Vibration Fault Diagnosis Method of Centrifugal Pump Based on EMD Complexity Feature and Least Square Support Vector Machine

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1 Avalable ole at Eergy Proceda 17 (1 ) Iteratoal Coferece o Future Electrcal Power ad Eergy Systems Vbrato Fault Dagoss Method of Cetrfugal Pump Based o EMD Complexty Feature ad Least Square Support Vector Mache Zhou ulog a,zhao Peg b a School of Eergy ad Power Egeerg,Northeast Dal Uversty,Jl 131, Cha b School of Eergy ad Power Egeerg,North Cha Electrc Power Uversty,Bejg 16, Cha Abstract Amg at the o-statoary ad o-learty characterstcs of the vbrato sgals of cetrfugal pump, a ew method based o complexty feature of Emprcal Mode Decomposto (EMD) ad Least Square Support Vector Mache (LS-SVM) s put forward. Frst of all, the Emprcal Mode Decomposto (EMD) method was used to decompose the vbrato sgals to a fte umber of statoary Itrsc Mode Fuctos (IMF), ad the complexty features of each IMF s extracted as the fault characterstcs vectors ad served as put parameters of LS-SVM classfer to dagoss fault. Applcato results showed that the proposed method s very effectve, whch ca better extract the olear features of the fault ad more exactly dagoss fault Publshed by Elsever by Elsever Ltd. Selecto Ltd. Selecto ad/or peer-revew ad/or peer-revew uder resposblty uder resposblty of Haa Uversty. of [ame orgazer] Ope access uder CC B-NC-ND lcese. Keywords : cetrfugal pump; fault dagoss; Emprcal Mode Decomposto; complexty; Least Square Support Vector Mache. 1.Itroducto Cetrfugal pump plays a mportat role dustres of Electrc power, petroleum ad chemcal, metallurgy, mechacal, ad mltary, as a result, t s ecessary to develop fault dagoss techque of cetrfugal pump. It has bee dscovered that fault types, extet, locato, ad cause are closely assocated wth vbrato sgals whch come about durg rotatg of cetrfugal pump, especally wth ampltude of vbrato, frequecy compoet cotaed the vbrato sgals, presetly, t s a effectve method of fault motorg ad dagoss, ad wdely applcato [1-3]. Formerly, fault sgature extracto of cetrfugal pump adopted Fourer trasform, t s uavodable the weakess tme doma aalyss. I recet decade, wavelet aalyss has bee appled sgal processg to extract the fault sgature, such as wavelet packet etropy [4], Autoregressve spectrum [5], etc. used to extract dfferet fault characterstcs. However, vbrato sgals are o-statoary, o-lear radomess, may problems exstg by far. Emprcal mode decomposto (EMD) s beleve to be a breakthrough sgal processg area recet Publshed by Elsever Ltd. Selecto ad/or peer-revew uder resposblty of Haa Uversty. Ope access uder CC B-NC-ND lcese. do:1.116/j.egypro

