函数波束形成改进FFT-FISTA算法及应用研究

PDF(4011 KB)

振动与冲击 ›› 2025, Vol. 44 ›› Issue (9) : 77-87.

振动理论与交叉研究

函数波束形成改进FFT-FISTA算法及应用研究

赵慎1，2，石少锦1，周超*3，李伟1，张锐1，李俊毅1

作者信息 +

Improved FFT-FISTA algorithm based on function beamforming and its application

ZHAO Shen1,2, SHI Shaojin1, ZHOU Chao*3, LI Wei1, ZHANG Rui1, LI Junyi1

Author information +

文章历史 +

摘要

基于快速傅里叶变换的快速迭代收缩阈值算法（fast iterative shrinkage threshold algorithm based on fast Fourier transform，FFT-FISTA）具有较高的计算效率，但其忽略点扩散函数的空间变化及卷绕误差，造成声源识别性能的损失，为此提出基于函数波束形成的改进FFT-FISTA算法。改进算法以函数波束形成输出作为FFT-FISTA算法的迭代输入，建立函数波束形成、声源分布及升幂空间转移不变点扩散函数的线性方程组，基于周期边界条件下的快速傅里叶变换进行迭代求解，使被运算的非周期函数变为一个周期函数，解决补零边界带来的波数泄漏问题，可提高运算准确性，进一步提升成像性能；通过指数运算锐化点扩散函数主瓣，拓展点扩散函数空间转移不变性假设的适用性。仿真和实验结果表明：相较于常规FFT-FISTA算法，改进算法能提升成像空间分辨率及动态范围，扩大FFT-FISTA算法的有效成像区域，压缩气体泄漏实验结果验证了改进算法的有效性。

Abstract

The Fast Iterative Shrinkage Threshold algorithm based on Fast Fourier transform (FFT-FISTA) has high computational efficiency, as it ignores the spatial variation of the point spread function and the winding error, resulting in the loss of sound source recognition performance. The improved algorithm takes the output of function beamforming as the iterative input of FFT-FISTA algorithm, establishes a linear equation system of function beamforming, sound source distribution and rising power spatial transfer invariant point spread function, and solves it iteratively based on the fast Fourier transform under the periodic boundary condition. The calculated non-periodic function is changed into a periodic function, which solves the problem of wavenumber leakage caused by the zero-filling boundary, which can improve the accuracy of the operation and further improve the imaging performance. The main lobe of the point spread function is sharpened by exponential operation, and the applicability of the assumption of spatial transfer invariance of the point spread function is expanded. The simulation and experimental results show that, compared with the conventional FFT-FISTA algorithm, the improved algorithm can improve the spatial resolution and dynamic range of the imaging, and expand the effective imaging area of the FFT-FISTA algorithm, and the experimental results of compressed gas leakage verify the effectiveness of the improved algorithm.

导出引用

赵慎1, 2, 石少锦1, 周超3, 李伟1, 张锐1, 李俊毅1. 函数波束形成改进FFT-FISTA算法及应用研究[J]. 振动与冲击, 2025, 44(9): 77-87

ZHAO Shen1, 2, SHI Shaojin1, ZHOU Chao3, LI Wei1, ZHANG Rui1, LI Junyi1. Improved FFT-FISTA algorithm based on function beamforming and its application[J]. Journal of Vibration and Shock, 2025, 44(9): 77-87

