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

Transcription

1 991. 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 1, 3 1 School of Reliability ad Systems Egieerig, Beihag Uiversity, Beijig , Chia State Key Laboratory of Virtual Reality Techology ad Systems, Beijig , Chia 3 Sciece & Techology Laboratory o Reliability & Evirometal Egieerig, Beijig , Chia 3 Correspodig author 1 luche@buaa.edu.c, hujiamegbrave@163.com, 3 liuhogmei@yahoo.com.c (Received 11 February 013; accepted 3 Jue 013) Abstract. A real-time diagosis of hydraulic pumps is very crucial for the reliable operatio of hydraulic systems. The mai purpose of this study is to propose a fault diagosis approach for hydraulic systems based o the empirical mode decompositio (EMD), autoregressive (AR) model, sigular value decompositio (SVD), ad Mahalaobis Taguchi system (MTS). The AR model effectively extracts the fault feature of vibratio sigals. However, it ca oly be applied to statioary sigals; the fault vibratio sigals of hydraulic pumps are o-statioary. To address this problem, the EMD method is used as a pretreatmet step to decompose the o-statioary vibratio sigals of hydraulic pumps. First, the vibratio sigals of hydraulic pumps are decomposed ito a fiite umber of statioary itrisic mode fuctios (IMF). The AR model of each IMF compoet is established. The AR parameters ad the remat s variace are regarded as the iitial feature vector matrices. Third, the sigular values are obtaied by applyig the SVD to the iitial feature vector matrices. Fially, these values serve as the fault feature vectors to be etered to the MTS, thereby classifyig the fault patter of the hydraulic pumps. The Taguchi methods are employed to reduce the redudat features ad extract the pricipal compoets. Experimetal aalysis results idicate that this method ca effectively accomplish the fault diagosis of hydraulic pumps. Keywords: hydraulic pump, fault diagosis, empirical mode decompositio, AR model, sigular value decompositio, Mahalaobis Taguchi system. 1. Itroductio A hydraulic pump is the heart of a hydraulic system. It reflects whether the operatio of the etire system is ormal or ot. Therefore, hydraulic pumps should be able to process coditio moitorig ad fault diagosis. Hydraulic pumps uder a abormal state are ormally accompaied with vibratio chages. Most mechaical faults are reflected by vibratio. Thus, vibratio diagosis is importat i this field ad is also the foremost topic of iterest for local ad foreig researchers [1, ]. I the fault diagosis of hydraulic pumps, fault sigals passed through the pump source outlet are ofte drowed by iterferece sigals because of complex fault mechaisms ad strog buzz durig the sigal extractio process. The effective fault characteristics are difficult to extract usig covetioal sigal processig methods. The hydraulic pump fault diagosis process basically cosists of three steps: (1) collectio of the hydraulic pump vibratio sigals; () extractio of the fault features; ad (3) patter recogitio ad fault diagosis. Steps ad 3 are the key steps i the fault diagosis of hydraulic pumps. Cosiderig that the fault vibratio sigals of hydraulic pumps are o-statioary, determiig how to obtai feature vectors from these sigals for fault diagosis is importat. Traditioal diagosis techiques obtai these vectors from the waveforms of the fault vibratio sigals i the time or frequecy domai, ad the costruct the criterio fuctios to determie the coditio of hydraulic pumps. However, cosiderig that the o-liear factors have distict effects o the vibratio sigals because of the complexity of the structure ad workig coditio of hydraulic pumps, obtaiig a accurate evaluatio of the fault coditio of hydraulic pumps oly through time or frequecy domai aalyses is difficult. VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 013. VOLUME 15, ISSUE. ISSN

