Research ArticleFault Diagnosis of a Hydraulic Pump Based onthe CEEMD-STFT Time-Frequency Entropy Method andMulticlass SVM Classifier

Wanlin Zhao12 Zili Wang12 Jian Ma12 and Lianfeng Li12

1Science amp Technology Laboratory on Reliability amp Environmental Engineering Beijing 100191 China2School of Reliability and Systems Engineering Beihang University Beijing 100191 China

Correspondence should be addressed to Jian Ma 09977buaaeducn

Received 27 April 2016 Accepted 23 August 2016

Academic Editor Ganging Song

Copyright copy 2016 Wanlin Zhao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The fault diagnosis of hydraulic pumps is currently important and significant to ensure the normal operation of the entire hydraulicsystem Considering the nonlinear characteristics of hydraulic-pump vibration signals and themodemixing problem of the originalEmpirical Mode Decomposition (EMD) method first we use the Complete Ensemble EMD (CEEMD) method to decompose thesignals Second the time-frequency analysismethods which include the Short-TimeFourier Transform (STFT) and time-frequencyentropy calculation are applied to realize the robust feature extraction Third the multiclass Support Vector Machine (SVM)classifier is introduced to automatically classify the fault mode in this paper An actual hydraulic-pump experiment demonstratesthe procedure with a complete feature extraction and accurate mode classification

1 Introduction

Hydraulic systems have been widely used in aeronauticsastronautics automobiles shipping and so on As the heartof a hydraulic system the performance of the hydraulic pumpsignificantly affects the entire hydraulic system [1] Thusachieving real-time fault diagnosis of the hydraulic pump isessential and urgent to maintain the entire system [2] Forthe hydraulic pump its structure is complex the relationshipamong its internal parameters is highly nonlinear and thereare strong couplings among various fault features As a resultan accurate mathematical model is difficult to establishTherefore data-driven diagnostic methods are commonlyused for hydraulic pumps based on their vibration signalsGenerally the entire fault diagnosis process can be considereda pattern identification problem that mainly includes twoimportant procedures feature extraction and mode classifi-cation

Many data-driven feature extraction methods haveemerged in recent years that are different from the traditional

time-domain analysis and frequency-domain analysis meth-ods The Empirical Mode Decomposition (EMD) whichwas developed by Huang et al is a time-frequency analysismethod and has advantages in addressing nonlinear andnonstationary signals [3] The EMD can decompose anysignal into intrinsic mode functions (IMFs) based on thelocal timescale of the data without using a priori basis [4]However the EMD faces a serious problem ldquomode mixingrdquowhere a notably disparate amplitude in a mode oscillates ornotably similar oscillations occur in differentmodes Becauseof this problem a new method was proposed EnsembleEmpirical Mode Decomposition (EEMD) which performsthe EMD over an ensemble of the signal plus Gaussian whitenoise to obtainmore regularmodesHowever the EEMDalsocreated new difficulties The reconstructed signal containsresidual noise and different realizations of signal plus noisemay produce different numbers of modes To overcome thesedifficulties another EMD method has been proposed andsuccessfully applied to vibration signal analysis completeEEMD (CEEMD) which provides an exact reconstruction

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 2609856 8 pageshttpdxdoiorg10115520162609856

2 Shock and Vibration

of the original signal and a better spectral separation ofthe modes [5 6] Han and van der Baan used CEEMD toanalyze the synthetic and real seismic data and obtained agood result [7] In our study CEEMD is selected to adaptivelydecompose signals into a small number of IMFs or modesand the Short-Time Fourier Transform (STFT) algorithm andtime-frequency entropy analysis method are simultaneouslyused to obtain the fault feature vectors composed by multi-scale time-frequency entropyThis feature extractionmethodis defined as the CEEMD-STFT time-frequency entropymethod

After the fault feature is extracted a classifier is exploitedto automatically achieve mode classification Support VectorMachine (SVM) is a powerful machine learning methodbased on the statistical learning theory and structural riskminimization principle that has been successfully applied tofault diagnosis and satisfactorily solved the overfitting andlocal optimal solution problem [8] However there are noelegant approaches to solve multiclass problems A betteralternative is provided by the construction of multiclass SVM[9] which is inherently two-class SVM classifiers In thispaper we build amulticlass SVM classifier to classify the faultmode over the feature vectors whose dimensions have beencompressed using the Principal Component Analysis (PCA)algorithm because the original feature vectors are always toolarge complex and variable for postprocessing

This paper is organized as follows Section 2 intro-duces the relevant feature extraction and mode classificationmethodology which includes the CEEMD STFT time-frequency entropy and multiclass SVM method Section 3describes the case study to validate the entire methodSection 4 presents the conclusions of this paper

2 Methodology

As shown in Figure 1 the complete fault diagnosis scheme hasthree elements data preprocessing fault feature extractionand fault mode classificationMore details are provided in thefollowing parts

21 Feature Extraction Based on the CEEMD-STFTTime-Frequency Entropy Method

211 Complete Ensemble EmpiricalMode Decomposition (CEEMD)

(A) Empirical Mode Decomposition (EMD) The EMD isan adaptive signal analysis method based on the signalcharacteristic local extrema which separate a signal into acertain number of IMF components To be considered anIMF a signal must satisfy two conditions (1) the numberof extrema and the number of zero-crossings must be equalor differ at most by one (2) the mean value of the envelopedefined by the local maxima and the envelope defined by thelocal minima is zero at any data location [10] Assume that119909(119905) is the signal to be decomposed the concrete steps of theEMD are shown as follows

Original signal Preprocessed data

CEEMD IMFs decomposed

STFT Time-frequency matrices

Entropy Time-frequency entropies

PCA Features compressed

Training multiclassSVM classifier

Training data

Testing withtrained classifier

Testing data

Classification results

Data

Featureextraction

Patternclassification

Fault diagnosis procedure of hydraulic pump

Figure 1 Entire fault diagnosis procedure

Step 1 (Initialization) Set 119896 = 0 where 119896 indicates the modeand the residual component 119903

0(119905) = 119909(119905)

Step 2 Calculate the mean envelope119898(119905)

119898 (119905) =[119890max (119903119896 (119905)) + 119890min (119903119896 (119905))]

2 (1)

where 119890max(119903119896(119905)) and 119890min(119903119896(119905)) are the upper and lowerenvelopes respectively which are obtained through cubic-spline interpolation on the localmaxima andminima of 119903

119896(119905)

Step 3 Compute the IMF candidate

119888119896+1

(119905) = 119903119896(119905) minus 119898 (119905) (2)

Step 4 Does 119888119896+1

(119905) satisfy the IMF properties

(i) Yes Set IMF119896+1

= 119888119896+1

(119905) and 119903119896+1

(119905) = 119903119896(119905)minusIMF

119896+1

let 119896 = 119896 + 1 and go to Step 2(ii) No Set 119888

119896+1(119905) as 119903

119896(119905) and go to Step 2

Step 5 Continue Steps 2ndash4 until 119903119896(119905) becomes a monotonic

function

Each obtained IMF through the EMD contains differentfrequency components of the signal from high to low fre-quencies and represent the inherent mode characteristics ofthe signal

(B) Ensemble EMD (EEMD) To solve the ldquomode mixingrdquoproblem Wu and Huang proposed the Ensemble EMD(EEMD) method [11] which defines the ldquotruerdquo modes as

Shock and Vibration 3

the mean of the corresponding IMFs that are obtained viaEMD over an ensemble of the original signal plus differentrealizations of finite variance white noise [12] Considering 119909as an example signal the EEMD algorithm can be describedas follows

Step 1 Generate

119909(119894)= 119909 + 120573119908

(119894) (3)

where 119908(119894) (119894 = 1 119868) are different realizations of whiteGaussian noise

Step 2 Each 119909(119894) (119894 = 1 119868) is fully decomposed by EMDto obtain the modes IMF(119894)

119896 where 119896 = 1 119870 indicates the

mode

Step 3 Assign IMF119896as the 119896th mode of 119909 which is obtained

by averaging the corresponding modes

IMF119896=1

119868

119868

sum119894=1

IMF(119894)119896 (4)

However the EEMDmethod has some disadvantages (1)the decomposition is not complete (2) different realizationsof signal plus white noise may generate different numbers ofmodes

