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Research Papers

A Comparison of Equivalent Source Method and Monopole Time Reversal Method for Noise Source Localization

[+] 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

Rong Zhou

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

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

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 18, 2018; final manuscript received April 19, 2018; published online May 17, 2018. Assoc. Editor: Nicole Kessissoglou.

J. Vib. Acoust 140(6), 061011 (May 17, 2018) (9 pages) Paper No: VIB-18-1029; doi: 10.1115/1.4040047 History: Received January 18, 2018; Revised April 19, 2018

The equivalent source method (ESM) and monopole time reversal method (MTRM) are two popular techniques for noise source localization. These two methods have some similar characteristics, such as using the pressure field measured by a microphone array as the input and using similar propagation matrices obtained from the Green's function. However, the spatial resolutions of results obtained by these two methods are different. The aim of this paper is to reveal the reason resulting in this difference from a theoretical analysis and compare the performance of these two methods using results from numerical simulations and experiments. Using the singular value decomposition (SVD) technique, the difference between the two methods is found to be only the diagonal matrices of singular values, and the two methods are equivalent after simply replacing the diagonal matrix in the MTRM with its inverse. Comparison of the results demonstrates that the ESM can calculate the real source strength and obtain a high spatial resolution due to the significant amplification of evanescent waves in the inverse process. However, it does not work when the signal-to-noise ratio (SNR) is low or the measurement distance is large. The performance of ESM under these situations can be significantly improved by introducing a regularization procedure. While the MTRM fails to calculate the real source strength and locate the source at low frequencies due to the loss of information of evanescent waves, it works well at high frequencies even with a low SNR and a large measurement distance.

