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Inverse identification of thermal parameters using reduced-basis method. (English) Zbl 1137.74361
Summary: A novel computational method is presented to inversely identify heat convection constants for complex engineering systems. A reduced-basis approach is developed as a forward solver for heat transfer analysis in order to significantly reduce the computational complexity in each forward analysis, which is crucial for the inverse analysis of complex systems. An intergeneration-projection genetic-algorithm (IP-GA) is introduced as the inverse procedure to speed up the process of finding the desired global minimum of the fitness function of error that leads to the parameters to be identified. As an example, identification of the heat convection constants of a typical microelectronic package are performed using the present method and the performance is examined comparing with other inverse identification methods. It is found that the reduced-basis method combined with the IP-GA significantly outperforms the conventional methods. The proposed inverse identification method is efficient enough even for online analysis of inverse problems due to both the use of the reduced-basis approach and the present inverse procedure.

MSC:
74G75 Inverse problems in equilibrium solid mechanics
74F05 Thermal effects in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
80A23 Inverse problems in thermodynamics and heat transfer
Software:
Genocop; Mfree2D
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[1] Prud’homme, C.; Rovas, D.V.; Veroy, K.; Machiels, L.; Maday, Y.; Patera, A.T.; Turinici, G., Reliable real-time solution of parametrized partial differential equations: reduced-basis output bound methods, J. fluid engrg., 124, 70-80, (2002)
[2] Machiels, L.; Maday, Y.; Oliveira, I.B.; Patera, A.T.; Rovas, D.V., Output bounds for reduced-basis approximations of symmetric positive definite eigenvalue problems, CR acad. sci. Paris ser. I, 331, 2, 153-158, (2000) · Zbl 0960.65063
[3] Santamarina, J.C.; Fratta, D., Introduction to discrete signals and inverse problems in civil engineering, (1998), ASCE Press USA
[4] Krishnan, B.; Navin, S.R., Inversion of composite material elastic constants from ultrasonic bulk wave phase velocity data using genetic algorithms, Composites pt. B, 29, 171-180, (1998)
[5] Sivakumar, K.; Iyengar, N.G.R.; Kalyanmoy, D., Optimum design of laminated composite plates with cutouts using a genetic algorithm, Compos. struct., 42, 265-270, (1998)
[6] Liu, G.R.; Chen, S.C., Flaw detection in sandwich plates based on time-harmonic response using genetic algorithm, Comput. methods appl. mech. engrg., 190, 42, 5505-5514, (2001) · Zbl 1014.74030
[7] Liu, G.R.; Han, X.; Xu, Y.G.; Lam, K.Y., Material characterization of functionally graded material by means of elastic waves and a progressive-learning neural network, Compos. sci. technol., 61, 10, 1401-1411, (2001)
[8] Xu, Y.G.; Liu, G.R.; Wu, Z.P., A novel hybrid genetic algorithm using local optimizer based on heuristic pattern move, Appl. artif. intell., 15, 7, 601-631, (2001)
[9] Liu, G.R.; Lam, K.Y., Scattering of SH waves by flaws in sandwich plates and its use in flaw detection, Compos. struct., 34, 3, 251-261, (1996)
[10] Wang, Y.Y.; Liu, G.R.; Lam, K.Y., Detection of flaws in sandwich plates, Compos. struct., 34, 4, 409-418, (1996)
[11] Wang, Y.Y.; Lam, K.Y.; Liu, G.R., Wave scattering of interior vertical crack in plates and the detection of the crack, Engrg. fract. mech., 59, 1, 1-16, (1998)
[12] Xu, Y.G.; Liu, G.R.; Wu, Z.P.; Hunag, X.M., Adaptive multilayer perceptron networks for detection of cracks in anisotropic laminated plates, Int. J. solids struct., 38, 5625-5645, (2001) · Zbl 1048.74024
[13] Holland, J.H., Adaptation in natural and artificial systems, (1975), The University of Michigan Press Ann Arbor
[14] Goldberg, D.E., Genetic algorithm in search optimization and machine learning, (1989), Addison Wesley Reading, MA · Zbl 0721.68056
[15] Michalewicz, Z., Genetic algorithm+data structures=evolution programs, (1994), Springer-Verlag New York · Zbl 0818.68017
[16] Davis, L., Handbook of genetic algorithms, (1991), Van Nostrand New York
[17] K. Krishnakumar, Micro-Genetic Algorithm for stationary and non-stationary function optimization, in: SPIE: Intelligent Control and Adaptive System, Philadelphia, PA, vol. 1196, 1989
[18] Gen, M.; Cheng, R.W., Genetic algorithm and engineering design, (1997), John Wiley and Sons Inc. New York
[19] Bar-Cohen, A.; Elperin, T.; Eliasi, R., θjc characterization of chip packages-justification limitations and future, IEEE trans. components hybrids manuf. technol., 12, 4, 724-731, (1989)
[20] Bar-Cohen, A.; Krueger, W.B., Thermal characterization of chip packages-evolutionary development of compact models, IEEE trans. components hybrids manuf. technol., 20, 4, 399-410, (1997)
[21] A. Ortega, A. Aranyosi, A. Griffin, S. West and D. Edwards, Compact thermal models of conduction cooled packages, in: Proceedings of the IEEE Fifth Annual SEMI-THERM Symposium, 1999, pp. 221-230
[22] Incropera, F.P.; De Witt, D.P., Fundamentals of heat and mass transfer, (2002), John Wiley and Sons New York
[23] ASE Group, Taiwan, Product Information, Available from <http://www.acegroup.com.tw>
[24] Zienkiewicz, O.C.; Taylor, R.L., The finite element method, (2000), McGraw-Hill New York · Zbl 0991.74002
[25] Liu, G.R.; Quek, S.S., The finite element method: A practical course, (2003), Butterworth Heinemann Oxford · Zbl 1027.74001
[26] Liu, G.R., Mesh free methods: moving beyond the finite element method, (2002), CRC Press Boca Raton, FL
[27] Liu, G.R.; Han, X., Computational inverse techniques for nondestructive evaluation, (2003), CRC Press Boca Raton, FL · Zbl 1067.74002
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