Mode separation in frequency–wavenumber domain through compressed sensing of far-field Lamb waves

This method based on Lamb waves shows great potential for long-range damage detection. Mode superposition resulting from multi-modal and dispersive characteristics makes signal interpretation and damage feature extraction difficult. Mode separation in the frequency–wavenumber (f–k) domain using a 1D sparse sensing array is a promising solution. However, due to the lack of prior knowledge about damage location, this method based on 1D linear measurement, for the mode extraction of arbitrary reflections caused by defects that are not in line with the sensor array, is restricted. In this paper, an improved compressed sensing method under the far-field assumption is established, which is beneficial to the reconstruction of reflections in the f–k domain. Hence, multiple components consisting of structure and damage features could be recovered via a limited number of measurements. Subsequently, a mode sweeping process based on theoretical dispersion curves has been designed for mode characterization and direction of arrival estimation. Moreover, 2D f–k filtering and inverse transforms are applied to the reconstructed f–k distribution in order to extract the purified mode of interest. As a result, overlapping waveforms can be separated and the direction of defects can be estimated. A uniform linear sensor array consisting of 16 laser excitations is finally employed for experimental investigations and the results demonstrate the efficiency of the proposed method.