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.

本文首次提出了模糊方法辅助的Levenberg-Marquardt (LM)算法求解逆传热问题。鉴于阻尼因子对LM算法求解不适定问题的一致性和效率的重要性，采用基于模糊逻辑理论的新方法在求解迭代步骤中调整阻尼因子的值。为了研究模糊LM算法的收敛速度、稳定性和鲁棒性，使用二次多项式、三次多项式和正弦函数三种不同的实验热通量求解一维传热问题，并将结果与​​经典算法进行比较。 LM算法。根据结果​​，通过将模糊逻辑与经典LM算法相结合，显着提高了不同噪声温度下逆问题求解的速度和收敛稳定性。此外，新方法的鲁棒性与 LM 算法相当。