La maîtrise des incertitudes dans un contexte industriel. 2nde partie : revue des méthodes de modélisation statistique physique et numérique

De Rocquigny, Étienne

Journal de la Société française de statistique, Tome 147 (2006) no. 3, pp. 73-106.

[1] Apostolakis G. (1999), The distinction between aleatory and epistemic uncertainties is important ; an example from the inclusion of aging effects in the PSA, PSA'99, Washington DC.

[2] Ardillon E., & De Rocquigny E. (2003), Probabilistic estimation of safety quantites for complex non-regular physical systems with uncertain parameters. Proc. 25th ESReDA Seminar, Paris.

[3] Beaudouin F., Munier B., Serquin Y. (1997), Multiattribute utility theory : Towards a more general framework, Proc. of the 1997 ESReDA seminar on decision analysis and its applications in safety and reliability.

[4] Bestion D. (2003), Final Report -§ 4.2 State of the Art on Uncertainty Evaluation, European Project for Future Advances in Sciences and Technology for Nuclear Engineering Thermal-Hydraulics (EUROFASTNET).

[5] Box G.E.P and Draper N.R (1987), Empirical Model Building and Response Surface, J. Wiley & Sons, Wiley Series in Probability and Mathematical statistics. | MR | Zbl

[6] Boyack B.E. (1990), Quantifying reactor safety margins-part I : an overview of the code scaling, applicability and uncertainty evaluation methodology, Nucl. Eng. Des. 119, 1-15.

[7] Cambier S. (2000), Approche probabilité pour la prise en compte de la dispersion de paramètres mécaniques - Application à la fatigue vibratoire de réseaux de tuyauteries, Thèse ENSAM Paris.

[8] Cambier S., Desceliers C., Soize S. (2003), Prise en compte probabiliste des incertitudes dans l'estimation du comportement sismique d'un circuit primaire. 7ème Colloque National AFPS.

[9] Cambier S., Guihot P., Coffignal G. (2002), Computational methods for accounting of structural uncertainties, applications to dynamic behavior prediction of piping systems. Structural Safety, 24 : 29-50.

[10] Chia C.-Y., Ayyub B.-M. (1994), Conditional sampling for simulation-based structural reliability assessment, Structural Safety et reliability, Schueller, Schonzuka & Yao (eds), Balkema, Rotterdam.

[11] Chick S.E. (2000), Bayesian Methods for Simulation, Proc. of the 2000 Winter Simulation Conference, Washington D.C.

[12] Corre B. (2003), Problématique des incertitudes en exploration-production pétrolière : application des plans d'expériences. Total Fina Elf, Séminaire « Plans d'Expériences Numériques » Ec. Mines St-Etienne.

[13] Cukier R.I., Levine H.B., Schuler K.E. (1978). Non-linear sensitivity analysis of multi-parameter model systems. Journal of computational physics 26, 1-42. | MR | Zbl

[14] De Crécy A. (1997), CIRCE : a tool for calculating the uncertainties of the constitutive relationships of Cathare2, 8th International Topical Meeting on Nuclear reactor Thermo-Hydraulics (NURETH8), Kyoto.

[15] Dempster A. P. (1967). Upper and lower probabilities induced by a multivalued mapping, Annals of Math. Statistics 38, 325-339. | MR | Zbl

[16] Dempster F., Laird N.M., Rubin D.B. (1977), Maximum likelihood from incomplete data from the EM algorithm, Journal of the Royal Statistical Society (Ser. B) 39, 1-38. | MR | Zbl

[17] De Rocquigny E. (2005), A simple Bayesian proposal to aggregate expert judgement and observations on epistemic and aleatory uncertainties - extensions and associated industrial needs, Proc. of the Workshop on the Use of Expert Judgment in Decision-Making, CEA & Eur. Comm. JRC Petten, Aix-en-Provence.

[18] De Rocquigny E. (2005), A statistical approach to control conservatism of robust uncertainty propagation methods ; application to accidental thermal hydraulics calculations, Proceedings of ESREL-05, Tri City, Poland.

[19] De Rocquigny E. (2005), Couplage mécano-probabiliste pour la fiabilité des structures - un cas industriel où la robustesse d'une surface de réponse est démontrable. Actes du 17ème Congrès Français de Mécanique. Troyes.

[20] De Rocquigny E. (2004), Tutoriel Incertitudes, présenté dans la Conférence Lambda-Mu 14, Bourges, Octobre 2004.

[21] De Rocquigny E. (2006), Problèmes ouverts - Sujet n° 1 « Statistiques, mesures et calcul scientifique inverse», www.jds2006.fr/prob-ouverts.php 38èmes Journ. Franc, de Stat., Clamart, 2006.

[22] Desceliers C., Soize C., Cambier S. (2003), Nonparametric-parametric model for random uncertainties in nonlinear structural dynamics -Application to earthquake engineering, to earthquake engineering and Structural Dynamics, 33, 315-327.

