In ultrasonic guided wave–based damage detection, the propagation distance recognition of wave packets is an essential step. However, it is difficult to perform direct distance extraction from guided wave signals since the multimode, mode conversion, and dispersion effects typically lead to wave packet overlapping and distortion. In addition, the identified damage location may be incorrect due to inevitable uncertainties in the procedure of propagation distance recognition and damage localization. Motivated by these difficulties, a novel two-stage approach for propagation distance recognition and damage localization is proposed based on sparse Bayesian learning framework. In the first stage, prior knowledge of a small number of wave packets contained in a signal is exploited to sparsely represent the guided wave signal and then the corresponding propagation distance and amplitude information of each wave packet can be obtained. In the next stage, only a small number of damages occurring in a structure are exploited and a vector consisting of the propagation distances extracted from the previous stage is used to match the atoms in a pre-defined over-complete distance dictionary matrix, to achieve our goal of localizing structural damage. Both procedures of the two stages are realized by the sparse Bayesian learning algorithm, which obtains the most probable value and the corresponding uncertainty. A sampling strategy is presented to transfer the uncertainty of the propagation distance recognition to the subsequent damage localization. Finally, the effectiveness of the proposed method is validated using numerical simulation and experimental investigation on aluminum plates. The proposed method is only valid for single damage localization in the present form, but it has the potential to be extended for multiple damage localization.
Unification of Sparse Bayesian Learning Algorithms for Electromagnetic Brain Imaging with the Majorization Minimization Framework