Abstract
The estimation of thermal boundary conditions occurring during heat treatment processes is an essential requirement for the characterization of heat transfer phenomena. In this work, the performance of five optimization techniques is studied. These models are the Conjugate Gradient Method, the Levenberg-Marquardt Method, the Simplex method, the NSGA II algorithm and a hybrid approach based on the NSGA II and Levenberg-Marquardt Method sequence. The models are used to estimate the heat transfer coefficient in 2D axis symmetrical case during transient heat transfer. The performance of the optimization methods is demonstrated using numerical experiments.
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References
Beck, J.V., Blackwell, B., St Clair, C.R., Jr.: Inverse Heat Conduction. Wiley, New York (1985)
Tikhonov, A.N., Arsenin, V.Y.: Solution of Ill-posed Problems. Winston, Washington, DC (1977)
Alifanov, O.M.: Inverse Heat Transfer Problems. Springer, Berlin/Heidelberg (1994)
Özisik, M.N., Orlande, H.R.B.: Inverse Heat Transfer: Fundamentals and Applications. Taylor & Francis, New York (2000)
Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7(4), 308–313 (1965)
Lagarias, J.C., Reeds, J.A., Wright, M.H., Wright, P.E.: Convergence properties of the Nelder-Mead simplex method in low dimensions. SIAM J. Optimiz. 9(1), 112–147 (1996)
Das, R.: A simplex search method for a conductive–convective fin with variable conductivity. Int. J. Heat Mass Transf. 54, 5001–5009 (2011)
Nelles, O.: Nonlinear System Identification. Springer, Berlin (2001)
Fletcher, R., Reeves, C.M.: Function minimization by conjugate gradients. Computer J. 7, 149–154 (1964)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Deb, K.: Multi-objective Optimization Using Evolutionary Algorithms. Wiley, Chichester, UK (2001)
Veldhuizen, D.A.V., Lamont, G.B.: Multi-objective evolutionary algorithms: analyzing the state-of-the-art. Evol. Comput. 8(2), 125–147 (2000)
Clark, J., Tye, R.: Thermophysical properties reference data for some key engineering alloys. High Temp. High Pressures 35/36, 1–14 (2003/2004)
Majorek, A., Scholtes, B., Müller, H., Macherauch, E.: Influence of heat transfer on development of residual stresses in quenched steel cylinders. Steel research No. 4, pp. 146–151 (1994)
Tensi, H.M., Stick, A.: Martens hardening of steel—prediction of temperature distribution and surface hardness. Mater. Sci. Forum 102–104, 741–775 (1992)
Acknowledgements
We acknowledge the financial support of this work by the Hungarian State and the European Union under the TÁMOP-4.2.1. B -11/2/KMR-2011-0001 project.
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Felde, I. (2016). Hybrid Optimization Approach for Determination of Thermal Boundary Conditions. In: Nádai, L., Padányi, J. (eds) Critical Infrastructure Protection Research. Topics in Intelligent Engineering and Informatics, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-28091-2_6
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DOI: https://doi.org/10.1007/978-3-319-28091-2_6
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