A new modified Levenberg-Marquardt algorithm for identifying the temperature-dependent conductivity of solids based on the radial integration boundary element method

Abstract

In this paper, combination of radial integration boundary element method (RIBEM) with complex variable and Levenberg-Marquardt algorithm (LMA) is firstly proposed to identify temperature-dependent conductivity in the inverse heat conduction problem. To obtain the simulative temperature, radial integration boundary element method is used to solve the transient nonlinear heat conduction problem with temperature-dependent conductivity. What’s more, RIBEM with complex variable, which transforms the real variables into complex ones in boundary element method, makes it possible to perform complex variable derivative method (CVDM) in LMA. Furthermore, because of the introduction of CVDM, the sensitivity coefficient matrix can be calculated accurately and efficiently, and then the identification of unknown variable can be achieved admirably in the inverse heat problem. Finally, different initial guess value and measurement errors are considered, respectively, and various numerical examples are presented to fully demonstrate the accuracy and feasibility of the proposed method in identifying temperature-dependent conductivity.