(C) Complete EEMD (CEEMD) To address the aforemen-tioned reconstruction error complete EEMD (CEEMD) wasproposed by Torres et al in 2011 [5] The procedure ofCEEMD is described as follows

Step 1 The first IMF is calculated in the identical method toEEMD First addwhite noise to the original signal and obtainthe first EMD component of the data with noise Repeatthe decomposition by adding different noise realizations andcompute the ensemble average to define it as the first IMF

1of

the original signal 119909 that is

IMF1=1

119868

119868

sum119894=1

1198641(119909 + 120576

0119908119894) (5)

where 119864119895(sdot) is defined as an operator and the 119895th mode can

be computed through EMD when it meets a new signal 119909 isthe raw signal119908119894 is the different white noise and 120576

0is a ratio

coefficient

Step 2 Calculate a unique first residue as

1199031= 119909 minus IMF

1 (6)

Then set 1199031+ 12057611198641(119908119894) (119894 = 1 119868) as the new signal

for decomposition When the first IMF component has beenobtained we must calculate the ensemble average as thesecond component IMF

2

IMF2=1

119868

119868

sum119894=1

1198641(1199031+ 12057611198641(119908119894)) (7)

Step 3 Repeat Steps 1-2 and we can obtain the (119896 + 1)th IMFcomponent IMF

119896+1

IMF119896+1

=1

119868

119868

sum119894=1

1198641(119903119896+ 120576119896119864119896(119908119894)) (8)

Step 4 Finally obtain the last residual function 119877 until theresidue cannot be decomposed Then 119877 = 119909 minus sum

119870

119896=1IMF119896

where 119870 is the total number of IMF The signal is describedas

119909 =

119870

sum119896=1

IMF119896+ 119877 (9)

The last step makes the proposed decomposition com-plete and provides an exact reconstruction of the originalsignal

212 Short-Time Fourier Transform (STFT) The time andfrequency information in each IMF relates to the samplingfrequency and changes with the signal itself so research onthe time-frequency domain characterization of signals hasbeen a key component of signal analysis [13] The STFT is apopular method to analyze nonstationary signals The STFTof the signal 119909(119905) is defined as

119883(119905 119891) = intinfin

minusinfin

119909 (120591) ℎ (120591 minus 119905) sdot 119890minus1198952120587119891120591

119889120591 (10)

where ℎ(119905) should be a low-pass filter and ℎ2 = 1 Note

that ℎ(120591 minus 119905) sdot 1198901198952120587119891120591 has its energy concentrated at time 119905 andfrequency 119891 Thus |119883(119905 119891)|2 can be considered the energyin 119909(119905) at frequency 119891 and time 119905 Generally one displays theenergy at each time and frequency pair that is

119875 (119905 119891) =1003816100381610038161003816119883 (119905 119891)

10038161003816100381610038162 (11)

119875(119905 119891) is known as the spectrogram (SP) of 119909(119905) [14]The spectrogram algorithm is an analysis algorithm that

produces a two-dimensional image representation of vibra-tion signals The Power Spectrum Density (PSD) function119875(119905 119891) is expressed as a Pseudo ColorMap (PCM) which is aspectrogramwith a time axis and a frequency axisThis time-frequency spectrum which can be called the ldquovisual lan-guagerdquo shows the modulation characteristics of the signals

213 Time-Frequency Entropy The time-frequency distri-bution of the vibration signal obtained through the STFTmethod presents modulation characteristic that is theenergy distribution changes at different moments Thereforea fault can be detected by comparing the energy distributionof the signals with and without fault conditions in the time-frequency domain which indicates that the energy variationin the time-frequency plane may indicate a fault occurrence[15] Because the spectrogram can provide an accurateenergy-frequency-time distribution the information entropytheory which measures the uniformity of the probabilitydistribution can be introduced to the time-frequency distri-bution to quantitatively describe the divergence in differentoperating conditions [16]

4 Shock and Vibration

Support vector

Support vector

Margin = 2120596

Figure 2 Illustration for data classification using a 2-class SVM

Let a time-frequency plane have 119873 blocks with equalareas where the information source for the entire plane is 119860and for each block is119882

119894(119894 = 1 119873) so the probability that

each information source appears in the entire system is

119873

sum119894=1

119902119894= 1 119902

119894=119882119894

119860 (119894 = 1 119873) (12)

According to the information entropy calculation [17] thetime-frequency entropy is defined as

119904 (119902) = minus

119873

sum119894=1

119902119894ln 119902119894 (13)

Now we can consider the time-frequency entropy of eachIMF as the extracted feature vectors which will be the inputof the mode classification

22 Mode Classification Based on the Multiclass SVM

221 Support Vector Machine (SVM) Support VectorMachine (SVM) which originated from the statisticallearning theory and an optimal separating hyper-plane in thecase of linear separation was developed by Cortes and hiscoworker [18] Through some nonlinear mapping functionsthe originalmode space ismapped into the high-dimensionalfeature space Z Then the optical separating hyper-plane isconstructed in the feature space Consequently the nonlinearproblem in the low-dimensional space corresponds to thelinear problem in the high-dimensional space

222 Two-Class SVM SVMs are primarily designed for 2-class classification problems To illustrate the basic principlea schematic diagram of 2-class SVM is shown in Figure 2where two different classes (circles and triangles) are classi-fied by a linear boundary 119867 and the distance between theboundary and the nearest data point in each class is maximal

Assume that the input vector is 119909 which is mapped intohigh-dimensional space Z through the nonlinear mappingfunction 120593(119909) and the linear function (120596 sdot 120593(119909)) + 119887 = 0 inthe high-dimensional feature space can be used to constructthe optimal classification hyper-plane The training data areset as 119909

119894 119910119894 119894 = 1 2 119897 119909

119894isin 119877119899 119910

119894isin minus1 +1 119910

119894is

the corresponding label of 119909119894 Then 120596 is a weight vector and

the margin is 1120596 The following constraint optimizationproblem is the solution of maximizing the margin 1120596

min 1

21205962+ 119862

119897

sum119894=1

120585119894

st 119910119894(120596 sdot 120593 (119909

119894) + 119887) ge 1 minus 120585

119894 119894 = 1 119897

120585119894ge 0 119894 = 1 119897

(14)

where coefficient 119862 is a penalty factor and 120585119894is a slack factor

[16]In addition using the duality theory of optimization

theory and Kernel function the final decision function isdescribed by

119891 (119909) = sgn( sum119909119894isin119878119881119904

119910119894120572119894(120593 (119909119894) sdot 120593 (119909)) + 119887)

= sgn( sum119909119894isin119878119881119904

119910119894120572119894119870(119909119894 119909) + 119887)

(15)

where 119870(119909119894 119909) is the kernel function which satisfies Mercer

condition the constants 120572119894are named Lagrange multipliers

and are determined in the optimization procedure The typ-ical kernel functions are the polynomial kernel Radial BasisFunction (RBF) kernel sigmoid kernel and linear kernel Inmany practical applications the RBF kernel has the highestclassification accuracy rate compared to the other kernelfunctions sowemainly consider the RBF kernel in this paper

The SVMwas originally designed for binary classificationand had good performance but it still faced many difficultiesin addressing multiclass classification problems The SVM isnot sufficient to handle a practical situation

223 Multiclass SVM Currently several methods based onthe SVM have been proposed for multiclass classificationsuch as ldquoone-against-allrdquo ldquoone-against-onerdquo and DirectedAcyclic Graph (DAG) Experiments indicate that the ldquoone-against-onerdquo and DAG-SVM methods are most suitablefor practical situation In this paper the ldquoone-against-onerdquomethod is selected for classification [19]

Let us suppose that the training data set is 119878 =

(1199091 1199101) (1199092 1199102) (119909

119897 119910119897) 119909119894isin 119877119899 and the ldquoone-against-

onerdquo method constructs 1198622119896= 119896(119896 minus 1)2 classifiers each of

which is trained using the data from two classes For examplewe should solve the following binary classification problemfor the training data from the 119894th and 119895th classes

min120596119894119895119887119894119895120585119894119895

1

2

1003817100381710038171003817100381712059611989411989510038171003817100381710038171003817

