Identification methods in nonlinear heat conduction. Part II: Inverse problem using a reduced model

International Journal of Heat and Mass Transfer

Volumn 48, Issue 1, 2005, Pages 119-133

  Girault, Manuel ^a   Petit, Daniel ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTABILITY AND DECIDABILITY; COMPUTER SIMULATION; HEAT CONDUCTION; NONLINEAR CONTROL SYSTEMS; OPTIMIZATION; THERMAL CONDUCTIVITY;

DETAILED MODELS (DM); EULER IMPLICIT SCHEME; REDUCED MODELS (RM);

IDENTIFICATION (CONTROL SYSTEMS);

HEAT CONDUCTION; HEAT TRANSFER; MATHEMATICAL ANALYSIS; MODEL;

EID: 9244248068     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2004.06.033     Document Type: Article

References (20)

1. J.V. Beck, B. Blackwell, C.R. St Clair, Inverse Heat Conduction: Ill-posed Problems, John Wiley, New York, 1985.
2. A.N. Tikhonov, V.Y. Arsenin, Solutions of Ill-Posed Problems, V.H. Winston, Washington, DC, 1977.
3. O.M. Alifanov, Inverse Heat Transfer Problems, Springer-Verlag, New York, 1994.
4. J.R. Shenefelt, R. Luck, R.P. Taylor, J.T. Berry, Solution to inverse heat conduction problems employing singular value decomposition and model-reduction, Int. J. Heat Mass Transfer 45 (1) (2002) 67-74.
5. Y. Jarny, M.N. Ozisik, J.P. Bardon, A general optimization method using adjoint equation for solving multidimensional inverse heat conduction, Int. J. Heat Mass Transfer 34 (11) (1991) 2911-2919.
6. C.H. Huang, S.P. Wang, A three dimensional inverse heat conduction problem in estimating surface heat flux by conjugate gradient method, Int. J. Heat Mass Transfer 42 (18) (1999) 3387-3403.
7. O.M. Alifanov, A.V. Nenarokomov, Three-dimensional boundary inverse heat conduction problem for regular coordinate systems, Inverse Problems in Engineering 7 (4) (1999) 335-362.
8. J.V. Beck, Nonlinear estimation applied to the nonlinear inverse heat conduction problem, Int. J. Heat Mass Transfer 13 (4) (1970) 703-716.
9. J.V. Beck, B. Litkouhi, C.RS.t. Clair, Efficient sequential solution of the nonlinear inverse heat conduction problem, Numer. Heat Transfer 5 (1982) 275-286.
10. A.M. Osman, K.J. Dowding, J.V. Beck, Numerical solution of the general two-dimensional inverse heat conduction problem, Trans. ASME 119 (1997) 38-45.
11. R. Pasquetti, C. Le Niliot, Boundary element approach for inverse heat conduction problems: application to a bidimensional transient numerical experiment, Numer. Heat Transfer B 20 (1991) 169-189.
12. E. Videcoq, D. Petit, Model reduction for the resolution of multidimensional inverse heat conduction problems, Int. J. Heat Mass Transfer 44 (10) (2001) 1899-1911.
13. M. Girault, D. Petit, E. Videcoq, The use of model reduction and function decomposition for identifying boundary conditions of a linear thermal system, Inverse Problems Eng. 11 (5) (2003) 425-455.
14. H.M. Park, O.Y. Chung, J.H. Lee, On the solution of inverse heat transfer problem using the Karhunen-Loève-Galerkin method, Int. J. Heat Mass Transfer 42 (1) (1999) 127-142.
15. H.M. Park, W.S. Jung, The Karhunen-Loève-Galerkin method for the inverse natural convection problems, Int. J. Heat Mass Transfer 44 (1) (2001) 155-167.
16. A.J. Newman, Model reduction via the Karhunen-Loève expansion, Part I: an exposition, Technical Research Report of the Institute for Systems Research, University of Maryland, 1996. 〈http://s.isr.umd.edu/TechReports/ ISR/1996/TR_96-32/TR_96-32.phtml〉.
17. M. Girault, D. Petit, Identification methods in nonlinear heat conduction, Part I: model reduction, Int. J. Heat Mass Transfer, submitted for publication.
18. D. Petit, R. Hachette, D. Veyret, A modal identification method to reduce a high order model: application to heat conduction modelling, International Journal of Modelling and Simulation 17 (3) (1997) 242-250.
19. J.V. Beck, B. Blackwell, A. Haji-Sheikh, Comparison of some inverse heat conduction methods using experimental data, Int. J. Heat Mass Transfer 39 (17) (1996) 3649-3657.
20. G. Blanc, M. Raynaud, T.H. Chau, A guide for the use of the function specification method for 2D inverse heat conduction problems, Rev. Générale de Thermique 37 (1) (1998) 17-30.