Sparse recovery of multiple dispersive guided-wave modes for defect localization using a Bayesian approach

Guided wave (GW) testing has become one of the most important nondestructive tools for evaluation of structural in-service degradation. Although GW testing was widely used to inspect and screen many engineering structures, there are still challenges associated with its applications, which mostly originate from the dispersive and multi-mode nature of GW signals as well as noise contamination. To deal with these challenges, an effective GW signal processing technique is introduced that enables one to accurately recover multiple modes from noisy dispersive GW signals for defect localization. To characterize the dispersion phenomenon, the chirp model is introduced first, which is derived from GW dispersion characteristics. Based on this model, an over-complete dictionary is designed by considering all possible defect locations (by discretization) and the propagation paths of GW modes caused by these defects. Then the prior knowledge that structural defects or damage typically occur in localized areas and correspondingly only a small number of modes are included in the GW signals is exploited by a robust sparse Bayesian learning (SBL) framework to reduce the ill-conditioning in the inverse problem. During the implementation of the robust SBL algorithm, irrelevant basis vectors in the dictionary are pruned out and the posterior probabilities of the small number nonzero basis coefficients corresponding to those “active” GW modes are established. After sparse representation of the GW signal, the information of propagation paths and group delays of GW modes are used to identify each GW mode and then localize defects. Illustrative results from numerical simulations and experiment studies on plate structures are presented to demonstrate the capability of the proposed method.