P. Brissonneau, ]. D. Jiles, and ]. E. Semail, Matériaux magnétiques en génie électriqueKedous-LeboucMatériaux magnétiques en génie électriquePhysique du génie électriqueContribution à la caractérisation et à la modélisation de matériaux magnétiques en vue d'une implantation dans un code de calcul de champ, Thèse de doctoratModélisation et caractérisation des matériaux magnétiques composites doux utilisés dans les machines électriques Thèse de doctorat, 1991.

G. Bertotti-]-m, R. Amar, and . Kaczmarek, General properties of power losses in soft ferromagnetic materials, IEEE Transactions on Magnetics, vol.24, issue.1, pp.621-630, 1995.
DOI : 10.1109/20.43994

A. Boglietti, A. Cavagnino, M. Lazzari, and M. Pastorelli, Two simplified methods for the iron losses prediction in soft magnetic materials supplied by PWM inverter, IEMDC 2001. IEEE International Electric Machines and Drives Conference (Cat. No.01EX485), pp.391-395, 2001.
DOI : 10.1109/IEMDC.2001.939331

A. Boglietti, A. Cavagnino, M. Lazzari, and M. Pastorelli, Predicting iron losses in soft magnetic materials with arbitrary voltage supply: an engineering approach, IEEE Transactions on Magnetics, vol.39, issue.2, pp.981-989
DOI : 10.1109/TMAG.2003.808599

A. Boglietti and A. Cavagnino, Iron loss prediction with PWM supply: An overview of proposed methods from an engineering application point of view, Proceedings of Industry Applications Conference, 42nd IAS Annual Meeting, pp.81-88, 2007.
DOI : 10.1016/j.epsr.2010.03.003

C. P. Steinmetz, On the law of hysteresis, American Institute of Electrical Engineers Transactions, vol.9, pp.3-64, 1982.

Y. Chen and P. Pillay, An improved formula for lamination core loss calculations in machines operating with high frequency and high flux density excitation, Industry Applications Conference, 37th IAS Annual meeting, pp.759-766, 2002.

D. M. Ionel, M. Popescu, S. J. Dellinger, T. J. Miller, R. J. Heideman et al., On the variation with flux and frequency of the core loss coefficients in electrical machines, IEEE Transactions on Industry Applications, vol.42, issue.3, pp.3-658, 2006.
DOI : 10.1109/TIA.2006.872941

M. Popescu and D. M. Ionel, A Best-Fit Model of Power Losses in Cold Rolled-Motor Lamination Steel Operating in a Wide Range of Frequency and Magnetization, IEEE Transactions on Magnetics, vol.43, issue.4, pp.1753-1756, 2007.
DOI : 10.1109/TMAG.2006.892291

D. M. Ionel, M. Popescu, M. I. Mcgilp, J. E. Miller, S. J. Dellinger et al., Computation of Core Losses in Electrical Machines Using Improved Models for Laminated Steel, IEEE Transactions on Industry Applications, vol.43, issue.6, pp.1554-1564, 2007.
DOI : 10.1109/TIA.2007.908159

Y. and O. Amor, Contribution à la modélisation de l'hystérésis magnétique en vue de l'analyse par éléments finis des systèmes de chauffage par induction, Thèse de doctorat, 2000.

F. C. Trutt, E. A. Erdélyi, and R. E. Hopkins, Representation of the Magnetization Characteristic of DC Machines for Computer Use, IEEE Transactions on Power Apparatus and Systems, vol.87, issue.3, pp.87-665, 1968.
DOI : 10.1109/TPAS.1968.292178

D. Jiles and D. Atherton, Theory of ferromagnetic hysteresis, Journal of Magnetism and Magnetic Materials, vol.61, issue.1-2, pp.48-60, 1986.
DOI : 10.1016/0304-8853(86)90066-1

Z. Wlodarski, Analytical description of magnetization curves, Physica B: Condensed Matter, vol.373, issue.2, pp.323-327, 2006.
DOI : 10.1016/j.physb.2005.12.242

N. Sadowski, N. J. Batistela, J. P. Bastos, and M. Lajoie-mazenc, An inverse Jiles-Atherton model to take into account hysteresis in time-stepping finite-element calculations, IEEE Transactions on Magnetics, vol.38, issue.2, pp.797-800, 2008.
DOI : 10.1109/20.996206

A. B. Ismail, Modélisation de la découpe des tôles ferromagnétiques-corrélation entre l'état mécanique et les propriétés magnétiques, Thèse de doctorat, 2007.

