Adaptive Determination of the Damping Coefficient of the Levenberg-Marquardt Algorithm Using Type-2 Fuzzy in Inverse Heat Transfer Problems

In this study, a combination of the Levenberg-Marquardt algorithm and the type-2 fuzzy method is used to solve an inverse heat transfer problem. Considering the essential role of the damping factor in the stability and efficiency of the Levenberg-Marquardt algorithm in solving ill-posed problems, a new method based on fuzzy logic theory is used to update the value of this parameter in the iteration of the solution. A cubic polynomial test case is estimated using classical, type-1, and type-2 fuzzy Levenberg-Marquardt methods for the boundary heat flux in a one-dimensional heat transfer problem. The evaluation criteria chosen are convergence speed and robustness. The results show that the use of the new method increases the speed of convergence. The robustness and the accuracy of the estimates is improved by using this new method compared to the conventional Levenberg-Marquardt method.