外文翻译--滚柱轴承初始故障诊断的方法 英文版

International Journal of Plant Engineering and Management V0112 No4 December 2007A Method for Incipient Fault Diagnosis of Roller BearingsFilter and Hilbert TransformZENG Qinghu，qw Ji，lg，LIU Guan-junCollege of Mechatronic Engineering and Automation，National University ofDefense Technology，Changsha 410073，PRChinaAbstract：Noise is the biggest obstacle that makes the incipient丘ult diagnosis results of roller bearingsincipient如ult of roller bearings based on the Wavelet Trans-扣m Correlation Filter and Hilbert Transform WritSare picked印加m the roller bearingsFirst，the weak扣ult information features如ult vibration signals妙琊e of a denoising characteristic of them Correlation Filter as the preprocessing of the Hilbert Envelope AnalysisThen，讯order to get知uh features frequency，de-noised wavelet of high scales which represent highfrequency signal were analyzed by Hilbert Envelope Spectrum AnalysisThe simulation signals and diagnosing examples analysis results reveal that the proposed method is more effective than the method ofdirect wavelet coefficientsHilbert Transform in denoising and clarifying roller bearing incipient知uhKey words：wavelet correlation Filter，Hilbea transform，envelope spectrum，fault diagnosis，rollerbearings1 IntroductionRoller bearings are frequently applied components in the vast majority of rotating machinesTheirrunning quality influences the working performance of equipmentAt present，the generally usedmethods for diagnosing roller bearing fault include FFvr spectrum analysis and high frequency demodulation analysis，but the two methods are deficientThe reasons are：(1)beating fault vibration sig-nals usually have unstable characteristics；(2)the feature information of roller bearing incipientfault is weak and the working condition is full of noise；feature information is inundated with noiseand difficulty identifiedSo how to pick up fault feature information and how to increase signal-tonoise ratio are the key technologies for diagnosing roller bearing incipient faultWavelet analysis came forth in the 1980sSince then，people began to use wavelet analysis to dealwith vibration signals and achieved some favorable effects卜31Almost all methods use WaveletTransform(WT)or Wavelet Pocket Translation(WPT)to pick up fault characteristics directly，which were not ideal when the working condition is full of strong noiseThe reason is that fault sig-nals are inundated with noise in each frequency channelThe Wavelet Transform Correlation Filter(WTCF)is based on the fact that sharp edges have large signals over many wavelet scales and noiseReceived 1 August 2007 万方数据A Method for Incipient Fault Diagnosis of Roller Bearings Based on the WaveletTmnsform Correlation Filter and Hilbert Tmnsform 193will die out swiftly with scale；the direct spatial correlation of wavelet coefficients at several adjacentscales sharpens and enhances edges and significant features while suppressing noise and small sharpfeatures；edges and significant features can be obtained from the noise，and noise is removed basedon threshold inspection；signal-to-noise ratio of wavelet coefficients of WTCF is much higher thanthat of wavelet coefficients of WTIn this papera new method of diagnosing incipient fault of rollerbearings based on WTCF and Hilbert Transform is proposedFirst，the weak fault information features are picked up from the roller beating fault vibration signals by use of a de-noising characteristicof the WTCF as the preprocessing of the Hilbert Envelope AnalysisThen，in order to get fault fea-turo frequency，denoised wavelet coefficients of high scales which represent a high frequency signalis analyzed by the Hilbert Envelope SpectrumThe simulation signals and diagnosing examples anal-ysis results reveal that the proposed method is more effective than the method of direct wavelet coef6cients-Hilbert Transform in denoising and clarifying roller bearing incipient fault2 Wavelet transfotin correlation filterThe de-noising idea of the Wavelet Transform Correlation Filter(WTCF)41 is based on the fact thatsharp edges have large signals over many wavelet scales and noise will die out