Localised wavenumber estimation and its application to waveguide discontinuities

Wave propagation methods have been widely investigated for the potential application to the detection and localisation of discontinuities in structural waveguides. In the low-mid frequency ranges, previous preliminary works that used the analytic signal theory have considered local wavenumber estimations based on the time domain for the purpose of localisation in mechanical structures. However, these have not fully exploited the potential of this approach. This is accomplished herein for a one-dimensional infinite-like waveguide by means of two methods applied in the spatial domain; namely the Hilbert transform via the wavenumber domain estimator and the Direct Quadrature method. Modifications are proposed to make these methods more suitable to the space-wavenumber application and for the purpose of localisation. A three-dimensional plot is proposed, where local divergences of the wavenumbers indicate the positions of the discontinuities for otherwise uniform waveguides. Numerical simulations and experiments show an accurate estimation of the local wavenumbers and validate the methods with the proposed modifications for the localisation of different types of discontinuities.