (2004) 169-181
39. Oberguggenberger M., and Fellin W. Reliability bounds through random sets: non-parametric methods and geotechnical applications. Computers and Structures 86 (2008) 1093-1101
40. Helton J.C., Johnson J.D., Oberkampf W.L., and Storlie C.B. A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Computer Methods in Applied Mechanics and Engineering 196 (2007) 3980-3998
41. Kriegler E. Imprecise Probability Analysis for Integrated Assessment of Climate Change. PhD Thesis, Universität Potsdam, 2005.
42. Aughenbaugh JM, Herrmann JW. A comparison of information management using imprecise probabilities and precise Bayesian updating of reliability estimates. In: Third international workshop on reliable engineering computing. Savannah, USA, 2008, pp. 107-136.
43. Aughenbaugh JM, Christiaan SD, Paredis JJ, Bras B. A comparison of probability bounds analysis and decision analysis in environmentally benign design and manufacture. In IDETC 2006: ASME Design Engineering and Technical Conferences and Computers and Information Engineering Conference. Philadelphia, USA, 2006.
44. Malak RJ, Aughenbaugh JM, Paredis CJJ (to appear). Multi-Attribute Utility Analysis in Set-Based Conceptual Design. Computer Aided Design.
45. Mourelatos ZP, Zhou J. Non-Probabilistic Design Optimization with Insufficient Data using Possibility and Evidence Theories. In: Muhanna RL, Mullen RL, editors. 'NSF workshop on reliable engineering computing'. Savannah, USA, 2006, pp. 391-418.
46. Simon C., Weber P., and Evsukoff A. Bayesian networks inference algorithm to implement Dempster Shafer theory in reliability analysis. Reliability Engineering & System Safety 93 (2008) 950-963
47. Yager R.R. Uncertainty modeling and decision support. Reliability Engineering and System Safety 85 (2004) 341-354
48. Rackwitz R. Reliability analysis - a review and some perspectives. Structural Safety 23 (2001) 365-395
49. Helton J.C., Johnson J.D., Oberkampf W.L., and Sallaberry C.J. Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty. Reliability Engineering and System Safety 91 (2006) 1414-1434
50. Hall J.W. Uncertainty-based sensitivity indices for imprecise probability distributions. Reliability Engineering and System Safety 91 (2006) 1443-1451
51. Ferson S., and Tucker W.T. Sensitivity in risk analyses with uncertain numbers (2006), Sandia National Laboratories, SAND2006-2801, Albuquerque, USA
52. de Rocquigny E. La maîtrise des incertitudes dans un contexte industriel-1re partie: Une approche méthodologique globale basée sur des exemples. Journal de la Société française de statistique 147 (2006) 33-71
53. de Rocquigny E. A simple Bayesian proposal to aggregate expert judgement and observations on epistemic and aleatory uncertainties-extensions and associated industrial needs. In: Proceedings of the workshop on the use of expert judgment in decision-making, CEA & Eur. Comm. JRC Petten'. Aix-en-Provence, France, 2005.
54. Ferson S., Hajagos J., Berleant D., Jianzhong Z., Troy Tucker W., Ginzburg L., et al. Dependence in Dempster-Shafer theory and probability bounds analysis (2004), Sandia National Laboratories, SAND2004-3072, Albuquerque, USA
55. Limbourg P., Savic R., Petersen J., and Kochs H.-D. Fault tree analysis in an early design stage using the Dempster-Shafer theory of evidence. In: Aven T., and Vinnem J.E. (Eds). Risk, reliability and societal safety vol. 2 (2007), Taylor and Francis, London 713-722
56. Wilks S.S. Determination of sample sizes for setting tolerance limits. Annals of Mathematical Statistics 12 (1941) 91-96