Estimation of the parameters of a Gaussian heat source by the Levenberg-Marquardt method: Application to the electron beam welding

International Journal of Thermal Sciences

Volumn 46, Issue 2, 2007, Pages 128-138

  Rouquette, S ^a   Guo, J ^a   Le Masson, P ^a  

^a UNIVERSITÉ DE BRETAGNE SUD   (France)

Author keywords

Electron beam welding; Inverse problem; Levenberg Marquardt method

Indexed keywords

ELECTRON BEAM WELDING; HEAT TRANSFER; INVERSE PROBLEMS; NONLINEAR SYSTEMS; PARAMETER ESTIMATION; PROBLEM SOLVING;

LEVENBERG-MARQUARDT METHOD; LIQUID ZONE; LONGITUDINAL SECTION;

HEAT FLUX;

EID: 33751245883     PISSN: 12900729     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijthermalsci.2006.04.015     Document Type: Article

References (21)

1. J. Guo, P. Le Masson, E. Artioukhine, T. Loulou, P. Rogeon, M. Carin, M. Dumons, J. Costa, Estimation of a source term in a two dimensional heat transfer problem: Application to an electron beam welding, in: 4th Int. Conf. Inverse Problems, Russia, 2003
2. Beck J.V., Blackwell B., and Clair C.R.St. Inverse Heat Conduction: Ill Posed Problems (1985), Wiley Interscience, New York
3. Alifanov O.M., Artyukhin E., and Rumyantsev A. Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems (1995), Begell House, New York
4. Jarny Y., Ozisik N., and Bardon J.P. A general optimization method using adjoint equation for solving multidimensional inverse heat conduction. Int. J. Heat Mass Transfer 62 (1991) 2911-2919
5. Silva Neto A.J., et al. Two dimensional inverse heat conduction problem of estimating the time-varying strength of a line source. J. Appl. Phys. 171 (1992) 5357-5362
6. Le Niliot C. The boundary element method for the time varying strength estimation of point heat sources: Application to a two-dimensional diffusion system. Numer. Heat Transfer B 33 (1998) 301-321
7. Le Niliot C., et al. Infrared thermography applied to the resolution of inverse heat conduction problems: Recovery of heat line sources and boundary conditions. Rev. Gen. Therm. 37 (1998) 629-643
8. Peneau S., et al. Front motion and convective heat flux determination in a phase change process. Inverse Problem Engrg. 4 (1996) 53-91
9. Keanini R., et al. Inverse finite element reduced mesh method for predicting multidimensional phase change boundaries and nonlinear solid face heat transfer. Int. J. Heat Mass Transfer 39 (1996) 1039-1049
10. Hsu Y.F., et al. An inverse finite element method for the analysis of stationary arc welding processes. J. Heat Transfer 108 (1986) 734-741
11. Ruan Y., et al. An inverse finite element technique to determine the change of phase interface location in two dimensional melting problems. Commun. Appl. Numer. Methods 7 (1991) 325-338
12. Zabaras N. Adjoint methods for inverse free convection problems with application to solidification processes. Computational Methods for Optimal Design and Control (1998), Birkhäuser, Basel 391-426
13. Karkhin V., et al. Solution of inverse heat conduction problem for determining heat input, weld shape, and grain structure during laser welding. Sci. Tech. Welding Jioning 7 4 (2002) 224-231
14. Levenberg K. A method for the solution of certain non linear problems in least squares. Quart. Appl. Math. 2 (1944) 4164-4168
15. Marquardt D.W. An algorithm for least squares estimation of non linear parameters. J. Soc. Ind. Appl. Math. 11 (1963) 431-441
16. M. Costantini, Simulation numérique du soudage par faisceau d'électrons, contribution au développement d'un modèle prédictif de l'apport d'énergie, Thèse de l'université Paris 6, 1995
17. M. Carin, et al., Experimental validation of a predictive model for numerical simulation of thermo-metallurgical phenomena during electron beam welding, in: 2nd Int. Conf. on Thermal Process Modelling and Computer Simulation, France, 2003
18. Rogeon P., et al. Numerical simulation of electron beam welding of metals: sensitivity study of a predictive model. In: Cerjak H., and Bhadeshia H.K.D.H. (Eds). Mathematical Modelling of weld Phenomena 5 (2001), Institute of Materials 913-943
19. Handbook of Sysweld (1994), Systus International
20. Ozisik M.N., and Orlande H.R.B. Inverse Heat Transfer: Fundamentals and Applications (2000), Taylor and Francis, New York
21. J. Guo, Estimation de la distribution énergétique induite par un faisceau d'électrons dans un matériau métallique - Application au cas du soudage d'un acier, Thèse de l'université de Bretagne Sud, 2005