A. C. Smith and . Edey, Influence of manufacturing processes on iron losses, Seventh International Conference on Electrical Machines and Drives, pp.77-85, 1995.
DOI : 10.1049/cp:19950839

A. Boglietti, A. Cavagnino, M. Lazzari, and M. Pastorelli, Effects of punch process on the magnetic and energetic properties of soft magnetic material, IEMDC 2001. IEEE International Electric Machines and Drives Conference (Cat. No.01EX485), pp.396-399, 2001.
DOI : 10.1109/IEMDC.2001.939332

A. Kedous-lebouc, B. Cornut, J. C. Perrier, P. Manfé, and T. Chevalier, Punching influence on magnetic properties of the stator teeth of an induction motor, Journal of Magnetism and Magnetic Materials, vol.254, issue.255, pp.255124-126, 2003.
DOI : 10.1016/S0304-8853(02)00803-X

A. Schoppa, J. Schneider, and C. D. Wuppermann, Influence of the manufacturing process on the magnetic properties of non-oriented electrical steels, Journal of Magnetism and Magnetic Materials, vol.215, issue.216, pp.215-21674, 2000.
DOI : 10.1016/S0304-8853(00)00070-6

A. Schoppa, H. Louis, F. Pude, and C. Rad, Influence of abrasive waterjet cutting on the magnetic properties of non-oriented electrical steels, Journal of Magnetism and Magnetic Materials, vol.254, issue.255, pp.370-372, 2003.
DOI : 10.1016/S0304-8853(02)00882-X

L. Min, X. Yu-de, W. Wei, . Zhou-juan, . Wu-guang-liang et al., Effect of annealing parameter on microstructure and magnetic properties of cold rolled non-oriented electrical steel, Transactions of nonferrous metals society of China, vol.17, pp.74-78, 2007.

A. Marco, . Da-cunha, C. Sebastião, and . Paolinelli, Effect of the Annealing Temperature on the Structure and Magnetic Properties of 2% Si Steel, Materials research, vol.5, pp.373-378, 2002.

M. Emura, F. J. Landgraf, W. Ross, and J. R. Barretta, The influence of cutting technique on the magnetic properties of electrical steels, Journal of Magnetism and Magnetic Materials, vol.254, issue.255, pp.255-358, 2003.
DOI : 10.1016/S0304-8853(02)00856-9

A. Boglietti, A. Cavagnino, L. Ferraris, and M. Lazzari, The annealing influence onto the magnetic and energetic properties in soft magnetic material after punching process, IEEE International Electric Machines and Drives Conference, 2003. IEMDC'03., pp.503-508, 2003.
DOI : 10.1109/IEMDC.2003.1211310

W. M. Arshad, T. Ryckebush, F. Magnussen, H. Lendenmann, B. Eriksson et al., Incorporating Lamination Processing and Component Manufacturing in Electrical Machine Design Tools, 2007 IEEE Industry Applications Annual Meeting, pp.94-102, 2007.
DOI : 10.1109/07IAS.2007.21

F. Libert and J. Soulard, Manufacturing methods of stator cores with concentrated windings, 3rd IET International Conference on Power Electronics, Machines and Drives (PEMD 2006), pp.676-680, 2006.
DOI : 10.1049/cp:20060194

A. Schoppa, J. Schneider, C. D. Wuppermann, and T. Bakon, Influence of welding and sticking of laminations on the magnetic properties of non-oriented electrical steels, Journal of Magnetism and Magnetic Materials, vol.254, issue.255, pp.255-367, 2003.
DOI : 10.1016/S0304-8853(02)00877-6

G. Bertotti, Physical interpretation of eddy current losses in ferromagnetic materials. I. Theoretical considerations, Journal of Applied Physics, vol.57, issue.6, pp.2110-2117, 1985.
DOI : 10.1063/1.334404

