Rolling Bearing Fault Diagnosis Based on EMD-TEO and Mahalanobis Distance

Transcription

1 Rollng Bearng Fault Dagnoss Based on EMD-TE and Mahalanobs Dstance Lu Chen, Hu Jameng, Lu Hongme and Wang Jng RLLG BEARG FAULT DAGSS BASED EMD-TE AD MAHALABS DSTACE. LU CHE, HU JAMEG, LU HGME AD WAG JG Lu Chen, Hu Jameng, Lu Hongme and Wang Jng, School of Relablty and Systems Engneerng, Behang Unversty, Bejng, 9, Chna,,, Scence & Technology on Relablty & Envronmental Engneerng Laboratory, Bejng 9, Chna E-mal: Abstract. A ntellgent rollng bearng fault dagnoss method s proposed on Emprcal Mode Decomposton (EMD) Teager Energy perator (TE) and Mahalanobs dstance. EMD can adaptvely decompose vbraton sgnal nto a seres of ntrnsc Mode Functons (MFs), that s, zero mean mono-component AM-FM sgnal. TE can estmate the total mechancal energy requred to generate sgnals, so t has good tme resoluton and self-adaptve ablty to the transent of the sgnal, whch shows the advantage to detect the sgnal mpact characterstcs. Wth regards to the mpulse feature of the bearng fault vbraton sgnals, TE can be used to detect cyclcal mpulse characterstc caused by bearng falure, gan the nstantaneous ampltude spectrum of each MF component, then dentfy the characterstc frequency of the nterestng and sngle MF component n bearng faults by means of Teager energy spectrum. The ampltude of the Teager energy spectrum n nner race fault frequency, outer fault frequency and the rato of the energy of the resonance frequency to the total energy were extracted as the feature vectors, whch were used as tranng samples and test samples separately for fault dagnoss. Then the Mahalanobs dstances between the real measure and dfferent type overalls of fault sample are calculated to classfy the real condton of rollng bearng. Expermental results was concluded that ths method can accurately dentfy and dagnose dfferent fault types of rollng bearng.. ntroducton Bearngs are an mportant element n a varety of ndustral applcatons such as machne tool and gearbox. An unexpected falure of the bearng may cause sgnfcant economc losses. For that reason, faults detecton of bearng has been the subject of ntensve research []. Sgnals generated by the rollng bearng falure often contan a large number of non-statonary components. The global frequency doman nformaton can be obtaned by fourer transform for sgnals contanng non-statonary composton, and the fault nformaton s dffcult to be extracted effectvely from spectrum overwhelmed by nose. Local nformaton of non-statonary sgnals can be extracted by wavelet transform. But the nformaton of hgh frequency s lost whch s caused by lack of the decomposton hgh-frequency part, so that the fault characterstcs of hgh frequency s dffcult to be extracted. Wavelet packet transform makes up for the lack of wavelet transform for hghfrequency decomposton. t can have a whole mult-level decomposton n the full-band sgnal, coupled wth good tme-frequency characterstcs. However, n terms of feature extracton of low sgnal to nose rato of the vbraton sgnal, t has no breakthrough. n ths paper, we present a ntellgent dagnoss method based on Emprcal Mode Decomposton (EMD) Teager Energy perator (TE) and Mahalanobs dstance. EMD s a fundamentally new approach to the decomposton of nonlnear and nonstatonary sgnal presented orgnally by Huang []. EMD can decompose adaptvely sgnal nto a fnte and usually small number of ntrnsc Mode Functons (MFs) whch are usually monocomponent Ampltude Modulaton-Frequency Modulaton (AM-FM) sgnals. Sgnal components wth ampltude modulaton characterstcs exst n hgh frequences, therefore, MFs ncludng hgh frequency are selected for further analyss. n ths paper, the approprate and nterested MF s selected to gan feature vectors for the nput of TE because To whom any correspondence should be addressed. VBREGEERG. VBREGEERG PRCEDA. VEMBER. VLUME. SS

