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

Abstract

For certain structure types and damage sizes, guided waves offer some distinct advantages for damage detection, such as range and sizing potential, greater sensitivity and cost effectiveness. Guided waves exhibit multiple modes; for Lamb waves there are two types; 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 facet leads to the 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 from 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 contain 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 made 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.

Informative Bayesian Tools for Damage Localisation by Decomposition of Lamb Wave Signals

“…The spatial sampling size is an important consideration in the experimental setup, as it directly relates to the wavenumber-bandwidth, as the reciprocal of the spatial sampling interval. Here, the second key process is the single-source decomposition [16], meaning decomposing a signal from one location, such as the voltage reading of a piezoelectric transducer. Section 3.2 begins here by explaining the details of the full-field multi-mode separation, which uses a forward-backward two-dimensional Fourier transform approach of masking the experimentally-determined dispersion curves.…”

“…After the nominal wave dictionary was determined and stored, it was used to decompose a Lamb wave signal from a single-source into the nominal and residual signals. This was done using a method first shown by Haywood-Alexander et al [16]. This method uses a Bayesian linear regression (BLR) technique, a description of which can be found in [34] and briefly in Appendix A.…”

“…Such an example would be for fibre-matrix composites, where the attenuation varies with respect to fibre-orientation [15]. Therefore, a method for single-source multi-mode decomposition was developed that only requires prior data on Lamb wave propagation in one direction [16].…”

“…However, for situations where the wave speed is unknown, localisation is still possible using an iterative optimisation procedure [18]. As one advantage of the decomposition strategy used here is its applicability for use with complex geometries and materials [16], it is important to also consider localisation in situations where confidence in prior wave velocity is limited. For such situations, it may be useful to take a probabilistic approach, such as in [19] and [20].…”

“…• The results produce inherent parametric features which are indicative of energy-based features of UGWs [16]. Features are commonly used in all stages of NDE/SHM strategies, and so minimising cost by reducing the number of computational steps required is advantageous.…”