J. V. Aguado, D. Borzacchiello, C. Ghnatios, F. Lebel, R. Upadhyay et al., A simulation app based on reduced order modeling for manufacturing optimization of composite outlet guide vanes. Advanced Modeling and Simulation in Engineering Sciences, vol.4, p.38, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01925863

D. C. Aiguilera, Advanced Numerical Simulations for Conventional and NonConventional Welding Processes : A Model Order Reduction Approach, p.38, 2017.

D. Albrecht, Calcul des déformations induites par un rechargement de type overlay, vol.88, p.117, 2013.

D. Albrecht, Etude des déformations sur tuyauteries dues à des rechargements de type overlay et patch : Modélisation et simulations thermiques, vol.112, p.117, 2013.

F. Alias and A. Pruvost, Appropriation et état des lieux de l'utilisation de la technique de réparation par rechargement overlay. D450712007073, p.110, 2012.

A. Ammar, B. Mokdad, F. Chinesta, and R. Keunings, A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids : Part ii : Transient simulation using space-time separated representations, Journal of Non-Newtonian Fluid Mechanics, vol.144, issue.2, p.37, 2007.
URL : https://hal.archives-ouvertes.fr/hal-01633241

A. Ammar, E. Pruliere, J. Férec, F. Chinesta, and E. Cueto, Coupling finite elements and reduced approximation bases, European Journal of Computational Mechanics/Revue Européenne de Mécanique Numérique, vol.18, issue.5-6, p.73, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01006702

A. Andrieu, Mécanismes et modélisation multi-échelle de la rupture fragile trans-et inter-granulaire des aciers rep en lien avec le vieillissement thermique, 2013.

J. Angles, Notice d'utilisation pour la simulation numérique du soudage, p.10, 2010.

O. Asserin, M. Afzali, F. Boitout, P. Gilles, and D. Lawrjaniec, Simulation numerique du soudage : Le projet multipartenaire musica, vol.25, p.26

J. Baiges, R. Codina, and S. Idelsohn, A domain decomposition strategy for reduced order models. application to the incompressible navier-stokes equations, Computer Methods in Applied Mechanics and Engineering, vol.267, p.73, 2013.

M. Barrault, Y. Maday, N. C. Nguyen, and A. T. Patera, An 'empirical interpolation'method : application to efficient reduced-basis discretization of partial differential equations, Comptes Rendus Mathematique, vol.339, issue.9, p.38, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00021702

G. Billard and D. Bergeot, Cahier des clauses techniques particulières pour rechargement des tubes amont et aval des tuyères app 001 et 002 yp sur les tuyauteries 5 app 535 ty-6 app 534 ty-6 app 535 ty. D5130DTMSFDI-RECHARGEMENT, p.110, 2008.

B. Bognet, F. Bordeu, F. Chinesta, A. Leygue, and A. Poitou, Advanced simulation of models defined in plate geometries : 3d solutions with 2d computational complexity, Computer Methods in Applied Mechanics and Engineering, vol.201, p.38, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01462825

M. Bonnet and A. Frangi, Analyse des solides déformables par la méthode des éléments finis. Ecole Polytechnique, p.20, 2005.

M. Brand, Incremental singular value decomposition of uncertain data with missing values, p.31, 2002.

K. Carlberg, C. Farhat, J. Cortial, and D. Amsallem, The gnat method for nonlinear model reduction : effective implementation and application to computational fluid dynamics and turbulent flows, Journal of Computational Physics, vol.242, p.38, 2013.

H. B. Cary, Modern welding technology, 1979.

S. Chaturantabut and D. C. Sorensen, Nonlinear model reduction via discrete empirical interpolation, SIAM Journal on Scientific Computing, vol.32, issue.5, p.48, 2010.

S. Chaturantabut and D. C. Sorensen, A state space error estimate for pod-deim nonlinear model reduction, SIAM Journal on numerical analysis, vol.50, issue.1, p.36, 2012.

F. Chinesta, A. Ammar, and E. Cueto, Proper generalized decomposition of multiscale models, International Journal for Numerical Methods in Engineering, vol.83, issue.8-9, p.37, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01007223

F. Chinesta, A. Leygue, F. Bordeu, J. V. Aguado, E. Cueto et al., Pgd-based computational vademecum for efficient design, optimization and control, Archives of Computational methods in Engineering, vol.20, issue.1, p.37, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01515083

J. Cognard, P. Ladeveze, and P. Talbot, A large time increment approach for thermo-mechanical problems, Advances in Engineering Software, vol.30, issue.9, p.37, 1999.

B. Cohen, Note technique : Justification des réparations effectuées en 2008 sur les lignes 5 app 534 et 535 ty du cnpe de gravelines. D4507081270, p.110, 2008.

A. Cosimo, A. Cardona, and S. Idelsohn, Improving the k-compressibility of hyper reduced order models with moving sources : applications to welding and phase change problems, Computer Methods in Applied Mechanics and Engineering, vol.274, p.36, 2014.