swiftly with scale；thedirect spatial correlation of wavelet coefficients at several adjacent scales sharpens and enhances edges and significant features while suppressing noise and small sharp features；edges and significantfeatures can be obtained from the noise and noise is removed based on threshold inspectionSignal-tonoise ratio of wavelet coefficients of WTCF is much higher than that of wavelet coefficients of WTThe WTCF have easily implemented and robust characteristics，and it can be as a signal processingtool applied to pick up incipient fault features of mechanical equipmentWe are using the directspatial correlation Corrl(m，玮)of wavelet transform contents at several adjacent scales to accuratelydetect the locations of edges or other significant features1一lCorrl(m，n)=I-Y(m+f，n)， 厅=1，2，N (I)#0Where N is the point number of a discrete signal，n is the translation index，m is the scale index，Ydenotes tlle wavelet transform data o“，l is the number of scales involved in the direct multiplicationmMl+1，and M is the total number at scalesUsually。we select l=2The presence of edgesor other significant features in a localized region of the signal allows the noisy background to be removedThe direct spatial correlation of edge-detection data over several scales sharpens and enhances major edges while suppressing noise and small sharp featuresIn this paper，the proposed a1gorithm makes use of the correlation characteristics to pick up significant features from the noiseThe algorithm is described briefly as follows：the filtered data is referred to as Yf,the initializationsof all elements are zero(I)Compute the correlation Corr2(m，n)for every wavelet scale m to obtain enhanced significantfeatures and suppressed noise(2)Rescale the power ofCorr2(m，n)to that of】，(m，n)and getNew Corr2(m，New Corr2(m，n)=Corr2(m，n)n)(2) 万方数据194 International Journal of Plant Engineering and Management V0112 No4 December 2007Where PY(m、=PCorr2(m)=Y(m，17,)2 (3)Corr2(rn，昂)2 (4)PY(m)is the mth scale wavelet coefficients and PCorr2(m)is the mth power of Corr2(m，n)(3)If INew Corr2(m，n)IIY(m，n)I，we accept the point as an edgePass Y(m，It)to rf，and reset y(m，乃)and Corr2(m，n)to 0Otherwise，we assume y(m，n)is produced by noiseand then retain y(m，n)and Corr2(m，n)(4)Return to(1)，repeat(2)and(3)until the power ofy(m，n)is nearly equal to the thresholdratio th(m)which is correlated with some reference noise power at the mth wavelet scaleThis procedure of power normalization，data value comparison，and edgebe iterated many times until the power of un-extracted data points in y(some reference noise power at the mth wavelet scale561On the start of the process，it isnoise will be extracted鹪edgesinformation extraction canm，n)is nearly equal tonecessary to estimate the reference noiseIn fact，we find that too muchthrough experiment analysis，to avoid this，we multiply i l，(m，n)I bya weight A(m)31 and impose that only when 1New Cbrr2(m，n)IA(m)Iy(m，It)I cail we extractr(m，n)鸥edgesThe detailed content of reference noise estimation refers to literature63 The method of diagnosing incipient fault of roller bearings based on the wave-let transform correlation filter and Hilbert transformHigh frequency scales wavelet coefficients acquired by WTCF denoising can not only divide mutatedvibration signals of roller bearing fault，but more important，it keeps the time information，which re-Sects the repetitive frequency and their changing rules and includes roller bearing fault information。“In order to get fault information effectively，it needs to do a Hilbert Transform on high fre-quency scales wavelet coefficients，and then to do Envelope Spectrum AnalysisIfd()is the wavelet coe蚯cient of one scale，and the hilbert Transform ofd(t)isci(t)：Hi d(t)-上r业dt1T J*t-r(5)And the envelope signal of wavelet coefficient d(t)isb(t)=d2(t)+ci2(t) (6)All fault characteristic frequencies of roller bearings are low compared with the sample frequency；low frequency spectrum analysis on Hilbert Envelope Signals of denoised wavelet coefficients is nec-essary to improve the envelope spectrum differentiate rateWhen directly do low frequency spectrumanalysis on discrete vibration signals笫(n)，菇(n)is necessarily re-sampledFor example，in orderto process 8 times spectrum analysis，firstly，a new data sequence名(m)is reformed by the datapoint which is sampled from茗(n)every other 8 points，and then frequency analysis of彳(m)isdoneThe relation between石(m)and并(n)is：(m)=戈(8m) m=I，2，膨 (7)When we do a low frequency spectrum analysis on the Hilbert Envelope Signal of wavelet coefficientd(t)，it is necessary to resample wavelet coefficient d(t)，but the resample rule is different from。 