Comparison of Methods for Different Timefrequency Analysis of Vibration Signal

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1 68 JOURNAL OF SOFTWARE, VOL. 7, NO., JANUARY 202 Compariso of Methods for Differet Timefrequecy Aalysis of Vibratio Sigal Lig Xiag Mechaical Egieerig Departmet, North Chia Electric Power Uiversity, Baodig 07003, Hebei Provice, Chia Aiju Hu Mechaical Egieerig Departmet, North Chia Electric Power Uiversity, Baodig 07003, Hebei Provice, Chia Abstract Vibratio problems i rotors ca be extremely frustratig ad may lead to greatly reduced reliability. By utilizig the proper data collectio ad aalysis techiques, the faults because of vibratio ca be discovered ad predicted. The sigal aalysis is importat i extractig fault characteristics i fault diagosis of machiery. The traditioal sigal aalysis ca ot settle for o-statioary vibratio sigal whose statistic properties are variat. To deal with o-statioary sigal, time-frequecy aalysis techiques are widely used. The experimet data of oil whip vibratio fault sigal were aalyzed by differet methods, such as short time Fourier trasform (STFT), Wiger-Ville distributio (WVD), Wavelet trasform (WT) ad Hilbert- Huag Trasform (HHT). The experimet data of rubbig vibratio faults sigal were also aalyzed by the HHT. Compared with these methods, it is demostrated that the time-frequecy resolutios of STFT ad WVD were icosistet, which were easy to cross or make sigal lower. WT had distict time-frequecy distributio, but it brought redudat compoet. HHT time-frequecy aalysis ca detect compoets of low eergy, ad displayed true ad distict time-frequecy distributio. Therefore, HHT is a very effective tool to diagose the faults of rotatig machiery. Idex Terms sigal aalysis, time-frequecy aalysis, vibratio, Hilbert-Huag trasform (HHT), fault diagosis I. INTRODUCTION Vibratio sigal aalysis has bee widely used i the faults detectio of rotatio machiery. May methods based o vibratio sigal aalysis have bee developed. These methods iclude power spectrum estimatio, fast Fourier trasform (FFT), evelope spectrum aalysis, which have bee proved to be effective i fault detectio. However, these methods are based o the assumptio of statioary ad liearly of the vibratio sigal. Therefore, ew techiques are eeded to aalyze vibratio for faults detectio i rotatig machiery. Effective detectio of Mauscript received Dec., 200; revised Ja. 5, 20; accepted Ja. 2, 20. project umber: o-statioary sigals is of great importace [-2], as they are precursors of potetial machie failures. However, their temporary ature makes the assumptio of sigal statioary as required by Fourier trasform ivalid, thus reducig its effectiveess. To deal with o-statioary ad o-liearity sigals, time-frequecy aalysis techiques such as the Short Time Fourier Trasform (STFT), Wiger-Ville distributio (WVD) ad Wavelet Trasform (WT) are widely used. The STFT uses slidig widows i time to capture the frequecy characteristics as fuctios of time. Therefore, spectrum is geerated at discrete time istats. A iheret drawback with STFT is the limitatio betwee time ad frequecy resolutios. A fier frequecy resolutio ca oly be achieved at the expese of time resolutio ad vice-versa. The Wiger-Ville distributio (WVD) is a basic time-frequecy represetatio, which is part of the Cohe class of distributio. The WVD possesses a great umber of good properties ad is of popular iterest for o-statioary sigal aalysis. The difficulty of WVD is the severe cross terms as idicated by the existece of egative power for some frequecy rages. The Wavelet Trasform (WT) provides a time-frequecy map of the sigal beig aalyzed[3-5]. It ca achieve high frequecy resolutio with sharper time resolutios. A very appearig feature of the wavelet aalysis is that it provides a uiform resolutio for all the scales. Limited by the size of the basic wavelet fuctio, the dowside of the uiform resolutio is uiformly poor resolutio. The Hilbert Huag trasform (HHT) is based o the istataeous frequecies resultig from the itrisic mode fuctios of the sigal beig aalyzed [6]; thus, it is ot costraied by the ucertaity limitatios with respect to the time ad frequecy resolutios to which other time-frequecy techiques are subject. I recet years, HHT has bee applied to idetificatio of damage time istat ad locatio i civil ad mechaical structures[7-2]. Usig HHT, the physical mass, dampig coefficiet, ad stiffess matrices of a multiple degree of freedom liear system could be idetified[3]. doi:0.4304/jsw

JOURNAL OF SOFTWARE, VOL. 7, NO., JANUARY 202 69 This paper ivestigates the utility of time-frequecy methods for vibratio sigal aalysis.