2 RLLG BEARG FAULT DAGSS BASED EMD-TE AD MAHALABS DSTACE. LU CHE, HU JAMEG, LU HGME AD WAG JG MF obtan more nformaton of sgnal characterstcs. TE s a nonlnear operator, whch can track the energy of the nterestng ntrnsc Mode Functons (MFs), gan the nstantaneous ampltude spectrum of each MF component and dentfy the characterstc frequency of bearng faults by means of Teager energy spectrum []. Moreover, the feature frequences of the nner race and outer race faults, the rato of the resonance frequency band energy to the total energy n the Teager energy spectrum were extracted as feature vectors, whch were used as tranng samples and test samples separately for fault dagnoss. TE also enable the extracton of bearng fault feature frequences for fault detecton. n end, the extracted features are classfed usng the Mahalanobs dstances for fault dagnoss of rollng bearng. The result shows that the proposed method s effectve.. Methodology.. EMD Algorthm orden E. Huang and hs colleagues developed a method of emprcal mode decomposton (EMD) n 998 []. Ths method decomposes sgnals nto MFs. The MF must satsfy two requrements as below: n a seres of data, the number of extreme value ponts and the zero-crossng pont must be equal or dffer by one pont at most. n any pont of tme axs, the average value of the upper and lower envelope s zero. The basc algorthm of EMD s as follows, theren x( t ) s the orgnal sgnal sequence () ntalze h x( t). () Search all the maxmum and mnmum values of h. () The upper and lower envelope s ftted by cubc-splne, and the mean value m of the upper and lower envelope s calculated. () The mean value of envelope s subtracted from the sequence h, h h m. (5) Repeat step ) ~ step ),untl h s an MF. (6) h, repeat the steps from () to (5) untl the last sequence m cannot be decomposed anymore. The result of EMD can be wrtten as below:.. Teager Energy perator (TE) The TE, ψ (.) s defned for contnuous-tme sgnal x( t ) as[5]: n x( t)= MF + rn () = [ ] [ ] ψ x( t) = xɺ ( t) x( t) ɺɺ x( t), () where xɺ ( t) and ɺɺ x( t) represent the frst and second tme dervatves of x( t ) respectvely. n fact, the output of the Teager Energy perator tracks the total energy requred to produce a sgnal. ( ) cos( ω ψ ) x t = A t + () where A represents the ampltude of the vbraton, ψ represents the ntal phase. At any tme the mechancal energy of the vbraton system s the sum of the potental energy of the sprng and the knetc energy of the mass: The total energy can be wrtten as E = k x( t) m x( t) + ɺ () 6 VBREGEERG. VBREGEERG PRCEDA. VEMBER. VLUME. SS 5-5