2 I the timig aalysis field, the autoregressive (AR) model is the most basic ad most widely used time-series model, but it is maily used i statioary processes. The AR model is a time sequece aalysis method with mature algorithms whose parameters comprise importat iformatio regardig the system coditio. A accurate AR model ca reflect the characteristics of a dyamic system. The autoregressio parameters of the AR model are also very sesitive to the coditio variatio [3, 4]. The vibratio sigals of hydraulic pumps with faults have shock characteristics. The AR model ca simulate trasiets, ad the frequecy respose fuctio of these pumps ca be calculated from the auto-regressio parameters of the AR model. Therefore, these parameters ca be effectively used to aalyze the coditio variatio of dyamic systems. The most apparet advatage of the AR model is that faults ca be idetified by the AR model parameters after the AR model of the vibratio sigals is established without costructig mathematical models ad studyig the fault mechaisms. The AR model has also bee successfully applied to fault diagoses i may cases. Whe the AR model is applied to ostatioary sigals, estimatig the autoregressio parameters by the least squares method or the Yule Walker equatio method is difficult; thus, the aalysis results are iaccurate if the AR model is directly applied to o-statioary hydraulic pump vibratio sigals. Sigals geerated by hydraulic pump failures traditioally ofte cotai a large umber of o-statioary compoets. The global frequecy domai iformatio ca be obtaied by performig a Fourier trasform o the sigals cotaiig o-statioary compoets, but the fault iformatio is difficult to be effectively extracted from a spectrum overwhelmed with oise. The local iformatio of o-statioary sigals ca be extracted by wavelet trasform. However, the high frequecy iformatio is lost because of the iability to decompose the high-frequecy part; thus, the fault characteristics of high frequecies is difficult to be extracted. The wavelet packet trasform compesates for the iability of the wavelet trasform to decompose high frequecies. The wavelet packet trasform ca perform a complete multi-level decompositio i the full-bad sigal, coupled with good time-frequecy characteristics. However, for some mechaical systems, this approach caot obtai a vibratio sigal feature extractio with a high sigal-to-oise ratio (SNR). To get rid of the disadvatages of the feature extractio methods above, a self-adaptive method, amely, empirical mode decompositio (EMD), for oliear ad o-statioary sigals was proposed by Huag [5, 6]. I the preset study, a effective method based o the EMD ad AR model is preseted to extract feature vectors. EMD is based o the local sigal characteristics ad could decompose complicated sigals ito a umber of itrisic mode fuctios (IMFs). The umber of decomposed IMFs is usually fiite, ad the IMF compoets geerated by EMD ca reflect the actual iformatio of the origial sigal. More importatly, the geerated IMF compoets are statioary; thus, the AR model of each IMF compoet ca be established. The iitial feature vectors of the fault vibratio sigals of hydraulic pumps are extracted with the combiatio of EMD ad the AR model. The feature vectors are composed of the autoregressio parameters ad remat s variace of the AR model. The feature vector matrices are decomposed to obtai the sigular value by sigular value decompositio (SVD). The Mahalaobis Taguchi system (MTS) is a multivariate patter recogitio tool that provides the basis to combie all the pertiet iformatio about a system ito a sigle metric usig the Mahalaobis distace (MD). It also presets a systematic way of determiig the key features required for aalysis based o the Taguchi methods. MTS is widely used i various diagostic applicatios that deal with data classificatio. I MTS, the MD is used to determie the degree of abormality, thereby idetifyig the workig coditio ad fault patters of hydraulic pumps. The Taguchi methods use orthogoal arrays (OAs) ad SNRs. These methods are also used to reduce the redudat features ad extract the pricipal compoets. The MD, itroduced by P. C. Mahalaobis i 1936 [7], is a multivariate geeralized measure used to determie the distace of a data poit to the mea of a group. The MD is measured i terms of the stadard deviatios from the mea of the samples ad provides a statistical measure of how well the 76 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 013. VOLUME 15, ISSUE. ISSN

