基于形态小波的轴承故障信号去噪和特征提取

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Sep．2013机 床 与 液 压Hydromechatronics Engineering Vo1．41 No．18DOI：10．3969／j．issn．1001-3881．2013．18．016Signal De-nosing and Fault Feature Extraction for BearingsBased on M orphological W aveletWANG Lili ，XIONG Jingqi，HAN Xing，QIN XiaopinUnive~ity of Electronic Science and Technology，Chengdu 61 1 731，China1．IntroductionAbstract：The traditional wavelet threshold de-noising method wil produce Pseudo-Gibbs phe-nomenon．In order to conquer the threshold method’s sho~ages，it has developed a variety ofimproved wavelet de-noising methods．Most of those methods just do some optimization to thewavelet thresholding．The optimized threshold method is based on relevant principles．FirstIy weintroduce this method simply，proved that this method is be~er than traditional threshold de-noi-sing．Diferent from the previous improved method．it can do some optimizations to traditionalwavelet threshold value．We take advantage of the morphological wavelet nonlinear filtering fea-tures，apply it to the signal de—noising and fault feature extraction for bearing fault diagnosis，andcompar its de-noising efect with the optimized threshold method based on relevant principles inpractice，test resu~s showed that the fault signal processing method based on MorphologicalWavelet is more efective and advanced.

Key words：roler bearing，Morphological Wavelet，Signal de—noising，feature extraction，fault di-agnosisRoller bearing is one of the most wildly usedparts in modem machinery and equipment，but it isalso prone to failure which could affect the operationof equipment and economic benefits，even bring a-bout production accident or critical human injuries.

Therefore，fault diagnosis for roller bearings is signif-icant.

In the process of running，the contact betweenan impaired point of a damaged bearing and the sur-face of adjacent part would cause an impact，whosefrequency is caled fault feature frequency of bearing.

This frequency can be used for bearing troubleshoot—ing and the key is to extract the fault feature parame—ters，which relates to the accuracy of fault diagnosis.

Received：2013—02—18WANG Lili．E—mail：kingquenl### 163．eomBecause the early fauh signal is weak，work environ—ment and the bearing itself have afected，and meas—urement process causes noisy pollution，it’s very dif-ficult to extract the signal feature．It means that de—noising for the early signal is a very important task.

Wavelet thresholding de—noising[1—2]pro-posed by Donoho[3]，namely soft thresholding andhard thresholding，has wildly used[4]．But in1995，Brace and Gao have proved that the hardthresholding always has a quite large variance mainlydue to discontinuity，and soft thresholding also has adeviation because of making the part over the systemrange shrink． For these reasons， many improvedthreshold methods『5—7]have been proposed so far.

This paper describes an improved thresholding meth-od，the optimized threshold method based on relevantprinciples，and con~rlns its advantages compared tothe traditional de—noising method，and then propose anew de—noising method． Morphological wavelet canbe applied to de-noisy signal and extract fault fea-ture．It evidently increases the eficiency of working78 Hydromechatronics Engineeringand accuracy of fault feature extraction2．The optimized threshold method basedon relevant principlesFault information always implicit in low frequen-cy signal or some stationary signal and noisy usuallyis high frequency signa1．So according to signal char-acteristic，using wavelet transformation can decom·pose these signal into diferent scale(corespond dif-ferent frequency bands)，then wavelet decompositioncoemcients processing and reconstruction can achievethe purpose of de—noising.

In strong noisy interference．the wavelet coefi.

cient of the useful signal is often higher than the nois-y signal，so using the same threshold to process thecoefficient maybe blot out the useful signa1．The tra—ditional de．noising method has defects which makesfault feature extraction has obvious deviation．For thisreason，we propose a threshold optimization method，that means to design the weight series matrix based0n the relevance of wavelet coemcients in the eorre-sponding position of each decomposed layer and opti—mize the weights of threshold，in order to make thede—noising thresholds of each level and each pointmore accurate，thus improve de—noising efect andmaintain the useful signal more completely and en—hance its the capacity of anti—interference.

3．The theory of the optimized thresholdmethod based on relevant principlesThe different propagation characteristics betweenthe signal and the noisy in each scales indicate thatthe signal wavelet transform has strong correlation andso does its edge，but the noisy doesn’t．Because thesignal is mainly distributed in low frequency or lowscale part，while the noise is predominant relative tothe signal in high frequency or high scales part.

Wavelet transformation has a strong de．corelation.