参考文献

[1] 褚志刚, 余立超, 杨洋, 等. CLEAN-SC波束形成声源识别改进[J]. 振动与冲击, 2019, 38(15): 87-94.
CHU Zhi-gang, YU Li-chao, YANG Yang, et al. Improved acoustic source identification based on CLEAN-SC beamforming[J]. Journal of Vibration and Shock, 2019, 38(15): 87-94.
[2] 杨洋, 倪计民, 褚志刚, 等. 基于互谱成像函数波束形成的发动机噪声源识别[J].内燃机工程,2012,33(03):82-87.
YANG Yang, NI Ji-min, CHU Zhi-gang, et al. Engine noise source identification based on beamforming of cross-spectral imaging function[J]. Chinese Internal Combustion Engine Engineering,2012,33(03):82-87.
[3] NING F L, 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.
[4] XIONG W, HE Q B, PENG Z K. Fibonacci array-based focused acoustic camera for estimating multiple moving sound sources[J]. Journal of Sound and Vibration, 2020, 478(115): 351-367.
[5] 王月, 杨超, 王岩松, 等. 基于压缩聚焦网格点的快速反卷积算法[J]. 振动与冲击, 2022, 41(06): 250-255.
WANG Yue, YANG Chao, WANG Yang-song, et al. Fast deconvolution algorithm based on compressed focus grid points[J]. Journal of Vibration and Shock, 2022, 41(06): 250-255.
[6] Dougherty R P. Functional beamforming[C]. Proceedings on CD of the 5th Berlin Beamforming Conference. Berlin: Berlin Beamforming Conference, 2014:1-25.
[7] 褚志刚, 段云炀, 沈林邦,等.函数波束形成声源识别性能分析及应用[J].机械工程学报,2017,53(04):67-76.
CHU Zhi-gang, DUAN Yun-yang, SHEN Ling-bang, et al. Performance analysis and application of functional beamforming sound source identification[J]. Journal of Mechanical Engineering, 2017, 53(04): 67-76.
[8] Brooks T F, Humphreys W M. A deconvolution approach for the mapping of acoustic sources (DAMAS) determined from phased microphone arrays[J].Journal of Sound & Vibration, 2006, 294(4):856-879.
[9] Ehrenfried K, Koop L. Comparison of Iterative Deconvolution Algorithms for the Mapping of Acoustic Sources[J]. AIAA Journal, 2007, 45(7):1-19.
[10] Beck A, Teboulle M. A fast Iterative Shrinkage-Thresholding Algorithm with application to wavelet-based image deblurring[C]//Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009, 19-24 April 2009, Taipei, Taiwan. IEEE, 2009.
[11] Sijtsma, Pieter. CLEAN based on spatial source coherence[J]. International Journal of Aeroacoustics, 2009, 6(4):357-374.
[12] Yardibi T, Bahr C, Zawodny N, et al. Uncertainty analysis of the standard delay-and-sum beamformer and array calibration[J]. Journal of Sound and Vibration, 2010, 329(13): 2654-2682.
[13] Brooks T F, Humphreys W M J. Extension of DAMAS Phased Array Processing for Spatial Coherence Determination (DAMAS-C)[C]//12th AIAA/CEAS Aeroacoustics Conference, Cambridge, Massachusetts, May 8-10, 2006.2006.
[14] 赵慎, 李伟, 覃业梅, 等. 传声器阵列函数反卷积声源成像算法研究[J]. 仪器仪表学报, 2023, 44(10): 112-119.
ZHAO Shen, LI Wei, QIN Ye-mei, et al. Functional deconvolutional approach for the mapping of acoustic sources algorithm of microphone array[J]. Chinese Journal of Scientific Instrument, 2023, 44(10): 112-119.
[15] 黄琳森, 徐中明, 张志飞, 等. 快速迭代收缩阈值声源识别算法及其改进[J]. 仪器仪表学报, 2021, 42(02): 257-265.
HUANG Ling-seng, XU Zhong-ming, ZHANG Zhi-fei, et al. A fast iterative shrinkage threshold sound source identification algorithm and its improvement[J]. Chinese Journal of Scientific Instrument, 2021, 42(02): 257-265.
[16] 王月, 杨超, 王岩松, 等. 基于互谱矩阵函数的多声源识别方法[J]. 振动、测试与诊断, 2023, 43(02): 277-281.
