Abstract
Inverse patch transfer functions (iPTF) method is an efficient technique for sound field reconstruction and separation of arbitrarily shaped sound sources in noisy acoustic environments. By applying Neumann boundary condition to a closed virtual cavity surrounding the source, the Helmholtz integral equation is simplified and can be solved with a Green's function satisfying the Neumann boundary condition. However, in the identification of sparsely distributed sources, ghost sources appear in the result solved by using the iPTF method with classic Tikhonov regularization methods and influence the accuracy of identification. In the present work, an evanescent Green's function with fast convergence of calculation is utilized, and a technique that combines the iPTF method and Fast Iterative Shrinkage-Thresholding Algorithm aimed at improving the performance for the identification of sparsely distributed source is proposed. Then double layer measurements, instead of using expensive p-u probes, are employed to acquire the normal velocity of the hologram surface. In numerical simulations, the normal velocities of two anti-phased piston sources are well reconstructed with high sparsity while a disturbing source is radiating in the sound field within the frequency band of 50 to 1000 Hz. Finally, an experiment on two baffled loudspeakers has been carried out. The results of simulations and experiments indicate that the proposed technique has obviously improved the accuracy of the iPTF method in the identification of sparsely distributed sources for the frequency band from 50 to 1000 Hz.
Highlights
Near-field acoustic holography (NAH) has been developed and used for the identification of sound sources and reconstruction of sound field through near-field measurements
The relative error of the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) is 4.42%, much less than 12.06% of the Tikhonov regularization. These results show that the FISTA combining with the Inverse patch transfer functions (iPTF) method is able to provide sparser and more accurate results than the iPTF method with Tikhonov regularization
Numerical and experimental validation of the iPTF method with FISTA is conducted with two baffled piston sources
Summary
Near-field acoustic holography (NAH) has been developed and used for the identification of sound sources and reconstruction of sound field through near-field measurements. To identify sources with an arbitrary structure in nonanechoic environment efficiently, the inverse patch transfer function method (iPTF) has been proposed [11]–[13]. Different from other NAH techniques, the iPTF method reconstructs the sound field with a high resolution by identifying the normal velocity of sound sources [13]. A key process of the iPTF method is to calculate the patch transfer function with the Green’s function of an enclosed volume fulfilling specific boundary conditions. A technique that introduced the idea of FISTA into the iPTF method is presented for the identification of sparsely distributed sources. A vibrating surface Sv radiates with a normal velocity vk in a noisy environment, where reflective waves and disturbing sources exist. After the velocity of the vibrating surface is solved, the sound field around the source can be reconstructed through the Rayleigh’s integral
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