Quantitative evaluation of crack based on the sparse decomposition of array Lamb wave propagation

Crack damage is one of the significant factors that may accumulate at the stress concentration area of engineering structures and cause catastrophic accidents. In this paper, we proposed a novel approach to identify the crack location and size by exploiting the reflections and diffractions of Lamb waves. The interaction mechanism between the crack and Lamb wave has been analyzed thoroughly, our analysis of the interaction between the crack and Lamb wave revealed that both reflections and diffractions carry valuable damage information that reflects the size and orientation of the crack. As the interaction coefficients between these two components and the crack are different, there are supposed to exist differences between them in the amplitude value. We implemented a threshold to classify the signals received from all paths into two groups: reflections and diffractions. Then we constructed an overcomplete dictionary of waveforms corresponding to different propagation distances to extract the damage information. Using sparse decomposition, the received signals were mapped to their corresponding propagation distances without the use of baseline signals. The diffractions allow us to determine the crack's tip points, while the reflections provide information about the edge points. The kinked crack's size and orientation were visualized based on the time-domain signals acquired in our experiment. We provided a comprehensive description of our algorithm and verified it through numerical simulation and experimental data. Our results show high agreement with actual cracks, demonstrating the efficacy of our proposed method.