V. Permiakov, 1D and 2D magnetization in electrical steels under uniaxial stresses, 2004.

G. Bertotti, Hysteresis in magnetism, For physicists, Materials Scientists, and Engineers, 1998.

K. Chwastek_ and J. Szczyglowski, An alternative method to estimate the parameters of Jiles???Atherton model, Journal of Magnetism and Magnetic Materials, vol.314, issue.1, pp.47-51, 2007.
DOI : 10.1016/j.jmmm.2007.02.157

D. Jiles, J. Thoelke, and M. Devine, Numerical determination of hysteresis parameters for the modeling of magnetic properties using the theory of ferromagnetic hysteresis, IEEE Transactions on Magnetics, vol.28, issue.1, pp.27-35, 1992.
DOI : 10.1109/20.119813

D. Lederer, H. Igarashi, A. Kost, and T. Honma, On the parameter identification and application of the Jiles-Atherton hysteresis model for numerical modelling of measured characteristics, IEEE Transactions on Magnetics, vol.35, issue.3, pp.1211-1214, 1999.
DOI : 10.1109/20.767167

A. J. Moses, N. Derebasi, G. Loisos, and A. Schoppa, Aspects of the cut-edge effect stress on the power loss and flux density distribution in electrical steel sheets, Journal of Magnetism and Magnetic Materials, vol.215, issue.216, pp.215-216, 2000.
DOI : 10.1016/S0304-8853(00)00260-2

G. Loisos and A. J. Moses, Effect of mechanical and Nd:YAG laser cutting on magnetic flux distribution near the cut edge of non-oriented steels, Journal of Materials Processing Technology, vol.161, issue.1-2, pp.151-155, 2005.
DOI : 10.1016/j.jmatprotec.2004.07.061

T. Nakata, M. Nakano, and K. Kawahara, Effects of Stress Due to Cutting on Magnetic Characteristics of Silicon Steel, IEEE Translation Journal on Magnetics in Japan, vol.7, issue.6, pp.453-457, 1992.
DOI : 10.1109/TJMJ.1992.4565422

K. Protassov, Analyse statistique des données expérimentales, Edp Sciences, 2002.

R. Veysseyere, Statistique et probabilité pour l'ingénieur, Edition Dunod, 2001.

F. Perrin, Prise en compte des données expérimentales dans les modèles probabilistes pour la prévision de la durée de vie des structures, Thèse de doctorat, 2008.

R. Rakotomalala, Comparaison de populations et tests non paramétriques, 2008.

S. Zheng, Modeling and Inclusion of Geometric Uncertainties in the Assessment of a Stator, Advanced Production System in KIMP, Arts et Métiers ParisTech, 2011.

K. Protassov, Analyse statistique des données expérimentales, Edp Sciences, 2002.

R. Veysseyere, Statistique et probabilité pour l'ingénieur, Edition Dunod, 2001.

F. Perrin, Prise en compte des données expérimentales dans les modèles probabilistes pour la prévision de la durée de vie des structures, Thèse de doctorat, 2008.

E. T. Jaynes, Information Theory and Statistical Mechanics, Physical Review, vol.106, issue.4, pp.620-630, 1957.
DOI : 10.1103/PhysRev.106.620

A. M. Djafari, A. E. Ouni, I. Masson, E. Allaire, and M. Zidi, Entropie en traitement du signalMaximum d'entropie et problèmes inverses en imagerieStochastic approach to estimate the arterial pressureApplication of maximum entropy principle for reliabilitybased design optimization, European Journal of Mechanics A/Solids, vol.28, pp.712-719, 2008.

I. J. Myung, Tutorial on maximum likelihood estimation, Journal of Mathematical Psychology, vol.47, issue.1, pp.90-100, 2003.
DOI : 10.1016/S0022-2496(02)00028-7

C. Soize, E. Capiez-lernout, J. Durand, C. Fernandez, and L. Gagliardini-b, Probabilistic model identification of uncertainties in computational models for dynamical systems and experimental validation, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.1, pp.150-163, 2008.
DOI : 10.1016/j.cma.2008.04.007

URL : https://hal.archives-ouvertes.fr/hal-00686138

K. Onder-cetina, A. Der-kiureghianb, and R. B. Seedb, Probabilistic models for the initiation of seismic soil liquefaction, Structural Safety, vol.24, issue.1, pp.67-82, 2002.
DOI : 10.1016/S0167-4730(02)00036-X

M. Livny, R. Ramakrishnan, and T. Zhang, Fast density and Probability estimation using CF-Kernel Method for very large databases, 1996.

