基于压缩感知的振动数据修复方法

张新鹏; 胡茑庆; 程哲; 钟华

doi:10.7498/aps.63.200506

摘要

为解决旋转机械振动信号丢失数据修复的问题，提出一种基于压缩感知原理的振动数据修复方法. 首先对采集到的不完整信号进行处理，将无信息输入时刻对应的数据用零元素填充得到有损信号，以单位矩阵为基础，根据有损信号中零元素的位置信息，构造对应于压缩感知框架下的观测矩阵；再根据待修复信号的特点并结合先验知识，构造或选择能够对振动信号进行稀疏表示的字典矩阵；然后使用高效且稳定的追踪算法，根据有损信号、观测矩阵以及字典矩阵重构原始信号，实现丢失振动数据的修复. 使用仿真数据检验方法的有效性；使用实测的轴承振动状态数据验证方法对于振动数据的适用性，并通过比较完整信号、有损信号和修复信号对应的时域和频域特征值来检验数据修复效果. 实验结果表明：本文方法能够有效地实现丢失数据的修复，且从统计特征的角度来看，相比于有损信号，修复信号能够更为准确地描述真实完整的振动信号.

关键词:

Abstract

A missing data recovery method based on compressed sensing is proposed for vibration data of rotating machinery. Firstly, the incomplete signal is transformed into lossy signal by setting the data values corresponding to the time without input as zeros. According to the indices of zero elements in lossy signal, the observation matrix in the frame of compressed sensing is constructed based on identity matrix. Secondly, the dictionary matrix with which the vibration signal can be represented sparsely is chosen or constructed according to the signal needed to be recovered and other prior knowledge. Finally, the original complete signal is recovered based on the lossy signal, observation matrix and dictionary matrix by using an effective and steady pursuit algorithm. The efficiency of the proposed method is validated with simulation data and practical bearing vibration data. Recovery results are discussed by comparing the characteristic values corresponding to the complete signal, lossy signal and recovered signal in time domain and frequency domain. The test results show that the proposed method can well achieve the missing data recovery, and from the view of statistical characteristics, the recovery signal can describe the complete vibration signal more accurately than the lossy signal.

Keywords:

作者及机构信息

1.
国防科学技术大学机电工程与自动化学院, 装备综合保障技术重点实验室, 长沙 410073

基金项目: 国家自然科学基金（批准号：51375484，51205401）资助的课题.

Authors and contacts

1.
Science and Technology on Integrated Logistics Support Laboratory, College of Mechatronics and Automation, National University of Defense Technology, Changsha 410073, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51375484, 51205401).

参考文献

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[25]	Candés E J, Tao T 2005 IEEE Trans. Inf. Theory 51 4203
[26]	Baraniuk R 2007 IEEE Signal Proc. Mag. 24 118
[27]	Davenport M 2010 Ph. D. Dissertation (Houston: Rice University)
[28]	Krahmer F, Ward R 2011 SIAM J. Math. Anal. 43 1269
[29]	Sun Y L, Tao J X 2014 Chin. Phys. B 23 078703
[30]	Wang L Y, Li L, Yan B, Jiang C S, Wang H Y, Bao S L 2010 Chin. Phys. B 19 088106
[31]	Pati Y C, Rezaiifar R, Krishnaprasad P S 1993 Twenty-seventh Asilomar Conference on Signal, System & Computers Pacific Grove, California, November 1-3, 1993 1 44
[32]	Mallat S, Davis G, Zhang Z 1994 SPIE J. Opt. Eng. 33 2183
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[34]	Sun C, He Z J, Zhang Z S, Chen X F, Cao H R, Ning X Y, Zou L M 2013 Chin. J. Mech. Engineer. 49 30 (in Chinese) [孙闯, 何正嘉, 张周锁, 陈雪峰, 曹宏瑞, 宁喜钰, 邹利民 2013 机械工程学报 49 30]

