Measurement of confined acoustic sources using near-field acoustic holography

Abstract

Due to excessive reverberation or to the presence of secondary noise sources, characterization of sound sources in enclosed space is rather difficult to perform. In this paper a process layer is used to recover the pressure field that the studied source would have radiated in free space. This technique requires the knowledge of both acoustic pressure and velocity fields on a closed surface surrounding the source. The calculation makes use of boundary element method and is performed in two steps. First, the outgoing pressure field is extracted from the measured data using a separation technique. Second, the incoming field then scattered by the tested source body is subtracted from the outgoing field to recover free field conditions. The studied source is a rectangular parallelepiped with seven mid-range loudspeakers mounted on it. It stands at 40 cm from the rigid ground of a semi-anechoic chamber which strongly modifies the radiated pressure field, especially on the underside. After the measured data have been processed, the loudspeaker positions are recovered with a fairly good accuracy. The acoustic inverse problem is also solved to calculate the velocity field on the source surface.

The Wave-Matching Boundary Integral Equation — An energy approach to Galerkin BEM for acoustic wave propagation problems

“…This also introduces the possibility that the relative weighting of the sensing of pressure and its surface-normal derivative might be optimised for a particular wave direction. This is done in [54] to eradicate 'front-back confusion' in planar arrays, and in [54][55][56] with spherical arrays to distinguish between waves arriving from outside or emanating from inside the array. Green's theorem is used to extend this to arbitrary shaped arrays in [57]; a similar formulation to this will be derived in two dimensions herein.…”

“…The first step is to acknowledge that the KHBIE, on which (50), (51), (56) and (57) are based, was derived from Green's theorem, so the result given by integration over would also be given by any other boundary so long as the two fields involved satisfy the Helmholtz equation for every point contained in the domain between and the new boundary. Here we are using the oscillatory functions to represent on the boundary, so these must satisfy this condition; for plane wave this will always be true.…”

Sound source identification in a noisy environment based on inverse patch transfer functions with evanescent Green's functions

“…The efficiency of the FST based on spherical harmonic expansions for the identification of sound sources in small spaces was investigated by Braikia et al [23]. To further remove the scattering on a target source from the outgoing field, an iBEM-NAH was proposed by Langrenne et al [24,25] to recover the free field conditions from noisy bounded space situations. The combination of SFT and ESM also gave a satisfactory solution to perform NAH in a noisy environment [26][27][28].…”

An equivalent source technique for recovering the free sound field in a noisy environment

“…Statistically optimized near-field acoustical holography (SONAH) has also been implemented by using a two-layer handheld array, 15,16 an array of pressure-velocity probes, [17][18][19] and a double-layer velocity transducer array. 20 The boundary element method can also be based on using a double-layer array 21,22 or Cauchy data. 23 Further, the equivalent source method (ESM) using double-layer pressure measurements 24 or single-layer pressure-velocity measurements 25, 26 have all recently been developed for the same purpose.…”