-. D. Fougère and . Verger, Estimation des distributions de revenu par des méthodes non paramétriques, INSEE Méthodes, pp.59-60

D. Faucher and -. Bobée, Nonparametric estimation of quantiles by the kernel method, Revue des sciences de l'eau, pp.2-515, 2002.
DOI : 10.7202/705467ar

I. Amadha-e and . Flachaire, Econométrie non paramétrique, Edition Economica, issue.67, 2008.

A. B. Tsybakov, Introduction à l'estimation non paramétrique, 2004.

N. Christopeit, Estimating parameters of an extreme value distribution by the method of moments, Journal of Statistical Planning and Inference, vol.41, issue.2, 1994.
DOI : 10.1016/0378-3758(94)90162-7

N. Hyvert, C. Perlot, P. Rougeau, A. Sellier, and F. Duprat, Approche probabiliste de la durabilité: intérêt pour l'optimisation des produits préfabriqués, p.10, 2006.

J. Lecoutre and P. Tassi, Statistique non paramétrique et robustesse, 1987.

P. Capéraà and B. Van-cutsem, Méthodes et modèles en statistique non paramétrique- Exposé fondamental, 1988.

S. Siegel and N. J. Castellan-jr, Non parametric statistics for the behavioral sciences, 1988.

R. Rakotomalala, Comparaison de populations et tests non paramétriques, 2008.

P. Paris and F. Erdogan, A Critical Analysis of Crack Propagation Laws, Journal of Basic Engineering, vol.85, issue.4, pp.528-534, 1963.
DOI : 10.1115/1.3656900

W. F. Wu and C. C. Ni, A study of stochastic fatigue crack growth modeling through experimental data, Probabilistic Engineering Mechanics, vol.18, issue.2, pp.107-118, 2003.
DOI : 10.1016/S0266-8920(02)00053-X

W. Shen, A. B. Soboyejo, and W. O. Soboyejo, Probabilistic modeling of fatigue crack growth in Ti???6Al???4V, International Journal of Fatigue, vol.23, issue.10, pp.917-925, 2001.
DOI : 10.1016/S0142-1123(01)00045-7

A. Mehrez, D. Doostan, D. Moens, and . Vandepitte, A Validation Study of a Stochastic Representation of Composite Material Properties from Limited Experimental Data, Proceedings of ISMA, 2010.

D. A. Virkler, B. M. Hillberry, and P. K. Goel, The Statistical Nature of Fatigue Crack Propagation, Journal of Engineering Materials and Technology, vol.101, issue.2, pp.148-153, 1979.
DOI : 10.1115/1.3443666

O. Ditlevsen and R. Olesen, Statistical analysis of the virkler data on fatigue crack growth, Engineering Fracture Mechanics, vol.25, issue.2, pp.177-195, 1986.
DOI : 10.1016/0013-7944(86)90217-1

Z. A. Kotulski, On efficiency of identification of a stochastic crack propagation model based on Virkler experimental data, Archives of Mechanics, vol.50, issue.5, pp.829-847, 1998.

A. E. Hassan, A Methodology for Validating Numerical Ground Water Models, Ground Water, vol.2, issue.6, pp.347-362, 2004.
DOI : 10.1029/98WR00003

P. Cornillon and E. M. Lober, Régression, théorie et application, 2007.

R. Kohavi, A Study of Cross-Validation and Bootstrap for Accuracy Estimation and Model Selection, Proceedings of the 14th international joint conference on Artificial intelligence, pp.1137-1143, 1995.

P. Refaeilzadeh, L. Tang, and H. Liu, Cross-Validation, 2008.
DOI : 10.1007/978-1-4899-7993-3_565-2

S. Arlot, A survey of cross-validation procedures for model selection, Statistics Surveys, vol.4, issue.0, pp.40-79, 2010.
DOI : 10.1214/09-SS054

URL : https://hal.archives-ouvertes.fr/hal-00407906

B. Efron and G. Gong, A Leisurely look at the bootstrap, the jackknife and cross validation, The American Statistician, vol.37, pp.36-48, 1983.

