Lamb wave imaging based on multi-frequency sparse decomposition

Abstract

Based on the assumption of damage sparsity, scattering signals can be directly sparsely decomposed in the time domain to obtain the scattering coefficients to generate images for indicating damage, which has been comprehensively studied in recent years. However, in these previous studies, the dimension of the constructed dictionary matrix is proportional to the product of the number of discrete imaging points and the signal length, which will cause the “dimensional disaster” problem. Considering the energy and useful information of the received Lamb wave signals are limited within a certain frequency bandwidth, a Lamb wave imaging method based on multi-frequency sparse decomposition in the frequency domain is proposed for damage localization in isotropic plate-like structures. A sparse representation model for the scattering signals in the frequency domain is established based on the constructed frequency domain dictionary matrix. Each single frequency component of the scattering signals obtained from the sensor array is sparsely decomposed one by one to obtain the frequency-dependent scattering coefficients. After that, images indicating damage locations can be generated by fusing the multi-frequency scattering coefficients. Both numerical simulations and experiments on aluminum plates are implemented to validate the proposed method, which provides an alternative tool for Lamb wave based damage localization. Results with a higher signal-to-noise ratio, fewer artifacts, and lower background noise are obtained compared with the conventional delay-and-sum and minimum variance distortionless response methods.