Defect detection combining multifrequency ultrasonic guided waves and topological derivative

Abstract

Ultrasonic guided waves are an attractive alternative to conventional methods.By analyzing these waves, the presence of aws may be detected. Mathematically, this is aninverse problem. A large variety of mathematical methods to solve inverse problems consist inminimizing an instrumental objective function, which gives the difference between the measuredand calculated signals. Among these, the topological derivative describes the sensitivity of theobjective function to in nitesimal inclusions on the material. In this work we investigate thereconstruction of an obstacle buried in an aluminium plate by a non-iterative method based onthe computation of topological derivatives. This is done by extending to the present context someideas by Funes et al. (2016) that gave very good results in the context of the two-dimensionalwave equation. The main purpose is to suitably combine multi-frequency data obtained viapiezoelectric emitters and receivers. In the rst part of the work, the method to detect defectsis described. In the second part, as a proof of the concept, some reconstruction examples areshown.