Thermal characterization of materials using Karhunen–Loève decomposition techniques – Part I. Orthotropic materials

Abstract

A new method for reliable thermal characterization of orthotropic, homogeneous materials is proposed. It is based on the use of Karhunen–Loève Decomposition (KLD) techniques in association with infrared thermography experiments or any other kind of experimental device providing dense data in the spatial coordinate. Main problem addressed in this paper is how to deal efficiently with large amount of rather noised experimental data. It is proven that orthogonal properties of KLD eigenfunctions and states allow achieving simple estimates of thermal diffusivities which depend only on the first and the second KLD eigenelements. This means that the 2D KLD approximation of the temperature field provides information enough for estimation purposes. As a result, a significant amplification of the signal/noise ratios is reached. Moreover, we prove that spatially uncorrelated noise has no effect on KLD eigenfunctions, the noise being entirely reported on states (time-dependent projection coefficients). This is particularly interesting because thermal diffusivities estimation involves spatial derivatives of the eigenfunctions calculation. Consequently, the proposed method results in an attractive combination of parsimony and robustness to noise. Indeed, because it does not require analytical solutions of the associated heat conduction problem, the method could be extended to application involving heterogeneous materials. The second part of the paper deals with this extension.