基于快速迭代柯西阈值的声场重建方法研究

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (6) : 272-279.

论文

基于快速迭代柯西阈值的声场重建方法研究

黄琳森，徐中明，昝鸣，张志飞，贺岩松

作者信息 +

Sound field reconstruction method based on a fast iterative Cauchy thresholding algorithm

HUANG Linsen, XU Zhongming, ZAN Ming, ZHANG Zhifei, HE Yansong

Author information +

文章历史 +

摘要

在声源识别领域，稳定且准确识别目标声源是一项极具挑战性的任务，尤其在中、低频范围内，因此论文提出快速迭代柯西阈值算法在中、低频段实现鲁棒性较强的声源识别和定位。通过蒙特卡罗分析，与三种经典罚函数方法Tikhonov正则化方法、宽带声全息算法和内点法求解方法相比，所提出的方法在中、低频段获得了稳定的声压重建结果，平均重建误差在5%以下，对声源识别逆问题具有良好的距离适应性和信噪比适应性。

Abstract

In the field of sound source identification, it is a challenging task to identify the target sound source stably and accurately, especially in the middle- and low-frequency range. This paper proposes a fast iterative Cauchy threshold algorithm (FICTA) to identify the sound source and achieve robust sound source location in the middle and low-frequency range. Compared with the other three classical penalty function methods (including Tikhonov regularization method, wideband acoustic holography algorithm and interior point method), the Monte Carlo Analysis shows that the proposed method could obtain the stable sound pressure reconstruction results whose average reconstruction error is below 5% in the medium- and low-frequency range, and it has favorable distance-adaptability and signal-to-noise ratio-adaptability to the inverse problem of the sound source identification.

导出引用

黄琳森，徐中明，昝鸣，张志飞，贺岩松. 基于快速迭代柯西阈值的声场重建方法研究[J]. 振动与冲击, 2023, 42(6): 272-279

HUANG Linsen, XU Zhongming, ZAN Ming, ZHANG Zhifei, HE Yansong. Sound field reconstruction method based on a fast iterative Cauchy thresholding algorithm[J]. Journal of Vibration and Shock, 2023, 42(6): 272-279

