A new approach for determining damping factors in Levenberg-Marquardt algorithm for solving an inverse heat conduction problem

Damping factor is a key parameter in Levenberg-Marquardt algorithm for solving inverse problems, which significantly affects the efficiency and the convergence stability of Levenberg-Marquardt algorithm and needs to be updated with the iterative number. A new approach is presented for determining damping factors in Levenberg-Marquardt algorithm in this paper, which relates the damping factor directly to the dimensionless objective function in inverse problems. Then, the accuracy, the efficiency, the convergence stability as well as the robustness of Levenberg-Marquardt algorithm are investigated in detail, for identifying temperature-dependent thermal conductivities by solving an inverse heat conduction problem. The results show that the LM algorithm using the new approach for determining damping factors is accurate and robust for identifying temperature-dependent thermal conductivities. The efficiency and the convergence stability of the LM algorithm are improved by using the new approach for determining damping factors. Moreover, the new approach is easy to implement.