The experimet data of oil whip vibratio fault sigal were aalyzed by differet methods, such as short time Fourier trasform (STFT), Wiger-Ville distributio (WVD), Wavelet trasform (WT) ad Hilbert-Huag

2 JOURNAL OF SOFTWARE, VOL. 7, NO., JANUARY This paper ivestigates the utility of time-frequecy methods for vibratio sigal aalysis. The theoretical backgrouds of each time-frequecy methods were itroduced, ad the simulatio was evaluated through experimetal studies performed o a test shaft. The experimet data of oil whip vibratio fault sigal were aalyzed by differet methods, such as short time Fourier trasform (STFT), Wiger-Ville distributio (WVD), Wavelet trasform (WT) ad Hilbert-Huag Trasform (HHT). The experimet data of rubbig vibratio faults sigal were also aalyzed by the HHT. Compared with these methods, it is demostrated that HHT is a very effective tool to aalyze o-statioary ad o-liearity sigals. II. STFT OF VIBRATION SIGNAL A. Short Time Fourier Trasform (STFT) Short Time Fourier Trasform (STFT) has a short data widow cetered at time. The widow is moved to a ew positio ad the calculatio repeated. STFT is defied for a sigle sample fuctio x() t, t, ω jωτ jωτ STFTx(, t ω) = x( τ) g ( τ) dτ = x( τ) g( τ t) e dτ =< x( τ), g( τ t) e > () gt, ( ) g( t) e jωτ ω τ = τ (2) Where g( τ ) =, gt, ω ( τ ) =, ad the widow fuctio g( τ ) is symmetrical. If the width of the widow is represeted by time duratio t, its frequecy badwidth is approximately ω. A feature of the STFT is that all spectral estimates have the same badwidth. B. 2.2 STFT of Oil Whip Sigal masses are to the fluid film bearig. The rotor kit is to go ustable place as the speed icreases. The rotor will develop oil whirl to oil whip. Whe the rotor ruig speed is ear the 2th rev, the rotor will develop oil whip. Because the frequecy of oil whirl approaches the high eccetricity atural resoat frequecy of the rotor. Durig oil whip the frequecy of the whip is early costat as rotor rpm is icreased. I Figure 2 the samplig data is show whe the rotor speed is 4800rpm. The three major frequecy compoets at 80Hz, 3Hz ad 5Hz were idetified, which are correspodig to fudametal frequecy, whip frequecy ad dimidiate frequecy of whip. I Figure 3 the STFT provides a time-frequecy distribute. The adjacet data widows have overlapped, so the time-frequecy spectrum of STFT geerated redudat iformatio. (a) Time sigal (b) Frequecy spectrum Figure 2. FFT of oil whip vibratio sigal Figure. Experimetal test rotor system To experimetally evaluate the effectiveess of timefrequecy methods for o-statioary vibratio sigal, systematic tests were coducted o a rotor test system (see Figure ). The test system cosisted of a oil pump assembly, a oil bearig assembly, a rotor kit shaft with oil bearig joural ad a preload frame. Tighte the set screws to firmly attach the rotor masses to the rotor. The rotor will whirl at a lower speed the closer the rotor Figure 3. STFT of oil whip vibratio sigal

70 JOURNAL OF SOFTWARE, VOL. 7, NO., JANUARY 202 III. WVD OF VIBRATION SIGNAL A. WVD ad SPWVD The fuctio (3) is called the Wiger-Ville distributio (WVD).

τ τ j 2πτ WVD x ( t, f ) = x t+ t- e d 2 x τ (3) 2 The smooth pseudo Wiger-Ville distributio (SPWVD) selects appropriate widow fuctio.

SPWVD of Oil Whip Sigal Figure 4 is time-frequecy diagram of SPWVD. It has high time-frequecy resolutio ad immuity of cross term iterferece.