参考文献

[1] 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 Lin-bang, et al. Performance analysis and application of functional beamforming sound source identification[J]. Journal of Mechanical Engineering, 2017, 53 (04): 67-76.
[2] 褚志刚，杨洋，王卫东，等. 基于波束形成方法的货车车外加速噪声声源识别[J]. 振动与冲击, 2012, 31(171): 66-70.
CHU Zhi-gang, YANG Yang, WANG Wei-dong, et al. Identification of truck noise sources under passby condition based on wave beamforming method[J]. Journal of Vibration and Shock, 2012, 31(171): 66-70.
[3] ZHANG Jie, XIAO Xin-biao, SHENG Xiao-zhen, et al. An acoustic design procedure for controlling interior noise of high-speed trains[J]. Applied Acoustics, 2020, 168: 107419.
[4] 张海滨，蒋伟康，闫肖杰. 运行列车辐射噪声源定位与声级定量分析研究[J]. 振动与冲击, 2015, 34(247): 88-92.
ZHANG Hai-bin, JIANG Wei-kang, YAN Xiao-jie. Running train noise source locating and quantitive prediction of sound pressure level[J]. Journal of Vibration and Shock, 2015, 34(247): 88-92.
[5] Merino-martínez R, Luesutthiviboon S, Zamponi R, et al. Assessment of the accuracy of microphone array methods for aeroacoustic measurements[J]. Journal of Sound and Vibration, 2020, 470: 115176.
[6] ZHANG Cui-qing, GAO Zhi-ying, CHEN Yong-yan, et al. Locating and tracking sound sources on a horizontal axis wind turbine using a compact microphone array based on beamforming[J]. Applied Acoustics, 2019, 146: 295-309.
[7] Williams E G, Maynard J D, Skudrzyk E. Sound source reconstructions using a microphone array[J]. Journal of the Acoustical Society of America, 1980, 68(1): 340-344.
[8] 张小正，毕传兴，张永斌，等. 基于Laplace变换的瞬态声场质点振速重建方法[J]. 机械工程学报, 2011, 47(19): 68-73.
ZHANG Xiao-zheng, BI Chuan-xing, ZHANG Yong-bin, et al. Method based on the Laplace transform for reconstructing the particle velocity in the transient acoustic field [J]. Journal of Mechanical Engineering, 2011, 47 (19): 68-73.
[9] 张志飞，陈思，徐中明，等. 基于反问题的正则化波束形成改进算法[J]. 仪器仪表学报, 2015, 36(08): 1752-1758.
ZHANG Zhi-fei, CHEN Si, XU Zhong-ming, et al. Modified algorithm of the inverse problem based regularized beamforming [J]. Chinese Journal of Scientific Instrument, 2015, 36 (08): 1752-1758.
[10] 苏俊博，朱海潮，毛荣富，等. 基于声辐射模态的声场重建中的测点优化方法[J]. 振动与冲击, 2017, 36(287): 145-150.
SU Jun-bo, ZHU Hai-chao, MAO Rong-fu, et al. Optimization of measurement points in reconstruction of acoustic field based on acoustic radiation modes[J]. Journal of Vibration and Shock, 2017, 36(287): 145-150.
[11] 向宇，石梓玉，陆静，等. 基于波叠加法的非共形近场声全息波函数的构造与选择[J]. 振动与冲击, 2020, 39(15): 183-192.
XIANG Yu, SHI Ziyu, LU Jing, et al. Construction and selection of nonconformal near-field acoustic holography wave function based on wave superposition method[J]. Journal of Vibration and Shock, 2020, 39(15): 183-192.
[12] WU Hai-jun, JIANG Wei-kang, ZHANG Hai-bin. A mapping relationship based near-field acoustic holography with spherical fundamental solutions for Helmholtz equation. Journal of Sound and Vibration, 2016, 373(7): 66-88.
[13] WU Hai-jun, JIANG Wei-kang. Experimental study of the mapping relationship based near-field acoustic holography with spherical fundamental solutions. Journal of Sound and Vibration, 2017, 394: 185-202.
[14] 宁方立，卫金刚，刘勇，等. 压缩感知声源定位方法研究[J]. 机械工程学报, 2016, 52(19): 42-52.
NING Fang-li, WEI Jin-gang, LIU Yong, et al. Study on sound sources localization using compressive sensing [J]. Journal of Mechanical Engineering, 2016, 52 (19): 42-52.
[15] HUANG Lin-sen, XU Zhong-ming, ZHANG Zhi-fei, et al. A ratio model of ℓ1/ ℓ2 norm for sound source identification[J]. Sensors, 2020, 20(18): 5290.
[16] 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 Lin-sen, 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.
[17] WANG Ran, ZHANG Chen-yu, YU Liang, et al. Sparsity-enhanced equivalent source method for acoustic source reconstruction via the Generalized Minimax-Concave penalty[J]. Mechanical Systems and Signal Processing, 2022, 167: 108508.
[18] BI Chuan-xing, LIU Yuan, XU Liang, et al. Sound field reconstruction using compressed modal equivalent point source method[J]. The Journal of the Acoustical Society of America,2017, 141(1): 73-79.
[19] BI Chuan-xing, LIU Yuan, ZHANG Yong-bin, et al. Extension of sound field separation technique based on the equivalent source method in a sparsity framework[J]. Journal of Sound and Vibration, 2019, 442: 125-137.
[20] 陈璐，郭世旭，王月兵，等. 基于近场声全息的重建算法分析与研究[J]. 计量学报, 2021, 42(10): 1335-1342.
CHEN Lu; GUO Shi-xu; WANG Yue-bing, et al. Analysis and Research of Reconstruction Algorithm Based on Near-field Acoustic Holography[J], Acta Metrologica Sinica, 2021, 42(10): 1335-1342.
[21] 扈宇，胡定玉，方宇，等. 基于稀疏贝叶斯学习的高分辨率Patch近场声全息[J]. 振动与冲击, 2018, 37(324): 104-110.
HU Yu;HU Dingyu;FANG Yu;XIAO Yue, et al. Super resolution patch near-field acoustic holography via sparse Bayesian learning[J]. Journal of Vibration and Shock, 2018, 37(324): 104-110.
[22] 张磊，曹跃云，杨自春. 迭代总体最小二乘正则化的近场声全息方法研究[J]. 振动与冲击, 2016, 35(281): 96-101.
ZHANG Lei, CAO Yue-yun, YANG Zi-chun. Near field acoustic holography based on Newton iteration total least square regularization[J]. Journal of Vibration and Shock, 2016, 35(281): 96-101.
