A new signal processing time-frequency transform for guided waves charcterization

Guided waves (GWs) have characteristic dispersive time-frequency representations (TFRs). Unfortunately, any TFR is subjected to the time-frequency uncertainty principle. This limits the capability of the TFR to distinguish multiple, closely spaced guided modes over a wide frequency range. To this aim we implemented a new time-frequency signal processing tool, that we call Warped Frequency Transform (WFT), that in force of a more flexible tiling of the time-frequency domain presents enhanced guided modes extraction capabilities. Such tiling can be chosen to match the spectro-temporal structure of the different propagating modes by selecting an appropriate warping map which generates non-linearly frequency modulated atoms. The proposed transformation is fast, invertible, and covariant to group velocity-delay shifts. In particular, in this work we propose design and calculation strategies for non-smooth maps tailored to Lamb Waves propagating in a single aluminium plate and to Flexural waves propagating in a hollow steel pipe. Time-transient guided wave propagation events are obtained artificially by means of dedicated Finite Element Simulations. The results show that the WFT limits interference patterns which appears with others TFRs and produces a sparse representation of the guided wave pattern that can be suitable for identification and characterization purposes.