Characterisation of the acoustic field radiated by a rail with a microphone array: The SWEAM method

Abstract

Beamforming methods are widely used for the identification of acoustic sources on rail-bound vehicles with microphone arrays, although they have limitations in case of spatially extended sources such as the rail. In this paper, an alternative method dedicated to the acoustic field radiated by the rail is presented. The method is called SWEAM for Structural Wavenumbers Estimation with an Array of Microphones. The main idea is to replace the elementary fields commonly used in beamforming (point sources or plane waves) by specific fields related to point forces applied on the rail. The vertical bending vibration of the rail is modelled using a simple beam assumption so that the rail vibration depends only on two parameters: the wavenumber and the decay rate of the propagative wave. Together with a radiation model based on a line of coherent monopoles, the acoustic field emitted by the rail is easily derived. The method itself consists in using the signals measured on a microphone array to estimate both the structural parameters and the global amplitude of this specific source. The estimation is achieved by minimising a least squares criterion based on the measured and modelled spectral matrices. Simulations are performed to evaluate the performance of the method considering one or several sources at fixed positions. The comparison of the simulated and reconstructed fields are convincing at most frequencies. The method is finally validated in the case of a single vertical excitation using an original set up composed of a 30m long experimental track excited by an electrodynamic shaker. The results show a great improvement of the wavenumber estimation in the whole frequency range compared with the plane wave beamforming method and a fair estimation of the decay rate. The underestimation of some low decay rates due to the poor selectivity of the criterion occurring in these cases requires further study.