In order to improve the sound field reconstruction accuracy of distributed structural source, a new near-field acoustic holography is established based on the element radiation superposition method (ERSM). In the proposed method, the surface of structural source is divided into several regular pistons. The sound field of structural source is considered as the superposition of sound field of pistons. Firstly, we compare the sound field calculated by ERSM with that by Rayleigh's integral. It is proved that ERSM is quite accurate in sound field prediction. Based on ERSM, a vibration acoustic transfer (VAT) function is derived. The VAT function has computable analytical expression and embodies the transfer relationship between the structural source surface and the radiated sound field. The VAT function can precisely characterize the acoustic propagation of continuous distributed coherent sources. Subsequently, we employ the VAT function to replace the Green's function, and apply the VAT function to sound field reconstruction. Different with the equivalent source method (ESM) which is widely used in sound field reconstruction, ERSM directly divides the piston-sources on the surface of structural source rather than constructing the equivalent point-sources on a plane behind the structural source. Furthermore, we introduce a weight matrix into ERSM and iteratively calculate the vibration velocity for a more accurate result, and we call the proposed method as iterative weighted ERSM (IWERSM). In this paper, the simulations and experiment of sound field reconstruction of a rectangular plate are performed. In the proposed method, the rectangular plate is divided into several rectangular pistons. The reconstruction results of ERSM and IWERSM are compared with that of ESM and iterative weighted ESM (IWESM) respectively. The reconstruction accuracies at different distances between the plate and array (test distances) are analyzed. The simulation results show the accuracy of ERSM and IWERSM are better than that of ESM and IWESM respectively. With the increase of test distance, the phenomenon is more obvious, and IWERSM even shows a good reconstruction accuracy while the test distance is more than half a wavelength. The experiment results also validate that ERSM and IWERSM have better reconstruction accuracy than ESM and IWESM respectively at the same test distance. In a word, the simulations and experiments demonstrate that the proposed method can improve the sound field reconstruction accuracy of regular structural source and expand the valid test distance of near-field acoustic holography.

Aiming at the problem of poor spatial resolution of low-frequency noise sources in a small-aperture spherical microphone array (SMA), this paper proposes a method for localizing and identifying low-frequency noise sources based on virtual-vector open SMA (‘p+v’ joint processing method of pressure and velocity). Firstly, a virtual open SMA with a larger aperture is obtained using a virtual array extrapolation method. In this method, the virtual SMA and the actual SMA are regarded as a dual-radius SMA, and velocity information is obtained using finite difference elements of the same direction (azimuth and elevation) array of the virtual and actual SMA. At the same time, the sound pressure at the velocity position is obtained using the virtual SMA extrapolation method and the virtual vector array element SMA, whereby both velocity and sound pressure information is obtained. Finally, the vector signal processing technology is introduced into the generalized inverse beamforming algorithm (GIB). After determining the vector transfer function of the ‘p+v’ joint processing mode, a low-frequency-noise-source localization and identification method based on the vector signal processing GIB is proposed. The simulation and experiment results show that a virtual SMA with a large aperture can be obtained using a virtual array extrapolation method, and the GIB with sound pressure and velocity joint processing has a better spatial resolution.

Nearfield acoustic holography (NAH) is a powerful tool for realizing sources identification and sound field reconstruction. The wave superposition (WS) based NAH is appropriate for the spatially extended sources and does not require the complex numerical integrals. Equivalent source method (ESM), as a classical WS approach, is widely used for its simplicity and efficiency. In ESM, a virtual source surface is introduced, on which the virtual point sources are taken as the assumed sources, and an optimal retreat distance needs to be considered. A newly proposed WS-based approach, the element radiation superposition method (ERSM), uses piston surface sources as the assumed sources without the need to choose a virtual source surface. To satisfy the use conditions of the pressure formula of pistons, the sizes of pistons are set to be as small as possible, which results in large numbers of pistons and sampling points. In this paper, transfer matrix modes (TMMs), which are composed of the singular vectors of the vibro-acoustic transfer matrix, are used as the sparse basis of piston normal velocities. Then, the compressive ERSM based on TMMs is proposed. Compared to the conventional ERSM, the proposed method maintains a good pressure reconstruction when the numbers of sampling points and pistons are both reduced. Besides, the proposed method is compared with the compressive ESM in a mathematical sense. Both simulations and experiments for a rectangular plate demonstrate the advantage of the proposed method over the existing methods.

The spatial resolution of near-field acoustic holography based on the equivalent source method (ESM) is closely related to the number of measurement points, the higher the number of measurement points, the higher the resolution. However, the number of measurement points in the actual measurement cannot be increased infinitely. To solve the contradiction between the resolution and the number of measurement points, this paper proposes an equivalent source density interpolation method (ESDIM). First, the equivalent source intensity is obtained using the sound pressure measured by the array element and the Green function, and the equivalent source intensity density is obtained based on the equivalent source intensity and grid area. Second, the Hermite interpolation function was used to obtain the interpolated equivalent source intensity density. However, as the number of interpolated grids increased, the resolution, computation, and running time of ESDIM increased, and the number of subdivided grids per unit grid was 9-25 in this study. Finally, the sound field was reconstructed based on the obtained interpolated equivalent source intensity and Green transfer function, and the reconstruction accuracies of ESDIM and ESM were compared and analyzed. The simulation and experimental data processing results showed that the resolution of the equivalent source intensity density interpolation method was higher than that of the equivalent source method.

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