基于高阶矩阵函数的广义逆波束形成改进算法

PDF(1238 KB)

振动与冲击 ›› 2017, Vol. 36 ›› Issue (10) : 98-103.

论文

陈思 2，张志飞 1，2，徐中明 1，2，贺岩松 1，2，黎术 2

作者信息 +

Modified Generalized Inverse Beamforming Based on High-order Matrix Function

Chen Si 1 Zhang Zhi-fei 1 Xu Zhong-ming 1 He Yan-song 1 Li Shu 1

Author information +

文章历史 +

摘要

广义逆波束形成是一种高效的声源识别定位方法，然而其计算稳健性易受随机噪声影响，阻碍了其声源识别动力学水平进一步提高。为改善广义逆波束形成声源识别方法的稳健性，基于高阶矩阵函数提出一种广义逆波束形成改进算法：定义了基于广义逆波束形成的正则化矩阵；对正则化矩阵与波束形成输出进行迭代运算；利用高阶矩阵函数对迭代求解所得广义逆波束形成输出的互谱进行优化。通过数值仿真详细分析了声源频率对波束形成矩阵函数阶次取值的影响，得到阶次的最优取值区间。最后通过数值模型和实验算例对单极子与相干声源进行定位识别，结果表明:改进算法在准确识别声源基础上能有效抑制旁瓣干扰，且具有更高的声源识别精度。

Abstract

Generalized inverse beamforming is an effective sound source locating method. But its calculation robustness is sensitive to random noises. For the sake of improving the robustness of generalized inverse beamforming, a modified algorithm based on high-order matrix function is proposed. The regularization matrix is defined based on generalized inverse beamforming and used in iteratively resolving beamforming output. At the same time, the high-order matrix function is incorporated into the cross spectra of beamforming output to optimize the effect of sound source localization. Moreover, to find the optimum range of matrix function order, the numerical simulation is implemented and the influence of sound source frequency on value selection of matrix function order is analyzed correspondingly. Finally, the identifications of both monopole and coherent sound sources are realized numerically and experimentally. The results show that the proposed modified algorithm can identify the source position with higher space resolution and less side-lobe.

导出引用

陈思 2，张志飞 1，2，徐中明 1，2，贺岩松 1，2，黎术 2. 基于高阶矩阵函数的广义逆波束形成改进算法[J]. 振动与冲击, 2017, 36(10): 98-103

Chen Si 1 Zhang Zhi-fei 1 Xu Zhong-ming 1 He Yan-song 1 Li Shu 1 . Modified Generalized Inverse Beamforming Based on High-order Matrix Function[J]. Journal of Vibration and Shock, 2017, 36(10): 98-103

参考文献

[1] 李兵，杨殿阁，邵林，等.基于波束形成和双目视觉的行驶汽车噪声源识别[J].汽车工程, 2008, 30(10): 889- 892.
LI Bing, YANG Dian-Ge, SHAO Lin, et al. Noise sources measurement and identification for moving automobiles [J]. Automotive Engineering, 2008, 30(10):889-892.
[2] J.J Christensen，J. Hald. Beamforming. B&K Technical Review 1．2004:1-31.
[3] Yong Thung Cho，Michael J. Roan. Adaptive near-field beamforming techniques for sound source imaging [J]. J. Acoust. Soc. Am, 2009, 125(2):944-957.
[4] 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(8): 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(8):1779-1786.
[5] Thomas F. Brooks, William M. Humphreys. A deconvolution approach for the mapping of acoustic sources (DAMAS) determined from phased microphone arrays [J]. Journal of Sound and Vibration, 2006, 294(4-5): 856-879.
[6] T. Suzuki. L1 generalized inverse beamforming algorithm resolving coherent/incoherent, distributed and multipole sources [J]. Journal of Sound and Vibration, 2011, 330(24): 5835-5851.
[7] 徐中明，黎术，贺岩松，等. 光滑L0范数广义逆波束形成[J].仪器仪表学报, 2014, 35(6):1276-1281.
XU Zhong-Ming, LI Shu, HE Yan-Song, et al. Smoothed L0 norm generalized inverse beamforming [J]. Chinese Journal of Scientific Instrument, 2014, 35(6): 1276-1281.
[8] J. Peng, J. Hampton, A. Doostan. A weighted L1 minimization approach for sparse polynomial chaos expansions[J]. Journal of Computational Physics, 2014, 267(15): 92-111.
[9] R. A. El-Attar, M. Vidyasagar, S. R. K. Dutta. Algorithm For L1-norm minimization with application to nonlinear L1-approximation [J]. Society for Industrial and Applied Mathematics, 1979, 16(1):70-86.
[10] D. Calvettia, S. Morigib, L. Reichelc,et al. Tikhonov regularization and the L-curve for large discrete ill-posed problems [J]. Journal of Computational and Applied Mathematics, 2000, 123(1): 423-446.
[11] Zou H, Hastie T. Regularization and variable selection via the elastic net [J]. Journal of the royal statistical society series b-statistical methodology, 2005, 67(2):301-320.
[12] P.A. Nelson, S.H. Yoon. Estimation of acoustic source strength by inverse methods: part I, conditioning of the inverse problem [J]. Journal of Sound and vibration ,2000, 233(4): 643-668.
[13] Takao Suzuki. L1 generalized inverse beam-forming algorithm resolving coherent/incoherent, distributed and multipole sources [J]. Journal of sound and vibration, 2011, 330 (24): 5835-5851.
[14] 郝燕玲，成怡，孙枫，等. Tikhonov正则化向下延拓算法仿真实验研究[J]. 仪器仪表学报, 2008, 29 (3): 605- 609.
HE Yanling, CHENG Yi, SUN Feng, et al. Simulation research on Tikhonov regularation algorithm in downward continuation[J]. Chinese Journal of Scientific Instrument, 2008, 29(3):605-609.
[15] 王薇，韩波，唐锦萍. 地震波形反演的稀疏约束正则化方法[J]. 地球物理学报, 2013, 56(1):289-297.
WANG Wei，HAN Bo，TANG Jinpin. ReguIarization method with sparsity constraints for seismic waveform inversion[J]. Chinese Journal of Geophysics, 2013, 56 (1):289-297.
[16] T. Padois, P.A. Gauthier, A. Berry. Inverse problem with beamforming regularization matrix applied to sound source localization in closed wind-tunnel using microphone array [J]. Journal of sound and vibration 2014, 333 (25): 6858-6868.
[17] P.A. Gauthier, C. Camier, Y. Pasco, et al. Beamforming regularization matrix and inverse problems applied to sound field measurement and extrapolation using microphone array[J]. Journal of Sound and Vibration, 2011, 330(24): 5852–5877.
[18] R.P. Dougherty. Functional beamforming[C]. The 5th Berlin beamforming conference (BeBeC)2014, Berlin, 2014, Paper BeBeC-2014-1.
[19] R. P. Dougherty. Functional beamforming for aero-acoustic source distributions[C]. The 20th AIAA aeroacoustics conference2014, Georgia, 2014, AIAA-2014-3066.