3 70 JOURNAL OF SOFTWARE, VOL. 7, NO., JANUARY 202 III. WVD OF VIBRATION SIGNAL A. WVD ad SPWVD The fuctio (3) is called the Wiger-Ville distributio (WVD). Wiger (932) used it first i quatum mechaics ad J.Ville (948) was the first to propose usig (3) for harmoic aalysis. τ τ j 2πτ WVD x ( t, f ) = x t+ t- e d 2 x τ (3) 2 The smooth pseudo Wiger-Ville distributio (SPWVD) selects appropriate widow fuctio. By slidig Wiger-Ville kerel fuctio, the cross elemets are restraied. The SPWVD is defied as: SPWVD x ( t, f ) = τ τ j 2πτ (4) x t u+ t-u- g( ) w( ) e d 2 x τ τ τ 2 B. SPWVD of Oil Whip Sigal Figure 4 is time-frequecy diagram of SPWVD. It has high time-frequecy resolutio ad immuity of cross term iterferece. But high resolutio caot be obtaied simultaeously i time ad i frequecy. The 2X frequecy of vibratio was weakeed. very log. The sigal x() t, is plotted alog the horizotal axis ad the wavelet fuctio ψ () t is plotted vertically. ψ () ( t b ) ab, t = a ψ (5) a 2 Where ab, are costats, ad a > 0. If x() t L ( R), Wavelet Trasform is defied as: t b WT x ( ab, ) = xt ( ) ψ ( ) dt a a (6) = x() t ψ () t dt = x(), t ψ () t ab, ab, B. WT of Oil Whip Sigal The structure of a o-statioary sigal ca be aalyzed with local features represeted by closelypacked wavelets of short legth. Vibratio characteristics ca be idetified readily from a wavelet map i which the mea-square value of the vibratio record is show distributed over wavelet scale ad positio. Coefficiet of cotiuous wavelet trasform was plotted o timefrequecy plae of oil whip sigal i Figure 5. 3-D timefrequecy distributio was show i Figure 6. The three major frequecy compoets at 80Hz, 3Hz ad 5Hz were idetified, which are correspodig to fudametal frequecy, whip frequecy ad dimidiate frequecy of whip. WT had distict time-frequecy distributio, but it brought redudat compoet decomposed i Figure 5. Figure 4. SPWVD of oil whip vibratio sigal IV. WT OF VIBRATION SIGNAL A. Wavelet Trasform (WT) Wavelet aalysis ivolves a fudametally differet approach. Istead of seekig to break dow a sigal ito its harmoics, which are global fuctios that go o for ever, the sigal is broke dow ito a series of local basis fuctios called wavelets. At the fiest scale, wavelets may be very short ideed; at a coarse scale, they may be Figure 5. The decomposed compoets of WT

JOURNAL OF SOFTWARE, VOL. 7, NO., JANUARY 202 7 Figure 6. WT of oil whip sigal V. HHT OF VIBRATION SIGNAL A.