3 ukow data set matches with the ideal oe. The advatage of the MD is that it is sesitive to the itervariable chages i the referece data. Therefore, it has traditioally bee used to classify observatios ito differet groups for diagoses [8]. The beefits of MTS as a patter recogitio ad data classificatio tool are summarized as follows. It is a robust methodology isesitive to variatios i multidimesioal systems. It ca hadle may differet types of data sets ad effectively cosolidates these data ito a useful metric. Implemetatio of MTS requires limited kowledge of statistics. It typically relies o simple arithmetic, cotextual kowledge, ad ituitio. Its success has bee demostrated i various practical applicatios.. Methodologies for hydraulic pump fault diagosis based o EMD-AR ad MTS.1. EMD method Huag et al. [5] developed EMD i The EMD method is developed based o the simple assumptio that ay sigal cosists of differet simple itrisic modes of oscillatios. Each liear or o-liear mode will have the same umber of extrema ad zero-crossigs. Oly oe extremum exists betwee successive zero-crossigs. Each mode should be idepedet of the others. I this way, each sigal could be decomposed ito a umber of IMFs, each of which must satisfy the followig defiitios [9]: (1) I the whole data set, the umber of extrema ad the umber of zerocrossigs must either be equal or differ by at most oe; () At ay poit, the mea value of the evelope defied by the local maxima ad the evelope defied by the local miima is zero. A IMF represets a simple oscillatory mode compared with the simple harmoic fuctio. With the defiitio, ay sigal x(t) ca be decomposed as follows: Step 1: Idetify all the local extrema, ad the coect all the local maxima by a cubic splie lie to give the upper evelope. Step : Repeat this procedure for the local miima to produce the lower evelope. Betwee them, the upper ad lower evelopes should cover all the data. Step 3: The mea of the upper ad lower evelope values is desigated as m 1 (t) ; the differece betwee the sigal x(t) ad m 1 (t) is the first compoet h 1 (t): x(t) m 1 (t) = h 1 (t). (1) Ideally, if h 1 (t) is a IMF, the h 1 (t) is the first compoet of x(t). A equivalet set of two first-order o-autoomous equatios is as follows: Step 4: If h 1 (t) is ot a IMF, h 1 (t) is treated as the origial sigal ad steps 1, ad 3 are repeated; the: h 1 (t) m 11 (t) = h 11 (t). () After repeated siftig, i.e., up to k times, h 1k (t) becomes a IMF, that is: h 1(k 1) (t) m 1k (t) = h 1k (t). (3) The, it is desigated as: c 1 (t) = h 1k (t). (4) The first IMF compoet from the origial data c 1 (t) should cotai the fiest scale or the shortest period compoet of the sigal. VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 013. VOLUME 15, ISSUE. ISSN

4 Step 5: Separatig c 1 (t) from x(t), we get: r 1 (t) = x(t) c 1 (t). (5) r 1 (t) is treated as the origial data, ad the above processes are repeated; therefore, the secod IMF compoet c (t) of x(t) ca be obtaied. Repeatig the process described above times, -IMFs of sigal x(t) ca be obtaied. The: r 1 (t) c (t) = r (t), r 1 (t) c (t) = r (t). (6) The decompositio process ca be stopped whe r (t) becomes a mootoic fuctio from which o more IMFs ca be extracted. Usig this procedure, ay sigal ca be decomposed. We fially obtai: x(t) = c j (t) + r (t). j=1 (7) Thus, the sigal is decomposed ito -empirical modes ad a residue r (t), which is the mea tred of x(t). Each IMF c 1 (t), c (t),, c (t) cotais lower-frequecy oscillatios tha the prior-extracted oe, while r (t) represets the cetral tedecy of sigal x(t). EMD has bee show to be a fast, effective, self-adaptive method for oliear ad ostatioary time series aalysis, but there is still a drawback worth otig: the ed effect, whereby distortio appears at the ed of the sigal i the decompositio process. I this paper, we employ the mirror periodic extedig method (MPM) to solve this problem... MTS The MTS starts by collectig data o ormal observatios. The MD is calculated usig certai characteristics to determie whether the MD has the ability to differetiate a ormal group from a abormal group. If the MD caot idetify the ormal group usig those particular characteristics, the a ew combiatio of characteristics are eeded to be examied. Whe the correct set of characteristics is determied, the Taguchi methods are employed to evaluate the effect of each characteristic. If possible, dimesioality is reduced by elimiatig those characteristics that do ot add value to the aalysis. The MTS cosists of the followig three stages [8, 10]...1. Stage 1: Costructio of the Mahalaobis Space (MS) Step 1: Calculate the mea for each characteristic i the ormal dataset as: x i = j=1 x ij. (8) Step : Calculate the stadard deviatio s i, for each characteristic (i = 1,, 3, ): s i = (X ij x i) j=1. 1 (9) 764 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 013. VOLUME 15, ISSUE. ISSN

