Research On Inverse Problem Of Thermal Conductivity Based On Levenberg-Marquardt Algorithm

Heat conduction inverse problem has important engineering application value in aerospace,petrochemical and other fields.The identification of thermo-physical parameters is an important research content in the inverse problem of heat conduction.For the transient heat conduction problem with constant coefficients,the domain integral in the integral equation is transformed into the boundary integral by using the dual reciprocity method,and the integral equation of the problem is discretized by linear elements to form an algebraic system of equations.The objective function of thermal conductivity inversion problem is established,the objective function is minimized by Levenberg-Marquardt(LM)algorithm,and the inversion result is obtained.The effects of iterative initial value and measurement error on the inversion results are discussed,and the effectiveness and stability of the least square method and the LM algorithm are compared.The LM algorithm has a larger convergence region than the least square method.It is a more efficient and stable inversion method.The relaxation factor can improve the convergence stability of the two methods,and the accuracy of the inversion results decreases with the increase of the measurement error.For the transient heat conduction problem with variable coefficients,the thermal conductivity varies with the spatial coordinates.The dual reciprocity method is used to deal with the domain integrals in the integral equation.For transient problems,the differential transformation method is introduced,which can overcome the shortcomings of the finite difference method and obtain accurate and stable numerical results.The numerical analysis model of two-dimensional transient heat conduction problem is constructed.The polynomial function is used to approximate the thermal conductivity,and the unknown thermal conductivity identification problem is transformed into the polynomial coefficient identification problem.The objective function of thermal conductivity inversion problem is established.The LM algorithm is used to optimize the objective function and the inversion results are obtained.The effects of the degree of polynomial function,the number of measuring points and the measurement errors on the inversion results are discussed.The effectiveness and stability of the conjugate gradient method and the LM algorithm are compared.Compared with the conjugate gradient method,the LM algorithm is more efficient and accurate,with less iteration steps and less computation time.It is an effective conversion method to approximate unknown thermal conductivity by using polynomial function.Increasing the number of measurement points,the inversion results are more accurate.The measurement error has a great influence on the inversion results.Reducing the measurement error,the inversion results are more accurate.