Vibration data recovery based on compressed sensing

Zhang Xin-Peng; Hu Niao-Qing; Cheng Zhe; Zhong Hua

doi:10.7498/aps.63.200506

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:

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).

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Cited By

[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 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 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 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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Vol. 63, Issue 20 - 2014-10-20

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