S. M. Lynch, Introduction to applied bayesian statistics and estimation for social scientists, 2006.
DOI : 10.1007/978-0-387-71265-9

R. Cross, A. Makeev, and E. Armanios, Simultaneous uncertainty quantification of fracture mechanics based life prediction model parameters, International Journal of Fatigue, vol.29, issue.8, pp.1510-1515, 2007.
DOI : 10.1016/j.ijfatigue.2006.10.027

A. O-'hagan and J. Forster, Kendall's advanced theory of statistics, Edition Chichester: J.Wiley&son, vol.2, 2004.

L. Mehrez1, A. Doostan, D. Moens1, and D. Vandepitte, A Validation Study of a Stochastic Representation of Composite Material Properties from Limited Experimental Data, Proceedings of ISMA, 2010.

R. L. Iman and W. J. Conover, A distribution-free approach to inducing rank correlation among input variables, Communications in Statistics - Simulation and Computation, vol.13, issue.4, pp.311-334, 1982.
DOI : 10.1080/00401706.1962.10490011

X. Zhang, GENERATING CORRELATIVE STORM VARIABLES FOR CLIGEN USING A DISTRIBUTION-FREE APPROACH, Transactions of the ASAE, vol.48, issue.2, pp.567-575, 2005.
DOI : 10.13031/2013.18331

I. Yang, Distribution-Free Monte Carlo Simulation: Premise and Refinement, Journal of Construction Engineering and Management, vol.134, issue.5, pp.352-360, 2008.
DOI : 10.1061/(ASCE)0733-9364(2008)134:5(352)

N. A. Shamm, J. W. Hall, and M. G. Anderson, Variance based sensitivity analysis of the probability of hydrologically induced slope instability, Comput. Geosci, vol.32, issue.6, pp.803-817, 2006.

R. E. Moore, R. B. Kearfott, and M. J. Cloud, Introduction to interval analysis, 2009.
DOI : 10.1137/1.9780898717716

Y. Rollet, Vers une maîtrise des incertitudes en calculs des structures composites, thèse de doctorat de l'école polytechnique, Mécanique et Matériaux, 2007.

K. O. Arras, An Introduction To Error Propagation: Derivation,Meaning and Examples of Equation, 1998.

B. Zidaric and D. Miljavec, J-A hysteresis model parameters estimation using GA, Advances in electrical and electronic engineering, pp.174-177, 2005.

J. V. Leite, S. L. Avila, N. J. Batistela, W. P. Carpes-jr, N. Sadowski et al., Real Coded Genetic Algorithm for Jiles???Atherton Model Parameters Identification, IEEE Transactions on Magnetics, vol.40, issue.2, pp.888-891, 2004.
DOI : 10.1109/TMAG.2004.825319

URL : https://hal.archives-ouvertes.fr/hal-00125380

P. R. Wilson, J. N. Ross, and A. D. Brown, Optimizing the Jiles-Atherton model of hysteresis by a genetic algorithm, IEEE Transactions on Magnetics, vol.37, issue.2, pp.989-993, 2002.
DOI : 10.1109/20.917182

D. Lederer, H. Igarashi, A. Kost, and T. Honma, On the parameter identification and application of the Jiles-Atherton hysteresis model for numerical modelling of measured characteristics, IEEE Transactions on Magnetics, vol.35, issue.3, pp.1211-1214, 1999.
DOI : 10.1109/20.767167

E. D. Hernandez, C. S. Muranaka, and J. R. Cardoso, Identification of the Jiles???Atherton model parameters using random and deterministic searches, Physica B: Condensed Matter, vol.275, issue.1-3, pp.212-215, 2000.
DOI : 10.1016/S0921-4526(99)00766-8

D. Miljavec and B. Zidaric, Introducing a domain flexing function in the Jiles???Atherton hysteresis model, Journal of Magnetism and Magnetic Materials, vol.320, issue.5, pp.763-768, 2008.
DOI : 10.1016/j.jmmm.2007.08.016

M. Toman, G. Stumberger, and D. Dolinar, Parameter Identification of the Jiles–Atherton Hysteresis Model Using Differential Evolution, IEEE Transactions on Magnetics, vol.44, issue.6, pp.1098-1101, 2008.
DOI : 10.1109/TMAG.2007.915947

Z. Wlodarski, The Jiles-Atherton model with variable pinning parameter, IEEE Transactions on Magnetics, vol.39, issue.4, 1990.
DOI : 10.1109/TMAG.2003.812716

