Inverse Heat Conduction Analysis of Cooling on Run Out Tables

Authors: M. S. Gadala, Khaled Ahmed, Elasadig Mahdi

Abstract:

In this paper, we introduced a gradient-based inverse solver to obtain the missing boundary conditions based on the readings of internal thermocouples. The results show that the method is very sensitive to measurement errors, and becomes unstable when small time steps are used. The artificial neural networks are shown to be capable of capturing the whole thermal history on the run-out table, but are not very effective in restoring the detailed behavior of the boundary conditions. Also, they behave poorly in nonlinear cases and where the boundary condition profile is different. GA and PSO are more effective in finding a detailed representation of the time-varying boundary conditions, as well as in nonlinear cases. However, their convergence takes longer. A variation of the basic PSO, called CRPSO, showed the best performance among the three versions. Also, PSO proved to be effective in handling noisy data, especially when its performance parameters were tuned. An increase in the self-confidence parameter was also found to be effective, as it increased the global search capabilities of the algorithm. RPSO was the most effective variation in dealing with noise, closely followed by CRPSO. The latter variation is recommended for inverse heat conduction problems, as it combines the efficiency and effectiveness required by these problems.

Keywords: Inverse Analysis, Function Specification, Neural Net Works, Particle Swarm, Run Out Table.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1100533

References:

[1] Alifanov, Oleg M., A. V. Nenarokomov, S. A. Budnik, V. V. Michailov, and V. M. Ydin. "Identification of thermal properties of materials with applications for spacecraft structures." Inverse Problems in Science and Engineering 12, no. 5 (2004): 579-594.
[2] Beck, James V. Inverse heat conduction: Ill-posed problems. James Beck, 1985.
[3] Beck, James Vere, and Kenneth J. Arnold. Parameter estimation in engineering and science. James Beck, 1977.
[4] Beck, J. V., B. Blackwell, and A. Haji-Sheikh. "Comparison of some inverse heat conduction methods using experimental data." International Journal of Heat and Mass Transfer 39, no. 17 (1996): 3649-3657.
[5] Al-Khalidy, Nehad. "A general space marching algorithm for the solution of two-dimensional boundary inverse heat conduction problems." Numerical Heat Transfer, Part B 34, no. 3 (1998): 339-360.
[6] Jarny, Yvon. "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, no. 7 (2001): 1309- 1322.
[7] Huang, Cheng-Hung, I-Cha Yuan, and Herchang Ay. "A threedimensional inverse problem in imaging the local heat transfer coefficients for plate finned-tube heat exchangers." International Journal of Heat and Mass Transfer 46, no. 19 (2003): 3629-3638.
[8] Girault, Manuel, Daniel Petit, and Etienne Videcoq. "The use of model reduction and function decomposition for identifying boundary conditions of a linear thermal system." Inverse Problems in Science and Engineering 11, no. 5 (2003): 425-455.
[9] Kim, H. K., and S. I. Oh. "Evaluation of heat transfer coefficient during heat treatment by inverse analysis." Journal of Materials Processing Technology 112, no. 2 (2001): 157-165.
[10] Louahlia-Gualous, H., P. K. Panday, and E. A. Artioukhine. "Inverse determination of the local heat transfer coefficients for nucleate boiling on a horizontal cylinder." Journal of heat transfer 125, no. 6 (2003): 1087-1095.
[11] Gadala, Mohamed S., and Fuchang Xu. "An FE-based sequential inverse algorithm for heat flux calculation during impingement water cooling." International Journal of Numerical Methods for Heat & Fluid Flow 16, no. 3 (2006): 356-385.
[12] Roudbari, Shawhin. "Self-Adaptive Finite Element Analysis." PhD diss., Cornell University, 2006.
[13] Silieti, M., E. Divo, and A. J. Kassab. "An inverse boundary element method/genetic algorithm based approach for retrieval of multidimensional heat transfer coefficients within film cooling holes/slots." Inverse Problems in Science and Engineering 13, no. 1 (2005): 79-98.
[14] Shiguemori, Elcio H., José Dem?Sio S. Da Silva, and Haroldo F. de Campos Velho. "Estimation of initial condition in heat conduction by neural network." Inverse Problems in Science and Engineering 12, no. 3 (2004): 317-328.
[15] Lecoeuche, S., G. Mercere, and S. Lalot. "Evaluating time-dependent heat fluxes using artificial neural networks." Inverse Problems in Science and Engineering 14, no. 2 (2006): 97-109.
[16] Ostrowski, Z., R. A. Bialstrokecki, and A. J. Kassab. "Solving inverse heat conduction problems using trained POD-RBF network inverse method." Inverse Problems in Science and Engineering 16, no. 1 (2008): 39-54.
[17] Hassan, Rania, Babak Cohanim, Olivier De Weck, and Gerhard Venter. "A comparison of particle swarm optimization and the genetic algorithm." In Proceedings of the 1st AIAA multidisciplinary design optimization specialist conference, pp. 18-21. 2005.
[18] Gosselin, Louis, Maxime Tye-Gingras, and François Mathieu-Potvin. "Review of utilization of genetic algorithms in heat transfer problems." International Journal of Heat and Mass Transfer 52, no. 9 (2009): 2169- 2188.
[19] Davis, Lawrence, ed. Handbook of genetic algorithms. Vol. 115. New York: Van Nostrand Reinhold, 1991.
[20] Clerc, Maurice. Particle swarm optimization. Vol. 93. John Wiley & Sons, 2010.
[21] Kennedy, James, James F. Kennedy, and Russell C. Eberhart. Swarm intelligence. Morgan Kaufmann, 2001.
[22] Vakili, S., and M. S. Gadala. "Effectiveness and efficiency of particle swarm optimization technique in inverse heat conduction analysis." Numerical Heat Transfer, Part B: Fundamentals 56, no. 2 (2009): 119- 141.
[23] Alrasheed, M. R., C. W. de Silva, and M. S. Gadala. "Evolutionary optimization in the design of a heat sink." Mechatronic Systems: Devices, Design, Control, Operation and Monitoring (2008).
[24] De Silva, Clarence W. Mechatronic Systems. Taylor and Francis, 2007.
[25] Urfalioglu, Onay. "Robust estimation of camera rotation, translation and focal length at high outlier rates." In Computer and Robot Vision, 2004. Proceedings. First Canadian Conference on, pp. 464-471. IEEE, 2004.