Ultrasonic waveguide signal decomposition using the synchrosqueezed wavelet transform for modal group delay computation

Due to the modal behavior of geometrically bounded media, ultrasonic guided waves propagate in waveguides as a combination of multiple dispersive wave packets, which can be simulated as a PDE-problem. Given an excitation in time and space, multiple eigen-modes derived from solving the PDE may propagate each with different dispersion characteristics and weight. Considering a broad-band pulse exciting from one side of a hollow cylindrical waveguide, the received signal at the other side consists of all propagating eigen-modes that can be considered approximately as the narrow band signals. The synchrosqueezed wavelet transform (SWT) is employed to sharpen the time-frequency representation (TFR) of the received waveguide signal. Using a ridge detection algorithm, we successively separate the synchrosqueezed TFR into several narrow band TFRs which can be identified as oscillatory components with time-varying frequency. Then those separated TFRs are reconstructed as narrow band signals using the inverse SWT. Based on an analytical model of the waveguide, we observe that the decomposed signals are similar to those dominant eigen-modes simulated above. Moreover, also the group delay and, therefore, the group velocity of each decomposed signal can be estimated well. This is of high interest when analyzing the characteristic of a given waveguide, such as acoustical property measurements or non-destructive testing.