5 Step 3: Normalize each characteristic. Form the ormalized data matrix Z, ad take its traspose Z ij, where: Z ij = (X ij x i) s i. (10) Step 4: Verify that the mea of the ormalized data is zero: z i = j=1 Z ij = 0. Step 5: Verify that the stadard deviatio of the ormalized data is oe: (11) s z = j=1 (Z ij z i) 1 = 1. (1) Step 6: Costruct the correlatio matrix C, for the ormalized data. Calculate the matrix elemets c ij, as follows: c ij = m=1 (Z imz jm ). 1 (13) Step 7: Calculate the iverse of the correlatio matrix c 1. Step 8: Calculate MD as: MD j = 1 k Z ij T C 1 Z ij, (14) where x ij is the i th characteristic i the j th observatio, is the umber of observatios, s i is the stadard deviatio of the i th characteristic, Z ij is the ormalized value of the i th characteristic i the j th observatios, s z is the stadard deviatio of the ormalized values, c is the correlatio matrix c 1 is the iverse of the correlatio matrix, MD j is the MD for the j th observatio, ad k is the umber of characteristics [11].... Stage : Idetificatio of the useful characteristics The useful characteristics are determied usig OAs ad SNRs. A OA is a table that lists the set of characteristics. It allows the effects of the presece or absece of a characteristic to be tested. The size of the OA is determied by the umber of characteristics ad the levels that they ca take. I the MTS, characteristics i the OA have two levels. Level-1 represets the presece of a characteristic, ad Level- represets the absece of a characteristic. For the abormal cases, the MD values are calculated usig the combiatio of the characteristics determied by the OA. The larger-the-sigal-the-better SNR is calculated as follows: η q = 10log [ 1 1 ], MD j j=1 (15) where η q is the SNR for the q th row of the OA, ad is the sample size of each abormality uder the cosideratio of the Taguchi aalysis. By obtaiig the average SNRs at Level-1 (t 1 ) ad VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 013. VOLUME 15, ISSUE. ISSN

6 Level- (t ) of each characteristic, the Gai i SNR ca be calculated as t 1 t. If t 1 t > 0, it meas this characteristic is useful; otherwise, it is useless or eve harmful for diagosis. Thus, characteristics with positive gai are selected for the detectio of abormalities ad the rest are discarded...3. Stage 3: Decisio makig I the fial stage, the applicatio uder ivestigatio is moitored by collectig data usig the MS. The MDs are calculated, ad if MD >> 1, the applicatio exhibits a abormal behavior ad appropriate corrective actios are eeded to be take. If MD 1, the the coditios are ormal [11]..3. Diagosis approach for hydraulic pump First, the fault vibratio sigal of the hydraulic pump X t, is decomposed by EMD ito IMFs, imf 1, imf,..., imf. Each compoet represets a differet characteristic iformatio. After the EMD method is applied to X t, the IMFs ca completely combie the characteristics of X t Therefore, the characteristics of X t ca be obtaied by extractig the characteristics of imf 1, imf,..., imf [9]. Secod, the followig AR model, AR(m), is established for each IMF compoet as: m X i (t) = φ ik X i (t k) + c i (t), (16) k=1 where φ ik (k = 1,,..., m) represet the parameters of the model, AR idicates a AR model of order m, c i (t) deotes the remat of the model ad is a white-oise sequece whose mea value is zero ad variace is σ i. The parameters φ ik (k = 1,,..., m) ca reflect the iheret characteristics of a hydraulic pump vibratig system. The variace of the remat σ i is closely related with the output characteristics of the system. φ ik (k = 1,,..., m) ad σ i ca be chose as the iitial feature vectors A i = [φ i1, φ i,..., φ im, σ i ]. The sigular values of the feature vector matrix are calculated to extract the feature vectors. Based o matrix theory, the sigular value of the matrix is the iheret characteristic of the matrix ad has good stability, that is, whe the matrix elemets ecouter small chages, the matrix sigular value oly slightly chages. Thus, the sigular values of the feature vector matrix obtaied by AR ca be extracted as mechaical compoet characteristics. However, the SVD also has its disadvatages, that is, for a space recostructio i the time series, embeddig dimesio ad delay decisios have o specific theoretical basis. The iitial feature vector matrix obtaied by AR could avoid this problem. Accordigly, the iitial feature vector A i, from IMF compoets costitutes the iitial feature vector matrix A, where A = (A 1, A,..., A N ) T. A is decomposed by SVD to extract the sigular value σ 1, σ,..., σ N, thereby extractig the fault feature vectors. The criterio of coditio idetificatio is the MD. The proposed diagosis method is illustrated i Fig. 1. The fault diagosis method for the hydraulic pump is as follows: (1) Acquire vibratio sigal samples at a certai samplig frequecy f s, uder each of the followig coditios: hydraulic pump is ormal, with valve plate wear, ad with slipper loosig. The 3 sigals are take as the samples. () Each sigal is decomposed by EMD, ad fiite umber of IMF compoets ca be obtaied. (3) Normalize each IMF compoet to obtai a ew compoet to elimiate the effect of the sigal amplitude o the variace of the remat σ i : 766 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 013. VOLUME 15, ISSUE. ISSN

