A Bayesian approach for quantification of model uncertainty

Reliability Engineering and System Safety

Volumn 95, Issue 7, 2010, Pages 777-785

  Park, Inseok ^a   Amarchinta, Hemanth K ^a   Grandhi, Ramana V ^a  

^a Wright State University   (United States)

Author keywords

Adjustment factor approach; Bayes' theorem; Model probability; Model uncertainty

Indexed keywords

BAYES' THEOREM; BAYESIAN; BAYESIAN APPROACHES; BEST MODEL; COMPETING MODELS; CONFIDENCE BANDS; ENGINEERING PROBLEMS; ENGINEERING SYSTEMS; EXPERIMENTAL DATA; LASER PEENING; MODEL PREDICTION; MODEL PROBABILITIES; MODEL SELECTION; MODEL UNCERTAINTIES; NONLINEAR VIBRATION SYSTEMS; STATISTICAL FRAMEWORK; SYSTEM RESPONSE;

BAYESIAN NETWORKS; PROBABILITY DENSITY FUNCTION; UNCERTAINTY ANALYSIS;

MATHEMATICAL MODELS;

EID: 77950925938     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2010.02.015     Document Type: Article

References (30)

1. Alvin K.F., Oberkampf W.L., Diegert K.V., and Rutherford B.M. Uncertainty quantification in computational structural dynamics: a new paradigm for model validation. Proceedings of the 16th international modal analysis conference, Santa Barbara, CA (1998) 1191-1198
2. Zio E., and Apostolakis G. Two methods for the structured assessment of model uncertainty by experts in performance assessments of radioactive waste repositories. Reliability Engineering and System Safety 54 2-3 (1996) 225-241
3. Reinert J.M., and Apostolakis G.E. Including model uncertainty in risk-informed decision making. Annals of Nuclear Energy 33 4 (2006) 354-369
4. Zhang R., and Mahadevan S. Model uncertainty and Bayesian updating in reliability-based inspection. Structural Safety 22 2 (2000) 145-160
5. Zouaoui F., and Wilson J.R. Accounting for input model and parameter uncertainty in simulation. Proceedings of the 2001 winter simulation conference, Arlington, VA (2001) 290-299
6. McFarland JM, Bichon BJ. Bayesian model averaging for reliability analysis with probability distribution model form uncertainty. In: Fiftieth AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Palm Springs, CA, 2009.
7. Bunge M. Foundations of physics (1967), Springer-Verlag, New York, NY
8. Burnham K.P., and Anderson D.R. Model selection and multi-model inference: a practical information-theoretic approach. 2nd ed (2002), Springer-Verlag, New York, NY
9. Vamos T. Epistemic background problems of uncertainty. In: First international symposium on uncertainty modeling and analysis, College Park, MD, USA, 1990. p. 96-100.
10. Link W.A., and Barker R.J. Model weights and the foundations of multimodel inference. Ecology 87 10 (2006) 2626-2635
11. Draper D. Assessment and propagation of model uncertainty. Journal of the Royal Statistical Society Series B 57 1 (1995) 45-97
12. Raftery A.E. Approximate Bayes factors and accounting for model uncertainty in generalized linear models. Biometrika 83 2 (1996) 251-266
13. Bayarri M.J., Berger J.O., Cafeo J., Garcia-Donato G., Liu F., Palomo J., et al. Computer model validation with functional output. Annals of Statistics 35 5 (2007) 1874-1906
14. Bayarri M.J., Berger J.O., Paulo R., Sacks J., Cafeo J.A., Cavendish J., et al. A framework for validation of computer models. Technometrics 49 2 (2007) 138-154
15. Kennedy M.C., and O'Hagan A. Bayesian calibration of computer models. Journal of the Royal Statistical Society Series B (Statistical Methodology) 63 3 (2001) 425-464
16. Xiong Y., Chen W., Tsui K.L., and Apley D.W. A better understanding of model updating strategies in validating engineering models. Journal of Computer Methods in Applied Mechanics and Engineering 198 15-16 (2009) 1327-1337
17. Jiang X, Yang RJ, Barbat S, Weerappuli P. Bayesian probabilistic PCA approach for model validation of dynamic systems. In: Proceedings of the SAE world congress and exhibition, Detroit, MI, April 2009.
18. AIAA. Guide for the verification and validation of computational fluid dynamics simulations (1998), American Institute of Aeronautics and Astronautics AIAA-G-077
19. ASME. Guide for verification and validation in computational solid mechanics (2006), American Society of Mechanical Engineers ASME V&V 10
20. McFarland JM, Mahadevan S, Swiler L, Giunta A. Bayesian calibration of the QASPR simulation. In: Forty-eighth AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Honolulu, HI, April 2007.
21. McFarland JM. Uncertainty analysis for computer simulations through validation and calibration. PhD thesis, Vanderbilt University, Nashville, TN, 2008.
22. Clemen R.T. Combining forecasts: a review and annotated bibliography. International Journal of Forecasting 5 4 (1989) 559-583
23. Barnard G.A. New methods of quality control. Journal of the Royal Statistical Society Series A 126 (1963) 255-258
24. Leamer E.E. Specification searches: ad hoc inference with nonexperimental data (1978), John Wiley & Sons, New York, NY
25. Nilsen T., and Aven T. Models and model uncertainty in the context of risk analysis. Reliability Engineering and System Safety 79 3 (2003) 309-317
26. Mosleh A., and Apostolakis G. The assessment of probability distributions from expert opinions with an application to seismic fragility curves. Risk Analysis 6 4 (1986) 447-461
27. He J.H. Variational approach for nonlinear oscillators. Chaos Solitons and Fractals 34 5 (2007) 1430-1439
28. Singh G, Grandhi RV, Stargel DS. Modeling and parameter design of a laser shock peening process. In: International journal for computational methods in engineering science and mechanics. Philadelphia, PA: Taylor and Francis; in print.
29. Amarchinta H.K., Grandhi R.V., Langer K., and Stargel D.S. Material model validation for laser shock peening process simulation. Modelling and Simulation in Materials Science and Engineering 17 1 (2009) paper id. 015010
30. Amarchinta HK, Grandhi RV, Clauer AH, Langer K, Stargel D. Simulation of residual stress induced by a laser peening process through inverse optimization of material models. Journal of Materials Processing Technology September 2009; submitted for publication.