L. De-lathauwer, B. D. Moor, and J. Vandewalle, A multilinear singular value decomposition, SIAM journal on Matrix Analysis and Applications, vol.21, issue.4, p.34, 2000.

L. Depradeux, Simulation numérique du soudage-acier 316L : validation sur cas tests de complexité croissante, p.16, 2004.

G. Dhatt and G. Touzot, Une présentation de la méthode des éléments finis, p.20, 1981.

R. Dony, Karhunen-loeve transform. The transform and data compression handbook, vol.1, p.29, 2001.

Y. Duan, F. Boitout, J. Leblond, and J. Bergheau, Simulation numérique du soudage de grandes structures par une approche locale/globale, Mécanique & Industries, vol.9, issue.2, p.25, 2008.

R. Everson and L. Sirovich, Karhunen-loeve procedure for gappy data, JOSA A, vol.12, issue.8, p.51, 1995.

L. D. Rossillon, Méthode simplifiée de simulation numérique du soudage multipasses, p.24, 2013.

A. Falco and A. Nouy, A proper generalized decomposition for the solution of elliptic problems in abstract form by using a functional eckart-young approach, Journal of Mathematical Analysis and Applications, vol.376, issue.2, p.38, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00461094

C. Farhat, P. Avery, T. Chapman, and J. Cortial, Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency, International Journal for Numerical Methods in Engineering, vol.98, issue.9, p.39, 2014.

Z. Feng, Processes and mechanisms of welding residual stress and distortion, p.12, 2005.

D. Galbally, K. Fidkowski, K. Willcox, and O. Ghattas, Non-linear model reduction for uncertainty quantification in large-scale inverse problems, International journal for numerical methods in engineering, vol.81, issue.12, p.38, 2010.

K. Ganesh, M. Vasudevan, K. Balasubramanian, N. Chandrasekhar, S. Mahadevan et al., Modeling, prediction and validation of thermal cycles, residual stresses and distortion in type 316 ln stainless steel weld joint made by tig welding process, Procedia Engineering, vol.86, issue.13, pp.767-774, 2014.

C. Ghnatios, F. Masson, A. Huerta, A. Leygue, E. Cueto et al., Proper generalized decomposition based dynamic data-driven control of thermal processes, Computer Methods in Applied Mechanics and Engineering, vol.213, p.37, 2012.
URL : https://hal.archives-ouvertes.fr/hal-01728702

M. A. Grepl, Y. Maday, N. C. Nguyen, and A. T. Patera, Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations, ESAIM : Mathematical Modelling and Numerical Analysis, vol.41, issue.3, p.35, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00112154

H. He, T. Wang, and G. Chen, A hybrid coordinates component mode synthesis method for dynamic analysis of structures with localized nonlinearities, Journal of Vibration and Acoustics, vol.138, issue.3, p.73, 2016.

H. Hotelling, New light on the correlation coefficient and its transforms, Journal of the Royal Statistical Society. Series B (Methodological), vol.15, issue.2, p.29, 1953.

P. Kerfriden, J. Passieux, S. P. , and -. Bordas, Local/global model order reduction strategy for the simulation of quasi-brittle fracture, International Journal for Numerical Methods in Engineering, vol.89, issue.2, p.73, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00614657

E. Kim, M. Bernier, O. Cauret, and J. Roux, A hybrid reduced model for borehole heat exchangers over different time-scales and regions, vol.77, p.73, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01068942

M. Kirby and L. Sirovich, Application of the karhunen-loeve procedure for the characterization of human faces, IEEE Transactions on Pattern analysis and Machine intelligence, vol.12, issue.1, p.37, 1990.

S. Kou, Welding metallurgy, vol.8, 2003.

K. Koudadje, Etude expérimentale et modélisation numérique du bain de fusion en soudage TIG d'aciers, 2013.

P. Ladevèze, Sur une famille d'algorithmes en mécanique des structures. Comptes-rendus des séances de l'Académie des sciences. Série 2, Mécanique-physique, chimie, sciences de l'univers, sciences de la terre, vol.300, p.37, 1985.

P. Ladevèze and P. Germain, La méthode à grand incrément de temps pour l'analyse de structures à comportement non linéaire décrit par variables internes. Comptes rendus de l'Académie des sciences. Série 2, Mécanique, Physique, Chimie, Sciences de l'univers, Sciences de la Terre, vol.309, issue.11, p.37, 1989.

D. Lawrjaniec, O. Asserin, F. Boitout, P. Gilles, H. Lieurade et al., Vers une simplification de la mise en oeuvre et une meilleure prédictibilité de la simulation du soudage, Soudage et techniques connexes, vol.64, p.26, 2010.

J. Lumley and B. Podvin, Dynamical systems theory and extra rates of strain in turbulent flows. Experimental thermal and fluid science, vol.13, p.39, 1996.