3 RLLG BEARG FAULT DAGSS BASED EMD-TE AD MAHALABS DSTACE. LU CHE, HU JAMEG, LU HGME AD WAG JG E = maω (5) Equaton (5) shows the nstantaneous total energy of the harmonc vbraton and the square of the ampltude s nversely proportonal to the square of the frequency. From the above equatons, we can get: ( ) = cos( + ) = ψ x t ψ A ωt ψ A ω (6) Contrastng to (5) and (6), there s only a dfference of a constant m/ between the output of the TE and the nstantaneous total energy of smple harmonc moton. n the dscrete case, the tme dervatves may be approxmated by tme dfferences. The dscrete-tme counterpart of TE becomes [6]: [ ] [ ] ψ x( n) = x( n) x( n ) x( n + ) (7) For the dscrete-tme sgnal, TE only need samples to calculate the energy of the sgnal at any tme. Therefore, TE has a good tme resoluton for the nstantaneous change of the sgnal, and can detect the transent components of the sgnal... Dagnoss approach for rollng bearng Fgure. Flow chart of the proposed method. The fault dagnoss method for the rollng bearng s as shown n Fgure: () Each sgnal s decomposed by EMD, and a fnte number of MF components can be obtaned. Select the approprate and nterestng ntrnsc Mode Functons (MFs) for the nput of TE. () TE gan the nstantaneous ampltude spectrum of each MF component and dentfy the characterstc frequency of bearng faults by means of Teager energy spectrum for fault detecton. Moreover, the feature frequences of the nner race and outer race faults, the rato of the resonance frequency band energy to the total energy n the Teager energy spectrum were extracted as feature vectors, whch were used as tranng samples and test samples separately. () The Mahalanobs dstances between the test sample and dfferent type overalls of fault samples are calculated to classfy the real condton of a rollng bearng. () dentfy the condton of the rollng bearng.. Case study.. Experment setup Ths paper uses the data from bearng data center of Case Western Reserve Unversty for testng and verfcaton. As shown n Fgure, test rg conssts of a hp (horsepower) motor (left), a torque converter / encoder (n), a dynamometer (rght) and the control crcut (not shown). A deep groove ball bearng of 65-RS JEM SKF s mounted n the motor. An acceleraton sensor nstalled on the magnetc base shell s used to collect vbraton datas. Vbraton sgnals collected by sensors nclude normal sgnal, nner race fault sgnal, outer race fault sgnal, and the samplng frequency s khz. The expermental datas were collected from groups of samples. t was composed of three types of condtons (normal, nner race fault, outer race fault), each of whch ncludes groups of samples. Here, the frst sx groups were selected as tranng samples, and the remanng four groups as testng VBREGEERG. VBREGEERG PRCEDA. VEMBER. VLUME. SS 5-5 6

4 RLLG BEARG FAULT DAGSS BASED EMD-TE AD MAHALABS DSTACE. LU CHE, HU JAMEG, LU HGME AD WAG JG samples. Fgure. Expermental setup... Feature extracton based on EMD-TE Fgure and Fgure show the MFs obtaned by EMD. The orgnal sgnal can be decomposed nto MFs and one resdue. The ampltudes of MF and MF are more lttle comparng wth others. So MF and MF can be abandoned. To select the nterested MF component for the nput of TE accordng to the objectve of fault dagnoss because MF contans the hghest sgnal frequences. The transent caused by the bearng faults s clearly captured. From Fgures and, t can be easly proven that the EMD decomposes vbraton sgnal very effectvely on an adaptve method. The ampltude of the Teager energy spectrum n nner race fault frequency, outer fault frequency and the rato of the energy of the resonance frequency to the total energy are extracted as the feature vectors. For avodng the error of the frequency leak, the weghted of Teager spectrum n fault frequency and f = Hz around were extracted as the feature vectors. MF MF MF resdual orgnal MF Fgure. MFs of the nner race vbraton sgnal. MF MF MF resdual orgnal MF Fgure. MFs of the outer race vbraton sgnal... Pattern Recognton... Fault detecton based on the TE. Cyclcal shock wll generate when the fault bearng works. The frequency of ths cyclcal shock reflects the reason of the bearng fault. Accordng to the parameters of the rollng bearngs, fault characterstc frequences of each element were calculated respectvely. The results are as follows: f nner =57.9Hz, f outer =.56Hz. The TE can be appled to each MF component, resultng n nstantaneous ampltude sgnal. Fgure 5 and Fgure 6 respectvely are nstantaneous ampltude of MF component for the nner race and outer race fault bearng. After the EMD, n addton to the effects of low frequency nose, when bearng fault mpact other parts, the peak of hgh-frequency vbraton sequence s obvous. The above results show that the nstantaneous ampltude spectrum of MF s to the best effect. 6 VBREGEERG. VBREGEERG PRCEDA. VEMBER. VLUME. SS 5-5