2

+ 119862[sum119894=1

120585119894119895

119905]

st [(120596119894119895sdot 119909119905) + 119887119894119895] minus 1 + 120585

119894119895

119905ge 0 if 119910

119905= 119894

[(120596119894119895sdot 119909119905) + 119887119894119895] + 1 minus 120585

119894119895

119905le 0

if 119910119905= 119895 120585

119894119895

119905ge 0

(16)

Shock and Vibration 5

Table 1 Six-dimensional fault features

Fault pattern No Feature 1 Feature 2 Feature 3 Feature 4 Feature 5 Feature 6

Normal

1 49681 39921 40155 36082 32670 265762 49732 39936 40145 36031 32395 26541sdot sdot sdot

20 47565 39406 41075 36274 33763 26567

Rotor wear

21 38933 42478 35822 37066 32937 2596622 38923 41903 35846 37407 32990 25675sdot sdot sdot

40 38991 39456 35417 36743 33190 25426

Swash plate wear

41 41123 34824 34975 36294 32926 2533242 41285 34886 35151 36196 33310 25820sdot sdot sdot

60 41782 34949 35132 35932 33496 26182

When testing is performed for the unknown sample 119909we construct all 119896(119896 minus 1)2 classifiers to realize the classdiscrimination andmake decisions using the following votingstrategy if sgn((120596119894119895 sdot 119909

119905) + 119887119894119895) 119909 is in the 119894th class then the

vote for the 119894th class is increased by one otherwise the 119895thclass is increased by one Finally we predict that 119909 is in theclass with the largest vote [20]

3 Experimental Verification

31 Experiment Setup The plunger pump test-rig is shownin Figure 3 from this test-rig the original vibration signalswere obtained to verify the proposed method The vibrationdata were obtained from the front side of the hydraulic pumpwith a stabilized motor speed of 528 rmin and a samplingrate of 1000Hz In this experiment two commonly occurringfaults were set swash plate wear and rotor wear Under threeconditions (two faulty conditions and the normal state) 20groups of samples (1024 sampling points for each group) wereselected for the analysis

32 Model for Fault Diagnosis of Hydraulic Pumps

321 Feature Extraction Based on the CEEMD-STFTand Time-Frequency Entropy

(1) CEEMD Model The parameters of the CEEMD modelwere set as follows the noise standard deviation (Nstd) was02 the Number of Realizations (NR) was 600 and themaximumnumber of sifting iterations allowed (MaxIter) was5000The original signals of each state were decomposed intoa series of IMFs the first six IMFs were selected for furtheranalysis as shown in Figure 4

(2) Procedure of the STFT and Time-Frequency EntropyAcquisitionThe parameters of STFT were selected as followsthe length of the window number of overlaps and samplingfrequency (fs) were 256 254 and 1000 respectively andthe length of the discrete Fourier transforms was equal to

Figure 3 Plunger pump test-rig

the window length Then the time-frequency matrices orspectrograms of each state were obtained in Figure 5

The time-frequency entropy of each state can be cal-culated based on the time-frequency matrices The time-frequency block was set as length = width = 64 and boththe lateral and longitudinal slip steps were 32 Then a six-dimensional time-frequency entropy was obtained for eachgroup which is one of the fault feature vectors All of the faultfeatures are listed in Table 1

(3) Feature Dimension Reduction Based on PCA To improvethe accuracy and robustness of the fault diagnosis dimensionreduction is necessary for the high dimensional fault featurevectors PCA which is an important and powerful methodsto extract the most significant information from data andcompress the size of the data [21] was used to acquire thethree-dimensional feature vectors in Table 2

The clustering result of the fault features is visuallydisplayed in Figure 6 which obviously shows a good perfor-mance of the hydraulic-pump fault mode classification

322 Fault Mode Classification Based on Multiclass SVMThe extracted fault feature sets were divided into trainingdata and testing data (the first ten groups were set as thetraining data and the remainder was set as the testing data forevery state) First the training multiclass SVM classifier was

6 Shock and Vibration

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

minus020

02

minus020

02

minus010

01

minus0050

005

minus010

01

04505

055

minus050

05

minus050

05

minus0050

005

minus0050

005

minus0020

002

minus0050

005

04505

055

minus050

05

minus0020

002

minus010

01

minus0020

002

minus0020

002

minus0020

002

046048

05

R(t)

minus050

05

R(t)

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

R(t)

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

Figure 4 First 6 IMFs of each state

Table 2 Feature vector set after dimension reduction

Fault pattern No Feature 1 Feature 2 Feature 3

Normal

1 41284 29741 564832 41327 29729 56553sdot sdot sdot

20 39954 29829 55353

Rotor wear

21 37289 20520 5258922 36789 20772 52629sdot sdot sdot

40 35266 21772 51467

Swash plate wear

41 32972 24613 5107842 33079 24822 51103sdot sdot sdot

60 33408 25041 51157

trained as previously proposed with the training data Thenthe trained classifier was used to classify the fault mode ofthe testing data and calculate the recognition accuracy Theclassification results of the testing data are shown in Table 3and Figure 7 These testing results verify that the recognition

performance is absolutely good and the multiclass SVMmethod is notably effective for mode classification

Combining the clustering figure and multiclass SVMclassification results the effectiveness and feasibility of thismethod for hydraulic-pump fault diagnosis were provenand a high classification performance was also obviouslyobtained

4 Conclusion

An effective method for the feature extraction and modeclassification of vibration signals has been performed in thispaper and this algorithm was successfully verified on practi-cal signals fromahydraulic pumpTheCEEMDmodel whichis an improvement of EMD and can solve the ldquomode mixingrdquoproblem was combined with the STFT analysis method andtime-frequency entropy calculation to extract the robust andsignificant fault feature Meanwhile the multiclass SVM clas-sifier was selected to process the small sample and multiple-fault situation and it obtained a perfect classification resultThen the accuracy and feasibility of this hydraulic-pumpfault diagnosis method were demonstrated Future work willconcentrate on the application of thismethod to other objectsor fields for signal analysis and fault diagnosis

Shock and Vibration 7

150 200 250 300 350

150 200 250 300 350

150 200 250 300 350

Freq

uenc

y (H

z)Fr

eque

ncy

(Hz)

Freq

uenc

y (H

z)

Time (ms)

Time (ms)

Time (ms)

minus40

minus60

minus80

minus100

minus120

minus140

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

050

100150200250300350400450500

050

100150200250300350400450500

050

100150200250300350400450500

minus100minus90minus80minus70minus60minus50minus40

minus100minus90minus80minus70minus60minus50minus40minus30minus20

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

Figure 5 Spectrograms of the first IMF of each state

Table 3 Classification results of the testing data

Fault pattern Actual label Index No Feature 1 Feature 2 Feature 3 Predicted label

Normal 1

1 11 40906 29178 55591 12 12 40961 29253 55036 1sdot sdot sdot sdot sdot sdot 110 20 39954 29829 55353 1

Rotor wear 2

11 31 37442 20107 51790 212 32 36416 21110 51027 2sdot sdot sdot sdot sdot sdot 220 40 35266 21772 51467 2

Swash plate wear 3

21 51 33093 25163 51968 322 52 33018 24982 52170 3sdot sdot sdot sdot sdot sdot 330 60 33408 25041 51157 3

8 Shock and Vibration

42414393837361st PC35343332182222nd PC

242628332

NormalRotor wear

Swash plate wear

5152535455565758

3rd

PC

Figure 6 Clustering result of the fault features

Index

Diagnosis results

Predicted labelsGround truth labels

1

2

3

Labe

l

1 2 3 4 5 6 7 8 910

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Figure 7 Classification results of the testing data

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This study was supported by the National Natural ScienceFoundation of China (Grant nos 51105019 and 51575021)as well as the Technology Foundation Program of NationalDefense (Grant no Z132013B002)

References

[1] Z Ruixiang L Tingqi H Jianding and Y Dongchao ldquoFaultdiagnosis of airplane hydraulic pumprdquo in Proceedings of the4th World Congress on Intelligent Control and AutomationShanghai China June 2002

[2] T Zhang and N Zhang ldquoVibration modes and the dynamicbehaviour of a hydraulic plunger pumprdquo Shock and Vibrationvol 2016 Article ID 9679542 7 pages 2016

