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Fuzzy Levenberg-Marquardt damping factor update strategy and Tikhonov regularization applied to a coupled conduction-radiation inverse heat transfer problem
Lucas C. S. Jardim, Diego C. Knupp, David A. Pelta, Carlos C. Corona, Orestes Llanes-Santiago and Antônio J. Silva Neto
The recently proposed Fuzzy Levenberg-Marquardt Damping Factor Updating Strategy (FLM) is used along with Tikhonov Regularization (TR) in order to solve a coupled conduction-radiation function estimation inverse problem. FLM consists of updating the Levenberg-Marquardt (LM) damping factor with the assist of Fuzzy Logic. To test the FLM algorithm combined with TR, a conduction-radiation problem is addressed, and it serves as test bed to the numerical experiments, where the objective is to obtain estimatives of parameters, such as the spatially variable scattering albedo, the thermal conductivity and the optical thickness, simultaneously, which is often performed separately. Two main test cases are presented, one considering only the radiation problem, used as benchmark, in order to investigate noise levels and hyperparameters. The second main test case deals with the coupled conduction-radiation heat transfer problem for different functional forms of the spatially variable scattering albedo. For all presented numerical experiments, good estimates were achieved for the sought functions and parameters. These results demonstrate that the methodology presented in this work, through the combination of the Fuzzy LM dampting factor updating strategy and the Tikhonov regularization scheme, may provide valuable tools for inverse heat transfer problems.
Keywords: Inverse Heat Conduction Radiation Problem, Levenberg-Marquardt, Fuzzy Logic, Tikhonov Regularization