Forward-propagation-free focusing MUSIC algorithm for Lamb waves

The multiple signal classification (MUSIC) algorithm is originally used for direction of arrival estimation and frequency identification. MUSIC-like algorithms have gained their popularity in structural health monitoring (SHM) owing to their super-resolution characteristic and the virtue of baseline independence. MUSIC essentially is a searching algorithm to find the best phase difference matching between the eigenvector from signal subspace and the presupposed steering vector. However, in the guided-wave-based SHM (in plate-like structure, the guided wave is Lamb wave), the dispersion effect will definitely lead to phase distortion. Therefore, Xu et al. presented a focusing MUSIC algorithm where the time reversal technique is adopted to eliminate the dispersion in the way of back propagation. Seeing that the phase difference information, which is necessary for MUSIC, disappears after back propagation, the damage scattered wave packet, obtained by window truncation, is forward propagated again at the constant group velocity to recover the time of flight information. Nevertheless, the forward propagation process is superfluous from the view of phase matching. In the presented forward-propagation-free focusing MUSIC (FPF-F MUSIC) algorithm (the simplified version of Xu's work), by revising the steering vector in the form of phase coincidence, the matching relation for MUSIC is modified from phase difference matching to phase alignment matching, so that the forward propagation and the steering vector traversal setting for every inspection point are all omitted. The damage localization performance of FPF-F MUSIC is verified on the aluminum plate with double through-hole and surface defects under uniform linear and circular arrays.