7 c i (t) c i(t) =. c i (t) dt (17) Fig. 1. Flow chart of the proposed method (4) Costruct the AR model for the ormalized compoet. Determie the order m, of the model usig the fial predictio error (FPE) criterio ad estimate the AR parameters φ ik (k = 1,,, m) ad the remat s variace σ i by the miimum squares method, where φ ik deotes the k th AR parameters of the i th IMF compoet. φ ik (k = 1,,, m) ad σ i ca be determied. These values ca be combied to costruct the iitial feature vector of the i th IMF compoet as follows: A j,i = [φ x,i1, φ x,i1,..., φ x,i1, σ x,i ], (18) where j = 1,, 3 deotes the ormal coditio, coditio with valve plate wear, ad coditio with slipper loosig. (5) Each sample i all coditios is decomposed by SVD to obtai m + 1 sigular values. Formally, the SVD of a m real or complex matrix M is a factorizatio of the form: M = U V, (19) where U is a m m real or complex uitary matrix, is a m rectagular diagoal matrix with oegative real umbers o the diagoal, ad V (the ojugate traspose of V) is a real or complex uitary matrix. The diagoal etries i,i of are kow as the sigular values of M. (6) Determie the MD betwee the testig data ad the bechmark space composed of the ormal traiig data as follows: VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 013. VOLUME 15, ISSUE. ISSN