[3] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciencesThe Royal Society vol 454 no 1971 pp 903ndash995 1998

[4] T Han D Jiang and N Wang ldquoThe fault feature extractionof rolling bearing based on EMD and difference spectrum

of singular valuerdquo Shock and Vibration vol 2016 Article ID5957179 14 pages 2016

[5] M E TorresMA Colominas G Schlotthauer and P FlandrinldquoA complete ensemble empirical mode decomposition withadaptive noiserdquo in Proceedings of the 36th IEEE InternationalConference on Acoustics Speech and Signal Processing (ICASSPrsquo11) pp 4144ndash4147 IEEE Prague Czech Republic May 2011

[6] L Zhao W Yu and R Yan ldquoGearbox fault diagnosis usingcomplementary ensemble empirical mode decomposition andpermutation entropyrdquo Shock and Vibration vol 2016 Article ID3891429 8 pages 2016

[7] J Han and M van der Baan ldquoEmpirical mode decompositionfor seismic time-frequency analysisrdquo Geophysics vol 78 no 2pp O9ndashO19 2013

[8] E Mayoraz and E Alpaydin ldquoSupport vector machines formulti-class classificationrdquo in Engineering Applications of Bio-Inspired Artificial Neural Networks pp 833ndash842 SpringerBerlin Germany 1999

[9] J Yang Y Zhang and Y Zhu ldquoIntelligent fault diagnosis ofrolling element bearing based on SVMs and fractal dimensionrdquoMechanical Systems and Signal Processing vol 21 no 5 pp2012ndash2024 2007

[10] M A Colominas G Schlotthauer andM E Torres ldquoImprovedcomplete ensemble EMD a suitable tool for biomedical signalprocessingrdquo Biomedical Signal Processing and Control vol 14no 1 pp 19ndash29 2014

[11] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise-assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[12] J Li C Liu Z Zeng and L Chen ldquoGPR signal denoising andtarget extraction with the CEEMD methodrdquo IEEE Geoscienceand Remote Sensing Letters vol 12 no 8 pp 1615ndash1619 2015

[13] S H Nawab T F Quatieri and J S Lim ldquoSignal reconstructionfrom short-time fourier transform magnituderdquo IEEE Transac-tions on Acoustics Speech and Signal Processing vol 31 no 4pp 986ndash998 1983

[14] H K Kwok andD L Jones ldquoImproved instantaneous frequencyestimation using an adaptive short-time Fourier transformrdquoIEEE Transactions on Signal Processing vol 48 no 10 pp 2964ndash2972 2000

[15] L Mingliang W Keqi S Laijun and Z Jianju ldquoApplyingempiricalmode decomposition (EMD) and entropy to diagnosecircuit breaker faultsrdquo OptikmdashInternational Journal for Lightand Electron Optics vol 126 no 20 pp 2338ndash2342 2015

[16] X Zhang Y Liang J Zhou and Y Zang ldquoA novel bearing faultdiagnosis model integrated permutation entropy ensembleempirical mode decomposition and optimized SVMrdquoMeasure-ment vol 69 pp 164ndash179 2015

[17] D Yu Y Yang and J Cheng ldquoApplication of timendashfrequencyentropy method based on HilbertndashHuang transform to gearfault diagnosisrdquo Measurement vol 40 no 9-10 pp 823ndash8302007

[18] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

[19] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

[20] Z Cai Q Ding and M Wang ldquoStudy on automated incidentdetection algorithms based on PCA and SVM for freewayrdquo inProceedings of the International Conference on Optoelectronicsand Image Processing (ICOIP rsquo10) Haikou China November2010

[21] S Wold K Esbensen and P Geladi ldquoPrincipal componentanalysisrdquo Chemometrics and Intelligent Laboratory Systems vol2 no 1ndash3 pp 37ndash52 1987

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

2 Shock and Vibration

of the original signal and a better spectral separation ofthe modes [5 6] Han and van der Baan used CEEMD toanalyze the synthetic and real seismic data and obtained agood result [7] In our study CEEMD is selected to adaptivelydecompose signals into a small number of IMFs or modesand the Short-Time Fourier Transform (STFT) algorithm andtime-frequency entropy analysis method are simultaneouslyused to obtain the fault feature vectors composed by multi-scale time-frequency entropyThis feature extractionmethodis defined as the CEEMD-STFT time-frequency entropymethod

After the fault feature is extracted a classifier is exploitedto automatically achieve mode classification Support VectorMachine (SVM) is a powerful machine learning methodbased on the statistical learning theory and structural riskminimization principle that has been successfully applied tofault diagnosis and satisfactorily solved the overfitting andlocal optimal solution problem [8] However there are noelegant approaches to solve multiclass problems A betteralternative is provided by the construction of multiclass SVM[9] which is inherently two-class SVM classifiers In thispaper we build amulticlass SVM classifier to classify the faultmode over the feature vectors whose dimensions have beencompressed using the Principal Component Analysis (PCA)algorithm because the original feature vectors are always toolarge complex and variable for postprocessing

This paper is organized as follows Section 2 intro-duces the relevant feature extraction and mode classificationmethodology which includes the CEEMD STFT time-frequency entropy and multiclass SVM method Section 3describes the case study to validate the entire methodSection 4 presents the conclusions of this paper

2 Methodology

As shown in Figure 1 the complete fault diagnosis scheme hasthree elements data preprocessing fault feature extractionand fault mode classificationMore details are provided in thefollowing parts

21 Feature Extraction Based on the CEEMD-STFTTime-Frequency Entropy Method

211 Complete Ensemble EmpiricalMode Decomposition (CEEMD)

(A) Empirical Mode Decomposition (EMD) The EMD isan adaptive signal analysis method based on the signalcharacteristic local extrema which separate a signal into acertain number of IMF components To be considered anIMF a signal must satisfy two conditions (1) the numberof extrema and the number of zero-crossings must be equalor differ at most by one (2) the mean value of the envelopedefined by the local maxima and the envelope defined by thelocal minima is zero at any data location [10] Assume that119909(119905) is the signal to be decomposed the concrete steps of theEMD are shown as follows

Original signal Preprocessed data

CEEMD IMFs decomposed

STFT Time-frequency matrices

Entropy Time-frequency entropies

PCA Features compressed

Training multiclassSVM classifier

Training data

Testing withtrained classifier

Testing data

Classification results

Data

Featureextraction

Patternclassification

Fault diagnosis procedure of hydraulic pump

Figure 1 Entire fault diagnosis procedure

Step 1 (Initialization) Set 119896 = 0 where 119896 indicates the modeand the residual component 119903

0(119905) = 119909(119905)

Step 2 Calculate the mean envelope119898(119905)

119898 (119905) =[119890max (119903119896 (119905)) + 119890min (119903119896 (119905))]

2 (1)

where 119890max(119903119896(119905)) and 119890min(119903119896(119905)) are the upper and lowerenvelopes respectively which are obtained through cubic-spline interpolation on the localmaxima andminima of 119903

119896(119905)

Step 3 Compute the IMF candidate

119888119896+1

(119905) = 119903119896(119905) minus 119898 (119905) (2)

Step 4 Does 119888119896+1

(119905) satisfy the IMF properties

(i) Yes Set IMF119896+1

= 119888119896+1

(119905) and 119903119896+1

(119905) = 119903119896(119905)minusIMF

119896+1

let 119896 = 119896 + 1 and go to Step 2(ii) No Set 119888

119896+1(119905) as 119903

119896(119905) and go to Step 2

Step 5 Continue Steps 2ndash4 until 119903119896(119905) becomes a monotonic

function

Each obtained IMF through the EMD contains differentfrequency components of the signal from high to low fre-quencies and represent the inherent mode characteristics ofthe signal

(B) Ensemble EMD (EEMD) To solve the ldquomode mixingrdquoproblem Wu and Huang proposed the Ensemble EMD(EEMD) method [11] which defines the ldquotruerdquo modes as

Shock and Vibration 3

the mean of the corresponding IMFs that are obtained viaEMD over an ensemble of the original signal plus differentrealizations of finite variance white noise [12] Considering 119909as an example signal the EEMD algorithm can be describedas follows

