基于DTCWPT和t-SNE的去噪方法及在故障诊断中的应用
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摘要
为了提取被强噪声淹没的机械设备振动信号中蕴含的微弱故障特征,依据有用信号和噪声在空间分布特性的不同,将流形学习的方法引入到信号降噪中,提出一种将双树复小波包(DTCWPT)和t分布随机近邻嵌入(t-SNE)结合的去噪方法,充分利用了DTCWPT分解的多尺度特性以及t-SNE的非线性降维能力。将振动信号进行双树复小波包分解,依据各尺度小波包系数Shannon熵值搜索最佳小波包基,利用提出的新的阈值函数,对最佳小波包基的小波包系数进行去噪并单支重构组成高维信号空间,然后,采用t-SNE提取高维空间的低维流形,对低维信号序列进一步采用阈值去噪,利用谱回归分析重构回一维信号序列。最后,通过对仿真信号与滚动轴承振动信号进行去噪,结果证实了方法具有良好的非线性去噪性能,将仿真信号的信噪比从-1提高到8.6 d B,并且能更有效的提取强噪声干扰下滚动轴承的故障特征频率。
In order to extract the week fault features contained in the vibration signal of the mechanical equipment with heavy noise,considering the difference of space distribution characteristics of useful signals and noises,a new de-nosing method based on dual-tree complex wavelet packet transform( DTCWPT) and t-distributed stochastic neighbor embedding( t-SNE) was proposed. The method could take full advantage of the multiscale properties of DTCWPT and the nonlinear dimensionality reduction ability of t-SNE. Firstly,the vibration signal was decomposed by DTCWPT,the Shannon entropy was used to seek the best basis of DTCWPT. And a new threshold function was proposed and employed to de-noise the wavelet coefficients of the best basis,then,the wavelet coefficients were reconstructed into a high dimensional space. Secondly,t-SNE was used to extract a low dimensional manifold,threshold de-nosing was further applied to process the low dimensional signal sequences,then the signals were reconstructed back into one dimensional time series by the method of spectral regression analysis. Finally,the noise reduction experiments to the simulated signal and vibration signal of a rolling bearing show that the proposed method has a better nonlinear noise reduction performance,the signal-to-noise ratio of the simulated signal is increased from-1 to 8. 6 d B,and it can be employed to extract the fault frequency of rolling bearing more effectively.
In order to extract the week fault features contained in the vibration signal of the mechanical equipment with heavy noise,considering the difference of space distribution characteristics of useful signals and noises,a new de-nosing method based on dual-tree complex wavelet packet transform( DTCWPT) and t-distributed stochastic neighbor embedding( t-SNE) was proposed. The method could take full advantage of the multiscale properties of DTCWPT and the nonlinear dimensionality reduction ability of t-SNE. Firstly,the vibration signal was decomposed by DTCWPT,the Shannon entropy was used to seek the best basis of DTCWPT. And a new threshold function was proposed and employed to de-noise the wavelet coefficients of the best basis,then,the wavelet coefficients were reconstructed into a high dimensional space. Secondly,t-SNE was used to extract a low dimensional manifold,threshold de-nosing was further applied to process the low dimensional signal sequences,then the signals were reconstructed back into one dimensional time series by the method of spectral regression analysis. Finally,the noise reduction experiments to the simulated signal and vibration signal of a rolling bearing show that the proposed method has a better nonlinear noise reduction performance,the signal-to-noise ratio of the simulated signal is increased from-1 to 8. 6 d B,and it can be employed to extract the fault frequency of rolling bearing more effectively.
引文
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[14]邬战军,牛敏,许冰,等.基于谱回归特征降维与后向传播神经网络的识别方法研究[J].电子与信息学部,2016,38(4):978-984.WU ZH J,NIU M,XU B,etal.Research on recognition method based on spectral regression and back propagation neural network[J].Journal of Electronics&Information Tecnology,2016,38(4):978-984.
[15]李慧,蔺启忠,王钦军,等.基于小波包变换和数学形态学结合的光谱去噪方法研究[J].光谱学与光谱分析,2010,30(3):644-648.LI H,LIN Q ZH,WANG Q J,etal.Research on spectrum denoising methods based on the combination of wavelet package transformation and mathematical morphology[J].Spectroscopy and Spectral Analysis,2010,30(3):644-648.
[16]The case western reserve university bearing data center.Bearings vibration data set[EB/OL].[2017-05-01].http://csegroups.case.edu/bearing data center/home.