2 94 Zhou ulog ad Zhao Peg / Eergy Proceda 17 ( 1 ) years, t s a self-adaptve sgal processg method ad sutable for o-statoary sgal aalyss. It wll be more accurate ad effectve to extract the sgature whe adoptg EMD method vbrato sgals processg of cetrfugal pump. hs paper adopts EMD method to decompose the vbrato sgal to calculate the complexty of trsc mode fucto (IMF) o each rakg, ad coducts the complexty as put feature vector of least-squares SVM. Expermetal dcates that t s a ew method for fault dagoss ad performace effectve estmatg cetrfugal pump fault types..emprcal Modedecomposto Method EMD s a tme-frequecy aalyss method, whch proposed by Dr. Huag [6] of NASA 1998, supposg ay sgals are comprsed by dfferet trsc mode fucto (IMF). IMF s defed by the followg codtos: over the etre data set, the umber of extreme pot must be equal to the umber of zero-crossgs or dffer at most by oe; the mea value of the evelope defed by the local maxmum value ad the evelope defed by the local mmum value s zero. Specfc algorthm refers to referece [6], tal sgals x (t) after EMD processg ca be express as: x( t) c r (1) Where, r s resdual error fucto, stads for average tred of sgals; IMF compoets c 1 (t), c (t),, c (t) cota dfferet elemets separately from low frequecy to hgh frequecy of sgals. 3.Complexty Extractoof Fault Sgals Based o Emd 3.1.Complexty Kolmogorov [8] proposed the symbol sequece complexty for the frst tme 1965, but he dd ot buld correspodg algorthm. he algorthm of complexty was provded by Lempel ad Zv [9] formato scece research, t made complexty applcato come true. he algorthm s as followg: Suppose sequece x } x, x,, x, recostruct the sequece, commad: { 1 N 1 s 1,, x x x x () Where, x ( x x x ) / 1 N N. Accordg to express (), tme sequece { x } ca be mapped to sequece {s }=s 1, s,, s N, where s = or 1. he complexty of geeratg the sequece, 1 s marked C. Frst, commad Q=s r+1 ad obta symbol sequece SQ from characters S=S 1, S,, S r, r<n the sequece, 1,ad commad SQ s the character strgs whch obtaed from symbol sequece SQ by subtractg the last character of the sequece, f Q ca be coped form substrg SQ, the addct the character to the ed, amed copy, f ot, called addto, addct at the ed of S=(s 1,, s r s r+1 s r+ ) to avod jog together, repeat the steps above. he umber of reflex the complexty C (N) of symbol sequece. Accordg to Lempel ad Zv, whe N, the complexty b(n) wll approach to a value b(n).

3 Zhou ulog ad Zhao Peg / Eergy Proceda 17 ( 1 ) b( N) lm C( N) N N / log N (3) Relatve complexty: C r ( N) C( N) / b( N) (4) Relatve complexty C r (N) reflects the approachg degree betwee a tme sequece ad a radom sequece, ad the relatve complexty C r (N) of a completely radom sequece s approachg to 1, but t wll be approachg to f t s a perodc sequece, the relatve complexty betwee two codtos s defed as C r (N) (, 1). Complexty reflects the structural characterstcs of the symbol sequece, ad ca be the characterstc parameter of system state [1]. 3..Fault Sgature Extractg Calculate complexty of the Itrsc Mode Fuctos (IMF) whch s obtaed from Emprcal Mode Decomposto; choose relatve complexty C r ( 1,, 8 ) of the frst 8 IMF compoets as the characterstc vector of dfferet states: [ C C C 8] (5) r1 r r 4.he Prcple of Support Vector Mache Classfer ad Parameters Selectg 4.1.he Prcple of Support Vector Mache Least Square Support Vector Mache (LS-SVM) [11] s ew learg method based o Support Vector Mache (SVM), adoptg quadratc loss fucto [1-13] to covert the quadratc programmg problem of SVM to ler equatos for soluto, t reduce the dffculty of calculato ad guaratee precso smultaeously, has bee wdely appled fault dagoss, flow patter detfcato ad power qualty classfcato [14-16]. o LS-SVM, t s optmzg-target: 1 w (6) m J LS (, ) w w, b, 1 s.t. y[ w ( x ) b] 1 1,,, (7) Where, s error pushg coeffcet, used for cotrollg J LS (w, ), troducg Lagrage fucto for soluto: Where, s Lagrage multpler, postve or egatve, dervato of w, b, ad separately of expresso above at extreme pot, commad them equal to zero. he codtos above make up a ler system, ts:

4 94 Zhou ulog ad Zhao Peg / Eergy Proceda 17 ( 1 ) I Z I - Z - - I w b 1 (8) Where: Z [ ( x 1) y1,, ( x) y], [ y 1,, y ], 1 [ 1,,1], [ 1,, ], [ 1,, ], I R s ut matrx. After elmatg w ad, expresso (8) s smplfed: ZZ b 1 I 1 (9) Defe ZZ [ q ] j expressed as followg form: ; applyg Mercer Codtos to matrx, the the elemets of the matrx q y y ( x ) ( x ) y y K( x x ) (1), j j j j Where, K x x ) s kerel fucto. Geerally, kerel fucto cotas polyomal fucto, RBF ( j kerel fucto ad sgmod kerel fucto, etc Radal Bass Fucto (RBF) kerel fucto s adopted ths paper, expresso: x x j K( xx j ) exp( ) ; o solve the expresso (9) wth least square method; the algorthm of LS-SVM, the quadratc programmg problem of SVM s coverted to ler equatos, fally, optmal classfcato fuctos: y( x) sg[ y (x ) b] (11) Although LS-SVM dagostc model s completeess theory, t stll beg choce problem of model parameters practce. Error pushg coeffcet ad kerel fucto parameter are mportat to classfcato precso. 4..Polytomous O classfcato, EMD cosders two type ssues: y = +1 stads for oe type sample; y = -1 stads for the other type. O mult-categores classfcato, covert ths problem to two categores by four kds codg scheme: mmum output codg, error correcto output codg, oe-to=may codg, oe-to-oe codg, ad mmum output codg s adopted ths paper. Amg at fault dagoss, four kd states cludg ormal, correct algmet, ubalace ad looseess are marked as = [1 3 4], the codes are as followg after mmum output codg: 1