[23] Devictor N. (1996) Fiabilité et mécanique : méthodes FORM/SORM et couplages avec des codes d'éléments finis par surfaces de réponse adaptative. PhD Université Blaise Pascal, Clermont-Ferrand.

[24] Devictor N., BOLADO LAVIN R. (eds) (2005), Proc. of the Workshop on the Use of Expert Judgment in Decision-Making, CEA & Eur. Comm. JRC Petten, Aix-en-Provence.

[25] Ditlevsen O. & Madsen H.O. (1996), Structural reliability Methods, John Wiley & Sons.

[26] Dubois D., Prade H. (1988), Possibility theory : an approach to computerized processing of uncertainty, New York, Plenum Press. | MR

[27] Duckstein L., Parent E. (1994), Engineering Risk in Natural Resources Management, NATO ASI Series.

[28] Dupuy J.P. (2002), Pour un catastrophisme éclairé - Quand l'Impossible est certain, Ed. du Seuil.

[29] Dutfoy A. (2001), Mefisto, The EDF Reliability Method to Propagate Uncertainties, Proc. of ICOSSAR 2001.

[30] Dutfoy A. (2000), Uncertainty propagation in radionuclide transport mo-delling for performance assessment of a nuclear waste repository, Proc. of PSAM5, Japan.

[31] Efron B., Tibshirani R.J. (1993), An introduction to the Bootstrap, Chapman & Hall. | MR | Zbl

[32] Faure C. (1996), Splitting of algebraic expressions for automatic differentiation, Proc. of the 2nd International Workshop on Computational Differentiation, 12-15 fév. 1996, Santa Fe. | Zbl

[33] Frey H.C., Rhodes D.S. (2005), Quantitative Analysis of Variability and Uncertainty in with Known Measurement Error : Methodology and Case Study, Risk Analysis Vol. 25, No3.

[34] Gille-Genest A. (1999), Utilisation des méthodes numériques probabilistes dans les applications au domaine de la Fiabilité des Structures, Thèse de l'Université Paris VI - EDF R&D.

[35] Granger Morgan M., Henrion M. (1990), Uncertainty - A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis, Cambridge University Press.

[36] Griewank A. (2000), Evaluating derivatives - Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia. | MR | Zbl

[37] Hascouet L., Pascual V. (2004), TAPENADE 2.1 user's guide, INRIA report, www.inria.fr/rrrt/rt-0300.html

[38] Helton J.C., Burmaster D.E. et al. (1996), Treatment of Aleatory and Epistemic Uncertainty, Special Issue of Rel. Eng. & Syst. Saf., vol. 54 n°2 et 3.

[39] Helton J.C., Davis F.J. (2003), Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems, Rel. Eng. & Syst. Saf. 81, 23-69.

[40] Helton J.C., Oberkampf W.L. (2004), Alternative Representations of Epistemic Uncertainty, Special Issue of Rel. Eng. & Syst. Saf., vol. 85 n°l-3.

[41] Henry Cl. (2004), Etat de la connaissance scientifique et mobilisation du principe de précaution, 3e Colloque international du réseau Monder, Paris, 12-15 sept.2004.

[42] Iooss B., Van Dorpe F., and Devictor N. (2006) Response Surfaces and Sensitivity Analysis for an Environmental Model of Dose Calculations. Rel. Eng. Sz Syst. Saf., à paraître.

[43] Jacques J., Lavergne C., Devictor N. (2006), Sensitivity Analysis in presence of model uncertainty and correlated outputs, Rel. Eng. and Syst. Saf., Elsevier, à paraître.

[44] Jourdan A. (2002), Approches Statistiques des Expériences Simulées, Rev. Statistique Appliquée, L(1), 49-64. | EuDML

[45] Kendall Mg. & Stuart ( 1943-1979), A, The Advanced Theory of Statistics (2 vol), Griffin & Co., London. | MR | Zbl

[46] Kleijnen J.P.C. and Sargent R.G. (2000), A methodology for fitting and validating metamodels in simulation, European Journal of Operational Research, 120, 14-29. | Zbl

[47] Knight F.H. (1921), Risk, Uncertainty and Profit, Hart, Schaffner & Marx.

[48] Kurowicka D., and Cooke R.M. (2002), Techniques for generic probabilistic inversion, Probabilistic Safety Assessment and Management, E.J. Bonano et al. (eds), Elsevier, 1543-1550.

[49] Kuschel N., Rackwitz R. (2000), Optimal design under time-variant reliability constraints, Structural Safety, Volume 22, Issue 2, 113-127.

[50] Lannoy A., et al. (1994), Méthodes avancées d'analyse des bases de données du retour d'expérience industriel, Coll. D.E.R.EDF, n°86, Eyrolles.

[51] Lebrun R. (2006), Modelling dependency with copulas in reliability analysis, a new approach to the FORM and SORM methods, submitted to 8th PSAM Conference.

