Agenda
As an inverse problem, sound source localization in three dimensions relies on two distinct cornerstones. One is the physical model chosen to describe the acoustic propagation of the sources to identify and the other is the algorithmic process used to derive information from measured acoustic data. Mainly focusing on the first point, an Equivalent Source Method (ESM) aiming at the simulation of realistic Frequency Response Functions (FRF) is proposed in this paper. The underlying idea is to substitute the acoustic behaviour of a radiating object by a set of acoustic monopoles calibrated with respect to the boundary condition on its skin. Such a method allows to perform 3D Conventional Beamforming (CBF) with FRF taking into account the acoustic environment and the influence of the radiating or scattering structure. Misleading sound source localization outcomes due to ground reflections or diffraction are therefore prevented. As a first step, the ESM process is validated thanks to the Spherical Related Transfer Function which provides a rigorous analytical framework for FRF comparison. ESM boils down to an inverse problem in itself upstream to CBF, and various ways of solving it are assessed. With a view to present an industrial application, FRF are computed on a car mesh and validated thanks to a commercial Finite Elements software. These FRF are then used to carry out 3D CBF with the experimental pressure scattered by an omnidirectional source placed near the rear-view mirror of the car, measured by a 160 microphones array in the Daimler automotive wind tunnel. At the cost of a brief study of CBF sensitivity to the FRF computation, the method yields promising results in comparison with the commonly used free field assumption. Finally, a strategy to include the contribution of wind tunnel convective effects at low Mach number is initiated. To this end, a geometric routine devised by R.K. Amiet is coupled with the ESM boundary condition step and assessed on wind tunnel measurements.