Topological sensitivity analysis in the context of ultrasonic non-destructive testing

This paper deals with the use of the topological derivative in detection problems involving waves. In the first part, a framework to carry out the topological sensitivity analysis in this context is proposed. Arbitrarily shaped holes and cracks with Neumann boundary condition in 2 and 3 space dimensions are considered. In the second part, a numerical example concerning the treatment of ultrasonic probing data in metallic plates is presented. With moderate noise in the measurements, the defects (air bubbles) are detected and satisfactorily localized by means of a single sensitivity computation.