Step 1 Generate

119909(119894)= 119909 + 120573119908

(119894) (3)

where 119908(119894) (119894 = 1 119868) are different realizations of whiteGaussian noise

Step 2 Each 119909(119894) (119894 = 1 119868) is fully decomposed by EMDto obtain the modes IMF(119894)

119896 where 119896 = 1 119870 indicates the

mode

Step 3 Assign IMF119896as the 119896th mode of 119909 which is obtained

by averaging the corresponding modes

IMF119896=1

119868

119868

sum119894=1

IMF(119894)119896 (4)

However the EEMDmethod has some disadvantages (1)the decomposition is not complete (2) different realizationsof signal plus white noise may generate different numbers ofmodes

(C) Complete EEMD (CEEMD) To address the aforemen-tioned reconstruction error complete EEMD (CEEMD) wasproposed by Torres et al in 2011 [5] The procedure ofCEEMD is described as follows

Step 1 The first IMF is calculated in the identical method toEEMD First addwhite noise to the original signal and obtainthe first EMD component of the data with noise Repeatthe decomposition by adding different noise realizations andcompute the ensemble average to define it as the first IMF

1of

the original signal 119909 that is

IMF1=1

119868

119868

sum119894=1

1198641(119909 + 120576

0119908119894) (5)

where 119864119895(sdot) is defined as an operator and the 119895th mode can

be computed through EMD when it meets a new signal 119909 isthe raw signal119908119894 is the different white noise and 120576

0is a ratio

coefficient

Step 2 Calculate a unique first residue as

1199031= 119909 minus IMF

1 (6)

Then set 1199031+ 12057611198641(119908119894) (119894 = 1 119868) as the new signal

for decomposition When the first IMF component has beenobtained we must calculate the ensemble average as thesecond component IMF

2

IMF2=1

119868

119868

sum119894=1

1198641(1199031+ 12057611198641(119908119894)) (7)

Step 3 Repeat Steps 1-2 and we can obtain the (119896 + 1)th IMFcomponent IMF

119896+1

IMF119896+1

=1

119868

119868

sum119894=1

1198641(119903119896+ 120576119896119864119896(119908119894)) (8)

Step 4 Finally obtain the last residual function 119877 until theresidue cannot be decomposed Then 119877 = 119909 minus sum

119870

119896=1IMF119896

where 119870 is the total number of IMF The signal is describedas

119909 =

119870

sum119896=1

IMF119896+ 119877 (9)

The last step makes the proposed decomposition com-plete and provides an exact reconstruction of the originalsignal

212 Short-Time Fourier Transform (STFT) The time andfrequency information in each IMF relates to the samplingfrequency and changes with the signal itself so research onthe time-frequency domain characterization of signals hasbeen a key component of signal analysis [13] The STFT is apopular method to analyze nonstationary signals The STFTof the signal 119909(119905) is defined as

119883(119905 119891) = intinfin

minusinfin

119909 (120591) ℎ (120591 minus 119905) sdot 119890minus1198952120587119891120591

119889120591 (10)

where ℎ(119905) should be a low-pass filter and ℎ2 = 1 Note

that ℎ(120591 minus 119905) sdot 1198901198952120587119891120591 has its energy concentrated at time 119905 andfrequency 119891 Thus |119883(119905 119891)|2 can be considered the energyin 119909(119905) at frequency 119891 and time 119905 Generally one displays theenergy at each time and frequency pair that is

119875 (119905 119891) =1003816100381610038161003816119883 (119905 119891)

10038161003816100381610038162 (11)

119875(119905 119891) is known as the spectrogram (SP) of 119909(119905) [14]The spectrogram algorithm is an analysis algorithm that

produces a two-dimensional image representation of vibra-tion signals The Power Spectrum Density (PSD) function119875(119905 119891) is expressed as a Pseudo ColorMap (PCM) which is aspectrogramwith a time axis and a frequency axisThis time-frequency spectrum which can be called the ldquovisual lan-guagerdquo shows the modulation characteristics of the signals

213 Time-Frequency Entropy The time-frequency distri-bution of the vibration signal obtained through the STFTmethod presents modulation characteristic that is theenergy distribution changes at different moments Thereforea fault can be detected by comparing the energy distributionof the signals with and without fault conditions in the time-frequency domain which indicates that the energy variationin the time-frequency plane may indicate a fault occurrence[15] Because the spectrogram can provide an accurateenergy-frequency-time distribution the information entropytheory which measures the uniformity of the probabilitydistribution can be introduced to the time-frequency distri-bution to quantitatively describe the divergence in differentoperating conditions [16]

4 Shock and Vibration

Support vector

Support vector

Margin = 2120596

Figure 2 Illustration for data classification using a 2-class SVM

Let a time-frequency plane have 119873 blocks with equalareas where the information source for the entire plane is 119860and for each block is119882

119894(119894 = 1 119873) so the probability that

each information source appears in the entire system is

119873

sum119894=1

119902119894= 1 119902

119894=119882119894

119860 (119894 = 1 119873) (12)

According to the information entropy calculation [17] thetime-frequency entropy is defined as

119904 (119902) = minus

119873

sum119894=1

119902119894ln 119902119894 (13)

Now we can consider the time-frequency entropy of eachIMF as the extracted feature vectors which will be the inputof the mode classification

22 Mode Classification Based on the Multiclass SVM

221 Support Vector Machine (SVM) Support VectorMachine (SVM) which originated from the statisticallearning theory and an optimal separating hyper-plane in thecase of linear separation was developed by Cortes and hiscoworker [18] Through some nonlinear mapping functionsthe originalmode space ismapped into the high-dimensionalfeature space Z Then the optical separating hyper-plane isconstructed in the feature space Consequently the nonlinearproblem in the low-dimensional space corresponds to thelinear problem in the high-dimensional space

222 Two-Class SVM SVMs are primarily designed for 2-class classification problems To illustrate the basic principlea schematic diagram of 2-class SVM is shown in Figure 2where two different classes (circles and triangles) are classi-fied by a linear boundary 119867 and the distance between theboundary and the nearest data point in each class is maximal

Assume that the input vector is 119909 which is mapped intohigh-dimensional space Z through the nonlinear mappingfunction 120593(119909) and the linear function (120596 sdot 120593(119909)) + 119887 = 0 inthe high-dimensional feature space can be used to constructthe optimal classification hyper-plane The training data areset as 119909

119894 119910119894 119894 = 1 2 119897 119909

119894isin 119877119899 119910

119894isin minus1 +1 119910

119894is

the corresponding label of 119909119894 Then 120596 is a weight vector and

the margin is 1120596 The following constraint optimizationproblem is the solution of maximizing the margin 1120596

min 1

21205962+ 119862

119897

sum119894=1

120585119894

st 119910119894(120596 sdot 120593 (119909

119894) + 119887) ge 1 minus 120585

119894 119894 = 1 119897

120585119894ge 0 119894 = 1 119897

(14)

where coefficient 119862 is a penalty factor and 120585119894is a slack factor

[16]In addition using the duality theory of optimization

theory and Kernel function the final decision function isdescribed by

119891 (119909) = sgn( sum119909119894isin119878119881119904

119910119894120572119894(120593 (119909119894) sdot 120593 (119909)) + 119887)

= sgn( sum119909119894isin119878119881119904

119910119894120572119894119870(119909119894 119909) + 119887)

(15)

where 119870(119909119894 119909) is the kernel function which satisfies Mercer

condition the constants 120572119894are named Lagrange multipliers

and are determined in the optimization procedure The typ-ical kernel functions are the polynomial kernel Radial BasisFunction (RBF) kernel sigmoid kernel and linear kernel Inmany practical applications the RBF kernel has the highestclassification accuracy rate compared to the other kernelfunctions sowemainly consider the RBF kernel in this paper

The SVMwas originally designed for binary classificationand had good performance but it still faced many difficultiesin addressing multiclass classification problems The SVM isnot sufficient to handle a practical situation

223 Multiclass SVM Currently several methods based onthe SVM have been proposed for multiclass classificationsuch as ldquoone-against-allrdquo ldquoone-against-onerdquo and DirectedAcyclic Graph (DAG) Experiments indicate that the ldquoone-against-onerdquo and DAG-SVM methods are most suitablefor practical situation In this paper the ldquoone-against-onerdquomethod is selected for classification [19]