A. Sklar, Fonctions de répartition à n dimensions et leurs marges, pp.229-231, 1959.

E. W. Frees and E. A. Valdez, Understanding Relationships Using Copulas, North American Actuarial Journal, vol.82, issue.5, p.1, 1997.
DOI : 10.1080/10920277.1998.10595667

B. Renard and M. Lang, Use of a Gaussian copula for multivariate extreme value analysis: Some case studies in hydrology, Advances in Water Resources, vol.30, issue.4, pp.897-912, 2007.
DOI : 10.1016/j.advwatres.2006.08.001

URL : https://hal.archives-ouvertes.fr/hal-00453788

M. Al-harthy, S. Begg, and R. B. Bratvold, Copulas: A new technique to model dependence in petroleum decision making, Journal of Petroleum Science and Engineering, vol.57, issue.1-2, pp.195-208, 2007.
DOI : 10.1016/j.petrol.2005.10.015

F. C. Wu and Y. P. Tsang, Second-order Monte Carlo uncertainty/variability analysis using correlated model parameters: application to salmonid embryo survival risk assessment, Ecological Modelling, vol.177, issue.3-4, pp.393-414, 2004.
DOI : 10.1016/j.ecolmodel.2004.02.016

N. Ilich, A matching algorithm for generation of statistically dependent random variables with arbitrary marginals, European Journal of Operational Research, vol.192, issue.2, pp.468-478, 2009.
DOI : 10.1016/j.ejor.2007.09.024

M. E. Johnson and J. S. Ramberg, Transformations of the Multivariate Normal Distribution with Applications to Simulation, 1977.

M. C. Cario and B. L. Nelson, Numerical Methods for Fitting and Simulating Autoregressive-to-Anything Processes, INFORMS Journal on Computing, vol.10, issue.1, pp.72-81, 1997.
DOI : 10.1287/ijoc.10.1.72

B. Biller and B. L. Nelson, Modeling and generation multivariate time series input processing using a vector autoregressive technique, ACM Transactions on Modeling and Computer Simulation, vol.18, issue.3, pp.211-237, 2003.

D. C. Charmpis and P. L. Panteli, A heuristic approach for the generation of multivariate random samples with specified marginal distributions and correlation matrix, Computational Statistics, vol.48, issue.3, pp.283-300, 2004.
DOI : 10.1007/BF02892061

R. B. Nelsen, An introduction to copulas, Lecture Notes in Statistics, vol.139, 1999.
DOI : 10.1007/978-1-4757-3076-0

H. Joe, Multivariate Models and Dependence Concepts, Monographs on Statistics and Applied Probability, 1997.

N. Pujol, L. Neppel, and R. Sabatier, Modélisation multivariée des précipitations maxannuelles par copules pour l'étude de stationnarité des pluies méditerranéennes françaises, congrès IWRA, 2008.

R. Ghanem and P. Spanos, Stochastic finite elements -A spectral approach, 1991.
DOI : 10.1007/978-1-4612-3094-6

R. Gaignaire, Contribution à la modélisation numérique en électromagnétisme statique stochastique, these de doctorat Arts et Métiers ParisTech, 2008.

D. H. Mac, Résolution numérique en électromagnétisme statique de problèmes aux incertitudes géométriques par la méthode de transformation : Application aux machines électriques, thèse de Doctorat, Arts et Métiers ParisTech, p.2012

K. Beddek, Propagation d'incertitudes dans les modèles éléments finis en électromagnétisme-Application au contrôle non destructif par courants de Foucault, thèse de Doctorat, p.2012

C. Cester, Etude des pertes magnétiques supplémentaires dans les machines asynchrones alimentées par onduleur à modulation de largeur d'impulsion, Thèse de Doctorat, INPG, 1996.

T. Chevalier, Modélisation et mesure des pertes fer dans les machines électriques, application à la machine asynchrone, Thèse de Doctorat, INPG, 1999.

T. Gautreau, Estimation des pertes fer dans les machines électriques. Modèle d'hystérésis loss surface et application aux machines synchrones à aimants, Thèse de Doctorat, INPG, 2005.

F. Preisach, Uber die magnetische nachwirfung, Zeitschrift fur Physik, pp.277-302, 1935.