Traveling distance estimation for dispersive Lamb waves through sparse Bayesian learning strategy

Lamb wave is a promising tool for the nondestructive testing and structural health monitoring (SHM) of plate-like structures. The dispersive effect is an intrinsic property of guided waves, making the energy of the incoming wave packets spreading out in time domain so that wave packets are easily overlapped, which causes the traveling distances of the wave packets hard to be estimated and thus degrades the resolution of imaging. Traveling distance estimation is the basis of damage localization in Lamb wave based SHM. To deal with these problems, a sparse Bayesian learning (SBL) strategy based method is proposed to sparsely estimate the traveling distance of each dispersive wave packet. To establish a spare representation model, an overcomplete dictionary with each atom corresponding to a dispersive Lamb wave is designed to decompose the measured dispersive signal in frequency domain. The sparse representation model is based on a prior knowledge that the number of wave packets in the measured signal is sparse comparing with the number of atoms of the designed dictionary. Then the distance spectrum, the amplitude coefficients in distance domain, can be sparsely recovered via the SBL strategy. Dispersion compensated signal can also be achieved using the distance spectrum and another designed non-dispersive dictionary. Results from simulations and experiments on a plate both demonstrate the effectiveness of the proposed method.