Beamforming for measurements under disturbed propagation conditions using numerically calculated Green’s functions

Abstract

Beamforming methods for sound source localization are usually based on free-field Green’s functions to model the sound propagation between source and microphones. This assumption is known to be incorrect for many industrial applications and the beamforming results can suffer from this inconsistency regarding both, main lobe width and dynamic range. The aim of this paper is to investigate whether the use of numerically calculated Green’s functions, which include the diffraction and reflection of the sound path between source and microphones, can improve the results of beamforming measurements. The current test cases of numerical and experimental investigations consist of a source placed in a short rectangular duct. The measurements are performed outside the duct in a semi-anechoic chamber. A typical example for this kind of installation is a fan with a heat exchanger. The Green’s functions for this test case are calculated numerically using the boundary element method. These tailored Green’s functions are used to calculate the corresponding beamforming steering vectors. Beamforming measurements are performed in this paper using a loudspeaker mounted in a disc as a reference source in the heat exchanger duct. The measurements are performed both with stationary and rotating disc. The stationary measurements are evaluated in the frequency domain. For the evaluation of the rotating measurements, a new beamforming method in the time domain is presented. This method also uses the stationary Green’s functions, which were calculated numerically in the frequency domain. It is also shown how the weighting of these tailored Green’s functions can be done for time domain beamforming. By means of different validation criteria it can be shown that the results with the numerical calculated Green’s functions are improved compared to free field beamforming. This is true both in the stationary and rotating case.