However．after transformed，each wavelet toemcientstill keeps much correlation． It means that core—sponding coeficients of wavelet coeficient have quitestrong relevance in different resolutions．Low resolu.

tion eoeficients and high resolution coeficients arecorelated．what is the inter．scale dependency．Basedon the different characteristic shown in each scalerange between the signal and the noisy，we can usethe correlation to locate the signal wavelet decomposi—tion coemcients in order to make optimization to therange of the signa1.

Defined corelative quantities of the adjacentscales wavelet coefficients in the same spatial positionis the product of those adjacent scales coeficients，denoted as：Corr￡(，m，n)= (1)Where L is the coemcient for calculation of theproduct，(m，n)means the spatial position of the co—efficient f extend sub．band coemcients to the samescale before product)，and J means the scale．Be—cause the location of some edge features wil deviatewith the scale changing．traditional threshold de—noi—sing method is easy to remove the signal and the nois—y simultaneously with using the same threshold foreach leve1．In order to solve the problems of tradi-tional thresholding．the optimized threshold methodbased on relevant principles calculates the corelationeoefficient，reduces the threshold in the position oflarge corelation coeficients，and enlarges the thresh·old in the position of small corelation coe佑cients，and sets a weight to each threshold of the wavelet co—efficients in order to adjust the threshold.

4．Simulation of the optimized thresholdmethod based on relevant principlesIn order to compare the cons and pros of thismethod with that of the traditional method ．we treatthe fault signal for simulation de—noising in differentways．Firstly，simulate the fault impact signal of theout ring ofthe bearing，shown in Fig．1(a)，and o。

verlav it with a low frequency interference and a fewof Gaussian white noise to get the noisy signal，shownin Figure 1(b)，then use the traditional thresholdingand threshold optimization method respectively basedon some relevant principles to de—noise and get theresult shown in Fig．1(c)，1(d).

As we see in Figure 1(c)，after traditionalthreshold de．noised．its signal has a lot of low fre—quency inference without obvious periodicity， thepeck?of the signal cannot be clearly reflected．Thesignal lack fidelity so severely that impede judgmentto the fault feature．In Figure 1(d)，we can accurate-ly extract the signal feature value by using the opti—mized threshold method based on relevant principles，low—frequency interference is substantialy completelyeliminate，the simulation signals in figure 1 can re—+兀WANG Lili，et al：Signal De—nosing and Fault Feature Extraction for BearingsBased on Morphological Wavelet 79flect the advantage that this improved algorithm willget more complete fault features clearly，what is tosay that this method has significantly improved con—pared with traditional thresholding method.

1．00．50 10 100 200 300(a)Original signal(c)Traditional thresholdde·noising methodO1 00 5O． 0 50 100 200 300fb、Noisy signal(d)the optimizing threshold methodbased on relevant principlesFig．1 De—noising efect of the optimized thresholdmethod based on relevant principles5．M orphological wavelet de—noisingDifferent with the previous improved method thatdo some optimization to traditional wavelet thresholdvalue，we take advantage of the morphological wave—let nonlinear filtering features，apply it to the signalde—noising and fauh feature extraction for bearingfault diagnosis，and compare its De—noising efect withthe optimized threshold method based on relevantprinciples in practice， descript its advantages anddisadvantages.

6．Transform theory of dual waveletThe diference between Morphological waveletand traditional classical linear wavelet transform isthat using corrosion or dilation operator instead of theoriginal linear decomposition operator． According tothe nonlinear wavelet framework and the signal de.

composition theory proposed by Goutsias and Heij.

mans[8]．Assuming geometric and respectivelyrepresent the j—th layer signal space and detail space.

Signal analysis refers to signal analysis operator ：— +i and detail analysis of operator ，’： —}+ldecompose along the direction of j increasing．Signalsynthesis refers to +1× +l syntheticalong thedirection ofj decreasing．This decomposition schemeis the dual wavelet decomposition． As shown inFig．2Fig．2 dual wavelet decompositionThe condition of the signal perfect reeonstrue.

tion：(0i。( )， ( ))= ， ∈ (2)( y)) ? )， + (3)【 ( (x,y))=y， ∈ +。，y∈ +Formula(3)is the condition for wavelet decom—position perfect reconstruction．formula(4)is thewavelet pyramid conditions which ensure that thewavelet decomposition and reconstruction processwithout loss of informati0n.

