Sparse signal processing and deep learning for guided waves NDT and SHM

Lamb-wave testing for Structural Health Monitoring (SHM) is complicated by the dispersive nature of wave modes, which deteriorates the wave spatial resolution and makes the experimental data hard to interpret. Mathematical operators such as the Warped Frequency Transform (WFT) are particularly suited for the analysis of Guided Waves (GWs). Indeed, WFT-based analysis methods are capable to achieve sparse representations of GW signals. These methods naturally lead to super-resolved and artifact-free representations, even in noisy environments, and are particularly effective to extract the information on the wave distance of propagation. The concept of sparse representations is also the basis of the so-called compressive sensing (CS) theory. CS proves that a signal which is sparse in a given representation can be compressed directly at the sampling stage. In this paper, a CS framework for Lamb wave field acquisitions with air-coupled probes or laser-Doppler vibrometers will be reviewed. Moreover, it will be shown how the capability to restore high-resolution details from CS input images can be improved dramatically by recent breakthroughs in deep learning and convolutional neural networks.