Multifrequency and multimodal sparse reconstruction in Lamb wave based structural health monitoring

In structural health monitoring, Lamb waves are employed extensively to examine and monitor thin structures, such as plates and shells. Typically, a network of piezoelectric transducers is attached to the structural plate member and used for both transmission and reception of the Lamb waves. The signals scattered from defects in the plate are recorded by employing the transducers in pitch-catch pairings. In this paper, we propose a multi-frequency, multi-modal sparse reconstruction approach for localizing defects in thin plates. We simultaneously invert Lamb wave based scattering models for both fundamental propagating symmetric and anti-symmetric wave modes, while exploiting the inherent sparsity of the defects. Dictionaries are constructed for both fundamental wave modes, which account for associated dispersion and attenuation as a function of frequency. Signals are collected at two independent frequencies; one at which the fundamental symmetric mode is dominant, and the other at which only the fundamental anti-symmetric wave mode is present. This provides distinct and separable multi-modal contributions, thereby permitting sparse reconstruction of the region of interest under the multiple measurement vector framework. The proposed defect localization approach is validated using simulated data for an aluminum plate.