Thermal characterization of materials using Karhunen-Loève decomposition techniques - Part II. Heterogeneous materials

Journal article

A new method for thermal characterization of heterogeneous materials has been proposed. As for homogeneous materials in the first part of the paper, the method is based on the use of Karhunen-Loève decomposition (KLD) techniques in association with infrared thermography experiments or any other experimental device providing dense data in the spatial coordinate. Orthogonal properties of KLD eigenfunctions and states are used for achieving simple estimates of thermal diffusivities. It has been proven that diffusivities can be estimated without explicit knowledge of variables and parameters related to heat exchanges at the interfaces (i.e. thermal conductivities, thermal contact resistances). Indeed, the diffusivities estimates only depend on some few KLD eigenelements. As a result, a significant amplification of the signal/noise ratios is reached. Moreover, it is shown 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 estimates involve spatial derivatives of the eigenfunctions. Consequently, the proposed method results in an attractive combination of parsimony and robustness to noise. The effectiveness of the method is illustrated through some simulated experimental applications. © 2012 Copyright Taylor and Francis Group, LLC.

Authors: Del Barrio, E; Dauvergne, J; Pradere, C

• Journal: Inverse Problems in Science and Engineering
• Volume: 20
• Issue: 8
• Pages: 1145-1174
• Publication date: 2012-12-01
• DOI: 10.1080/17415977.2012.658517
• EISSN: 1741-5985
• ISSN: 1741-5977
• Language: English
• Keywords: thermal characterization; Karhunen-Loève decomposition; singular values decomposition; infrared thermography