4 JOURNAL OF SOFTWARE, VOL. 7, NO., JANUARY Figure 6. WT of oil whip sigal V. HHT OF VIBRATION SIGNAL A. Hilbert-Huag Trasform (HHT) The HHT represets the sigal beig aalyzed i the time-frequecy domai by combiig the empirical mode decompositio (EMD) with the Hilbert trasform [6]. I cotrast to the Fourier spectral aalysis by which a series of sie ad cosie fuctios of costat amplitudes are used to represet each costituet frequecy compoets i the sigal, the HHT techique is based o the istataeous frequecy calculatio that results from the Hilbert trasform of the sigal. Geerally, the Hilbert trasform for ay sigal is defied as x( τ ) H[ xt ( )] = yt ( ) = dτ (7) π t τ Where H () deotes the Hilbert trasform operatio. Theoretically, ay aalytic sigal z(t) ca be expressed by the sum of its real part x(t) ad imagiary part y(t), with the latter beig the Hilbert trasform of the real part. zt () = xt () + jyt () (8) Equatio (8) ca be rewritte i a polar coordiate system as () zt () = ate () jθ t (9) From the istataeous phase θ () t, the istataeous frequecy ω() t of the sigal ca be derived as d( θ ()) t ytxt &() () ytxt ()&() ω() t = = (0) 2 2 dt x () t + y () t Accordigly, the real part x(t) of the sigal ca be writte i terms of the amplitude ad istataeous frequecy as a time-depedet fuctio j () t dt xt () =R ( zt ()) =R ( ate () ω ) () Where the symbol R () deotes the real part of the sigal z(t). To effectively costruct frequecy spectrum of a vibratio sigal that cotais multiple-frequecy compoets, the sigal eeds to be first decomposed ito moo-compoet fuctios, by meas of EMD [6]. Decompositio of such a sigal is based o the followig observatios. ) The sigal has at least two extrema, i.e., oe maximum ad oe miimum. 2) The characteristic time scale is clearly defied by the time lapse betwee successive alteratios of local maxima ad miima of the sigal. 3) If the sigal has o extrema but cotais iflectio poits, the it ca be differetiated oe or more times to reveal the extrema. The EMD techique decomposes the sigal ito a umber of Itrisic Mode Fuctios (IMFs), each of which is a moo-compoet fuctio. The, the Hilbert trasform is applied to calculate the istataeous frequecies of the origial sigal. After idetifyig all the local maxima ad miima of the sigal, the upper ad lower evelopes are geerated through curve fittig. Therefore, the cubic splie fuctio was employed i the preseted study. The mea values of the upper ad lower evelopes of the sigal m () t are calculated as m () t = ( xup () t + xlow ())/2 t (2) Where xup () t ad xlow() t are the upper ad lower evelopes of the sigal, respectively. Accordigly, the differece betwee the sigal x() t ad the evelopes of the sigal m () t, which is deoted as h () t, is give by h() t = x() t m() t (3) Due to the approximatio ature of the curve fittig method, h () t has to be further processed (by treatig h () t as the sigal itself ad repeatig the process cotiually) util it satisfies the followig two coditios. ) The umber of extrema ad the umber of zerocrossigs are either equal to each other or differ by at most oe. 2) At ay poit, the mea value betwee the evelope defied by local maxima ad the evelope defied by the local miima is zero. Through the iteratio process (for a total of times), the differece betwee the sigal ad the mea evelope values, is deoted as h () t = h () t m () t (4) k ( k ) k Where mk is the mea evelope value after the kth iteratio, ad h ( k ) () t is the differece betwee the sigal ad the mea evelope values at the (k-)th iteratio. The fuctio h k () t is the defied as the first IMF compoet ad expressed as c() t = h k () t (5) After separatig c () t from the origial sigal x() t, the residue is obtaied as

the sigal x() t as r2() t = r() t c2(), t L, r() t = r () t c() t (7) The sigal decompositio process is termiated whe r () t becomes a mootoic fuctio, from which o further IMFs ca be extracted.

5 72 JOURNAL OF SOFTWARE, VOL. 7, NO., JANUARY 202 r() t = x() t c () t (6) Subsequetly, the residue r () t ca be treated as the ew sigal, ad the above-illustrated iteratio process is repeated to extract the rest of the IMFs iheret to the sigal x() t as r2() t = r() t c2(), t L, r() t = r () t c() t (7) The sigal decompositio process is termiated whe r () t becomes a mootoic fuctio, from which o further IMFs ca be extracted. By substitutig (7) ito (6), the sigal x() t is decomposed ito a umber of itrisic mode fuctios that are the costituet compoets of the sigal. As a result, the sigal x() t ca be expressed as x() t = ci() t + r() t (8) i= Where ci () t represets the ith itrisic mode fuctio, r t is the residue of the sigal decompositio. ad () Equatio (8) provides a complete descriptio of the empirical mode decompositio process [6], which ca be evaluated by checkig the amplitude error betwee the recostructed ad the origial sigal. Based o (7) (0) ad (8), () ca be modified as I which j i () t dt ai te =R ω (9) i= xt () ( () ) a () t = c () t + H[ c ()] t ad ω () t = 2 2 i i i (ta ( [ i()]/ i())/ d H c t c t dt. The term r () t i (2) is ot icluded i (3) as it is a mootoic fuctio ad does ot cotribute to the frequecy cotet of the sigal. Comparig (20) with the Fourier-based represetatio of a sigal x() t give by Where both A i ad jωit xt () =R ( Ae ) (20) Ωi i= i are costats, it becomes evidet that the EMD process eables flexible represetatio of a dyamic sigal by revealig its timedepedet amplitude ad the characteristic frequecy compoets at various time istaces. The sigal is thus represeted by a time-frequecy distributio. The uderlyig HHT of the sigal is mathematically defied as HHT( t, ω) = HHT( t, ω) a ( t, ω ) i i i i= i= (2) HHT i ( t, ω) represets the time-frequecy distributio obtaied from the ith IMF of the sigal. The symbol deotes by defiitio, ad combies the amplitude ad istataeous frequecy of the sigal together. B. HHT of oil whip sigal The first 8 mode of HHT was displayed I Figure 7. Compared with decomposed based o WT i Figure 5, the mode of HHT had little residual. Time-frequecy distributio was show i Figure 8. The three major frequecy compoets at 80Hz, 3Hz ad 5Hz were idetified, which are more distict. I compariso, the i Hilbert Huag trasform (HHT) is based o the istataeous frequecies resultig from the itrisic mode fuctios of the sigal beig aalyzed; thus, it is ot costraied by the ucertaity limitatios with respect to the time ad frequecy resolutios to which other timefrequecy techiques are subject. The test results that HHT provides a more effective time-frequecy distribute. Figure 7. The mode of HHT for oil whip sigal Figure 8. HHT of oil whip vibratio sigal