Let us suppose that the training data set is 119878 =

(1199091 1199101) (1199092 1199102) (119909

119897 119910119897) 119909119894isin 119877119899 and the ldquoone-against-

onerdquo method constructs 1198622119896= 119896(119896 minus 1)2 classifiers each of

which is trained using the data from two classes For examplewe should solve the following binary classification problemfor the training data from the 119894th and 119895th classes

min120596119894119895119887119894119895120585119894119895

1

2

1003817100381710038171003817100381712059611989411989510038171003817100381710038171003817

2

+ 119862[sum119894=1

120585119894119895

119905]

st [(120596119894119895sdot 119909119905) + 119887119894119895] minus 1 + 120585

119894119895

119905ge 0 if 119910

119905= 119894

[(120596119894119895sdot 119909119905) + 119887119894119895] + 1 minus 120585

119894119895

119905le 0

if 119910119905= 119895 120585

119894119895

119905ge 0

(16)

Shock and Vibration 5

Table 1 Six-dimensional fault features

Fault pattern No Feature 1 Feature 2 Feature 3 Feature 4 Feature 5 Feature 6

Normal

1 49681 39921 40155 36082 32670 265762 49732 39936 40145 36031 32395 26541sdot sdot sdot

20 47565 39406 41075 36274 33763 26567

Rotor wear

21 38933 42478 35822 37066 32937 2596622 38923 41903 35846 37407 32990 25675sdot sdot sdot

40 38991 39456 35417 36743 33190 25426

Swash plate wear

41 41123 34824 34975 36294 32926 2533242 41285 34886 35151 36196 33310 25820sdot sdot sdot

60 41782 34949 35132 35932 33496 26182

When testing is performed for the unknown sample 119909we construct all 119896(119896 minus 1)2 classifiers to realize the classdiscrimination andmake decisions using the following votingstrategy if sgn((120596119894119895 sdot 119909

119905) + 119887119894119895) 119909 is in the 119894th class then the

vote for the 119894th class is increased by one otherwise the 119895thclass is increased by one Finally we predict that 119909 is in theclass with the largest vote [20]

3 Experimental Verification

31 Experiment Setup The plunger pump test-rig is shownin Figure 3 from this test-rig the original vibration signalswere obtained to verify the proposed method The vibrationdata were obtained from the front side of the hydraulic pumpwith a stabilized motor speed of 528 rmin and a samplingrate of 1000Hz In this experiment two commonly occurringfaults were set swash plate wear and rotor wear Under threeconditions (two faulty conditions and the normal state) 20groups of samples (1024 sampling points for each group) wereselected for the analysis

32 Model for Fault Diagnosis of Hydraulic Pumps

321 Feature Extraction Based on the CEEMD-STFTand Time-Frequency Entropy

(1) CEEMD Model The parameters of the CEEMD modelwere set as follows the noise standard deviation (Nstd) was02 the Number of Realizations (NR) was 600 and themaximumnumber of sifting iterations allowed (MaxIter) was5000The original signals of each state were decomposed intoa series of IMFs the first six IMFs were selected for furtheranalysis as shown in Figure 4

(2) Procedure of the STFT and Time-Frequency EntropyAcquisitionThe parameters of STFT were selected as followsthe length of the window number of overlaps and samplingfrequency (fs) were 256 254 and 1000 respectively andthe length of the discrete Fourier transforms was equal to

Figure 3 Plunger pump test-rig

the window length Then the time-frequency matrices orspectrograms of each state were obtained in Figure 5

The time-frequency entropy of each state can be cal-culated based on the time-frequency matrices The time-frequency block was set as length = width = 64 and boththe lateral and longitudinal slip steps were 32 Then a six-dimensional time-frequency entropy was obtained for eachgroup which is one of the fault feature vectors All of the faultfeatures are listed in Table 1

(3) Feature Dimension Reduction Based on PCA To improvethe accuracy and robustness of the fault diagnosis dimensionreduction is necessary for the high dimensional fault featurevectors PCA which is an important and powerful methodsto extract the most significant information from data andcompress the size of the data [21] was used to acquire thethree-dimensional feature vectors in Table 2

The clustering result of the fault features is visuallydisplayed in Figure 6 which obviously shows a good perfor-mance of the hydraulic-pump fault mode classification

322 Fault Mode Classification Based on Multiclass SVMThe extracted fault feature sets were divided into trainingdata and testing data (the first ten groups were set as thetraining data and the remainder was set as the testing data forevery state) First the training multiclass SVM classifier was

6 Shock and Vibration

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

minus020

02

minus020

02

minus010

01

minus0050

005

minus010

01

04505

055

minus050

05

minus050

05

minus0050

005

minus0050

005

minus0020

002

minus0050

005

04505

055

minus050

05

minus0020

002

minus010

01

minus0020

002

minus0020

002

minus0020

002

046048

05

R(t)

minus050

05

R(t)

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

R(t)

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

Figure 4 First 6 IMFs of each state

Table 2 Feature vector set after dimension reduction

Fault pattern No Feature 1 Feature 2 Feature 3

Normal

1 41284 29741 564832 41327 29729 56553sdot sdot sdot

20 39954 29829 55353

Rotor wear

21 37289 20520 5258922 36789 20772 52629sdot sdot sdot

40 35266 21772 51467

Swash plate wear

41 32972 24613 5107842 33079 24822 51103sdot sdot sdot

60 33408 25041 51157

trained as previously proposed with the training data Thenthe trained classifier was used to classify the fault mode ofthe testing data and calculate the recognition accuracy Theclassification results of the testing data are shown in Table 3and Figure 7 These testing results verify that the recognition

performance is absolutely good and the multiclass SVMmethod is notably effective for mode classification

Combining the clustering figure and multiclass SVMclassification results the effectiveness and feasibility of thismethod for hydraulic-pump fault diagnosis were provenand a high classification performance was also obviouslyobtained

4 Conclusion

An effective method for the feature extraction and modeclassification of vibration signals has been performed in thispaper and this algorithm was successfully verified on practi-cal signals fromahydraulic pumpTheCEEMDmodel whichis an improvement of EMD and can solve the ldquomode mixingrdquoproblem was combined with the STFT analysis method andtime-frequency entropy calculation to extract the robust andsignificant fault feature Meanwhile the multiclass SVM clas-sifier was selected to process the small sample and multiple-fault situation and it obtained a perfect classification resultThen the accuracy and feasibility of this hydraulic-pumpfault diagnosis method were demonstrated Future work willconcentrate on the application of thismethod to other objectsor fields for signal analysis and fault diagnosis

Shock and Vibration 7

150 200 250 300 350

150 200 250 300 350

150 200 250 300 350

Freq

uenc

y (H

z)Fr

eque

ncy

(Hz)

Freq

uenc

y (H

z)

Time (ms)

Time (ms)

Time (ms)

minus40

minus60

minus80

minus100

minus120

minus140

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

050

100150200250300350400450500

050

100150200250300350400450500

050

100150200250300350400450500

minus100minus90minus80minus70minus60minus50minus40

minus100minus90minus80minus70minus60minus50minus40minus30minus20

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

Figure 5 Spectrograms of the first IMF of each state

Table 3 Classification results of the testing data

Fault pattern Actual label Index No Feature 1 Feature 2 Feature 3 Predicted label

Normal 1

1 11 40906 29178 55591 12 12 40961 29253 55036 1sdot sdot sdot sdot sdot sdot 110 20 39954 29829 55353 1

Rotor wear 2

11 31 37442 20107 51790 212 32 36416 21110 51027 2sdot sdot sdot sdot sdot sdot 220 40 35266 21772 51467 2

Swash plate wear 3

21 51 33093 25163 51968 322 52 33018 24982 52170 3sdot sdot sdot sdot sdot sdot 330 60 33408 25041 51157 3

8 Shock and Vibration

42414393837361st PC35343332182222nd PC

242628332

NormalRotor wear

Swash plate wear

5152535455565758

3rd

PC

Figure 6 Clustering result of the fault features

Index

Diagnosis results

Predicted labelsGround truth labels

1

2

3

Labe

l

1 2 3 4 5 6 7 8 910

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Figure 7 Classification results of the testing data

