An improvement of the generalized discrete Fourier series based patch near-field acoustical holography

摘要

Patch near-field acoustic holography (NAH) is an effective tool for reconstructing sound field with a small microphone array. The generalized discrete Fourier series based near-field acoustic holography (GDFS-NAH) is a natural patch NAH method. Although Fourier-based, the spectral leakage is greatly reduced in GDFS-NAH by using generalized discrete Fourier series rather than discrete Fourier transform, as more wavenumber components are used in the reconstruction. However, more wavenumber components also lead to the instability in a noisy case. In this study, the GDFS-NAH is improved by remodeling the reconstruction processing and introducing the sparse regularization. Different from the original GDFS-NAH, in which the pressure on the measurement plane is decomposed into discrete Fourier series, the reconstruction model is reformulated by decomposing the particle velocity on the reconstruction plane, which will avoid the inversion in the original model. Meanwhile, the problem is solved by using sparse regularization, which will suppress the influence of high wave number components and promote the stability. Numerical results show that the proposed method can effectively improve the reconstruction accuracy within 100-2000 Hz, and is capable of interpolating the sound filed simultaneously. The advantages of the proposed method are also verified by experiments. (C) 2020 Elsevier Ltd. All rights reserved.