JOURNAL OF SOFTWARE, VOL. 7, NO., JANUARY 202 73 C.

I the followig the HHT is applied i early local rubbig, circumferetial rubbig. By comparig the HHT with origial method, the obvious advatage ad validity ca be clearly expressed.

Usig EMD method, the origial vibratio sigals of rubbig faults ca be decomposed ito itrisic modes.

6 JOURNAL OF SOFTWARE, VOL. 7, NO., JANUARY C. HHT of early local rubbig sigal To experimetally evaluate the effectiveess of HHT for o-statioary vibratio sigal aalysis, systematic tests were coducted o a rotor test system. I the followig the HHT is applied i early local rubbig, circumferetial rubbig. By comparig the HHT with origial method, the obvious advatage ad validity ca be clearly expressed. characteristic of early local rubbig ca ot be displayed i FFT spectral diagram. Figure 0 displays the empirical mode decompositio i eight IMFs. Usig EMD method, the origial vibratio sigals of rubbig faults ca be decomposed ito itrisic modes. The decompositio idetifies eight modes: c-c8, which represets the differet frequecy compoets exited by the ier race defects, c8 is the residue, respectively. Mode c cotais the highest sigal frequecies, mode c2 the ext higher frequecy bad ad so o. Mode c3 cotais the fudametal frequecy, ad modes c4-c7 cotais differetial frequecies, whose amplitudes are very small. But they ca be characteristics of early local rubbig. (a) Time sigal (b) Frequecy spectrum Figure 9. Time ad spectral diagram of early local rubbig sigals Figure. HT of early local rubbig fault sigals I Figure the HHT result of the early local rubbig fault vibratio sigal is illustrated. The eergy distributig of vibratios at ormal ad compressiodecreasig coditios is give i Figure 3, ad their frequecies are computed usig (5), respectively. As shower i two figures, the eergy of core vibratio maily focuses o the fudametal frequecy, a little exists roud about /2X, /3X ad high frequecies 2X, 3X ad so o. But differetial frequecies ca be cosidered as the characteristics of early local rubbig. Therefore, HHT is a very effective tool to diagose the early faults of rotor system. Ad it provides ew meas for state detectio ad fault diagosis of rotatig machie. Figure 0. Time of early local rubbig fault sigals by EMD The vibratio sigal of early local rubbig fault is measured ad show i Figure 9(a). Its spectrum i Figure 9(b) reveals the fudametal frequecy at 3Hz. The fudametal frequecy was obvious, but the twice rotatioal frequecy (2X) is egligible ad the V. CONCLUSION The experimet data of oil whip vibratio fault sigal were aalyzed by differet methods, such as short time Fourier trasform (STFT), Wiger-Ville distributio (WVD), Wavelet trasform (WT) ad Hilbert-Huag Trasform (HHT). Compared with these methods, it is demostrated that the time-frequecy resolutios of STFT ad WVD were icosistet, which were easy to cross or make sigal lower. WT had distict timefrequecy distributio, but it brought redudat compoet. HHT time-frequecy aalysis ca detect

Research is beig cotiued to systematically ivestigate the suitability ad costraits of the HHT for o-statioary sigal aalysis, usig vibratio sigals from differet faults.