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This study was supported by the National Natural ScienceFoundation of China (Grant nos 51105019 and 51575021)as well as the Technology Foundation Program of NationalDefense (Grant no Z132013B002)

References

[1] Z Ruixiang L Tingqi H Jianding and Y Dongchao ldquoFaultdiagnosis of airplane hydraulic pumprdquo in Proceedings of the4th World Congress on Intelligent Control and AutomationShanghai China June 2002

[2] T Zhang and N Zhang ldquoVibration modes and the dynamicbehaviour of a hydraulic plunger pumprdquo Shock and Vibrationvol 2016 Article ID 9679542 7 pages 2016

[3] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciencesThe Royal Society vol 454 no 1971 pp 903ndash995 1998

[4] T Han D Jiang and N Wang ldquoThe fault feature extractionof rolling bearing based on EMD and difference spectrum

of singular valuerdquo Shock and Vibration vol 2016 Article ID5957179 14 pages 2016

[5] M E TorresMA Colominas G Schlotthauer and P FlandrinldquoA complete ensemble empirical mode decomposition withadaptive noiserdquo in Proceedings of the 36th IEEE InternationalConference on Acoustics Speech and Signal Processing (ICASSPrsquo11) pp 4144ndash4147 IEEE Prague Czech Republic May 2011

[6] L Zhao W Yu and R Yan ldquoGearbox fault diagnosis usingcomplementary ensemble empirical mode decomposition andpermutation entropyrdquo Shock and Vibration vol 2016 Article ID3891429 8 pages 2016

[7] J Han and M van der Baan ldquoEmpirical mode decompositionfor seismic time-frequency analysisrdquo Geophysics vol 78 no 2pp O9ndashO19 2013

[8] E Mayoraz and E Alpaydin ldquoSupport vector machines formulti-class classificationrdquo in Engineering Applications of Bio-Inspired Artificial Neural Networks pp 833ndash842 SpringerBerlin Germany 1999

[9] J Yang Y Zhang and Y Zhu ldquoIntelligent fault diagnosis ofrolling element bearing based on SVMs and fractal dimensionrdquoMechanical Systems and Signal Processing vol 21 no 5 pp2012ndash2024 2007

[10] M A Colominas G Schlotthauer andM E Torres ldquoImprovedcomplete ensemble EMD a suitable tool for biomedical signalprocessingrdquo Biomedical Signal Processing and Control vol 14no 1 pp 19ndash29 2014

[11] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise-assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[12] J Li C Liu Z Zeng and L Chen ldquoGPR signal denoising andtarget extraction with the CEEMD methodrdquo IEEE Geoscienceand Remote Sensing Letters vol 12 no 8 pp 1615ndash1619 2015

[13] S H Nawab T F Quatieri and J S Lim ldquoSignal reconstructionfrom short-time fourier transform magnituderdquo IEEE Transac-tions on Acoustics Speech and Signal Processing vol 31 no 4pp 986ndash998 1983

[14] H K Kwok andD L Jones ldquoImproved instantaneous frequencyestimation using an adaptive short-time Fourier transformrdquoIEEE Transactions on Signal Processing vol 48 no 10 pp 2964ndash2972 2000

[15] L Mingliang W Keqi S Laijun and Z Jianju ldquoApplyingempiricalmode decomposition (EMD) and entropy to diagnosecircuit breaker faultsrdquo OptikmdashInternational Journal for Lightand Electron Optics vol 126 no 20 pp 2338ndash2342 2015

[16] X Zhang Y Liang J Zhou and Y Zang ldquoA novel bearing faultdiagnosis model integrated permutation entropy ensembleempirical mode decomposition and optimized SVMrdquoMeasure-ment vol 69 pp 164ndash179 2015

[17] D Yu Y Yang and J Cheng ldquoApplication of timendashfrequencyentropy method based on HilbertndashHuang transform to gearfault diagnosisrdquo Measurement vol 40 no 9-10 pp 823ndash8302007

[18] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

[19] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

[20] Z Cai Q Ding and M Wang ldquoStudy on automated incidentdetection algorithms based on PCA and SVM for freewayrdquo inProceedings of the International Conference on Optoelectronicsand Image Processing (ICOIP rsquo10) Haikou China November2010

[21] S Wold K Esbensen and P Geladi ldquoPrincipal componentanalysisrdquo Chemometrics and Intelligent Laboratory Systems vol2 no 1ndash3 pp 37ndash52 1987

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 3

the mean of the corresponding IMFs that are obtained viaEMD over an ensemble of the original signal plus differentrealizations of finite variance white noise [12] Considering 119909as an example signal the EEMD algorithm can be describedas follows

Step 1 Generate

119909(119894)= 119909 + 120573119908

(119894) (3)

where 119908(119894) (119894 = 1 119868) are different realizations of whiteGaussian noise

Step 2 Each 119909(119894) (119894 = 1 119868) is fully decomposed by EMDto obtain the modes IMF(119894)

119896 where 119896 = 1 119870 indicates the

mode

Step 3 Assign IMF119896as the 119896th mode of 119909 which is obtained

by averaging the corresponding modes

IMF119896=1

119868

119868

sum119894=1

IMF(119894)119896 (4)

However the EEMDmethod has some disadvantages (1)the decomposition is not complete (2) different realizationsof signal plus white noise may generate different numbers ofmodes

(C) Complete EEMD (CEEMD) To address the aforemen-tioned reconstruction error complete EEMD (CEEMD) wasproposed by Torres et al in 2011 [5] The procedure ofCEEMD is described as follows

Step 1 The first IMF is calculated in the identical method toEEMD First addwhite noise to the original signal and obtainthe first EMD component of the data with noise Repeatthe decomposition by adding different noise realizations andcompute the ensemble average to define it as the first IMF

1of

the original signal 119909 that is

IMF1=1

119868

119868

sum119894=1

1198641(119909 + 120576

0119908119894) (5)

where 119864119895(sdot) is defined as an operator and the 119895th mode can

be computed through EMD when it meets a new signal 119909 isthe raw signal119908119894 is the different white noise and 120576

0is a ratio

coefficient

Step 2 Calculate a unique first residue as

1199031= 119909 minus IMF

1 (6)

Then set 1199031+ 12057611198641(119908119894) (119894 = 1 119868) as the new signal

for decomposition When the first IMF component has beenobtained we must calculate the ensemble average as thesecond component IMF

2

IMF2=1

119868

119868

sum119894=1

1198641(1199031+ 12057611198641(119908119894)) (7)

Step 3 Repeat Steps 1-2 and we can obtain the (119896 + 1)th IMFcomponent IMF

119896+1

IMF119896+1

=1

119868

119868

sum119894=1

1198641(119903119896+ 120576119896119864119896(119908119894)) (8)

Step 4 Finally obtain the last residual function 119877 until theresidue cannot be decomposed Then 119877 = 119909 minus sum

119870

119896=1IMF119896

where 119870 is the total number of IMF The signal is describedas

119909 =

119870

sum119896=1

IMF119896+ 119877 (9)

The last step makes the proposed decomposition com-plete and provides an exact reconstruction of the originalsignal

212 Short-Time Fourier Transform (STFT) The time andfrequency information in each IMF relates to the samplingfrequency and changes with the signal itself so research onthe time-frequency domain characterization of signals hasbeen a key component of signal analysis [13] The STFT is apopular method to analyze nonstationary signals The STFTof the signal 119909(119905) is defined as

119883(119905 119891) = intinfin

minusinfin

119909 (120591) ℎ (120591 minus 119905) sdot 119890minus1198952120587119891120591

119889120591 (10)

where ℎ(119905) should be a low-pass filter and ℎ2 = 1 Note

that ℎ(120591 minus 119905) sdot 1198901198952120587119891120591 has its energy concentrated at time 119905 andfrequency 119891 Thus |119883(119905 119891)|2 can be considered the energyin 119909(119905) at frequency 119891 and time 119905 Generally one displays theenergy at each time and frequency pair that is

119875 (119905 119891) =1003816100381610038161003816119883 (119905 119891)

10038161003816100381610038162 (11)

