基于不动点迭代的增广拉格朗日声源识别算法

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (14) : 243-252.

论文

贺岩松1，2，贾晨阳1，黄琳森1，昝鸣1，徐中明1，2

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Augmented Lagrangian algorithm based on fixed point iteration for sound source identification

HE Yansong1,2， JIA Chenyang1， HUANG Linsen1， ZAN Ming1, XU Zhongming1,2

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摘要

等效源法近场声全息是进行声源识别的重要方法。传统的基于Tikhonov正则化方法局限于相对低的频率，进行高频声源的声场重建时效果较差，而基于最速下降法的宽带声全息(wideband acoustic holography, WBH)方法则在中高频效果较好。为了拓宽声场重建的频率范围并提高声源识别分辨率，本文提出一种基于增广拉格朗日方法(augmented Lagrangian method, ALM)的等效源法声源识别算法，该方法将L1范数正则化模型转化为增广拉格朗日方程的最小化问题，并应用不动点迭代求解得到声源强度。通过仿真与实验表明，与Tikhonov正则化、宽带声全息和快速迭代收缩阈值算法(fast iterative shrinking threshold algorithm, FISTA)三种方法对比，本文所提方法适用于更宽的频率范围，且对不同的全息距离和信噪比具有很好的适应性。
关键词：等效源法；声源识别；压缩感知；增广拉格朗日方法（ALM）

Abstract

Near-field acoustic holography based on the equivalent source method is an important method for sound source identification. The conventional Tikhonov regularization method is limited to relatively low frequencies, and the effect of the sound field reconstruction of high-frequency sound sources is poor. While the wideband acoustic holography （WBH）method based on the steepest descent method has better effects at middle-to-high frequencies. In order to widen the frequency range of sound field reconstruction and to improve the resolution of sound source identification, this paper proposes an equivalent source method based on augmented Lagrangian method（ALM） for sound source identification, which transforms the L1-norm regularized model into the minimization problem of augmented Lagrangian equation, and fixed-point iteration is applied to gain the source strength. Simulations and experiments results show that, compared with the three methods of Tikhonov regularization, wideband acoustic holography and fast iterative shrinking threshold algorithm（FISTA）, the proposed method is suitable for a wider frequency range and has good adaptability to different holographic distances and signal-to-noise ratios.
Key words: equivalent source method; sound source identification; compressive sensing; augmented Lagrangian method（ALM）

导出引用

贺岩松1，2，贾晨阳1，黄琳森1，昝鸣1，徐中明1，2. 基于不动点迭代的增广拉格朗日声源识别算法[J]. 振动与冲击, 2022, 41(14): 243-252

HE Yansong1,2， JIA Chenyang1， HUANG Linsen1， ZAN Ming1, XU Zhongming1,2. Augmented Lagrangian algorithm based on fixed point iteration for sound source identification[J]. Journal of Vibration and Shock, 2022, 41(14): 243-252

