Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced. To this end, several configurations are detailed and effects of noisy observations are investigated.
@article{bwmeta1.element.bwnjournal-article-amcv26i3p623bwm,
author = {Sara Beddiaf and Laurent Autrique and Laetitia Perez and Jean-Claude Jolly},
title = {Heating source localization in a reduced time},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {26},
year = {2016},
pages = {623-640},
zbl = {1304.65213},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv26i3p623bwm}
}
Sara Beddiaf; Laurent Autrique; Laetitia Perez; Jean-Claude Jolly. Heating source localization in a reduced time. International Journal of Applied Mathematics and Computer Science, Tome 26 (2016) pp. 623-640. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv26i3p623bwm/
[000] Alifanov, O.M. (1994). Inverse Heat Transfer Problems, Springer-Verlag, Berlin. | Zbl 0979.80003
[001] Alifanov, O.M., Artyukhin, E.A. and Rumyantsev, S.V. (1995). Extreme Methods for Solving Ill Posed Problems with Applications to Inverse Heat Transfer Problems, Begell House, New York, NY. | Zbl 1006.35001
[002] Autrique, L., Chaussavoine, C., Leyris, J. and Ferriere, A. (2000). Optimal sensor strategy for parametric identification of a thermal system, Proceedings of IFACSYSID 2000, Santa Barbara, CA, USA.
[003] Autrique, L., Leyris, J. and Ramdani, N. (2002). Optimal sensor location: An experimental process for the identification of moving heat sources, Proceedings of the 15th World Congress IFAC, Barcelona, Spain.
[004] Beck, J. and Arnold, K. (1977). Parameter Estimation in Engineering and Science, John Wiley and Sons, New York, NY. | Zbl 0363.62020
[005] Chen, M., Berkowitz-Mattuck, J.B. and Glaser, P.E. (1963). The use of a kaleidoscope to obtain uniform flux over a large area in a solar or arc imaging furnace, Applied Optics 2(3): 265-271.
[006] Daouas, N. and Radhouani, M. (2004). A new approach of the Kalman filter using future temperature measurements for nonlinear inverse heat conduction problem, Numerical Heat Transfer 45(6): 565-585.
[007] Daouas, N. and Radhouani, M. (2007). Experimental validation of an extended Kalman smoothing technique for solving nonlinear inverse heat conduction problems, Inverse Problems in Science and Engineering 15(7): 765-782. | Zbl 1157.80319
[008] Egger, H., Heng, Y., Marquardt, W. and Mhamdi, A. (2009). Efficient solution of a three-dimensional inverse heat conduction problem in pool boiling, Inverse Problems 25(9), Article ID: 095006. | Zbl 1173.35726
[009] Girault, M., Videcoq, E. and Petit, D. (2010). Estimation of time-varying heat sources through inversion of a low order model built with the modal identification method from in-situ temperature measurements, Journal of Heat and Mass Transfer 53: 206-219. | Zbl 1180.80055
[010] Hager, W. and Zhang, H. (2006). A survey of nonlinear conjugate gradient method, Pacific Journal of Optimization 2(1): 35-58. | Zbl 1117.90048
[011] Hasanov, A. and Pektas, B. (2013). Identification of an unknown time-dependent heat source term from overspecified Dirichlet boundary data by conjugate gradient method, Computers and Mathematics with Applications 65(1): 42-57. | Zbl 1268.65129
[012] Huang, C. and Chen, W. (1999). A three-dimensional inverse forced convection problem in estimating surface heat flux by conjugate gradient method, International Journal of Heat and Mass Transfer 43(17): 3171-3181. | Zbl 1094.76566
[013] Isakov, V. (1998). Inverse Problems for Partial Differential Equations, Springer-Verlag, New York, NY. | Zbl 0908.35134
[014] Jarny, Y., Ozisik, M. and Bardon, J. (1991). A general optimization method using adjoint equation for solving multidimensional inverse heat conduction, International Journal of Heat and Mass Transfer 34(11): 2911-2919. | Zbl 0729.73930
[015] Khachfe, R. and Jarny, Y. (2000). Numerical solution of 2-D nonlinear inverse heat conduction problems using finite-element techniques, Numerical Heat Transfer B 37(1): 45-67.
[016] Khachfe, R. and Jarny, Y. (2001). Determination of heat sources and heat transfer coefficient for two-dimensional heat flow numerical and experimental study, International Journal of Heat and Mass Transfer 44(7): 1309-1322. | Zbl 0979.80005
[017] Kolodziej, J., Mierzwiczak, M. and Ciakowski, M. (2010). Application of the method of fundamental solutions and radial basis functions for inverse heat source problem in case of steady-state, International Communications in Heat and Mass Transfer 37(2): 121-124.
[018] Lefèvre, F. and Le Niliot, C.L. (2002). Multiple transient point heat sources identification in heat diffusion: Application to experimental 2D problems, Journal of Heat and Mass Transfer 45(9): 1951-1964.