5 5.Aalyss of Dagoss Example Zhou ulog ad Zhao Peg / Eergy Proceda 17 ( 1 ) c (16) Cetrfugal pump s BA-6A, maxmum rotate speed 3r/m, flow rate m 3 /h, pressure head 5.m, effcecy 65.6%, heght of sucto 7.m, adoptg ope system; electromotor type s JZS-51-1, prcpal voltage 38V, rotate speed 47~9r/m, frequecy 5Hz. o measure radal dsplacemet by o-cotact eddy dsplacemet trasducer, stalled o support of the cetrfugal pump vertcal ad horzotal drecto; the vertcal surface of cetrfugal pump coupler s measuremet surface, to measure axal dsplacemet by stall the strumet horzotally. he measuremet sgal s cludg ormal, mass ubalace, rotor correct algmet, ad vbrato dsplacemet sgal of foudato looseess. he rotate speed crease from 5r/m to 9r/m durg the expermet, samplg whle creasg every r/m by INV36fF data acqusto ut, samplg frequecy s 8Hz, samplg umbers 496. o smulate mass ubalace by fxg a bolt to dsk whch s stall to coupler. o smulate rotor correct algmet by dsassemblg the coupler, make t devate from cetre ad coect together. Loose the bolt a lttle of electromotor foudato to smulate foudato looseess. he test system s show fgure electromotor -valve 3-dsplacemet trasducer4-ext pressure 5-etrace pressure 6-cetrfugal pump 7-turbe flow-meter 8-water tak. Fgure 1 Cetrfugal pump testg equpmet Sgal Iput Fgure EMD Feature IMFCompoet Feature LSSVM Decomposto Complexty Classfcato Extracto Iput he flow chart of fault dagoss based o EMD ad LS-SVM Fgure 3 me doma waveforms of four states Fgure 4 he spectral dagram of vbrato sgals four states

6 944 Zhou ulog ad Zhao Peg / Eergy Proceda 17 ( 1 ) he flow chart of cetrfugal pump fault dagoss based o EMD ad LS-SVM s show fgure. Fault dagoss detals: o obta the data of cetrfugal pump dfferet states. 15 groups data of each state are selected radomly from the whole test data to be trag samples, ad the others are test data. me doma oscllograph ad frequecy spectrogram of four states cludg ormal, correct algmet, ubalace ad looseess are show fgure 3 ad fgure 4. It s dffcult to dstgush four kd states from frequecy spectrogram, ad eeds feature extracto further. he complexty of 8 IMFs of four type vbrato sgals accout for 98.77% of total complexty 8 max C r / Cr ( 1 1, max s maxmum decomposto umber of EMD). It dcates that the frst 8 IMFs cotag majorty formato of the sgal, the complexty of frst 8 IMFs s eough. wo group feature vectors of EMD complexty extracted from four kds States s show table 1. he 8 complexty etropy E obtaed from expresso E C r log C r based o EMD s show table 1 ad fgure 5. here are 4 types states of complexty etropy, but t s ot very clear. For the purpose of dstgushg the dfferet states relably ad wth accuracy, to dstgush the dfferece by puttg the complexty feature vector to LS-SVM for dagoss. able lst out the fault dagoss result of EMD eergy ad EMD sgular value feature, by whch for the purpose of comparg the effect of dagoss by EMD complexty wth other EMD features. ABLE I. 6.Cocluso Feature vectors States C r1 C r C r3 C r4 C r5 C r6 C r7 C r8 E Normal Normal Icorrect algmet Icorrect algmet ubalace ubalace looseess looseess hs paper presets a fault dagoss method of cetrfugal pump based o EMD complexty feature. he complexty of vbrato sgal vares alog wth the state of cetrfugal pump, frstly, to obta umbers of statoary Itrsc Mode Fuctos (IMF) by EMD method ad calculate ts complexty, whch the varato of complexty of dfferet frequecy sectos s captured; the, the complexty are served as vectors of LS-SVM for classfcato, comparg to EMD eergy ad sgular value, t performace hgher accuracy. 1 Fgure 5 Complexty etropy of four state

