Three-Dimensional Reconstruction of Thermal Volumetric Sources from Surface Temperature Fields Measured by Infrared Thermography

Abstract

Non-destructive testing (NDT) of materials and structures is a very important industrial issue in the fields of transport, aeronautics and space as well as in the medical domain. Active infrared thermography is an NDT method that consists of providing an external excitation to cause an elevation of the temperature field in the material, consequently allowing evaluation of the resulting temperature field at the surface. However, thermal exciters that are used (flash lamps, halogen, lasers) act only on the surface of the sample. On the other hand, several energy conversion systems can lead to the generation of volumetric sources; the phenomena of thermo-acoustics, thermo-induction, thermomechanics or thermochemistry can be cited. For instance, ultrasonic waves can generate volumetric heat sources if the material is viscoelastic or if there is a defect. The reconstruction of these sources is the initial process for the quantification of parameters responsible for the heating. Characterizing a heat source means reconstructing its geometry and the supplied power. Identification of volumetric heat sources from surface temperature fields is a mathematically ill-posed problem. The main cause of the issue is the diffusive nature of the temperature. In this work, 3D reconstruction of the volumetric heat sources from the resulting surface temperature field, measured by infrared thermography, is studied. An analysis of the physical problem enables specifying the limits of the reconstruction. In particular, a criterion on the achievable spatial resolution is defined, and a reconstruction limitation for in-depth sources is highlighted.

Bayesian Inference for 3D Volumetric Heat Sources Reconstruction from Surfacic IR Imaging

“…Then, Figure 4 enables the obtained probability to be determined for three different signal-to-noise ratios: SNR = 10 (a), SNR = 50 (b), and SNR = 100 (c). One can note that the method is not so sensitive to the noise compared to literature methods [8,12,15]: for SNR = 50 and 100, the probability at the source position is superior to 0.95, while for SNR = 10, the probability is 0.30, which can be questionable in absolute terms but not in the case where the other source position probabilities are equal to 0.…”

“…In [11,12], the authors tested different deterministic inversion methods, highlighting some crucial tricks:…”

“…The discretization of the sample along the x and y directions is given by the IR camera (pixel of 290 µm × 290 µm), which leads to n x = 126, n y = 72. The discretization along the z direction is defined as n z = 16 [11,12]. The probabilistic approach reconstruction algorithm is then applied, and the solution obtained is illustrated in Figure 10, representing the probability of the presence of the source at each point of the sample.…”

“…Finally, an important point to highlight is the execution time of the program. The calculation, run on a laptop computer (the least powerful of the computers tested) lasted 8.35 s. To compare, in [12], the proposed reconstruction method based on SVD and regularization allows estimating the sources for the same experimental problem. Even if a reduction of the study domain is applied, the execution time of the program is particularly long, more than 6 h are necessary to reconstruct the same sources.…”

3D reconstruction of thermal volumetric sources from surface temperature fields measured by infrared thermography

“…28, run on a laptop computer (the least powerful of the computers tested) lasted 8.35 s. To compare, in Ref. 29, the proposed reconstruction method based on SVD and regularization allows estimating the sources for the same experimental problem. Even if a reduction of the study domain is applied, the execution time of the program is particularly long, more than 6 h are necessary to reconstruct the same sources.…”