8 MD j = 1 k x j R 1 x j, (0) where R 1 is the iverse of the correlatio matrix R, MD j is the MD for the j th observatio, ad k is the umber of characteristics. (7) Establish the orthogoal table, optimize the bechmark space, reduce the redudat features, ad extract the pricipal characteristics by Taguchi methods. The MD values for all of the datasets are re-calculated by usig the optimized algorithm. (8) Idetify the fault coditio of the hydraulic pump. 3. Case study 3.1. Experimetal setup I this study, a test pluger pump rig, as show i Fig., was tested ad aalyzed to verify the preseted fault diagosis method. I the experimet, two commoly occurrig faults i the pluger pump were set, amely, slipper loosig ad valve plate wear. Uder three coditios, icludig the two faulty coditios ad the ormal state, the vibratio sigal was acquired from the ed face of the pluger pump with a stabilized motor speed of 58 r/mi, ad samplig rate of 1000 Hz. Twelve samples were acquired uder the ormal coditio ad four samples were obtaied for each of the two fault states. Amog these samples, the first eight ormal samples were used to costruct the bechmark space, ad the remaiig samples were used for testig. 3.. Feature extractio Fig.. Experimetal test pluger pump rig The feature vectors were determied by the proposed method. The vectors were calculated usig the first eight IMF compoets. Fig. 3 shows the acceleratio vibratio sigal of the hydraulic pump with a ormal sigal. It is decomposed ito eight IMFs by EMD. As show i Fig. 4, each IMF compoet has a distict time characteristic scale. The system coditio is maily decided by the first several AR parameters ad the remat variace. The order of the model m, was determied by FPE criterio. This order is differet from the umber of IMF compoets, wherei the maximum ad miimum compoets are 6 ad 9, respectively. I this case, the first seve AR parameters φ ik (k = 1,,,7) ad σ i were chose. These values costitute the eight-dimesio vector. The extracted feature vectors are listed i Table 1 (oly the feature vectors of the first four IMF compoets from oe sample i each coditio are listed i Table 1 because of space limitatios). A ji (j = 1,, 3; i = 1,, 3,, 8) deotes the feature vector of the i th IMF compoet uder the j th coditio, where j deotes the ormal coditio, coditio with valve plate wear, ad coditio with slipper loosig, ad i deotes the first eight IMF compoets. The feature vector matrixes were decomposed to obtai the sigular value by SVD. The extracted sigular values are listed i Tables ad 3. The 768 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 013. VOLUME 15, ISSUE. ISSN

9 extracted sigular values for the model traiig (Table ) are used to costruct the bechmark space i calculatig the MD, ad the others (Table 3) are used for testig. Fig. 3. Acceleratio vibratio sigal of the hydraulic pump with a ormal sigal Fig. 4. Decomposed results of the hydraulic pump vibratio sigal show i Fig. 3 by EMD Coditio Normal Valve plate wear Slipper loosig Model feature vectors Table 1. Feature vector compoets extracted by AR Feature vectors compoets φ i,1 φ i, φ i,3 φ i,4 φ i,5 φ i,6 φ i,7 σ i A 1, A 1, A 1, A 1, A, A, A, A, A 3, A 3, A 3, A 3, VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 013. VOLUME 15, ISSUE. ISSN

10 Table. Extracted sigular values for model traiig Sample Coditio Normal Table 3. Extracted sigular values for testig Sample Coditio Normal coditio Valve plate wear Slipper loosig Patter recogitio Fault diagosis based o the MD After obtaiig the feature vectors usig the proposed methods, the MD values of the testig samples for the three coditios ca be obtaied. The experimetal results are listed i Table 4, wherei the MD betwee all the testig samples (Table 3) ad the bechmark space composed of the traied ormal samples (Table ) are show. Table 4 cotais the mea, miimum, ad maximum MDs for the three coditios. Separatig the three coditios is easy by comparig the sizes of the MD values. These results verified that the MD method is very effective for fault detectio ad isolatio. Table 4. Mea, miimum ad maximum MD values Normal coditio Valve plate wear Slipper loosig Mea e e+4 Mi-max e e e e Algorithm optimizatio by Taguchi methods First, the appropriate OA L 9 ( 8 ) is selected, which is used for the two abormal datasets to idetify which characteristic is useless. Cosiderig the differet characteristics of each lie measurig project, ie differet bechmark spaces are formed. The larger-the-better SNR is calculated. Tables 5 ad 6 show the results of the OA ad SNR aalysis for the valve plate wear ad slipper loosig testig datasets. t 1 ad t i Tables 5 ad 6 respectively deote the sum of the measuremet feature project SNRs i Level-1 ad Level-. From Tables 5 ad 6, the eergies of the 6 th ad 7 th bad should be excluded from the feature vector because they do ot display a positive SNR for fault diagosis. After the key features were 770 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 013. VOLUME 15, ISSUE. ISSN

