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Decomposition of multi-mode signals using dispersion curves and Bayesian linear regression

For certain structure types and damage sizes, guided waves offer some distinct advantages for damage detection, such as distance and sizing potential, greater sensitivity and cost effectiveness. Guided waves exhibit in multiple modes, of which for Lamb waves there are two shapes; symmetric and antisymmetric. In damage detection regimes, information and features of individual modes, which propagate from a single source, are useful for localisation and sizing of damage. This leads to motivation to decompose a single signal into the individual modes that are received in the wave-packet. Decomposition of wave modes is possible in full-field Lamb wave data through a forward-backward, two-dimensional Fourier transform method that involves dispersion curve information; though this method cannot be applied directly to signals at a single location. By using this method, the expected nominal waves can be determined for a given propagation distance; i.e. the individual wave modes expected to be present regardless of damage. In the presence of damage, residual signals will be present which contains information on the damage. In this paper, a Bayesian linear regression technique is used to decompose single multi-mode signals into their individual wave modes, which is then used to determine any residual signals. This decomposition is done by determining the expected shape and size of individual mode signals from the full-field decomposed waves. The information inferred by this method both before and after the wave has propagated through damage is studied.