Single atom convolutional matching pursuit: Theoretical framework and application to Lamb waves based structural health monitoring

Lamb Waves (LW) based Structural Health Monitoring (SHM) aims to monitor the health state of thin structures. An Initial Wave Packet (IWP) is sent in the structure and interacts with boundaries, discontinuities, and with eventual damages thus generating many wave packets. An issue with LW based SHM is that at least two LW dispersive modes simultaneously exist. Matching Pursuit Method (MPM), which approximates a signal as a sum of delayed and scaled atoms taken from a known dictionary, is limited to nondispersive signals and relies on a priori known dictionary and is thus inappropriate for LW-based SHM. Single Atom Convolutional MPM, which addresses dispersion by decomposing a signal as delayed and dispersed atoms and limits the learning dictionary to only one atom, is alternatively proposed here. Its performances are demonstrated on numerical and experimental signals and it is used for damage monitoring. Beyond LW-based SHM, this method remains very general and applicable to a large class of signal processing problems.