A sparse approximation method for Ultrasonic Monitoring the degradation of adhesive joints

Ultrasonic pulse-echo methods have played a significant role in monitoring the integrity of adhesive joints along their service life. However, since for thin layers the echoes from two successive interfaces overlap in time, it is difficult to extract the parameters of the individual echoes. Over the last decade, sparse approximation methods have been extensively used to address this issue. These methods employ a large dictionary of elementary functions (atoms) and attempt to select the smallest subset of atoms (sparest approximation) that represent the ultrasonic signal accurately. In order to obtain highly sparse results, the dictionary should contain atoms which are similar to the anticipated ultrasonic echoes. However, when ultrasonically monitoring layered joints for long periods, it is expected that the ultrasonic echoes’ shape will change significantly due to degradation of the layers. This will enforce the design of a large dictionary which includes all possible echo waveforms during the monitoring period. Using such a large dictionary may degrade the accuracy of the approximation and will result in high computational cost. In this paper we propose to apply a sparse approximation method, utilizing a small dictionary, just for signals measured before the degradation started. Then, we update the obtained atoms in order to find approximations for signals acquired after the degradation started. Our atom modification procedure is based on a physical model describing only the changes which occurred during the degradation period. The effectiveness of the proposed method is demonstrated through simulations and experiments involving environmentally degraded samples.