J. L. Lumley, Atmospheric turbulence and radio wave propagation, p.29, 1967.

J. Maton, , vol.5, p.6, 2014.

A. Michaut, Note technique : Etude des réparations de la ligne 1 app 534 ty-6 au niveau des tubes 14 et 16 de la tranche 1 de gravelines. D4507081681, p.110, 2009.

A. Nouy, A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.23, p.37, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00455635

C. Of, ASME Boiler and pressure Vessel Code. Code cases n-561-1. alternative requirements for wall thickness restoration of class 2 and high energy class 3 carbon steel piping section xi, p.109, 1998.

S. Perotto, A. Ern, and A. Veneziani, Hierarchical local model reduction for elliptic problems : a domain decomposition approach, Multiscale Modeling & Simulation, vol.8, issue.4, p.38, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00377492

E. Prulière, J. Férec, F. Chinesta, and A. Ammar, An efficient reduced simulation of residual stresses in composite forming processes, International Journal of Material Forming, vol.3, p.38, 2010.

A. Quarteroni, A. Manzoni, and F. Negri, Reduced basis methods for partial differential equations : an introduction, vol.92, p.35, 2015.

A. Radermacher and S. Reese, Model reduction in elastoplasticity : proper orthogonal decomposition combined with adaptive sub-structuring, Computational Mechanics, vol.54, issue.3, p.73, 2014.

D. Ryckelynck, Réduction a priori de modèles thermomécaniques, Comptes Rendus Mécanique, vol.330, issue.7, p.27, 2002.

D. Ryckelynck, A priori hyperreduction method : an adaptive approach, Journal of computational physics, vol.202, issue.1, p.68, 2005.

D. Ryckelynck, Hyper-reduction of mechanical models involving internal variables, International Journal for Numerical Methods in Engineering, vol.77, issue.1, p.51, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00359157

D. Ryckelynck and D. M. Benziane, Multi-level a priori hyper-reduction of mechanical models involving internal variables, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.17, p.39, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00461492

D. Ryckelynck, F. Chinesta, E. Cueto, and A. Ammar, On the a priori model reduction : overview and recent developments, Archives of Computational methods in Engineering, vol.13, issue.1, p.31, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01007164

D. Ryckelynck, L. Gallimard, and S. Jules, Estimation of the validity domain of hyper-reduction approximations in generalized standard elastoviscoplasticity. Advanced Modeling and Simulation in Engineering Sciences, vol.2, p.61, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01237733

D. Ryckelynck, K. Lampoh, and S. Quilicy, Hyper-reduced predictions for lifetime assessment of elasto-plastic structures, Meccanica, vol.51, issue.2, p.42, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01295849

D. Ryckelynck, F. Vincent, and S. Cantournet, Multidimensional a priori hyperreduction of mechanical models involving internal variables, Computer Methods in Applied Mechanics and Engineering, vol.225, p.39, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00705783

P. Saini, C. M. Arndt, and A. M. Steinberg, Development and evaluation of gappy-pod as a data reconstruction technique for noisy piv measurements in gas turbine combustors, Experiments in Fluids, vol.57, issue.7, p.37, 2016.

L. Sirovich, Turbulence and the dynamics of coherent structures. i. coherent structures, Quarterly of applied mathematics, vol.45, issue.3, p.29, 1987.

N. T. Trinh, Sur la modélisation du comportement thermomécanique et métal-lurgique des aciers. Application au procédé de soudage et de traitements thermiques, 2008.

L. R. Tucker, Some mathematical notes on three-mode factor analysis, Psychometrika, vol.31, issue.3, p.34, 1966.

M. Turlure, Ecart nécessitant une analyse mécanique. analyse de nocivité des indications non volumiques dans la soudure circulaire a3-a4 de l'échangeur 0se002ex de cruas, vol.09083, p.110, 2009.

Y. Ueda, H. Murakawa, and N. Ma, Welding deformation and residual stress prevention, p.12, 2012.

S. Volkwein, Model reduction using proper orthogonal decomposition, Lecture Notes, Institute of Mathematics and Scientific Computing, p.31, 2011.

L. X. Wang and R. V. Melnik, Model reduction applied to square to rectangular martensitic transformations using proper orthogonal decomposition, Applied numerical mathematics, vol.57, issue.5-7, p.35, 2007.

K. Willcox, Unsteady flow sensing and estimation via the gappy proper orthogonal decomposition, Computers & fluids, vol.35, issue.2, p.37, 2006.

Y. Zhang, A. Combescure, and A. Gravouil, Efficient hyper reduced-order model (hrom) for parametric studies of the 3d thermo-elasto-plastic calculation, Finite Elements in Analysis and Design, vol.102, p.39, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01442852

Y. Zhang, A. Combescure, and A. Gravouil, Modèle thermique hyper-réduit avec source mobile : formulation dans le repère mobile. S01 Modélisation avancée en mécanique des solides et des fluides, p.39, 2015.