Application of a topological derivative based inversion method to infrared thermography damage detection and electromagnetic imaging

Resumen

Novel and faster non-destructive methods are of paramount interest in the industry. In this thesis we study of a new algorithm to detect the presence of cracks or defects in thin plates from a set of thermograms of one of its sides while is heated by a lamp. This algorithm consists in formulating a misfit functional between the measured data on the faulty plate, and the simulated measurements that would be obtained with a virtual healthy plate. The topological derivative of this functional is computed and the points where it attains its lowest values are considered to be the estimated position of the defects. This type of algorithm for domain identification based on the topological derivative has been very successful in other areas like electromagnetic imaging, or acoustic imaging. In thesis we tested the algorithm on synthetic data, that is, thermograms generated numerically. The method has shown very promising results: with a small number of multi-frequency experiments the cracks can be easily identified. As a complement, the already studied topological derivative method in electromagnetic imaging was validated against experimental data. The data used was kindly made public by the Institute Fresnel, and supposes a known benchmark in the inverse problem community. The topological derivative based method demonstrated to handle without problem the experimental data, giving results as good as the other methods while doing it in a much faster way.