Sparse estimation of propagation distances in Lamb wave inspection

The arrival Lamb waves of a receiver usually contain multiple wave packets corresponding to different propagation distances. It is important to accurately identify the propagation distances in Lamb wave inspection and structural health monitoring for damage location. While techniques such as multiplying group velocity and time of flight are simple and capable of estimating propagation distances, their performance is limited because accurate identification of time of flights is also a challenging task. Here a novel approach to estimate propagation distances leading to high resolution from arrival Lamb waves is presented that exploits the sparsity of distance spectrum. The unit pulse response is obtained between the transmitter and receiver and then decomposed into a sparse linear combination of propagation distance-based components. The components are pre-computed from Lamb wave propagation and scattering models, and are used to construct an overcomplete dictionary for sparse decomposition. The distance spectrum is obtained by solving a sparse reconstruction problem. Both synthetic signals with noise and experimental signals recorded on an aluminum plate are investigated. The results demonstrate the effectiveness of the proposed method.