基于EMD和BCS的振动信号数据修复方法
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摘要
为改善振动信号修复效果,引入贝叶斯压缩感知(BCS)理论,并提出一种基于经验模态分解(EMD)的贝叶斯压缩感知修复方法,以解决连续缺失信号修复问题。针对随机缺失信号,根据压缩感知修复原理,利用贝叶斯压缩感知算法进行修复;针对连续缺失信号,先对其进行经验模态分解,对分解得到的所有基本模式分量利用多任务贝叶斯压缩感知算法进行修复,最终将所有修复的基本模式分量累加得到整体信号。利用西储大学公开轴承数据进行修复实验,发现所提方法在时频域指标、误差、信噪比、峰值信噪比等方面均优于正交匹配追踪和正则化正交匹配追踪算法。从修复效果角度验证,发现该方法成功还原了外圈故障信号基本模式分量中的故障特征频率,达到了修复的目的。
In order to improve the repairing effect of vibration signal, Bayesian compressed sensing(BCS) theory is introduced, and a Bayesian compressed sensing-based repairing method with empirical mode decomposition(EMD) is proposed to solve the problem of continuously missing signal restoration. For the randomly missing signals, Bayesian compressed sensing algorithm is designed to repair them based on the principle of compressed sensing-based repairing. While for the continuously missing signals, empirical mode decomposition is firstly performed on them, and then all the basic mode components obtained by decomposition are repaired by multi-task Bayesian compressed sensing algorithm. Finally, all the repaired mode components are accumulated to get the whole signal. Experiments on open bearing data from Case Western Reserve University show that the proposed method is superior to orthogonal matching pursuit and regularized orthogonal matching pursuit in time-frequency domain, error, signal-to-noise ratio and peak signal-to-noise ratio. From the perspective of repairing effect, it is found that this method successfully restores the fault feature frequency in the basic mode components of the outer ring fault signal, and achieves the purpose of repairing.
In order to improve the repairing effect of vibration signal, Bayesian compressed sensing(BCS) theory is introduced, and a Bayesian compressed sensing-based repairing method with empirical mode decomposition(EMD) is proposed to solve the problem of continuously missing signal restoration. For the randomly missing signals, Bayesian compressed sensing algorithm is designed to repair them based on the principle of compressed sensing-based repairing. While for the continuously missing signals, empirical mode decomposition is firstly performed on them, and then all the basic mode components obtained by decomposition are repaired by multi-task Bayesian compressed sensing algorithm. Finally, all the repaired mode components are accumulated to get the whole signal. Experiments on open bearing data from Case Western Reserve University show that the proposed method is superior to orthogonal matching pursuit and regularized orthogonal matching pursuit in time-frequency domain, error, signal-to-noise ratio and peak signal-to-noise ratio. From the perspective of repairing effect, it is found that this method successfully restores the fault feature frequency in the basic mode components of the outer ring fault signal, and achieves the purpose of repairing.
引文
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[2] DONOHO D L.Compressed sensing [J].IEEE Transactions on Information Theory,2006,52 (4):1289-1306.
[3] 王强,张培林,王怀光,等.机械振动信号分块自适应压缩感知算法[J].仪器仪表学报,2017,38(2):312-319.WANG Q,ZHANG P L,WANG H G,et al.Adaptive blocked compressed sensing algorithm for the machinery vibration signal [J].Chinese Journal of Scientific Instrument,2017,38(2):312-319.
[4] 孙洁娣,乔艳雷,温江涛.压缩感知域智能天然气管道泄漏孔径识别[J].仪器仪表学报,2017,38(12):3071-3078.SUN J D,QIAO Y L,WEN J T.Pipeline leak aperture identification based on compressed sensing [J].Chinese Journal of Scientific Instrument,2017,38(12):3071-3078.
[5] JI S,XUE Y,CARIN L.Bayesian compressive sensing [J].IEEE Transactions on Signal Process,2008,56 (6):2346-2356.
[6] TORKAMANI R,SADEGHZADEH R A.Bayesian compressive sensing using wavelet based Markov random fields [J].Signal Processing:Image Communication,2017 (58):65-72.
[7] 罗堪,李建清,王志刚,等.心电压缩感知恢复先验块稀疏贝叶斯学习算法[J].仪器仪表学报,2014,35(8):1883-1889.LUO K,LI J Q,WANG ZH G,et al.Prior-block sparse Bayesian learning algorithm for compressed sensing based ECG recovery [J].Chinese Journal of Scientific Instrument,2014,35(8):1883-1889.
[8] 马文洁.贝叶斯压缩感知在DOA估计中的应用研究[D].哈尔滨:哈尔滨工业大学,2014.MA W J.DOA estimation through Bayesian compressive sensing algorithm [D].Harbin:Harbin Institute of Technology,2014.
[9] SELESNICK I W,SLYKE R V,GULERYUZ O G.Pixel recovery via l1 minimization in the wavelet domain [J].International Conference on Image Processing,2004(3):1819-1822.
[10] 宁方立,何碧静,韦娟.基于lp范数的压缩感知图像重建算法研究[J].物理学报,2013,62(17):174212.NING F L,HE J B,WEI J.An algorithm for image reconstruction based on lp norm [J].Acta Physica Sinica,2013,62(17):174212.
[11] ELAD M,STARCK J L,QUERRE P,et al.Simultaneous cartoon and texture image impainting using morphological component analysis(MCA) [J].Applied & Computational Harmonic Analysis,2005,19(3):340-358.
[12] 张新鹏,胡茑庆,程哲,等.基于压缩感知的振动数据修复方法[J].物理学报,2014,63(20):200506.ZHANG X P,HU N Q,CHENG ZH,et al.Vibration data recovery based on compressed sensing [J].Acta Physica Sinica,2014,63(20):200506.
[13] 余路,曲建岭,高峰,等.基于过完备字典的缺失振动数据压缩感知重构算法[J].系统工程与电子技术,2017,39(8):1871-1877.YU L,QU J L,GAO F,et al.Missing vibration data reconstruction using compressed sensing based on over-complete dictionary [J].Systems Engineering and Electronics,2017,39(8):1871-1877.
[14] JI S,DUNSON D,CARIN L.Multi-task compressive sensing [J].IEEE Transactions on Signal Process,2009,57(1):92-106.
[15] 高强,段晨东,赵艳青,等.最大相关波形延拓的经验模式分解端点效应抑制方法[J].振动与冲击,2013,32(2):62- 66.GAO Q,DUAN CH D,ZHAO Y Q,et al.A maximal correlation waveform extension method for end effects reduction of empirical mode decomposition [J].Journal of Vibration and Shock,2013,32(2):62- 66.
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