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Research Papers

Analytical Passive Time Reversal Method Combined With Equivalent Source Method for Sound Source Localization in an Enclosure

[+] Author and Article Information
Chuan-Xing Bi

Institute of Sound and Vibration Research,
Hefei University of Technology,
193 Tunxi Road,
Hefei 230009, China
e-mail: cxbi@hfut.edu.cn

Yong-Chang Li

Institute of Sound and Vibration Research,
Hefei University of Technology,
193 Tunxi Road,
Hefei 230009, China
e-mail: lyc19490@163.com

Yong-Bin Zhang

Institute of Sound and Vibration Research,
Hefei University of Technology,
193 Tunxi Road,
Hefei 230009, China
e-mail: ybzhang@hfut.edu.cn

Rong Zhou

School of Mechanical Engineering,
Hefei University of Technology,
193 Tunxi Road,
Hefei 230009, China
e-mail: zhourong2015@hfut.edu.cn

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 9, 2018; final manuscript received January 13, 2019; published online March 4, 2019. Assoc. Editor: Zhongquan Charlie Zheng.

J. Vib. Acoust 141(3), 031014 (Mar 04, 2019) (8 pages) Paper No: VIB-18-1293; doi: 10.1115/1.4042818 History: Received July 09, 2018; Revised January 13, 2019

The analytical passive time reversal method (APTRM) is a powerful technique for sound source localization. In that technique, it generally requires that the frequency response function relating the measurement point to the focusing point should be known in advance. However, inside an enclosure of arbitrary shape, there is no theoretical formulation of this frequency response function, and using the APTRM with the free-field Green's function might lead to inaccurate localization of sound sources. This paper proposes a method combining the APTRM with the equivalent source method (ESM) to locate sound sources in an enclosure of arbitrary shape. In this method, the frequency response function relating the measurement point to the focusing point inside the enclosure is first calculated numerically using the ESM, and then the APTRM with this numerical frequency response function is used to realize the localization of sound sources. Numerical simulations in a rectangular enclosure and an enclosure of arbitrary shape as well as an experiment in a rectangular wooden cabinet are performed to verify the validity of the proposed method. The results demonstrate that the frequency response function in an enclosure can be accurately calculated using the ESM; based on measurements with a spherical array composed of 48 microphones, the proposed method can effectively locate the sound sources in enclosures of different shapes and work stably under the situation of low signal-to-noise ratio.

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Figures

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Fig. 1

The schematic diagram of ESM

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Fig. 2

Coordinates of microphones on the spherical array

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Fig. 3

The schematic diagram of the rectangular enclosure

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Fig. 4

The magnitudes of the frequency response function between points A(0.2 m, 0.2 m, 0.2m) and B(0.8 m, 0.8 m, 0.8 m) in the rectangular enclosure calculated by the ESM and the modal model

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Fig. 5

The localization results at two frequencies of 1500 and 2000 Hz. Black spots in the figures indicate the actual locations of sound sources. The different colors in the figures indicate different normalized amplitudes of the time-reversed fields.

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Fig. 6

The curve of SFR of the proposed method in the frequency range from 100 to 2000 Hz

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Fig. 7

The curve of SFR of the proposed method in the SNR range from 0 to 40 dB at 2000 Hz

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Fig. 8

A simplified car model

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Fig. 9

The localization results at two frequencies of 1500 and 2000 Hz, respectively. Black spots in the figures indicate the actual locations of sound sources. The different colors in the figures indicate different normalized amplitudes of the time-reversed fields.

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Fig. 10

The curve of SFR of the proposed method in the frequency range from 100 to 2000 Hz

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Fig. 11

The curve of SFR of the proposed method in the SNR range from 0 to 40 dB at 2000 Hz

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Fig. 12

The experimental setup

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Fig. 13

The magnitudes of the frequency response function between points A(0.2 m, 0.2 m, 0.2 m) and B(0.6 m, 0.3 m, 1.2 m) calculated by the ESM and the modal model

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Fig. 14

The localization results at two frequencies of 1500 and 2000 Hz, respectively. Black spots in the figures indicate the actual locations of sound sources. The different colors in the figures indicate different normalized amplitudes of the time-reversed fields.

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Fig. 15

The curve of SFR of the proposed method in the frequency range from 100 to 2000 Hz

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