5 RLLG BEARG FAULT DAGSS BASED EMD-TE AD MAHALABS DSTACE. LU CHE, HU JAMEG, LU HGME AD WAG JG Therefore, the MF s selected to dentfy the characterstc frequency of bearng faults through the Teager energy spectrum. n Fgure 7, TE hghlghts the cyclcal mpact characterstcs, the fault characterstc frequency(57hz, close to f nner ) and the frequency doublng of the rollng bearng wth nner race fault can be clearly dentfed. Therefore, the MF s related to the nner race defect of the bearng and can be selected as a sutable dagnostc feature n the analyss of the nner race defect. n Fgure 8, the fault characterstc frequency (7Hz, close to f outer ) and the frequency doublng of the ball bearng wth outer race fault can be clearly dentfed. Therefore, the MF s related to the nner race defect of the bearng and can be selected as a sutable dagnostc feature n the analyss of the outer race defect Fgure 5. nstantaneous ampltude of MF n the nner race fault condton Fgure 6. nstantaneous ampltude of MF for the outer race fault condton X: 7 Y: X: 57 Y: Fgure 7. Teager energy spectrum of the nner race fault condton Fgure 8. Teager energy spectrum of the outer race fault condton.... ntellgent fault dagnoss based on Mahalanobs dstance. Calculate and compare the d X, G =,,, G : normal; G : nner race fault; G : outer race fault from mahalanobs dstance ( ) ( ) the unknown test sample X to the three overall G, then dentfy the test sample X belong to the the smallest dstance. The crteron s that f d ( X, G ) mn d ( X, Gj ) G of =, the sample s determned from the overall G [7]. Fnally, t s dstngushed ts category of the fault accordng to the "proxmty" prncple. The results are shown n Table. VBREGEERG. VBREGEERG PRCEDA. VEMBER. VLUME. SS 5-5 6

6 RLLG BEARG FAULT DAGSS BASED EMD-TE AD MAHALABS DSTACE. LU CHE, HU JAMEG, LU HGME AD WAG JG Table. The results of fault dagnoss G G G Mn Mod F F F F F F F F F F F F (,,, ) (,,, ) (,,, ) = : Mahalanobs dstance of the four testng samples under normal condton = : Mahalanobs dstance of the four testng samples under nner race fault = : Mahalanobs dstance of the four testng samples under outer race fault F : normal F : nner race fault F : outer race fault. Conclusons n ths paper, a method for fault dagnoss of rollng bearng s presented based on a newly developed sgnal processng technque named as EMD-TE and Mahalanobs dstance. The EMD-TE can extract the transent mpact feature of the faulty bearng and fault detecton, and the Mahalanobs dstance can classfy the bearng falure mode. EMD acts as a mult-band flter and can adaptvely decompose complex sgnal nto a seres of MFs, that s, zero mean mono-component AM-FM sgnal. TE tracks the modulaton energy of the nterestng ntrnsc Mode Functons (MFs) for feature vectors. And TE can be used to detect perod mpulse characterstc of bearng localzed damage, and then dentfy the characterstc frequency of bearng faults by means of Teager energy spectrum. The expermental results show the robustness and the effectveness of ths proposed method. Acknowledgements Ths research was supported by the atonal atural Scence Foundaton of Chna (Grant os. 678, 5755 and 559), as well as the Technology Foundaton Program of atonal Defense (Grant o. ZB). References [] L H, Fu Lhu and Zhang Y P 9 nternatonal Conference on Measurng Technology and Mechatroncs Automaton [] Huang E, Shen Z and Long S R 999 Annual Revew of Flud Mechancs 7-57 [] Wang T J, Feng Z P, Hao R J and Chu F L Journal of vbraton and shock [] Huang E, Shen Z and Long S R et al 998 Proc. R. Soc. Lond. A [5] Potamanos A and Maragos P. 99 Sgnal Processng 7 95 [6] Maragos P, Kaser J F and Qu T F 99 EEE Transactons on Sgnal Processng 5 [7] Zhang D X and Wu X P 9 Anhu Unversty Journal:atural Scence 6 VBREGEERG. VBREGEERG PRCEDA. VEMBER. VLUME. SS 5-5