A New Approach For Determining Damping Factors In Levenberg-marquardt Algorithm And Its Applications In Inverse Heat Conduction Problems

With the rapid development of computer and progress of research methods,inverse problems of 'the results for reasons,the phenomenon of seeking essence' are encountered in many fields,such as the chemical industry,civil engineering,mechanical engineering and the aerospace.In aeronautics and astronautics areas,temperature-dependent thermo-physical properties of TPS materials or boundary conditions are often required to be estimated,which belongs to inverse heat conduction problems.Due to the ill posedness of inverse heat conduction problems,their solutions have been being investigated.In this thesis,the Levenberg-Marquardt algorithm is used for solving the inverse heat conduction problems,which has the merit of high accuracy and efficiency.In the Levenberg-Marquardt algorithm,damping factors are key parameters,which significantly affect the efficiency and the convergence stability and needs to be updated with the iterative number.Firstly,a new approach is proposed for determining damping factors in Levenberg-Marquardt algorithm based on a lot of numerical tests,which relates the damping factor directly to the dimensionless objective function in inverse problems.Then,the accuracy,the efficiency,the convergence stability and the robustness of the Levenberg-Marquardt algorithm are investigated in detail,for identifying temperature-dependent thermal conductivities and estimating the boundary heat flux,by solving one-dimensional and three-dimensional problems.Finally,the conclusion is given.The numerical results show that the LM algorithm using the new approach for determining damping factors is accurate and robust.In addition,the efficiency and the convergence stability of the Levenberg-Marquardt algorithm are improved by using the new approach for determining damping factors,compared with the existing three methods.