A new damping strategy of Levenberg-Marquardt algorithm with a fuzzy method for inverse heat transfer problem parameter estimation

Abstract

In this paper for the first time, the Levenberg-Marquardt (LM) algorithm assisted by a fuzzy method is presented to solve an inverse heat transfer problem. Given the importance of the damping factor in the consistency and efficiency of the LM algorithm in solving ill-posed problems, a new method based on fuzzy logic theory is used to adjust the value of the damping factor during the solution iteration step. In order to investigate the convergence speed, stability and robustness of the fuzzy LM algorithm, a one-dimensional heat transfer problem is solved using three different experimental heat fluxes including quadratic polynomial, cubic polynomial, and sine function, and the results are compared with classical LM algorithm. According to the results, the speed and the convergence stability of the solution of an inverse problem for different noisy temperatures are significantly improved by combining fuzzy logic with classical LM algorithm. Also, the new method robustness is comparable with the LM algorithm.