万方数据A Method for Incipient Fault Diagnosis of Roller Bearings Based on the WaveletTransform Correlation Filter and Hilbert Transfornl 195the aforementioned rule of discrete vibration signal resampleBecause every time a decomposed resuh of wavelet transform is obtained by resampling one point from two points，the sample frequencydecreases by one halfFurthermore，resample frequency will decrease by the rate of 2一along withthe augment of scale J，so when we do a spectrum analysis on the Hilbert Envelope Signal of everyscale wavelet coefficient，the resample interval needs to decrease by the rate of 2一。along with theaugment of scale JFor example，when we do 8 times spectrum analysis on the Hilbert Envelope Sig-nal of wavelet coefficient dl(I)，the resample interval is 4 points in the dl layerIn this paper，theHilhert Envelope Signal of high frequency scales wavelet coefficient dt(t)，which is denoised byWTCF，is re-sampled based on the aforementioned resample rule，and then we do a power spectrumanalysisThe process for diagnosing incipient fault of rollerbearings based on WTCF and Hilbert Transformis divided into two phases(shown in Figure 1)：(1)Based on the denoising idea of WaveletTransform Correlation Filter(WTCF)，the directspatial correlation of wavelet coefficients at sever-al adjacent scales sharpens and enhances edgesand significant features while suppressing noiseand small sharp featuresEdges and significantfeatures can be obtained from the noise and noiseis removed based on threshold inspection，SignaltoNoise of wavelet coefficients of W-ICF is muchHigII signal-tonoise wavelet coefficients which arede-noised by WTCFlHigh frequency scales wavelet coefficient吐(，)isprocessed by Hilbert transformlLow frequency spectrum analysis on Hilbert envelopesignal ofwavelet coefficienthigher than that of the wavelet coefficients Figure l The flow chart of fault diagnosis method basedof WT on WrcF and Hilbert transform(2)High frequency scales wavelet coefficient dl(t)，which is de-noised by WTCF，is processed byHilbert Transform Envelope Spectrum Analysis，and then we can get the feature frequency of thefault4 Simulation analysisThe analyzed data are obtained as follows：(1)The impulse train of 120 Hz imitates passing vibration，which has a single fault point；(2)A single harmonic of 3000 Hz with an exponential decay imitatesthe natural frequency excited is added；(3)Two low component frequencies of 20 Hz and 130 Hz imitate factors such as unbalance，misalignment，mechanical looseness etc，are added；(4)Strong whiteGaussian noise is added to imitate environmental disturbancesSample frequency is 16384 HzFigure 2(a)presents the original vibration signal and the fault frequency is 1 20 HzThe fault 8ig-nal is inundated with noiseFigure 2(b)presents the envelope spectrum analysis of a direct waveletcoefficient-Hilbert Transform，there is no means to judge whether the fault existsFigure 2(c)shows the envelope spectrum analysis of the WTCFHilbea Transform；the fault frequency 1 20 Hzand its higher harmonics are clearly observed 万方数据196 International Journal of Plant Engineering and Management V0112 No4 December 20075 Analysis of diagnosis example fIn order to validate the validity and practica-吾bility of the proposed method based on WTCF星and Hilbert Transform in diagnosing the incip-墨ient fault of a roller bearing，several mainfaults of roller bearings testbed are analyzedTester and test data come from USA Case e吕Western Reserve University electric engineer-吾ing lab91In the tester。