Assume that there is a plus operator 4-in thesignal space as well as operator f。： +l—} andf ： +1_÷ meet the conditions：( ，Y)= ( ) (Y)∈ +1，Y∈ +1 (4)Then 、m are called signal synthesis operator anddetails synthesis operator．If it is assumed that V0=VI： W1= R2，morphological Haar wavelet is ob.

tained：( )(n) x(2n)一x(2n+1)toj ( )(n)= (2n)一 (2n+1)The basic ideas of Morphological Wavelet is when u.

sing the wavelet algorithm ，using nonlinear morpho.

1ogical operator to replace the original linear opera—tor，in order to realize nonlinear filtering.

7．Decomposition method of M orphologicalW aveletThe basic principles of morphological wavelettransform and some major nature are introduced a.

bove．from the morphological wavelet applicability
，the morphological wavelet applied to nonlinear time.

varying signal analysis is feasible．Using diferent op.

erator can get different morphological filter． In thispaper，morphological median wavelet was adopted
，which based on partly features of signals to signal de.

composition，with updates to the adaptive nature ofsense.

Suppose A is a struetural element．the one．di.

80 Hydromechatronics Engineeringmensionalmorphological median operatorcan be ob—tained as：咖 ： ( )(n)=x(2n)+median(O，x(2n一1)一x(2n一2)，x(2n+1)一x(2n)) (6)： ( )(凡)= (2n+1)一 (2n) (7)Composite operator is：( )(2n)= ( )(2n+1)= (n)(8)8．Simulation and analysis results(9)In order to verify the application features to ex.

tract the signal impact component of morphological—wavelet，compared its de—noising effect with the opti—mized threshold method based on relevant principles，and ilustrate whether the morphological waveletmethod is better．Then we analyze specifc instances0f faulf signal diagnosis．In order to analyze the denoising capacity of improved algorithm to the actualbearing fault，we use the bearing failure experimentaldata from Case Western Reserve University，The specifc parameters listed in Tab．1.

Tab．1 main parameters of experimental platformExperiments bearing speed is 1 797 r／min，sam—pling frequency is 12 000 Hz．Failure is the inner ringfault，fault diameter is 0．178 mm，fault depth is 0．28m m .

Characteristic frequency：= (1+ d c。s )=162 Hz(10)is bearing contact angle．z is number of rolling ele—ments.

Fig．3 is the time—domain waveform graph inclu—ding the original signal and de-nosing signa1.

In Fig．3，by comparing the time domain wave—form figure to each other，we can see that two meth.

ods are effective for noise elimination，the fault fea—turesand frequency doubling composition of the mot—phological wavelet is more prominent than the opti—mized threshold method based on relevant principles.

However，if just according to the time-domain wave—form analysis，we can’t observe the fault feature.

Therefore，the collected signal needs spectrum analy—sis as shown in Fig．4.

o 2o． 0 2o o l o 2 o 3 o 4 o 5 o 6 o 7 o 8 o 9 1 ot／s(a)Oringinal signal0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0t／sfb1 Morphological wavelet de-noising0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0t／s(c)The optimizing threshold method based on relevant principlesFig．3 Time domain wave~rm figure oforiginal signaland de—noise signal2001O0OlO0 150 200 250 300 350 400 450 500f／Hz5000(a)Oringinal signal100 15O 200 250 300 350 400 450 500f／Hz(b)Morphological wavelet de—noising0 010O O050100 l50 200 250 300 350 400 450 500f／Hz(e)The optimizing threshold method based on relevant principlesFig．4 Fault feature extractionAfter observing the signal spectrum obtained byvarious de—noisingmethods in figure 4，we found thatit has been decomposed and extracted by the methodof morphological median wavelet，peak points in thefigure were162 Hz，324 Hz and 483 Hz．since the lat—ter two frequency components is substantially an inte.

ger multiple of 1 62 Hz，belong to the double frequen—cy component．There is suficient reason to believethat the fault feature frequency of the signal extractedby the method of morphological wavelet is 162 Hz.

This is consistent with the theoreticaI value of thebearing inner ring fault feature~equency we calculat一2 0 2 5 O 5 ” 一n) O I ，【 一 帆 n
0 一帆m =一 ) = 。．1)
+ 甜WANG Lili，et al：Signal De-nosing and Fault Feature Extraction for BearingsBased on Morphological W aveleted above．which can determine the inner ring racefailure．The partially enlarged spectrum after process。

ing by the optimized threshold method based on rele—vant principles in figure 4 shows that the peak valuein 162 Hz，295 Hz and 455 Hz were very prominent，those two peaks behind can be basically consideredthe double frequency component of 162 Hz，so we canalso consider the fault feature frequency extracted bythis method is162 Hz．its feature extraction is also rel-atively accurate，but if we compared its multiple fre—quency components with those extracted by the meth一0d of morphological wavelet，we could clearly seethat the signal de．noised by the method of morpholog—ical wavelet is more accurate.

