31 Mai – Thesis defense - Hamza Hafidi Alaoui

10 h30 University of Bordeaux (Talence campus)

Ultrasonic topological imaging of periodic media.

The detection, localization and monitoring of the evolution of defects in periodic media and waveguides is a major issue in the field of Non Destructive Testing (NDT). Wave propagation in such media is complex, for example when the velocity depends on the frequency (dispersion) or direction of propagation (anisotropy). The signature of the defect can also be "embedded" in the acoustic field reflected by the structure (reverberation or multiple diffusion). It is to resolve these kinds of problems that the Topological Optimization (TO) has been adapted to the problems of diffraction of the acoustic waves by infinitesimal defects in order to obtain reflectivity images of the inspected media.  The method can be applied to all kinds of environments, regardless their complexity, provided an exact simulation of the wave propagation in a defectless medium is performed. Inspired by the TO, the work of this thesis proposes to implement qualitative imaging methods adapted to the specificities of Phononic Crystals (PC) and waveguides.
First, we focus on the description of the mathematical formalism of Topological Optimization and Full Waveform Inversion (FWI). Although these methods do not try to solve the same inverse problems, we highlight their similarities. In a second step, we apply Topological Imaging (TI) to the inspection in pulse echo configuration of weakly heterogeneous media. Thirdly, we draw inspiration from TI to define a new variant of this term called Hybrid Topological Imaging (HTI). We apply these methods for the pulse echo configuration inspection of PCs created by steel rods immersed in water. We compare the performance of these methods according to the type of defect in the PC. Numerical simulations for some case studies are supported by conclusive experimental trials. In a fourth step, we adapt the TI to a pitch catch configuration in order to implement a method of Structural Health Monitoring (SHM) of waveguides. In this regard, we have developed a new imaging method that is better suited than TI to pitch catch configurations.

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