7 Zhou ulog ad Zhao Peg / Eergy Proceda 17 ( 1 ) ABLE II. Dagoss results total Classfcato accuracy / % feature ormal Icorrect algmet ubalace looseess Eergy Sgular Complexty Referece [1] Huag Wehu, Xa Sogbo, Lu Ruya. Prcple, echque ad Applcato of Equpmet Fault Dagoss. he frst edto. Bejg Scece Press, 1996:1-5. [] Lu B, Lg S F. O the selecto of formatve wavelets for machery dagoss. Mechacal Systems & Sgal Processg, 1999, 13(1):145~16. [3] Adrate M A, Messa A R, Rvera C A, et al. Idetfcato of stataeous attrbutes of torsoal shaft sgals usg the Hlbert trasform. IEEE rasactos o Power Systems, 4, 19(3): 14~149. [4] Zhag Log, Xog Guolag, Lu Hesheg. Fault dagoss for hgh voltage crcut breakers wth mproved characterstc etropy of wavelet packet [J]. Proceedgs of the CSEE, 7, 7(1): 13-18( Chese). [5] Zhou ulog, Lu Chagx, Zhao Peg, et al. Fault dagoss methods for cetrfugal pump based o autoregressve ad cotuous Hdde Markov Model[J]. Proceedgs of the CSEE, 8,8():86-93( Chese). [6] Huag N E, She Z, Log S R, et al. he emprcal mode decomposto ad the Hlbert spectrum for olear ad o-statoary tme seres aalyss [C]. Proc. Roy. Soc. Lodo. A, 1998, 454: [7] Huag N E, She Z, Log S R. A ew vew of olear water waves: he Hlbert spectrum [J]. Aual Revew. Flud Mechacs. 1999, (31): [8] Kolmogorov A N. hree approaches to the quattatve defto of formato [J]. Problems Iformato rasmssos, 1965, 1 (1):1-7. [9] Lempel A, Zv J. O the complexty of fte sequece [J]. IEEE ras form heory, 1976, (1): [1] ag Dgx, Hu Naoqg, Zhag Chaozhog. Early fault detecto of electrc mache rotor-bearg system based o complexty measure aalyss [J]. Proceedgs of the CSEE, 4, 4(11): 16-19( Chese). [11] Suykes JAK, Vadewalle J. Least squares support vector mache classfers [J]. Neural Processg Letters, 1999, 9(3):93-3. [1] Lukas L, Suykes J A K, Vadewalle J. Least squares support vector maches classfers: A mult two-spral bechmark problem[c]. Proc of the Idoesa Studet Scetfc Meetg. Machester, 1: [13] Suykes J A K, Lukas L, Vadewalle J. Square least squares support vector mache classfers[c]. Proc of the Europea Symposum o Artfcal Neural Networks. Bruges, :37-4. [14] Wag ayog, He Hulog, Wag Guofeg, et al. Rollg-beargs fault dagoss based-o emprcal mode decomposto ad least square support vector mache [J]. Chese joural of mechacal egeerg, 7, 43(4):88-9. [15] Su B, Zhou ulog, Zhao Peg, et al. Idetfcato method for gas-lqud two-phase flow regme based o sgular value decomposto ad least square support vector mache[j]. Nuclear power egeerg, 8(6):6-66( Chese). [16] Zhag Mgqua, Lu Huj. Applcato of LS-SVM classfcato of power qualty dsturbaces [J]. Proceedgs of the CSEE, 8, 8(1): 16-11( Chese).