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Optimal Regularization Methods for Inverse Heat Transfer Problems

[+] Author Affiliations
Kei Okamoto, Ben Q. Li

Washington State University, Pullman, WA

Paper No. HT-FED2004-56395, pp. 825-834; 10 pages
  • ASME 2004 Heat Transfer/Fluids Engineering Summer Conference
  • Volume 4
  • Charlotte, North Carolina, USA, July 11–15, 2004
  • Conference Sponsors: Heat Transfer Division and Fluids Engineering Division
  • ISBN: 0-7918-4693-8 | eISBN: 0-7918-3740-8
  • Copyright © 2004 by ASME


The Tikhonov regularization method has been used to find the unknown heat flux distribution along the boundary when the temperature measurements are known in the interior of a sample. Mathematically, the inverse problem is ill-posed, though physically correct, and prone to instability. This paper discusses the fundamental issues concerning the selection of optimal regularization parameters for inverse heat transfer calculations. Towards this end, a finite-element-based inverse algorithm is developed. Five different methods, that is, the maximum likelihood (ML), the ordinary cross-validation (OCV), the generalized cross-validation (GCV), the L-curve method, and the discrepancy principle, are evaluated for the purpose of determining optimal regularization parameters. An assessment of these methods is made using 1-D and 2-D inverse steady heat conduction problems where analytical solutions are available. The optimal regularization method is also compared with the Levenberg-Marquardt method for inverse heat transfer calculations. Results show that in general the Tikhonov regularization method is superior over the Levenberg-Marquardt method when the input data errors are noisy. With the appropriately determined regularization parameter, the inverse algorithm is applied to estimate the heat flux of spray cooling of a 3-D microelectronic component with an embedded heating source.

Copyright © 2004 by ASME
Topics: Heat transfer



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