[52] Lecoutre J.P., Tassi P. (1987), Statistique non paramétrique et robustesse, Economica.

[53] Lemaire M. (2005), Fiabilité des Structures, Coll. Génie Civil, Hermès-Lavoisier.

[54] Mahé P., De Rocquigny E. (2005), Incertitudes non observables en calcul scientifique industriel - Etude d'algorithmes simples pour intégrer dispersion intrinsèque et ébauche d'expert, 37èmes Journ. Franc. de Stat., Pau, 2005.

[55] Mckay M.D. (1996), Application of Variance-Based Methods to NUREG-1150 Uncertainty Analyses, USNRC 1996.

[56] Miquel J. (1984), Guide pratique d'estimation des probabilités de crues, Eyrolles.

[57] Myers R.H. (1971), Response surface methodology, Allyn and Bacon, Inc., Boston.

[58] Nelsen R.B. (1999), An introduction to copulas, SPRINGER. | MR

[59] Olivi L., (1984), Response surface methodology, Handbook for Nuclear Safety Analysis, J.R.C., European Commission.

[60] Pendola M. (2000), Fiabilité des Structures en contexte d'incertitudes statistiques et d'écarts de modélisation, Thèse de l'Université Clermont II.

[61] Persoz M., Hugonnard-Bruyère S., Venturini V., Meister E. (2000), Deterministic and probabilistic assessments of the reactor pressure vessel structural integrity with user-friendly software, ASME Press. Vess. &; Piping.

[62] Procaccia H., Morilhat P. (1996), Fiabilité des structures des installations industrielles, Coll. D.E.R. EDF, n°94, Eyrolles.

[63] Quiggin J. (1982), A theory of anticipated utility, Journal of Economic Behavior and Organization, Vol. 3, pp. 323-343.

[64] Reiss R.D., Thomas M. (2001), Statistical Analysis of Extreme Values, Ed. Birkhauser. | MR

[65] Royset J.O., Der Kiureghlan A., and Polak E. (2001), Reliability-based optimal structural design by the decoupling approach, Rel. Eng. & Syst. Saf., Vol. 73, Issue 3, pp. 213-221.

[66] Rowe W.D. (1994), Understanding Uncertainty, Risk Analysis, Vol. 14. n°5, pp. 743-750.

[67] Rubinstein R.Y. (1981), Simulation and the Monte-Carlo Method, Wiley. | MR | Zbl

[68] Saltelli A., Bolado R. (1998), An alternative way to compute the Fourier Amplitude Sensitivity Test, Computational Statistics and data analysis, 26, 445-460. | Zbl

[69] Saltelli A., Tarantola S., Campalongo F., Ratto M. (2004), Sensitivity analysis in practice : a guide to assessing scientific models, Wiley. | MR | Zbl

[70] Saporta G. (1990), Probabilités, Analyse de Données et Statistique, Ed. Technip. | Zbl

[71] Shannon C. E., (1948), A mathematical theory of communication, Bell Systems Technical Journal, Vol. 27, pp. 379-423, 623-656. | MR | Zbl

[72] Sobol I.M. (1993), Sensitivity estimates for non-linear mathematical models, Mathematical Modelling and Computational Experiments. | MR | Zbl

[73] Soize C. (2000), A non-parametric model of random uncertainties for reduced matrix models in structural dynamics, Probab. Engrg. Mech. 15 (3) 277-294.

[74] Sudret B., Guédé Z., Lemaire M. (2005), Probabilistic assessment of thermal fatigue in nuclear components, Nucl. Eng. Des., 235, 219-235.

[75] Sudret B., Der Kiureghian A. (2000), Stochastic Finite Elements and Reliability - A state-of-the-art report, Report n° UCB/SEMM-2000/08.

[76] Sudret B. (2005), Des éléments finis stochastiques spectraux aux surfaces de réponses stochastiques : une approche unifiée, 17ème Congrès Français de Mécanique, Troyes, August 2005.

[77] Talagrand O., Courtier P. (1987), Variational assimilation of meteorological observations with the adjoint vorticity equation, I : theory. Q. J. R. Meteorol. Soc. 113.

[78] Tarantola (1987), Inverse Problem Theory and methods for data fitting and model parameter estimation, Elsevier - Amsterdam et Tarantola ( 2004), Inverse Problem Theory and methods for model parameter estimation, SIAM. | MR

[79] Von Neumann J., Morgenstern O., (1944), Theory of games and economic behavior, Princeton University Press. | MR | Zbl

[80] Walter E., Pronzato L. (1994), Identification de Modèles Paramétriques à partir de données expérimentales, Coll. MASC, Masson. | MR

[81] Wilks S. S. (1941), Determination of sample sizes for setting tolerance limits, Ann. Math. Statist. 12, pp. 91-96. | MR | Zbl