A New Hybrid Method for Solving Inverse Heat Conduction Problems

Abstract

Solving the inverse problems, especially in the field of heat transfer, is one of the challenges of engineering due to its importance in industrial applications. It is well-known that inverse heat conduction problems (IHCPs) are severely ill-posed, which means that small disturbances in the input may cause extremely large errors in the solution. This paper introduces an accurate method for solving inverse problems by combining Tikhonov's regularization and the genetic algorithm. Finding the regularization parameter as the decisive parameter is modelled by this method, a few sample problems were solved to investigate the efficiency and accuracy of the proposed method. A linear sum of fundamental solutions with unknown constant coefficients assumed as an approximated solution to the sample IHCP problem and collocation method is used to minimize residues in the collocation points. In this contribution, we use Morozov's discrepancy principle and Quasi-Optimality criterion for defining the objective function, which must be minimized to yield the value of the optimum regularization parameter.