Entropy- and tikhonov-based regularization techniques applied to the backwards heat equation

The goal of this paper is to analyze the performance of different regularization techniques for an inverse heat conduction problem (IHCP): the estimation of the initial condition. The inverse problem is formulated as a nonlinear constrained optimization problem, and a regularization term is added to...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2000-10, Vol.40 (8), p.1071-1084
Main Authors: Muniz, W.B., Ramos, F.M., de Campos Velho, H.F.
Format: Article
Language:English
Subjects:
Backwards heat equation
Maximum entropy principle
Tikhonov regularization
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Summary:The goal of this paper is to analyze the performance of different regularization techniques for an inverse heat conduction problem (IHCP): the estimation of the initial condition. The inverse problem is formulated as a nonlinear constrained optimization problem, and a regularization term is added to the objective function with the help of a regularization parameter. Three classes of regularization methods have been considered: Tikhonov regularization, maximum entropy principle, and truncated singular value decomposition. Concerning the entropíc methodology, two new techniques are introduced and good results were obtained using synthetic data corrupted with noise. The Morozov's discrepancy principle is used to find out the regularization parameter.
ISSN:0898-1221
1873-7668
DOI:10.1016/S0898-1221(00)85017-8