Sparse Signal Processing Technique in Multimodal Dispersive SHM

Abstract

One of the main challenges in developing structural health monitoring algorithms is the multimodal and dispersive nature of the wave propagation. Structural health monitoring makes use of the wave propagation information in order to determine the distance between the measuring equipment and the defect from the reflections caused by the defect. The geometrical information from different sensor locations is then used to determine the spatial position of the defect. The inverse problem approach makes use of the knowledge of the whole mapping between the defect and the reflections. This mapping, also called forward operator, combines the wave propagation and the geometrical information in a natural way. Once the forward mapping is known, a regularization approach can be applied in order to reconstruct the defect out of the reflections in a stable way. The main aim of this paper is to find a formulation of the forward model for an isotropic multimodal dispersive medium, which contains all important features of wave propagation, but is simple enough in order to be used in a regularization approach. As we assume the defects to be few and small in size compared to the whole medium, our solution will be sparse in mathematical sense. In this case, sparse regularization approach is the most appropriate one to solve the inverse problem. We illustrate the application of the proposed method for defect detection by means of simulated Lamb waves.