施引文献

[1]	Gu Y, Li Q, Xu B J, Zhao Z 2014 Chin. Phys. B 23 017804
[2]	Gao W, Zha F S, Song B Y, Li M T 2014 Chin. Phys. B 23 010701
[3]	Yu G Y, Song Y F, He X, Zheng X X, Tan D W, Chen J, Yang Y Q 2012 Chin. Phys. B 21 043402
[4]	Liang X X, Ban S L 2004 Chin. Phys. 13 71
[5]	Donoho D L 2006 IEEE Trans. Inf. Theory 52 1289
[6]	Candés E J, Romberg J, Tao T 2006 IEEE Trans. Inf. Theory 52 489
[7]	Candés E J 2006 Proceedings of International Congress of Mathematicians (Switzerland: European Mathematical Society Publishing House) p1433
[8]	Bai X, Li Y Q, Zhao S M 2013 Acta Phys. Sin. 62 044209 (in Chinese) [白旭, 李永强, 赵生妹 2013 物理学报 62 044209]
[9]	Zhao S M, Zhuang P 2014 Chin. Phys. B 23 054203
[10]	Candés E J, Wakin M 2008 IEEE Signal Proc. Mag. 25 21
[11]	Donoho D L, Tsaig Y 2006 Signal Process. 86 533
[12]	Candés E J, Tao T 2006 IEEE Trans. Inf. Theory 52 5406
[13]	Chan W L, Charan K, Takhar D, Kelly K F, Baraniuk R G, Mittleman D M 2008 Appl. Phys. Lett. 93 121105
[14]	Katz O, Bromberg Y, Silberberg Y 2009 Appl. Phys. Lett. 95 131110
[15]	Lustig M, Donoho D, Pauly J M 2007 Magn. Reson. Med. 58 1182
[16]	Herman M, Strohmer T 2009 IEEE Trans. Signal Process 57 2275
[17]	Bajwa W U, Haupt J 2007 IEEE Trans. Signal Process 53 3629
[18]	Bobin J, Starck J L, Ottensamer R 2008 Appl. Math. Comput. 206 980
[19]	Elad M 2007 IEEE Trans. Signal Process 55 5695
[20]	Selesnick I, van Slyke R, Guleryuz O 2004 International Conference on Image Processing (ICIP) Singapore, October 24-27, 2004 p1819
[21]	Elad M, Starck J L, Querre P, Donoho D L 2005 Appl. Comput. Harmon A 19 340
[22]	Zhang Y 2006 Rice University CAAM Technical Report Houston, USA, October, 2006 TR 06-15
[23]	Ning F L, He B J, Wei J 2013 Acta Phys. Sin. 62 174212 (in Chinese) [宁方立, 何壁静, 韦娟 2013 物理学报 62 174212]
[24]	Feng B C, Fang S, Zhang L G, Li H, Tong J J, Li W Q 2013 Acta Phys. Sin. 62 112901 (in Chinese) [冯丙辰, 方晟, 张立国, 李红, 童节娟, 李文茜 2013 物理学报 62 112901]
[25]	Candés E J, Tao T 2005 IEEE Trans. Inf. Theory 51 4203
[26]	Baraniuk R 2007 IEEE Signal Proc. Mag. 24 118
[27]	Davenport M 2010 Ph. D. Dissertation (Houston: Rice University)
[28]	Krahmer F, Ward R 2011 SIAM J. Math. Anal. 43 1269
[29]	Sun Y L, Tao J X 2014 Chin. Phys. B 23 078703
[30]	Wang L Y, Li L, Yan B, Jiang C S, Wang H Y, Bao S L 2010 Chin. Phys. B 19 088106
[31]	Pati Y C, Rezaiifar R, Krishnaprasad P S 1993 Twenty-seventh Asilomar Conference on Signal, System & Computers Pacific Grove, California, November 1-3, 1993 1 44
[32]	Mallat S, Davis G, Zhang Z 1994 SPIE J. Opt. Eng. 33 2183
[33]	DeVore R A, Temlyakov V N 1996 Adv. Comput. Math. 5 173
[34]	Sun C, He Z J, Zhang Z S, Chen X F, Cao H R, Ning X Y, Zou L M 2013 Chin. J. Mech. Engineer. 49 30 (in Chinese) [孙闯, 何正嘉, 张周锁, 陈雪峰, 曹宏瑞, 宁喜钰, 邹利民 2013 机械工程学报 49 30]

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