[23] Chardon G, Daudet L, Peillot A, et al. Near-field acoustic holography using sparse regularization and compressive sampling principles[J]. The Journal of the Acoustical Society of America, 2012, 132(3): 1521-1534.
[24] Fernandez-grande E, Xenaki A, Gerstoft P. A sparse equivalent source method for near-field acoustic holography[J]. The Journal of the Acoustical Society of America, 2017, 141(1): 532-542.
[25] Hald J. A comparison of iterative sparse equivalent source methods for near-field acoustical holography[J]. The Journal of the Acoustical Society of America, 2018, 143(6): 3758-3769.
[26] YU Liang, Antoni J, ZHAO Han, et al. The acoustic inverse problem in the framework of alternating direction method of multipliers[J]. Mechanical Systems and Signal Processing, 2021, 149: 107220.
[27] XU Zong-ben, ZHANG Hai, WANG Yao, et al. ℓ1/2 regularization[J]. SCIENCE CHINA Information Sciences, 2010, 53(6): 1159–1169.
[28] Selesnick I. Sparse regularization via convex analysis[J]. IEEE Transactions on Signal Processing, 2017, 65(17): 4481-4494.
[29] CAI Gai-gai, Wang Shi-bin, Chen Xue-feng, et al. Reweighted generalized minimax-concave sparse regularization and application in machinery fault diagnosis[J]. ISA Transactions, 2020.
[30] ZHANG Ben-xin, ZHU Guo-pu, ZHU Zhi-bin. A TV-log nonconvex approach for image deblurring with impulsive noise[J]. Signal Processing, 2020, 174: 107631.
[31] SUN Yu-li, CHEN Hao, TAO Jin-xu, et al. Computed tomography image reconstruction from few views via Log-norm total variation minimization[J]. Digital Signal Processing, 2019, 88: 172-181.
[32] Malioutov D, Aravkin A. Iterative log thresholding[C]. 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2014: 7198-7202.
[33] DENG Yue, DAI Qiong-hai, LIU Ri-sheng, et al. Low-rank structure learning via nonconvex heuristic recovery[J]. Ieee Transactions on Neural Networks and Learning Systems, 2013, 24(3): 383-396.
[34] SHI Ke-han, DONG Gang, GUO Zhi-chang. Cauchy noise removal by nonlinear diffusion equations[J]. Computers & Mathematics with Applications, 2020, 80(9): 2090-2103.
[35] QU Shen-ming, HU Rui-min, CHEN Shi-hong, et al. Face hallucination via Cauchy regularized sparse representation[C]. 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2015: 1216-1220.
[36] WAN T, Canagarajah N, Achim A. Segmentation of noisy colour images using cauchy distribution in the complex wavelet domain[J]. IET Image Processing, 2011, 5(2): 159-170.
[37] Karakuş O, Achim A. On solving SAR imaging inverse problems using nonconvex regularization with a cauchy-based penalty[J]. IEEE Transactions on Geoscience and Remote Sensing, 2020: 1-13.
[38] Tikhonov A N. On the solution of ill-posed problems and the method of regularization[J]. Dokl Akad Nauk SSSR, 1963, 151(3): 501–504.
[39] Gade S, Hald J, Ginn K B. Wideband acoustical holography[J]. Sound and Vibration, 2016, 50(4): 8-13.
[40] SHI Tong-yang, Bolton J S. A comparison of near-field acoustical holography methods applied to noise source identification[J]. SAE Technical Paper, 2019, 2019-01-1533.
[41] Valdivia N P. Advanced equivalent source methodologies for near-field acoustic holography[J]. Journal of Sound and Vibration, 2019, 438: 66-82.
[42] BAI M R. Application of BEM (boundary element method)‐based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries[J]. The Journal of the Acoustical Society of America, 1992, 92(1): 533-549.
[43] Grant M, Boyd S. CVX: Matlab software for disciplined convex programming. cvxr.com/cvx,2013.
[44] Suzuki T. ℓ1 generalized inverse beam-forming algorithm resolving coherent/incoherent, distributed and multipole sources[J]. Journal of Sound and Vibration, 2011, 330(24): 5835-5851.
[45] 赵永峰，杨涛. 基于平滑ℓ0范数的压缩感知近场声全息方法[J]. 压电与声光, 2018, 40(01): 73-78.
ZHAO Yong-feng, YANG Tao. Near-field acoustic holography based on compressive sensing by using the smoothed ℓ0 norm method[J], Piezoelectrics & Acoustooptics, 2018, 40(01): 73-78.
[46] Candès E J, WAKIN M B, BOYD S P. Enhancing Sparsity by Reweighted ℓ1 Minimization[J]. Journal of Fourier Analysis and Applications, 2008, 14(5): 877-905.
[47] PING Guo-li, CHU Zhi-gang, YANG Yang, et al. Wideband holography based spherical equivalent source method with rigid spherical arrays[J]. Mechanical Systems and Signal Processing, 2018, 111: 303-313.
[48] SHI Tong-yang, LIU Yang-fan, Bolton J S. Spatially sparse sound source localization in an under-determined system by using a hybrid compressive sensing method[J]. Journal of the Acoustical Society of America, 2019, 146(2): 1219-1229.
[49] Combettes P L, Pesquet J C. Fixed-Point Algorithms for Inverse Problems in Science and Engineering, Springer New York, New York, 2011: 185-212.
[50] Casandjian, C., Challamel, N., Lanos, C., et al. Cardano's Method. In Reinforced Concrete Beams, Columns and Frames. John Wiley & Sons, New Jersey, 2013: 221-228.
[51] YANG Yong-xin, CHU Zhi-gang, YANG Yang, et al. Two-dimensional Newtonized orthogonal matching pursuit compressive beamforming[J]. The Journal of the Acoustical Society of America, 2020, 148(3): 1337-1348.