Combining multi-frequency ultrasonic guided waves and topological derivative
Abstract »Non-destructive testing using conventional ultrasonic methods is slow because the test region is limited to the area below the probe, which then has to be moved on the surface to inspect the whole structure. Ultrasonic guided waves are an attractive alternative because the elastic waves emitted at one location travel over a long distance. By analyzing these waves (i.e., the returning echoes or change of dispersion relationships), the presence of flaws may be detected. Mathematically, this is an inverse problem. A large variety of mathematical methods to solve inverse problems consist in minimizing an instrumental objective function, which gives the difference between the measured and calculated (via convenient modelization) signals. Among these, the topological derivative describes the sensitivity of the objective function to infinitesimal inclusions on the material. Topological derivatives are used nowadays in a variety of fields, including image processing, shape optimization, and crack detection. In particular, in the context of two-dimensional sound propagation in a homogenous medium, the method has been recently improved using multi-frequency signals to deal with situations in which only a limited number of sound emitters and receivers is used, which moreover are concentrated in small regions. Based on these promising results, a project has been initiated to combine topological derivatives with actual experimental runs on guided waves. The aim of this talk will be to present the first steps in this direction.