11 idetified, the MD values for all of the testig datasets were recalculated. The compariso betwee the iitial ad optimized MDs for each dataset is listed i Table 7. The optimized MDs are more stable ad distiguishable tha the iitial MDs, thereby verifyig that the Taguchi methods are very effective i reducig the redudat characteristics ad extractig the priciple compoets. Therefore, MTS ca effectively coduct a fault diagosis of hydraulic pumps. Table 5. Results of the OA ad SNR aalysis for the valve plate wear dataset SNR t t t 1 t Useful Y Y Y Y Y N N Y Table 6. Results of the OA ad SNR aalysis for the slipper loosig dataset SNR t t t 1 t Useful Y Y Y Y Y N N Y Table 7. Compariso betwee the iitial ad optimized MDs Normal coditio Iitial Optimized Mea Mi-max Valve plate wear Iitial Optimized Mea 6.375e e+ Mi-max e e e e+ Slipper loosig Iitial Optimized Mea e e+3 Mi-max e e e e+3 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 013. VOLUME 15, ISSUE. ISSN

12 4. Coclusios The characteristic iformatio of the hydraulic pumps ca be effectively isolated ad highlighted by EMD-AR ad SVD combied with MTS. The AR model simulates the characteristics ad workig coditio of hydraulic pump systems. However, the AR model ca oly aalyze statioary sigals; thus, i this study, a pretreatmet o the vibratio sigals is carried out by EMD before the AR model is established. The IMF compoets ot oly reflect the actual iformatio cotaied i the sigal, but are also statioary. The IMF compoets obtaied by EMD highlights the differet local characteristic iformatio of the origial sigal, which is useful for fault feature extractio. Usig the AR model combied with SVD ot oly accurately reflects the hydraulic pump operatio state, but also sigificatly compresses the iput dimesio of the MTS. The Taguchi methods offer a systematic way to determie the pricipal features based o the MD, which is a more effective method for fault diagosis. Ackowledgemets This study is supported by the Natioal Natural Sciece Foudatio of Chia (Grat Nos , ad ) ad by the Techology Foudatio Program of Natioal Defese (Grat No. Z13010B004). Refereces [1] S. P. Wag, Z. K. Yua, G. Q. Yag Study o fault diagosis of data fussio i hydraulic pump. Chia Mechaical Egieerig, Vol. 16, Issue 4, 005, p [] W. L. Jiag, S. Q. Zhag, Y. Q. Wag Wavelet trasform method for fault diagosis of hydraulic pump. Chiese Joural of Mechaical Egieerig, Vol. 37, Issue 6, 001, p [3] H. Dig, Y. Wu, S. Z. Yag Fault diagosis by time series aalysis. Applied Time Series Aalysis, World Scietific Publishig Co., Sigapore, [4] Y. Wu, S. Z. Yag Applicatio of several time series models i predictio. Applied Time Series Aalysis, World Scietific Publishig Co., Sigapore, [5] N. E. Huag, Z. She, S. R. Log A ew view of oliear water waves: the Hilbert spectrum. Aual Review of Fluid Mechaics, Vol. 31, 1999, p [6] P. C. Mahalaobis O the geeralized distace i statistics. Proceedigs, Natioal Istitute of Sciece of Idia, Vol. 1, p [7] G. Taguchi, R. Jugulum The Mahalaobis Taguchi strategy. A Patter Techology System, Wiley, New York, 00. [8] N. E. Huag, Z. She, Steve R. Log The empirical mode decompositio ad the Hilbert spectrum for oliear ad o-statioary time series aalysis. Proc. R. Soc. Lod., Vol. 454, Issue 1971, 1998, p [9] J. S. Cheg, D. J. Yu, Y. Yag A fault diagosis approach for roller bearigs based o EMD method ad AR model. Mechaical Systems ad Sigal Processig, Vol. 0, Issue, 006, p [10] G. Taguchi, S. Chowdury, Y. Wu The Mahalaobis Taguchi System. McGraw-Hill, New York, 001. [11] S. Ahmet, S. Jagaatha Mahalaobis Taguchi system (MTS) as a progostics tool for rollig elemet bearig failures. Joural of Maufacturig Sciece ad Egieerig, Vol. 13, Issue 5, VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 013. VOLUME 15, ISSUE. ISSN