A novel inverse method for identification of 3D thermal conductivity coefficients of anisotropic media by the boundary element analysis

摘要

This paper presents a new numerical inverse method for identifying the six components of the thermal conductivity tensor of a 3D anisotropic medium with an arbitrary shape. The unknowns are inversely calculated using heat conduction problems with extra information at some boundary sampling points. For better stability, the inverse method uses data supplied from more than one steady-state heat conduction problem. Since all sampling points are taken to be on boundary surfaces for the sake of easy access, the boundary element method (BEM) for direct calculation is employed for the sensitivity analyses. The off-diagonal components of the thermal conductivity tensor must satisfy three nonlinear inequality constraints, which make the inverse analysis even more challenging. To overcome this difficulty, the inverse problem is formulated in terms of the principal thermal conductivities along with the rotation angles of principal axes, by which the three constraints disappear. For the inverse analysis, the damped Gauss-Newton method is adopted for the optimization process. In the end, numerical examples are presented, showing that the proposed method can yield reliable solutions even in cases with relatively large measurement error and with initial guesses far from the exact solution.