Prediction of average propagation characteristics in polygonal reverberant plates for experimental feature extraction

While exploitation of reverberant signals inside bounded media of low acoustic attenuation is customary in room acoustics, it is not so common in NDT&E. Yet, such diffuse signals potentially contain useful quantitative information about the medium and source(s) properties and are very sensitive to either localised or distributed structural changes. Provided proper data extraction techniques are available, it could therefore be advantageously exploited for structural characterisation using only a small set of sensors. Specifically, in this work, we aim at retrieving either information about the source position, or about the mechanical properties of a plate-shaped structure. A statistical time-domain description of the reverberant propagation in plates is developed using the image source method. The average density of received wavepackets due to multiple reflections at the medium boundaries is deduced from the spatial distribution of the image sources. Then, the mathematical expectation (or ensemble average) of the signal envelope or correlation function is theoretically derived, taking into account the dispersive nature of the plate wave (Lamb waves). The relationships between the reverberation properties and structural parameters such as the group velocity and the plate surface are thus explicitly expressed. A major point is that the reverberant behaviour is shown to be governed by a limited set of parameters, thus leading to a significant reduction of the problem complexity. First, by comparison with both numerical and experimental results, the model is shown to correctly predict the average reverberation behaviour of polygonal plates of various shapes and sizes. Then, by fitting the late envelopes of experimental signals to the theoretical expressions provided by the model, a number of terms involving the values of structural parameters can be estimated. Finally, by considering additional relations obtained from the early characteristics (treated in a determ- nistic manner) of the reverberation signals, it is shown possible to extract useful structural parameters. Possible practical applications in terms of structural characterisation and/or source localisation without any time measurement nor trigger synchronisation between the source and the receiver, and without the knowledge of the emitted signal are illustrated. These results show promising potential in the scope of blind parameter estimation or passive source or defect detection.