Simultaneous Inverse Identification of Transient Thermal Properties and Heat Sources Using Sparse Sensor Information
Publication: Journal of Engineering Mechanics
Volume 133, Issue 12
Abstract
A study is presented herein on the simultaneous inverse identification of transient internal heat generation, transient thermal diffusivity, and constant convection coefficients. The formulations of the direct and inverse problems are presented in the context of finite-element analysis and nonlinear optimization, respectively. A real-coded genetic algorithm was used to solve the inverse problem because of the global convergence properties of this optimization technique. It was found through numerical studies that heat generation and thermal conductivity as functions of time can be simultaneously and consistently estimated from sparse sensor information, as long as convection coefficients are known. However, treating convection coefficients as unknown may significantly affect the accuracy of the estimated thermal diffusivity function and to a lesser extent, the accuracy of the heat generation function. The numerical experiments showed, however, that the Biot number can be accurately estimated when the convection coefficients are not well known. These results can have wide and important implications in problems related to monitoring and quality control of structures.
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Acknowledgments
This work was partly supported by the Intelligence Community Postdoctoral Research Fellowship Program. This research was conducted using the resources of the Cornell Theory Center, which receives funding from Cornell University, New York State, federal agencies, foundations, and corporate partners.
References
Abou, K. R., and Jarny, Y. (1999). “Estimation of heat sources within two dimensional shaped bodies.” Proc., Inverse Problems in Engineering: Theory and Practice, Port Ludlow, Wash., 309–316.
Alifanov, O. M. (1994). Inverse heat transfer problems, Springer-Verlag, Berlin.
AlNajem, N. M. (1993). “Inverse heat generation problem in a hollow cylinder.” Proc., Inverse Problems in Engineering: Theory and Practice, Palm Coast, Fla., 243–251.
Aquino, W., and Brigham, J. C. (2006). “Self-learning finite elements for inverse estimation of thermal constitutive models.” Int. J. Heat Mass Transfer, 49, 2466–2478.
Beck, J. V. (1985). Inverse heat conduction: Ill-posed problems, Wiley, New York.
Bye, G. C. (1983). Portland cement—Composition, production, and properties, Pergamon, New York.
Divo, E., Kassab, A., and Rodriguez, F. (2000). “Characterization of space dependent thermal conductivity with a BEM-based genetic algorithm.” Numer. Heat Transfer, Part A, 37(8), 845–875.
Foster, N. F., and Dulikravich, G. S. (1997). “Three-dimensional aerodynamic shape optimization using genetic and gradient search algorithms.” J. Spacecr. Rockets, 34(1), 36–42.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning, Addison-Wesley, Boston.
Holland, J. H. (1975). Adaptation in natural and artificial systems, Univ. of Michigan Press, Ann Arbor, Mich.
Huang, C. H., and Chin, S. C. (2000). “A two-dimensional inverse problem in imaging the thermal conductivity of a nonhomogeneous medium.” Int. J. Heat Mass Transfer, 43(22), 4061–4071.
Jang, H. Y., Tuan, P. C., Chen, T. C., and Chen, T. S. (2006). “Input estimation method combined with the finite-element scheme to solve IHCP hollow cylinder inverse heat conduction problems.” Numer. Heat Transfer, Part A, 50, 263–280.
Lin, J. H., Chen, C. K., and Yang, Y. T. (2001). “Inverse method for estimating thermal conductivity in one-dimensional heat conduction problems.” J. Thermophys. Heat Transfer, 15(1), 34–41.
Marin, L., and Lesnic, D. (2003). “BEM first-order regularization method in linear elasticity for boundary identification.” Comput. Methods Appl. Mech. Eng., 192(16–18), 2059–2071.
Mitchell, M. (1999). An introduction to genetic algorithms, MIT Press, Cambridge, Mass.
Paul, C., Lipson, H., and Cuevas, F. J. V. (2005). “Evolutionary form-finding of tensegrity structures.” Proc., GECCO 2005—Genetic and Evolutionary Computation Conference, Washington, D.C., 3–6.
Ponterosso, P., Fishwick, R. J., Fox, D. S. J., Liu, X. L., and Begg, D. W. (2000). “Masonry arch collapse loads and mechanisms by heuristically seeded genetic algorithm.” Comput. Methods Appl. Mech. Eng., 190(8–10), 1233–1243.
Rayward-Smith, V. J., Osman, I. H., Reeves, C. R., and Smith, G. D. (1996). Modern heuristic search methods, Wiley, New York.
Reddy, J. N. (2004). An introduction to nonlinear finite element analysis, Oxford University Press Inc., New York.
Rodrigues, F. A., Orlande, H. R. B., and Dulikravich, G. S. (2004). “Simultaneous estimation of spatially dependent diffusion coefficient and source term in a nonlinear 1D diffusion problem.” Math. Comput. Simul., 66(4–5), 409–424.
Scarpa, F., Milano, G., and Pescetti, D. (1993). “Thermophysical properties estimation form transient data: Kalman versus Gauss approach.” Proc., Inverse Problems in Engineering: Theory and Practice, Palm Coast, Fla., 109–116.
Silva, A. J., and Ozisk, M. N. (1993). “The estimation of space and time dependent strength of a volumetric heat source in a one-dimensional plate.” Int. J. Heat Mass Transfer, 37(6), 909–915.
Su, J., and Hewitt, G. F. (2004). “Inverse heat conduction problem of estimating time-varying heat transfer coefficient.” Numer. Heat Transfer, Part A, 45, 777–789.
Tadi, M. (2000). “Evaluation of a two-dimensional conductivity function based on boundary measurements.” J. Heat Transfer, 122(2), 367–371.
Truffart, B., Jarny, Y., and Delaunay, D. (1993). “A general optimization algorithm to solve 2-D boundary inverse heat conduction problems using finite elements.” Inverse problems in engineering: Theory and practice, Palm Coast, Fla., 53–60.
Zabaras, N., and Yang, G. Z. (1997). “A functional optimization formulation and implementation of an inverse natural convection problem.” Comput. Methods Appl. Mech. Eng., 144(3–4), 245–274.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 12 • December 2007
Pages: 1341 - 1351
Copyright
© 2007 ASCE.
History
Received: Aug 30, 2006
Accepted: Feb 27, 2007
Published online: Dec 1, 2007
Published in print: Dec 2007
Notes
Note. Associate Editor: Arif Masud
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