×

A modified genetic algorithm for solving the inverse heat transfer problem of estimating plan heat source. (English) Zbl 1148.80371

Summary: This work considers a new approach for solving the inverse heat conduction problem of estimating unknown plan heat source. It is shown that the physical heat transfer problem can be formulated as an optimization problem with differential equation constraints. A modified genetic algorithm is developed for solving the resulting optimization problem. The proposed algorithm provides a global optimum instead of a local optimum of the inverse heat transfer problem with highly-improved convergence performance. Some numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.

MSC:

80A23 Inverse problems in thermodynamics and heat transfer
80M25 Other numerical methods (thermodynamics) (MSC2010)
80M50 Optimization problems in thermodynamics and heat transfer
90C29 Multi-objective and goal programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Beck, J. V.; Blackwell, B.; Jr., C. R. St Clair: Inverse heat conduction, (1985) · Zbl 0633.73120
[2] Tikhonov, A. N.; Arsenin, V. Y.: Solution of ill-posed problem, (1977) · Zbl 0354.65028
[3] Blackwell, B.: Efficient technique for the numerical solution of one-dimensional inverse problem of heat conduction, Numer. heat transfer, 229-238 (1981)
[4] Huang, C. -H.; Chen, C. -W.: A boundary element-based inverse problem in estimating transient boundary conditions with conjugate gradient method, Int. J. Numer. meth. Eng. 42, 943-965 (1998) · Zbl 0944.74078 · doi:10.1002/(SICI)1097-0207(19980715)42:5<943::AID-NME395>3.0.CO;2-V
[5] Huang, C. -H.; Chen, C. -W.: A three-dimensional inverse forced convection problem in estimating surface heat flux by conjugate gradient method, Int. J. Heat mass transfer 43, 3171-3181 (2000) · Zbl 1094.76566 · doi:10.1016/S0017-9310(99)00330-0
[6] Huang, C. -H.; Hsiao, J. -H.: A non-linear fin design problem in determining the optimum shape of spine and longitudinal fins, Commun. numer. Meth. eng. 19, 111-124 (2003) · Zbl 1013.65066 · doi:10.1002/cnm.575
[7] Huang, C. -H.; Huang, C. -Y.: An inverse biotechnology problem in estimating the optical diffusion and absorption coefficients of tissue, Int. J. Heat mass transfer 47, 447-457 (2003) · Zbl 1053.80013 · doi:10.1016/j.ijheatmasstransfer.2003.07.011
[8] Alander, J. T.: Population size, building blocks, fitness landscape and genetic algorithm search efficiency in combinatorial optimization: an empirical study, Practical handbook of genetic algorithms: complex coding systems (1999)
[9] Ansari, N.; Hon, E.: Computational intelligence for optimization, (1997) · Zbl 0890.68111
[10] Bierwith, C.; Malfeld, D. C.: Production scheduling and rescheduling with genetic algorithms, Evol. comput. 7, 1-17 (1999)
[11] Falkenauer, E.: Genetic algorithms and grouping problem, (1998) · Zbl 0803.68037
[12] Koza, J. R.: Hierarchical automatic function definition in genetic programming, Foundations of genetic algorithms 2 (1993)
[13] Rasmussen, S.; Barrettt, C. L.: Elements of a theory of simulation, (1995)
[14] Scott, S. D.; Seth, S.; Samal, A.: A synthesizable VHDL coding of a genetic algorithm, Practical handbook of genetic algorithms: complex coding systems (1999)
[15] Vainio, M.; Schonberg, T.; Halme, A.; Jakubik, P.: Optimization in performance of a robot society in structured environments through genetic algorithms, (1995)
[16] Liu, G. R.; Zhou, J. -J.; Wang, J. G.: Coefficient identification in electronic system cooling simulation through genetic algorithm, Comp. struct. 80, 23-30 (2002)
[17] Raudensky, M.; Horsky, J.; Krejsa, J.; Slama, L.: Usage of artificial intelligence methods in inverse problems for estimation of material parameters, Int. J. Num. meth. Heat fluid flow 6, No. 8, 19-29 (1996) · Zbl 0965.80501 · doi:10.1108/eb017555
[18] Liu, G. R.; Lee, J. -H.; Patera, A. T.; Yang, Z. L.; Lam, K. Y.: Inverse identification of thermal parameters using reduced-basis method, Comput. meth. Appl. mech. Eng. 194, 3090-3107 (2005) · Zbl 1137.74361 · doi:10.1016/j.cma.2004.08.003
[19] Holland, J. H.: Adaptation in natural and artificial system, (1975) · Zbl 0317.68006
[20] Raudensky, M.; Woodbury, K. A.; Kral, J.; Brezina, T.: Genetic algorithm in solution of inverse heat conduction problems, Num. heat transfer, part B 28, 293-306 (1995)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.