[019] Le Niliot, C. and Lefèvre, F. (2001). A method for multiple steady line heat sources identification in diffusive system: Application to an experimental 2D problem, Journal of Heat and Mass Transfer 44(7): 1425-1438. | Zbl 0979.80006
[020] Le Niliot, C. and Lefèvre, F. (2004). A parameter estimation approach to solve the inverse problem of point heat sources identification, International Journal of Heat and Mass Transfer 47(4): 827-841. | Zbl 1052.80004
[021] Lormel, C., Autrique, L. and Claudet, B. (2004). Mathematical modeling of skin behavior during a laser radiation exposure, Proceedings of the 2nd European Survivability Workshop, Noordwijk, The Netherlands.
[022] Mechhoud, S., Witrant, E., Dugard, L. and Moreau, D. (2013). Combined distributed parameters and source estimation in tokamak plasma heat transport, Proceedings of the European Control Conference, Zurich, Switzerland.
[023] Mierzwiczak, M. and Kolodziej, J. (2010). Application of the method of fundamental solutions and radial basis functions for inverse transient heat source problem, Computer Physics Communications 181(12): 2035-2043. | Zbl 1219.65101
[024] Mierzwiczak, M. and Kolodziej, J. (2011). The determination of heat sources in two dimensional inverse steady heat problems by means of the method of fundamental solutions, Inverse Problems in Science and Engineering 19: 777-792. | Zbl 1269.65117
[025] Mierzwiczak, M. and Kolodziej, J. (2012). Application of the method of fundamental solutions with the Laplace transformation for the inverse transient heat source problem, Journal of Theoretical and Applied Mechanics 50(4): 1011-1023.
[026] Mohammadiun, M., Rahimi, A. and Khazaee, I. (2011). Estimation of the time-dependent heat flux using the temperature distribution at a point by conjugate gradient method, International Journal of Thermal Sciences 50(12): 2443-2450.
[027] Morozov, V. (1994). Methods for Solving Incorrectly Posed Problems, Springer-Verlag, New York, NY.
[028] Museux, N., Perez, L., Autrique, L. and Agay, D. (2012). Skin burns after laser exposure: Histological analysis and predictive simulation, Burns 38(5): 658-667.
[029] Park, H., Chung, O. and Lee, J. (1999). On the solution of inverse heat transfer problem using the Karhunen-Love-Galerkin method, International Journal of Heat and Mass Transfer 42: 127-142. | Zbl 0952.65069
[030] Perez, L., Gillet, M. and Autrique, L. (2007). Parametric identification of a multi-layered intumescent system, Proceedings of the 5th International Conference: Inverse Problems (Identification, Design and Control), Moscow, Russia.
[031] Perez, L. and Vergnaud, A. (2016). Observation strategies for mobile heating source tracking, High Temperatures, High Pressures 45(1): 57-76.
[032] Powell, M. (1977). Restart procedures for the conjugate gradient method, Mathematical Programming 12(1): 241-254. | Zbl 0396.90072
[033] Prudhomme, M. and Nguyen, T.H. (1998). On the iterative regularization of inverse heat conduction problems by conjugate gradient method, International Communications in Heat and Mass Transfer 25(7): 999-1008.
[034] Rakotoniaina, J., Breitenstein, O. and Langenkamp, M. (2002). Localization of weak heat sources in electronic devices using highly sensitive lock-in thermography, Materials Science and Engineering B: Solid-State Materials for Advanced Technology 91: 481-485.
[035] Renault, N., André, S., Maillet, D. and Cunat, D. (2008). A two-step regularized inverse solution for 2-D heat source reconstruction, Journal of Thermal Sciences 47(7): 827-841.
[036] Renault, N., André, S., Maillet, D. and Cunat, D. (2010). A spectral method for the estimation of a thermomechanical heat source from infrared temperature measurements, Journal of Thermal Sciences 49(8): 1394-1406.
[037] Rouquette, S., Autrique, L., Chaussavoine, C. and Thomas, L. (2007a). Identification of influence factors in a thermal model of a plasma-assisted chemical vapor deposition process, Inverse Problems in Science and Engineering 15(5): 489-515. | Zbl 1202.76149
[038] Rouquette, S., Guo, J. and Masson, P.L. (2007b). 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 46(2): 128-138.
[039] Silva Neto, A. and Ozisik, M. (1993). Simultaneous estimation of location and timewise-varying strength of a plane heat source, Numerical Heat Transfer A 24(4): 467-477.
[040] Tarantola, A. (2005). Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM Society for Industrial and Applied Mathematics, Philadelphia, PA. | Zbl 1074.65013
[041] Weinstock, R.P. (1952). Calculus of Variations, McGraw, New York, NY. | Zbl 0049.19503
[042] Yi, Z. and Murio, D. (2002). Source term identification in 1D IHCP, Journal of Computers and Mathematics with Applications 47(10/11): 1921-1933. | Zbl 1063.65102
[043] Zhou, J., Zhang, Y., Chen, J. and Feng, Z. (2010). Inverse estimation of surface heating condition in a three-dimensional object using conjugate gradient method, International Journal of Heat and Mass Transfer 53: 2643-2654. | Zbl 1191.80040