Influence of Typical Factors on Acoustic Source Identification of Grid-free Compressive Beamforming

doi:10.3901/JME.2022.05.98

Abstract

Abstract: Based on microphone array measurement and compressive sensing theory, the grid-free compressive beamforming acoustic source identification method, which treats the target area as a continuum, has good application prospects in military, industrial,environmental and other fields. Monte Carlo simulation and validation experiment are used to investigate the effects of four typical factors （source coherence, the minimum separation of sources, noise interference and the number of data snapshots） on the performance of grid-free compressive beamforming. The results show that this method is suitable for sources with arbitrary coherence and data with any number of snapshots; the conditions to obtain accurate results with high probability is that the sources are sufficiently separate （with a rectangular array and single data snapshot, the minimum separation of sources is usually required to be not less than 1/√AB, where A and B are the number of rows and columns of the rectangular array, respectively） and the noise interference is not strong （with single data snapshot, the signal-to-noise ratio is usually required to be better than 15 d B）; when the sources are not completely coherent, increasing the data snapshot will relax the requirements for source separation and the intensity of noise interference; when the sources are completely coherent, increasing the data snapshot will only relax the requirement for the intensity of noise interference. The disclosure of the influence of typical factors is of guiding significance in the proper application of grid-free beamforming and the correct analysis of the results of acoustic source identification.

Key words: acoustic source identification, grid-free compressive beamforming, typical factors, influence

CLC Number:

TB52

YANG Yang, CHU Zhi-gang, YANG Yong-xin. Influence of Typical Factors on Acoustic Source Identification of Grid-free Compressive Beamforming[J]. Journal of Mechanical Engineering, 2022, 58(5): 98-107.

References

[1] XENAKI A,GERSTOFT P,MOSEGAARD K. Compressive beamforming[J]. Journal of the Acoustical Society of America,2014,136(1):260-271.
[2] GERSTOFT P,XENAKI A,MECKLENBRAUKER C F. Multiple and single snapshot compressive beamforming[J]. Journal of the Acoustical Society of America,2015,138(4):2003-2014.
[3] NING F,WEI J,QIU L,et al. Three-dimensional acoustic imaging with planar microphone arrays and compressive sensing[J]. Journal of Sound and Vibration,2016,380:112-128.
[4] NING F,PAN F,ZHANG C,et al. A highly efficient compressed sensing algorithm for acoustic imaging in low signal-to-noise ratio environments[J]. Mechanical Systems and Signal Processing,2018,112:113-128.
[5] BU H,HUANG X,ZHANG X. High-resolution acoustical imaging for rotating acoustic source based on compressive sensing beamforming[C]//Proceedings of the 25th AIAA/CEAS Aeroacoustics Conference,20-23 May 2019,Delft,Netherlands. AIAA-2019-2410.
[6] YANG Z,XIE L,ZHANG C. Off-grid direction of arrival estimation using sparse Bayesian inference[J]. IEEE Transactions on Signal Processing,2013,61(1):38-43.
[7] PARK Y,SEONG W,GERSTOFT P. Block-sparse two-dimensional off-grid beamforming with arbitrary planar array geometry[J]. Journal of the Acoustical Society of America,2020,147(4):2184-2191.
[8] PARK Y,GERSTOFT P. Compressive 2-D off-grid DOA estimation for propeller cavitation localization[C]//2020 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP),4-8 May 2020,Barcelona,Spain. 2020:4612-4616.
[9] 樊小鹏,余立超,褚志刚,等.二维动态网格压缩波束形成声源识别方法[J].机械工程学报,2020,56(22):46-55. FAN Xiaopeng,YU Lichao,CHU Zhigang,et al. Two-dimensional dynamic grid compressive beamforming for acoustic source identification[J]. Journal of Mechanical Engineering,2020,56(22):46-55.
[10] YANG Y X,CHU Z,YANG Y,et al. Two-dimensional Newtonized orthogonal matching pursuit compressive beamforming[J]. Journal of the Acoustical Society of America,2020,148(3):1337-1348.
[11] XENAKI A,GERSTOFT P. Grid-free compressive beamforming[J]. Journal of the Acoustical Society of America,2015,137(4):1923-1935.
[12] PARK Y,CHOO Y,SEONG W. Multiple snapshot grid free compressive beamforming[J]. Journal of the Acoustical Society of America,2018,143(6):3849-3859.
[13] ANG Y Y,NGUYEN N,GAN W S. Multiband grid-free compressive beamforming[J]. Mechanical Systems and Signal Processing,2020,135:106425.
[14] YANG Y,CHU Z,PING G. Two-dimensional multiple-snapshot grid-free compressive beamforming[J]. Mechanical Systems and Signal Processing,2019,124:524-540.
[15] YANG Y,CHU Z,YANG L,et al. Enhancement of direction-of-arrival estimation performance of spherical ESPRIT via atomic norm minimisation[J]. Journal of Sound and Vibration,2021,491:115758.
[16] CHI Y,SCHARF L L,PEZESHKI A,et al. Sensitivity to basis mismatch in compressed sensing[J]. IEEE Transactions on Signal Processing,2011,59(5):2182-2195.
[17] YANG Z,XIE L,STOICA P. Vandermonde decomposition of multilevel Toeplitz matrices with application to multidimensional super-resolution[J]. IEEE Transactions on Information Theory,2016,62(6):3685-3701.
[18] JO B,CHOI J W. Parametric direction-of-arrival estimation with three recurrence relations of spherical harmonics[J]. Journal of the Acoustical Society of America,2019,145(1):480-488.
[19] YANG Y,CHU Z,XU Z,et al. Two-dimensional grid-free compressive beamforming[J]. Journal of the Acoustical Society of America,2017,142(2):618-629.
[20] YANG Y,CHU Z,PING G,et al. Resolution enhancement of two-dimensional grid-free compressive beamforming[J]. Journal of the Acoustical Society of America,2018,143(6):3860-3872.
[21] LIU M,DONG C,DONG Y,et al. Superresolution 2D DOA estimation for a rectangular array via reweighted decoupled atomic norm minimization[J]. Mathematical Problems in Engineering,2019,2019:6797168.
[22] LIU Y,CHU Z,YANG Y. Iterative Vandermonde decomposition and shrinkage-thresholding based two-dimensional grid-free compressive beamforming[J]. Journal of the Acoustical Society of America, 2020,148(3):EL301-EL306.
[23] DUMITRESCU B. Positive trigonometric polynomials and signal processing applications[M]. Dordrecht, Netherlands:Springer,2007.
[24] BOYD S,VANDENBERGHE L. Convex optimization[M]. Cambridge,UK:Cambridge University Press,2004.
[25] YANG Z,XIE L. Exact joint sparse frequency recovery via optimization methods[J]. IEEE Transactions on Signal Processing,2016,64(19):5145-5157.