Linear Sampling Method applied to Non Destructive Testing of an elastic waveguide: theory, numerics and experiments

This paper presents an application of the Linear Sampling Method to ultrasonic Non Destructive Testing of an elastic waveguide. In particular, the NDT context implies that both the solicitations and the measurements are located on the surface of the waveguide and are given in the time domain. Our strategy consists in using a modal formulation of the Linear Sampling Method at multiple frequencies, such modal formulation being justified theoretically in [1] for rigid obstacles and in [2] for cracks. Our strategy requires the inversion of some emission and reception matrices which deserve some special attention due to potential ill-conditioning. The feasibility of our method is proved with the help of artificial data as well as real data.