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Research Papers

Functional Generalized Inverse Beamforming Based on the Double-Layer Microphone Array Applied to Separate the Sound Sources

[+] Author and Article Information
Shu Li

State Key Laboratory of Mechanical Transmission,
Chongqing University,
No. 174 Shazhengjie, Shapingba,
Chongqing 400044, China
e-mail: leeshu@cqu.edu.cn

Zhongming Xu

State Key Laboratory of Mechanical Transmission,
Chongqing University,
No. 174 Shazhengjie, Shapingba,
Chongqing 400044, China
e-mail: xuzm@cqu.edu.cn

Yansong He

College of Automotive Engineering,
Chongqing University,
No. 174 Shazhengjie, Shapingba,
Chongqing 400044, China
e-mail: hys68@cqu.edu.cn

Zhifei Zhang

State Key Laboratory of Mechanical
Transmission,
Chongqing University,
No. 174 Shazhengjie, Shapingba,
Chongqing 400044, China
e-mail: z.zhang@cqu.edu.cn

Shaoyu Song

State Key Laboratory of Mechanical
Transmission,
Chongqing University,
No. 174 Shazhengjie, Shapingba,
Chongqing 400044, China
e-mail: songshaoyu@163.com

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 30, 2015; final manuscript received December 3, 2015; published online January 27, 2016. Assoc. Editor: Sheryl M. Grace.

J. Vib. Acoust 138(2), 021013 (Jan 27, 2016) (8 pages) Paper No: VIB-15-1289; doi: 10.1115/1.4032305 History: Received July 30, 2015; Revised December 03, 2015

Beamforming based on microphone array measurements is a popular method for identifying sound sources. However, beamforming has many limitations that limit their precision. These limitations are addressed in research. To separate the contributions which come from two sides of the microphone array more accurately, an innovative beamforming method based on a double-layer microphone array, called functional generalized inverse beamforming (FGIB), is proposed to improve beamforming performance. This method, which involves the use of a priori beamforming regularization matrix and a matrix function to redefine the inverse problem, is combined with the advantages of both generalized inverse beamforming (GIB) and functional beamforming. Compared with GIB, with reduced iterations, the computational efficiency of FGIB is greatly improved. The dynamic range of the proposed method can be modestly improved as order v increases. Furthermore, the sidelobes gradually disappear and the mainlobes become narrower. Both simulations and experiments have shown that the sources are correctly located and separated. The proposed FGIB demonstrates the good performance when compared to other beamforming methods in terms of resolution and sidelobes level.

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Figures

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Fig. 1

Geometry used in simulated measurements on monopole point sources

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Fig. 2

The numerical results of two monopole sources at 1 kHz: (a) SOAP, (b) FGIB with v = 1, (c) FGIB with v = 5, and (d) FGIB with v = 10

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Fig. 3

The numerical results of the source in front of the array at 1 kHz: (a) SOAP, (b) FGIB with v = 1, (c) FGIB with v = 5, and (d) FGIB with v = 10

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Fig. 4

The numerical results of the sources at 2.5 kHz: (a) SOAP, (b) FGIB with v = 1, (c) FGIB with v = 5, and (d) FGIB with v = 10

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Fig. 5

Arrangement of the virtual microphone array and the sound sources: (a) the virtual microphone array and (b) the measuring order of three microphones

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Fig. 6

Contour plots of reconstructed sound distribution at 1.5 kHz: (a) FDBF, (b) SOAP, (c) FGIB with v = 2, and (d) FGIB with v = 4

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Fig. 7

Contour plots of reconstructed sound distribution at 3 kHz: (a) FDBF, (b) SOAP, (c) FGIB with v = 2, and (d) FGIB with v = 4

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Fig. 8

Contour plots of reconstructed sound distribution in front of the array at 3 kHz: (a) FDBF, (b) SOAP, (c) FGIB with v = 2, and (d) FGIB with v = 4

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