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References

Maynard, J. D. , Williams, E. G. , and Lee, Y. , 1985, “ Nearfield Acoustic Holography—Part I: Theory of Generalized Holography and the Development of NAH,” J. Acoust. Soc. Am., 78(4), pp. 1395–1413. [CrossRef]
Cassereau, D. , and Fink, M. , 1993, “ Focusing With Plane Time-Reversal Mirrors: An Efficient Alternative to Closed Cavities,” J. Acoust. Soc. Am., 94(4), pp. 2373–2386. [CrossRef]
de Rosny, J. , and Fink, M. , 2007, “ Focusing Properties of Near-Field Time Reversal,” Phys. Rev. A, 76(6), p. 065801. [CrossRef]
Fannjiang, A. C. , 2009, “ On Time Reversal Mirrors,” Inverse Probl., 25(9), p. 095010. [CrossRef]
Klemm, M. , Craddock, I. J. , Leendertz, J. A. , Preece, A. , and Benjamin, R. , 2008, “ Improved Delay-and-Sum Beamforming Algorithm for Breast Cancer Detection,” Int. J. Antennas Propag., 4, pp. 264–276.
Rakotoarisoa, I. , Fischer, J. , Valeau, V. , Marx, D. , and Prax, C. , 2014, “ Time-Domain Delay-and-Sum Beamforming for Time-Reversal Detection of Intermittent Acoustic Sources in Flows,” J. Acoust. Soc. Am., 136(5), pp. 2675–2686. [CrossRef] [PubMed]
Besson, A. , Carrillo, R. E. , Bernard, O. , Wiaux, Y. , and Thiran, J. P. , 2016, “ Compressed Delay-and-Sum Beamforming for Ultrafast Ultrasound Imaging,” IEEE International Conference on Image Processing (ICIP), Phoenix, AZ, Sep. 25–28, pp. 2509–2513.
Williams, E. G. , and Maynard, J. D. , 1980, “ Holographic Imaging Without the Wavelength Resolution Limit,” Phys. Rev. Lett., 45(7), pp. 554–557. [CrossRef]
Loyau, T. , Pascal, J. C. , and Gaillard, P. , 1988, “ Broadband Acoustic Holography Reconstruction From Acoustic Intensity Measurement—I: Principle of the Method,” J. Acoust. Soc. Am., 84(5), pp. 1744–1750. [CrossRef]
Veronesi, W. A. , and Maynard, J. D. , 1989, “ Digital Holography Reconstruction of Sources With Arbitrarily Shaped Surfaces,” J. Acoust. Soc. Am., 85(2), pp. 588–598. [CrossRef]
Zhang, Y. , Zhang, X. Z. , Bi, C. X. , and Zhang, Y. B. , 2017, “ An Inverse Direct Time Domain Boundary Element Method for the Reconstruction of Transient Acoustic Field,” ASME J. Vib. Acoust., 139(2), p. 021013. [CrossRef]
Wang, Z. , and Wu, S. F. , 1997, “ Helmholtz Equation-Least Method for Reconstructing the Acoustic Pressure Field,” J. Acoust. Soc. Am., 102(4), pp. 2020–2032. [CrossRef]
Wu, S. F. , and Zhao, X. , 2002, “ Combined Helmholtz Equation-Least Squares Method for Reconstructing the Acoustic Radiation From Arbitrarily Shaped Objects,” J. Acoust. Soc. Am., 112(1), pp. 179–188. [CrossRef] [PubMed]
Sarkissian, A. , 2005, “ Method of Superposition Applied to Patch Near-Field Acoustic Holography,” J. Acoust. Soc. Am., 118(2), pp. 671–678. [CrossRef]
Bi, C. X. , Chen, X. Z. , Chen, J. , and Zhou, R. , 2005, “ Nearfield Acoustic Holography Based on the Equivalent Source Method,” Sci. China Ser. E, 48(3), pp. 338–353. [CrossRef]
Valdivia, N. P. , and Williams, E. G. , 2006, “ Study of the Comparison of the Methods of Equivalent Sources and Boundary Element Methods for Near-Field Acoustic Holography,” J. Acoust. Soc. Am., 120(6), pp. 3694–3705. [CrossRef] [PubMed]
Bi, C. X. , Dong, B. C. , Zhang, X. Z. , and Zhang, Y. B. , 2017, “ Equivalent Source Method-Based Nearfield Acoustic Holography in a Moving Medium,” ASME J. Vib. Acoust., 139(5), p. 051017. [CrossRef]
Zhang, X. Z. , Bi, C. X. , Zhang, Y. B. , and Xu, L. , 2017, “ A Time-Domain Inverse Technique for the Localization and Quantification of Rotating Sound Sources,” Mech. Syst. Signal Process., 90, pp. 15–29. [CrossRef]
Tanter, M. , Thomas, J. L. , and Fink, M. , 2000, “ Time Reversal and the Inverse Filter,” J. Acoust. Soc. Am., 108(1), pp. 223–234. [CrossRef] [PubMed]
Higley, W. J. , Roux, P. , and Kuperman, W. A. , 2006, “ Relationship Between Time Reversal and Linear Equalization in Digital Communications,” J. Acoust. Soc. Am., 120(1), pp. 35–37. [CrossRef]
Prada, C. , and Thomas, J. L. , 2003, “ Experimental Subwavelength Localization of Scatterers by Decomposition of the Time Reversal Operator Interpreted as a Covariance Matrix,” J. Acoust. Soc. Am., 114(1), pp. 235–243. [CrossRef] [PubMed]
Davy, M. , Minonzio, J. G. , de Rosny, J. , Prada, C. , and Fink, M. , 2009, “ Influence of Noise on Subwavelength Imaging of Two Close Scatterers Using Time Reversal Method: Theory and Experiments,” Prog. Electromagn. Res., 98, pp. 333–358. [CrossRef]
Koopmann, G. H. , Song, L. , and Fahnline, J. B. , 1989, “ A Method for Computing Acoustic Fields Based on the Principle of Wave Superposition,” J. Acoust. Soc. Am., 86(6), pp. 2433–2438. [CrossRef]
Fink, M. , Prada, C. , Wu, F. , and Cassereau, D. , 1989, “ Self Focusing in Inhomogeneous Media With Time Reversal Acoustic Mirrors,” IEEE Ultrasonics Symposium, Montreal, QC, Canada, Oct. 3–6, pp. 681–686.
Hillion, P. , 2006, “ Acoustic Pulse Reflection at a Time-Reversal Mirror,” J. Sound Vib., 292(3–5), pp. 488–503. [CrossRef]
Cassereau, D. , Wu, F. , and Fink, M. , 1990, “ Limits of Self-Focusing Using Closed Time-Reversal Cavities and Mirrors—Theory and Experiment,” IEEE Ultrasonics Symposium, Honolulu, HI, Dec. 4–7, pp. 1613–1618.
Lerosey, G. , de Rosny, J. , Tourin, A. , and Fink, M. , 2007, “ Focusing Beyond the Diffraction Limit With Far-Field Time Reversal,” Science, 315(5815), pp. 1120–1122. [CrossRef] [PubMed]
de Rosny, J. , and Fink, M. , 2002, “ Overcoming the Diffraction Limit in Wave Physics Using a Time-Reversal Mirror and a Novel Acoustic Sink,” Phys. Rev. Lett., 89(12), p. 124301. [CrossRef] [PubMed]
Bavu, É. , Besnainou, C. , Gibiat, V. , de Rosny, J. , and Fink, M. , 2007, “ Subwavelength Sound Focusing Using a Time-Reversal Acoustic Sink,” Acta Acust. Acust., 93(5), pp. 706–715. https://www.researchgate.net/publication/225102488_Subwavelength_sound_focusing_using_a_time-reversal_acoustic_sink
Bavu, É. , and Berry, A. , 2009, “ High-Resolution Imaging of Sound Sources in Free Field Using a Numerical Time-Reversal Sink,” Acta Acust. Acust., 95(4), pp. 595–606. [CrossRef]
Conti, S. G. , Roux, P. , and Kuperman, W. A. , 2007, “ Near-Field Time-Reversal Amplification,” J. Acoust. Soc. Am., 121(6), pp. 3602–3606. [CrossRef] [PubMed]
Bi, C. X. , Li, Y. C. , Zhang, Y. B. , and Xu, L. , 2017, “ Super-Resolution Imaging of Low-Frequency Sound Sources Using a Corrected Monopole Time Reversal Method,” J. Sound Vib., 410, pp. 303–317. [CrossRef]
Kim, G. T. , and Lee, B. H. , 1990, “ 3-D Sound Source Reconstruction and Field Reprediction Using the Helmholtz Integral Equation,” J. Sound Vib., 136(2), pp. 245–261. [CrossRef]
Borgiotti, G. V. , 1990, “ The Power Radiated by a Vibrating Body in an Acoustic Fluid and Its Determination From Boundary Measurements,” J. Acoust. Soc. Am., 88(4), pp. 1884–1893. [CrossRef]
Photiadis, D. M. , 1990, “ The Relationship of Singular Value Decomposition to Wave-Vector Filtering in Sound Radiation Problems,” J. Acoust. Soc. Am., 88(2), pp. 1152–1159. [CrossRef]
Williams, E. G. , 2001, “ Regularization Methods for Near-Field Acoustical Holography,” J. Acoust. Soc. Am., 110(4), pp. 1976–1988. [CrossRef] [PubMed]
Yoon, S. H. , and Nelson, P. A. , 2000, “ Estimation of Acoustic Source Strength by Inverse Methods—Part II: Experimental Investigation of Methods for Choosing Regularization Parameters,” J. Sound Vib., 233(4), pp. 665–701.
Harker, B. M. , and Anderson, B. E. , 2013, “ Optimization of the Array Mirror for Time Reversal Techniques Used in a Half-Space Environment,” J. Acoust. Soc. Am., 133(5), pp. EL351–EL357. [CrossRef] [PubMed]