参考文献

[1] Wan Q, Jiang W K. Near field acoustic holography (NAH) theory for cyclostationary sound field and its application[J]. Journal of Sound & Vibration, 2006, 290(3-5):956-967.
[2] 何元安,何祚镛,姜军.基于声强测量的近场声全息及其在水下声源声辐射分析中的应用[J]. 声学学报,1996,21(04): 297-305.
HE Yuan-an, He Zuo-yong. Nearfield acoustic holography based on intensity measurement and application in radiating analysis of underwater sound sources[J]. Acta Acoustica, 1996,21(04):297-305.
[3] Williams E G, Maynard J D, Skudrzyk E. Sound source reconstruction using a microphone array[J]. Journal of the Acoustical Society of America, 1980, 68(1): 30-345.
[4] 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.
[5] Bai M R. Application of BEM (boundary element method) based acoustic holography to radiation analysis[J]. Journal of the Acoustical Society of America, 1992, 92(2):533-549.
[6] Kim B K, Ih J G. On the reconstruction of the vibro-acoustic field over the surface enclosing an interior space using the boundary element method[J]. Journal of the Acoustical Society of America, 1996, 105(5): 3003-3016.
[7] Koopmann G H, Song L, Fahnline J. A method for computing acoustic fields based on the principle of wave superposition[J]. Journal of the Acoustical Society of America, 1989, 86(5):2433-2438.
[8] Wang Z, Wu S F. Helmholtz Equation-Least Method for reconstructing the acoustic pressure field [J]. Journal of the Acoustical Society of America, 1997, 102(4): 2020-2032.
[9] Fahnline J B, Koopmann G H. A numerical solution for the general radiation problem based on the combined methods of superposition and singular-value decomposition[J]. Journal of the Acoustical Society of America, 1991, 90(5): 2808-2819.
[10] Hald J. Patch near-field acoustical holography using a new statistically optimal method [C]// INTER-NOISE and NOISE-CON Congress and Conference Proceedings.Jeju ：Institute of Noise Control Engineering, 2003.
[11] Cho Y T, Bolton J T, Hald J. Source visualization by using statistically optimized near-field acoustical holography in cylindrical coordinates[J]. Journal of the Acoustical Society of America, 2005, 118(4): 2355-2364.
[12] Tikhonov A N. Solution of incorrectly formulated problems and the regularization method[J]. Soviet Mathematics Doklady, 1963, 4(4): 1035–1038.
[13] Schuhmacher A, Hald J, Rasmussen K B. Sound source reconstruction using inverse boundary element calculations [J]. Journal of the Acoustical Society of America, 2003, 113(1): 114–127.
[14] Delillo T, Isakov V, Valdivia N, et al. The detection of the source of acoustical noise in two dimensions[J]. Siam Journal on Applied Mathematics, 2001, 61(6): 2104–2121.
[15] Magalhães, Marcelo Bruno S, Tenenbaum R A. Sound Sources Reconstruction Techniques: A Review of Their Evolution and New Trends[J]. Acta Acustica united with Acustica, 2004, 90(2):199-220.
[16] Chardon G, Daudet L, Peillot A, et al. Near-field acoustic holography using sparse regularization and compressive sampling principles[J]. Journal of the Acoustical Society of America, 2012, 132(3):1521-1534.
[17] Gade S, Hald J, Ginn K. Wideband acoustical holography[J]. Sound & Vibration, 2016, 50(2):8-13.
[18] Hald, J. Fast wideband acoustical holography[J]. Journal of the Acoustical Society of America, 2016, 139(4):1508-1517.
[19] Fernandez-Grande E, Xenaki A, Gerstoft P. A sparse equivalent source method for near-field acoustic holography[J]. Journal of the Acoustical Society of America, 2017, 141(1):532-542.
[20] 张晋源，杨洋，褚志刚. 压缩波束形成声源识别的改进研究[J]. 振动与冲击, 2019, 38(01):203-207.
ZHANG Jin-yuan, YANG Yang, CHU Zhi-gang. Improvement of compressive beamforming acoustic source identification[J]. Journal of Vibration and Shock, 2019, 38(01):203-207.
[21] Hald J. A comparison of iterative sparse equivalent source methods for near-field acoustical holography[J]. Journal of the Acoustical Society of America, 2018, 143(6):3758-3769.
[22] 樊小鹏，张鑫，褚志刚，等.分裂增广拉格朗日收缩反卷积声源识别算法[J]. 振动与冲击, 2020,39(23):141-147.
FAN Xiao-Peng, ZHANG Xin, CHU Zhi-gang et al. Split augmented lagrange contraction deconvolution algorithm for sound source identification[J]. Journal of Vibration and Shock, 2020, 39(23):141-147.
[23] Kang M, Kang M, Jung M. Inexact accelerated augmented Lagrangian methods[J]. Computational Optimization & Applications, 2015, 62(2):373-404.
[24] Yi-Fen K E, Chang-Feng M A. An accelerated augmented Lagrangian method for linearly constrained convex programming with the rate of convergence O(1/k2)[J]. Applied Mathematics: A Journal of Chinese Universities, 2017(01):121-130.
[25] Sun M, Liu J. An accelerated proximal augmented Lagrangian method and its application in compressive sensing[J]. Journal of Inequalities & Applications, 2017, 2017(1):263.
[26] Hale E T, Yin W, Zhang Y. Fixed-point continuation for l1-minimization: Methodology and convergence[J]. Siam Journal on Optimization, 2008, 19(3):1107-1130.