7 74 JOURNAL OF SOFTWARE, VOL. 7, NO., JANUARY 202 compoets of low eergy, ad displayed true ad distict time-frequecy distributio. Therefore, as a timefrequecy sigal decompositio techique, the Hilbert- Huag trasform provides a effective tool for aalyzig vibratio sigal. Research is beig cotiued to systematically ivestigate the suitability ad costraits of the HHT for o-statioary sigal aalysis, usig vibratio sigals from differet faults. Furthermore, itegratio of the EMD process with evelopig spectrum aalysis is also beig ivestigated, with the goal of realizig a adaptive sigal demodulatio approach to accout for varyig machie coditios i real-world applicatios. ACKNOWLEDGMENT This work was supported by Project of the Natioal Sciece Foudatio of Chia. REFERENCES [] R. Ya ad R. Gao, Complexity as a measure for machie health evaluatio, IEEE Tras. Istrum. Meas., vol. 53, o. 4, pp , Aug [2] B. Craft, O-lie surveillace moitorig i discrete maufacturig applicatios, SKF Reliability Syst., 2002, Applicatio Note CM3066. [3] C.Wag ad R. Gao, Wavelet trasform with spectral post-processig for ehaced feature extractio, IEEE Tras. Istrum. Meas., vol. 52, o., pp , [4] R. Ya ad R. Gao, A efficiet approach to machie health evaluatio based o harmoic wavelet packet trasform, Robotics Comput. Itegrated Mauf., vol. 2, pp , [5] R. Gao ad R. Ya, Nostatioary sigal processig for bearig health moitorig, It. J. Mauf. Res., vol., o., pp. 8 40, [6] N. E. Huag, Z. She, ad S. R. Log, The empirical ode decompositio ad the Hilbert spectrum for oliear ad ostatioary time series aalysis, i Proc. Royal. Soc. Lodo. A, 998, vol. 454, pp [7] N. E. Huag, Z. She, ad S. R. Log, A ew view of oliear water waves: The Hilbert spectrum, Au. Rev. Fluid Mechaics, vol. 3, pp , 999. [8] D. Beral ad B. Gues, A examiatio of istataeous frequecy as a damage detectio tool, i Proc. 4th Egieerig Mechaics Cof., Austi, TX, [9] Yag B Z,Iterpretatio of crackiduced rotor o-liear respose usig istataeous frequecy[j]. Mechaical Systems ad Sigal Processig,2004,8(4): [0] J. N. Yag, Y. Lei, S. Li, S., ad N. E. Huag, Hilbert- Huag based approach for structural damage detectio, J. Eg. Mechaics, vol. 30, o., pp , [] J. N. Yag, Y. Lei, S. Pa, ad N. E. Huag, System idetificatio of liear structure based o Hilbert-Huag spectral aalysis. Part : Normal modes, Earthquake Eg. Structural Dy., vol. 32, pp , [2] F.Hlawatsch, W.Kozek, The Wiger distributio of a liear sigal space, IEEE trasactio o sigal processig, Vol.4, o.3, pp ,993. [3] R. Balocchi, D. Meicucci, E. Satarcagelo, L. Sebastiai, A. Gemigai, B. Ghelarducci, ad M. Varaii, Derivig the respiratory sius arrhythmia from the heartbeat time series usig empirical mode decompositio, Chaos, Solitos, Fractals, vol. 20, pp. 7 77, Lig Xiag was bor i Hubei Provice, Chia, i 97. She received the B.Sc.ad M.Sc. degrees i mechaical egieerig system, from the North Chia Electric Power Uiversity, Baodig City, Chia, i 993 ad 998, respectively. She received the Ph.D. degree i electrical power egieerig system, from the North Chia Electric Power Uiversity, Baodig City, Chia, i Her mai research iterests iclude the coditio moitorig ad fault diagosis. She is a associate professor of Dept. Mechaical Egieerig of North Chia Electric Power Uiversity. Aiju Hu was bor i Hebei Provice, Chia, i 97. He received the B.Sc.ad M.Sc. degrees i mechaical egieerig system, from the North Chia Electric Power Uiversity, Baodig City, Chia, i 993 ad 998, respectively. He received the Ph.D. degree i thermal power egieerig system, from the North Chia Electric Power Uiversity, Baodig City, Chia, i His mai research iterests iclude the coditio moitorig ad fault diagosis. He is a associate professor of Dept. Mechaical Egieerig of North Chia Electric Power Uiversity.

1. Introduction (Received 11 February 2013; accepted 3 June 2013)

1. Introduction (Received 11 February 2013; accepted 3 June 2013) 991. Applicatio of EMD-AR ad MTS for hydraulic pump fault diagosis Lu Che, Hu Jiameg, Liu Hogmei 991. APPLICATION OF EMD-AR AND MTS FOR HYDRAULIC PUMP FAULT DIAGNOSIS. Lu Che 1,, 3, Hu Jiameg 1, Liu Hogmei