Figures

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Fig. 1

The configuration of the measurement system

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Fig. 2

The diagram of ESM

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Fig. 3

The diagram of MTRM

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Fig. 4

Comparison between the ESM and the MTRM

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Fig. 5

The configuration of the simulation system

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Fig. 6

Localization results at 100 and 2000 Hz when Δz = 0.05 m and SNR = 40 dB. The two “+” give the locations of the two sources.

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Fig. 7

The curves of SFR of MTRM (line with ◻ marks) and ESM with (line with ○ marks) and without (line with * marks) the use of TSVD in the frequency range from 100 to 2000 Hz when Δz = 0.05 m and SNR = 40 dB

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Fig. 8

Localization results at 100 and 2000 Hz when Δz = 0.05 m and SNR = 10 dB. The two “+” give the locations of the two sources.

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Fig. 9

The curves of SFR of MTRM (line with □ marks) and ESM with (line with ○ marks) and without (line with * marks) the use of TSVD at 2000 Hz in the SNR range from 10 to 40 dB when Δz = 0.05 m

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Fig. 10

Localization results at 100 and 2000 Hz when Δz = 0.2 m and SNR = 40 dB. The two “+” give the locations of the two sources.

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Fig. 11

The curves of SFR of MTRM (line with ◻ marks) and ESM with (line with ○ marks) and without (line with * marks) the use of TSVD at 2000 Hz in the measurement distance range from 0.05 to 0.5 m when SNR = 40 dB

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Fig. 12

(a) The experimental setup and (b) the relative position of the two loudspeakers

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Fig. 13

Experimental localization results at 100 and 2000 Hz when Δz = 0.05 m. The two “+” give the locations of the two sources.

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Fig. 14

Experimental curves of SFR of MTRM (line with ◻ marks) and ESM with (line with ○ marks) and without (line with * marks) the use of TSVD in the frequency range from 100 to 2000 Hz when Δz = 0.05 m

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Fig. 15

Experimental localization results at 100 and 2000 Hz when Δz = 0.2 m. The two “+” give the locations of the two sources.

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Fig. 16

Experimental curves of SFR of MTRM (line with ◻ marks) and ESM with (line with ○ marks) and without (line with * marks) the use of TSVD at 2000 Hz in the measurement distance range from 0.05 to 0.5 m

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