WANG Yue, YANG Chao, WANG Yan-song, et al. Multi source identification method based on cross spectral matrix function[J]. Journal of Vibration, Measurement & Diagnosis, 2023, 43(02): 277-281.
[17] DOUGHERTY R P. Extensions of DAMAS and benefits and limitations of deconvolution in beamforming[C]. 11th AIAA/CEAS Aeroacoustics Conference, Monterey, CA, 2005: AIAA-2005-2961.
[18] EHRENFRIED E, KOOP L. Comparison of iterative deconvolution algorithms for the mapping of acoustic sources[J]. AIAA JOURNAL, 2007, 45(7): 1584–1595.
[19] LYLLOFF O, FERNANDEZ-GRANDE E. Improve the efficiency of deconvolution algorithms for sound source localization[J]. Journal Acoustical Society of America, 2015, 138(1): 172-180.
[20] 杨洋, 褚志刚, 江洪, 等. 反卷积DAMAS2波束形成声源识别研究[J]. 仪器仪表学报, 2013, 34(08): 1779-1786.
YANG Yang, CHU Zhi-gang, JIANG Hong, et al. Research on DAMAS2 beamforming sound source identification[J]. Chinese Journal of Scientific Instrument, 2013, 34(08): 1779-1786.
[21] Brusniak L. DAMAS2 validation for flight test airframe noise measurements[C]//Proceedings of the 2nd Berlin Beamforming Conference. 2008: 12.
[22] 褚志刚, 杨洋. 基于非负最小二乘反卷积波束形成的发动机噪声源识别[J]. 振动与冲击, 2013, 32(23): 75-81.
CHU Zhi-gang, YANG Yang. Engine noise source identification based on non-negative least squares deconvolution beamforming [J] Vibration and Shock, 2013, 32(23): 75-81.
[23] MAYNARD J D, WILLIAMS E G, LEE Y. Nearfield acoustic holography: I. Theory of generalized holography and the development of NAH[J]. Journal of the Acoustical
Society of America, 1985, 78(4): 1395-1413.
[24] XENAKI A, JACOBSEN F, TIANA-ROIG E, et al. Improving the resolution of beamforming measurements on wind turbines[C/CD]// Proceedings of 20th International Congress on Acoustics, 23-27 August 2010, Sydney, Australia.
[25] Xenaki A, Jacobsen F, Fernandez-Grande E. Improving the resolution of three-dimensional acoustic imaging with planar phased arrays[J]. Journal of Sound and Vibration, 2012, 331(8): 1939-1950.
[26] Chu Z, Chen C, Yang Y, et al. Improvement of Fourier-based fast iterative shrinkage-thresholding deconvolution algorithm for acoustic source identification[J]. Applied Acoustics, 2017, 123: 64-72.
[27] Yoon S H, Nelson P A. A method for the efficient construction of acoustic pressure cross-spectral matrices[J].Journal of Sound & Vibration, 2000, 233(5):897-920.
[28] Dougherty R P. Functional beamforming for aeroacoustic source distributions[C]//20th AIAA/CEAS aeroacoustics conference. 2014: 3066.
[29] Brigham E O. The fast Fourier transform and its applications[M]. Prentice-Hall, Inc., 1988.
[30] Brigham E O, Morrow R E. The fast Fourier transform[J]. IEEE spectrum, 1967, 4(12): 63-70.
[31] Chan R H, Ng M K. Conjugate gradient methods for Toeplitz systems[J]. SIAM review, 1996, 38(3): 427-482.
[32] Gray R M. Toeplitz and circulant matrices: A review[J]. Foundations and Trends® in Communications and Information Theory, 2006, 2(3): 155-239.
[33] Allen C S, Blake W K, Dougherty R P, et al. Aeroacoustics Measurements[M]. Springer, 2002.
[34] 杨洋, 褚志刚. 高性能波束形成声源识别方法研究综述[J]. 机械工程学报, 2021, 57(24): 166-183.
YANG Yang, CHU Zhi-gang. A Review of High-performance Beamforming Methods for Acoustic Source Identification[J]. Journal of Mechanical Engineering, 2021, 57(24): 166-183.