The peak points extracted by the traditionalwavelet de．noising method in the figure were164 Hz，323 Hz and 485 Hz。the feature frequency was 164Hz，the result is a certain discrepancies comparedwith the two improved de．noising method，the error isrelatively large．We can obviously found that the twoimproved de—noising method is superiority to the tra—ditional method of wavelet de．noising．And the verac—itv of the method of morphological wavelet relative tothe optimized threshold method based on relevantprinciples.

Then let’s analyze the efect of various de-noi·sing methods by MSE and SNR，as shown in Tab．2：Tab．2 the comparison of mean square errorand signal·-to-noise ratioThrough the analysis and comparison of MSEand SNR，we can clearly find that the two improvedde—noising method can achieve much higher SNR andfar lower MSE than the traditional wavelet method，they are able to achieve a beter de—noising effect.

While through the comparison of two improved meth—ods，we realize that morphological wavelet de-noisingmethod is better than the optimized threshold methodbased on relevant principles． And in the partial en—larged spectrum graph，we can figuratively see thatthe feature frequency and the ~equency doublingcomponents extracted by the morphological waveletde—noising method is closer to the theoretical value.

To further compare the pros and cons of the twoimproved approaches，we compared their program runtime using Matlab simulation program．Morphologicalwavelet de．noising took 2．352 428 seconds to get theresult，The optimized threshold method based on rel-evant principles took 4．834161 s to get the result，ofcourse．the nln time in diferent configuration envi—ronment will vary ，but in the same configuration 0p。

crating environment，morphological wavelet de—noi—sing is much quicker than the optimized thresholdmethod based Oil relevant principles，computing efi-ciency is improved by 51％ .

9．Conclusions1)In the existing improved wavelet de—noisingmethod，the optimized threshold method based onrelevant principles can achieve effect far superior totraditional wavelet de—noising method.

2)With the on—linear filtering characteristics ofmorphological wavelet，applying it to nonlinear time—varying signal processing analysis is feasible．We ap’plied morphological wavelet to the bearing fault signalde—noising and feature extraction in this paper.

3)Analyzing the simulation results，we provedthat the diagnostic accuracy and eficiency has beengreatly improved by using the method of morphologi—cal wavelet de-noising compared with those previousimproved threshold methods，we can extract the fea。

ture frequency accurately in the early stage of bearingfailure，so morphological wavelet de—noising methodis a good method f0r bearing fault diagnosis． It issuitable for on．1ine fauh features analysis.

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基于形态小波的轴承故障信号去噪和特征提取王李立 ，熊静琪，韩 星，秦枭品电子科技大学，成都 611731摘要：针对传统小波阈值去噪所产生的 Pseudo—Gibbs现象，已发展 出各种改进的小波去噪方法，基于相关原则优化阈值方法就是其中的一种。介绍了该方法的原理，证明其优于传统阈值去噪的特性。

与以往的对阈值进行改进不同，将形态小波用于信号处理当中，对轴承早期故障特征进行提取，并经过数据仿真和故障轴承实例分析 ，将该方法的去噪效果和基于相关原则优化 阈值方法进行对比，验证了该方法的有效性和先进性。

关键词：滚动轴承；形态小波；信号去噪；特征提取；故障诊断中图分类号：TH13(Continued on 58 page)[5] The Editorial Committee of Anti—Wear and Erosion Re—sistance and Surface Technology of materials．Introduc—tion of Material Corrosion Resistant and Surface Technol—ogy[M]．Beijing：China Machine Press，1986.

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GU Hongwu．The Efect of Some Surface ModifcationProcesses on Wear and Corrosion Resistance of Stee1『J].

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热处理解决传统车床方刀架故障的分析与探讨冯小飞 ，郑卫刚 ，江丽桃武汉理工大学 a．能源与动力工程学院．b．工程训练中心，武汉 430063摘要：传统车床方刀架在使用中经常出现偏移现象，存在小滑板上销孔套筒磨损过大的问题，影响了h．x-精度，降低了工作效率。以 CA6140车床为例进行研究发现，其销孔套筒的材料为45号钢，按传统热处理方式对其进行处理后耐磨度不够。通过现代热处理工艺来强化45号钢的耐磨性能，从而解决了实际生产中车床方刀架的故障。

关键词 ：销孔套筒；磨损；45号钢 ；亚温淬火；表面热处理中图分类号：TH16