[2]吴定海,张培林,任国全,等.基于双树复小波包的发动机振动信号特征提取研究[J].振动与冲击,2010,29(4):160-164.WU D H,ZHANG P L,REN G Q,etal.Feature extraction of an engine vibration signal based on dual-tree wavelet package transformation[J].Journal of Vibration and Shock,2010,29(4):160-164.
[3]WANG Y X,HE Z J,ZI Y Y.Enhancement of signal denoising and multiple fault signatures detecting in rotating machinery using dual-tree complex wavelet transform[J].Mechanical System and Signal Processing,2010,24(1):119-137.
[4]胥永刚,孟志鹏,陆明.基于双树复小波包变换的滚动轴承故障诊断[J].农业工程学报,2013,29(10):49-56.XU Y G,MENG ZH P,LU M.Fault diagnosis of rolling bearing based on dual-tree complex wavelet packet transform[J].Transactions of the Chinese Society of Agricultural Engineering,2013,29(10):49-56.
[5]阳建宏,徐金梧,杨德斌,等.基于主流形识别的非线性时间序列降噪方法及其在故障诊断中的应用[J].机械工程学报,2006,42(8):154-158.YANG J H,XU J W,YANG D B,etal.Noise reduction method for nonlinear time series based on principal manifold learning and its application to fault diagnosis[J].Transactions of the Chinese Society of Agricultural Engineering,2006,42(8):154-158.
[6]WANG G B.Signal denoise method based on fractal dimension,the higher order statistics and local tangent space arrangement[J].Journal of Computers,2012,7(6):1482-1489.
[7]苏祖强,萧红,张毅,等.基于小波包分解与主流形识别的非线性降噪[J].仪器仪表学报,2016,37(9):1954-1960.SU Z Q,XIAO H,ZHANG Y,etal.Nonlinear noise reduction method based on wavelet packet decomposition and principle manifold learning[J].Chinese Journal of Scientific Instrument,2016,37(9):1954-1960.
[8]王奉涛,陈守海,闫达文,等.双偶树小波流形域降噪方法及其在故障诊断中的应用[J].机械工程学报,2014,50(21):159-163.WANG F T,CHEN SH H,YAN D W,etal.Noise reduction based on dual tree complex wavelet transform unfolding and its application in fault diagnosis[J].Journal of Mechanical Engineering,2014,50(21):159-163.
[9]MAATEN L V D,HINTON G.Visualizing data using tSNE[J].Journal of Machine Learning Research,2008,9(11):2579-2605.
[10]COIFMAN R R,WICKERHAUSER M V.Entropy based algorithms for best basis selection[J].IEEE Transactions on Information Theory,1992,38(2):713-718.
[11]赫彬,张雅婷,白艳萍.基于ICA-CEEMD小波阈值的传感器去噪方法[J].振动与冲击,2017,36(4):226-332.HE B,ZHANG Y T,BAI Y P.A method for sensor signal de-noising based on ICA-CEEMD wavelet threshold[J].Journal of Vibration and Shock,2017,36(4):226-332.
[12]石明江,罗仁泽,付元华,等.小波和能量特征提取的旋转机械故障诊断方法[J].电子测量与仪器学报,2015,29(8):1114-1120.SHI M J,LUO R,FU Y H,etal.Fault diagnosis of rotating machinery based on wavelet and energy feature extraction[J].Journal of Electronic Measurement and Instrumentation,2015,29(8):1114-1120.
[13]马婧华,汤宝平,宋涛.基于自适应本征维数估计流形学习的相空间重构降噪方法[J].振动与冲击,2015,34(11):29-34.MA J H,TANG B P,SONG T.Phase space reconstruction method for vibration signal’s noise reduction based on adaptive intrinsic dimension estimation manifold learning[J].Journal of Vibration andShock,2015,34(11):29-34.
[14]邬战军,牛敏,许冰,等.基于谱回归特征降维与后向传播神经网络的识别方法研究[J].电子与信息学部,2016,38(4):978-984.WU ZH J,NIU M,XU B,etal.Research on recognition method based on spectral regression and back propagation neural network[J].Journal of Electronics&Information Tecnology,2016,38(4):978-984.
[15]李慧,蔺启忠,王钦军,等.基于小波包变换和数学形态学结合的光谱去噪方法研究[J].光谱学与光谱分析,2010,30(3):644-648.LI H,LIN Q ZH,WANG Q J,etal.Research on spectrum denoising methods based on the combination of wavelet package transformation and mathematical morphology[J].Spectroscopy and Spectral Analysis,2010,30(3):644-648.
[16]The case western reserve university bearing data center.Bearings vibration data set[EB/OL].[2017-05-01].http://csegroups.case.edu/bearing data center/home.