threephase indue善嚣tion motors whose power is 15 kW is joined稍tll a power meter and a torque sensor by oneself-calibration coupling，to drive fansDatais gathered by the vibration acceleration sell-o80r which is a vertically fixed shell of the sup-童porting beating of the induction motors export-童shaftSimulating three running states of roller罾beatings：(1)outer race slight fault；(2)in、ner race slight fault；(3)ball slight fault，andthe defect size is 018 mmIn the three running states，the work frequency of bearingf is30 Hz，outer race fault feature frequency工u1ris 916 Hz，inner race fault feature frequencyf。，is 1484 Hz，and ball fault feature frequency五棚is 1 196 HzSampling point is 4096，samplingfrequency is 12 kHzTime field wave shape of three incipient weakfaults are shown in Figure 3；we know from Figure 3 that the incipient fault signal is very weakand basically inundated with noise；it is difficultto distinguish the existence of fault and fault feature frequency，especially as the ball fault iscompletely inundated with noiseFigure 4 shows the envelope spectrum analysis ofthe WTCFHilbert Transform5O0 500 1000 1500 2000 2500 3000 3500 4000Sample point(a)Original vibration signalFrequency(Hz)(b)The envelope spectrum analysis ofdirectwavelet coefncientHilbert TransformFrequency(Hz)(c)The envelope spectrum analysis ofWTCFHilbert TransforrnFigure 2 Simulation vibration signal analysis30一)曼25詈0拿一25O5005(a)Outer race fault(b)Inner lace fault2048Data pointN(c)BalI faultFigure 3 Time field wave shape of originalvibration signalWhen there is outer race fault，Figure 4(a)presents the envelope spectrum analysis of the WTCFHilbert Transform，there are distinct spectrum lines in the outer race fault feature frequency fom，(916Hz)and its hi。gh frequenciesWhen there is inner race fault，Figure 4(b)illustrates the envelope spectrum analysis of the WTCF 万方数据A Method for Incipient Fault Diagnosis of Roller Bearings Ba8ed on the WaveJetTmnafo珊Conel8tion Filter and Hilbert Tmndorm 197一Hilbert Tran8fo肌；there are distinct spectmm lines in the inner race fault feature fi。(1484 nz)叭dwork frequency f(30 Hz)of the bearingsWhen there is ball fauIt，Figure 4(c)shows the envelope spectrum analysis of the WTCF-HilbenTransfo珊：there are distinct spectrum lines in the ball fault feature fb。lI(1 1 96 nz)FigIlle 5 shows the envelope spectrum analysis of direct wavelet coefficient-HilbertTransformfromFigure 5(a)删d(b)，we know that when there are outer racefaults and inner race faults,the meh。od c眦diagnolse the existence of fault，but the amplitude of fault frequency is not distinctand the di-agnosis e讹ct is not good，when there is ball fault；the envelope spectrum analY81sof dlrect w8VeletcoefficientHilbert Tran8f0眦can not diagnose the existence of fault as shown in Figure 5(c)p 10。暑05O0，6吖吕q已 O3=L宣0016O08Frequency(az)(a)Outer race faultP邑名量Eg1O050 0OFrequency(Hz)(b)Inner race faultFrequency(Hz)(C)Ball faultFigure 4 The envelope spectrum analysis ofWTCFHiIberr TransformO603OFrequency(Hz)(a)Outer race fault0016O080Frequency(Hz)(b)Inner race faultFrequency(Hz)(C)Ball faultOFigure 5 The envelope spectrum analysis of directwavelet coemeientHilbert Transform6 ConclusiOIISWhen there are ineipient faults of roller bearings，very weak fault feature signals are often inundatedwith vib眦ion signals and noise，the de-noising of the vibration signal is a main approach ot diagnosing ineipient fauh of roiler bearingsIn this paper，an approach of diagnosing incipient fault of roller bearin98 i8 Proposed ba8ed 0n the Wavelet Transform Correlation Filter and Hilbert TransformFirstthe weak fault infomation features are picked up from the roller bearings fault vibration signal8r0J二I一i一疋k卫一等皇11Qg_sIIl一。口君II岛暑一IIIo口暑11dlIl一乙叠一u口暑II口暑 万方数据198 International Journal of Plant Engineering and Management V0112 No4 December 2007by use of a de-noising characteristic of the Wavelet Correlation Filter as the preprocessing of the Hil-bert Envelope Analysis；Then，in order to get fault features frequency，de-noised wavelet coefficients of high scales which represent a high frequency signal is analyzed by the Hilbert EnvelopeSpectrumThe simulation signals and diagnosing examples analysis results reveal that the proposedmethod iS more effective than the method of direct wavelet eoefficients。Hilber