119875(119905 119891) is known as the spectrogram (SP) of 119909(119905) [14]The spectrogram algorithm is an analysis algorithm that

produces a two-dimensional image representation of vibra-tion signals The Power Spectrum Density (PSD) function119875(119905 119891) is expressed as a Pseudo ColorMap (PCM) which is aspectrogramwith a time axis and a frequency axisThis time-frequency spectrum which can be called the ldquovisual lan-guagerdquo shows the modulation characteristics of the signals

213 Time-Frequency Entropy The time-frequency distri-bution of the vibration signal obtained through the STFTmethod presents modulation characteristic that is theenergy distribution changes at different moments Thereforea fault can be detected by comparing the energy distributionof the signals with and without fault conditions in the time-frequency domain which indicates that the energy variationin the time-frequency plane may indicate a fault occurrence[15] Because the spectrogram can provide an accurateenergy-frequency-time distribution the information entropytheory which measures the uniformity of the probabilitydistribution can be introduced to the time-frequency distri-bution to quantitatively describe the divergence in differentoperating conditions [16]

4 Shock and Vibration

Support vector

Support vector

Margin = 2120596

Figure 2 Illustration for data classification using a 2-class SVM

Let a time-frequency plane have 119873 blocks with equalareas where the information source for the entire plane is 119860and for each block is119882

119894(119894 = 1 119873) so the probability that

each information source appears in the entire system is

119873

sum119894=1

119902119894= 1 119902

119894=119882119894

119860 (119894 = 1 119873) (12)

According to the information entropy calculation [17] thetime-frequency entropy is defined as

119904 (119902) = minus

119873

sum119894=1

119902119894ln 119902119894 (13)

Now we can consider the time-frequency entropy of eachIMF as the extracted feature vectors which will be the inputof the mode classification

22 Mode Classification Based on the Multiclass SVM

221 Support Vector Machine (SVM) Support VectorMachine (SVM) which originated from the statisticallearning theory and an optimal separating hyper-plane in thecase of linear separation was developed by Cortes and hiscoworker [18] Through some nonlinear mapping functionsthe originalmode space ismapped into the high-dimensionalfeature space Z Then the optical separating hyper-plane isconstructed in the feature space Consequently the nonlinearproblem in the low-dimensional space corresponds to thelinear problem in the high-dimensional space

222 Two-Class SVM SVMs are primarily designed for 2-class classification problems To illustrate the basic principlea schematic diagram of 2-class SVM is shown in Figure 2where two different classes (circles and triangles) are classi-fied by a linear boundary 119867 and the distance between theboundary and the nearest data point in each class is maximal

Assume that the input vector is 119909 which is mapped intohigh-dimensional space Z through the nonlinear mappingfunction 120593(119909) and the linear function (120596 sdot 120593(119909)) + 119887 = 0 inthe high-dimensional feature space can be used to constructthe optimal classification hyper-plane The training data areset as 119909

119894 119910119894 119894 = 1 2 119897 119909

119894isin 119877119899 119910

119894isin minus1 +1 119910

119894is

the corresponding label of 119909119894 Then 120596 is a weight vector and

the margin is 1120596 The following constraint optimizationproblem is the solution of maximizing the margin 1120596

min 1

21205962+ 119862

119897

sum119894=1

120585119894

st 119910119894(120596 sdot 120593 (119909

119894) + 119887) ge 1 minus 120585

119894 119894 = 1 119897

120585119894ge 0 119894 = 1 119897

(14)

where coefficient 119862 is a penalty factor and 120585119894is a slack factor

[16]In addition using the duality theory of optimization

theory and Kernel function the final decision function isdescribed by

119891 (119909) = sgn( sum119909119894isin119878119881119904

119910119894120572119894(120593 (119909119894) sdot 120593 (119909)) + 119887)

= sgn( sum119909119894isin119878119881119904

119910119894120572119894119870(119909119894 119909) + 119887)

(15)

where 119870(119909119894 119909) is the kernel function which satisfies Mercer

condition the constants 120572119894are named Lagrange multipliers

and are determined in the optimization procedure The typ-ical kernel functions are the polynomial kernel Radial BasisFunction (RBF) kernel sigmoid kernel and linear kernel Inmany practical applications the RBF kernel has the highestclassification accuracy rate compared to the other kernelfunctions sowemainly consider the RBF kernel in this paper

The SVMwas originally designed for binary classificationand had good performance but it still faced many difficultiesin addressing multiclass classification problems The SVM isnot sufficient to handle a practical situation

223 Multiclass SVM Currently several methods based onthe SVM have been proposed for multiclass classificationsuch as ldquoone-against-allrdquo ldquoone-against-onerdquo and DirectedAcyclic Graph (DAG) Experiments indicate that the ldquoone-against-onerdquo and DAG-SVM methods are most suitablefor practical situation In this paper the ldquoone-against-onerdquomethod is selected for classification [19]

Let us suppose that the training data set is 119878 =

(1199091 1199101) (1199092 1199102) (119909

119897 119910119897) 119909119894isin 119877119899 and the ldquoone-against-

onerdquo method constructs 1198622119896= 119896(119896 minus 1)2 classifiers each of

which is trained using the data from two classes For examplewe should solve the following binary classification problemfor the training data from the 119894th and 119895th classes

min120596119894119895119887119894119895120585119894119895

1

2

1003817100381710038171003817100381712059611989411989510038171003817100381710038171003817

2

+ 119862[sum119894=1

120585119894119895

119905]

st [(120596119894119895sdot 119909119905) + 119887119894119895] minus 1 + 120585

119894119895

119905ge 0 if 119910

119905= 119894

[(120596119894119895sdot 119909119905) + 119887119894119895] + 1 minus 120585

119894119895

119905le 0

if 119910119905= 119895 120585

119894119895

119905ge 0

(16)

Shock and Vibration 5

Table 1 Six-dimensional fault features

Fault pattern No Feature 1 Feature 2 Feature 3 Feature 4 Feature 5 Feature 6

Normal

1 49681 39921 40155 36082 32670 265762 49732 39936 40145 36031 32395 26541sdot sdot sdot

20 47565 39406 41075 36274 33763 26567

Rotor wear

21 38933 42478 35822 37066 32937 2596622 38923 41903 35846 37407 32990 25675sdot sdot sdot

40 38991 39456 35417 36743 33190 25426

Swash plate wear

41 41123 34824 34975 36294 32926 2533242 41285 34886 35151 36196 33310 25820sdot sdot sdot

60 41782 34949 35132 35932 33496 26182

When testing is performed for the unknown sample 119909we construct all 119896(119896 minus 1)2 classifiers to realize the classdiscrimination andmake decisions using the following votingstrategy if sgn((120596119894119895 sdot 119909

119905) + 119887119894119895) 119909 is in the 119894th class then the

vote for the 119894th class is increased by one otherwise the 119895thclass is increased by one Finally we predict that 119909 is in theclass with the largest vote [20]

3 Experimental Verification

31 Experiment Setup The plunger pump test-rig is shownin Figure 3 from this test-rig the original vibration signalswere obtained to verify the proposed method The vibrationdata were obtained from the front side of the hydraulic pumpwith a stabilized motor speed of 528 rmin and a samplingrate of 1000Hz In this experiment two commonly occurringfaults were set swash plate wear and rotor wear Under threeconditions (two faulty conditions and the normal state) 20groups of samples (1024 sampling points for each group) wereselected for the analysis

32 Model for Fault Diagnosis of Hydraulic Pumps

321 Feature Extraction Based on the CEEMD-STFTand Time-Frequency Entropy

(1) CEEMD Model The parameters of the CEEMD modelwere set as follows the noise standard deviation (Nstd) was02 the Number of Realizations (NR) was 600 and themaximumnumber of sifting iterations allowed (MaxIter) was5000The original signals of each state were decomposed intoa series of IMFs the first six IMFs were selected for furtheranalysis as shown in Figure 4

(2) Procedure of the STFT and Time-Frequency EntropyAcquisitionThe parameters of STFT were selected as followsthe length of the window number of overlaps and samplingfrequency (fs) were 256 254 and 1000 respectively andthe length of the discrete Fourier transforms was equal to

Figure 3 Plunger pump test-rig

the window length Then the time-frequency matrices orspectrograms of each state were obtained in Figure 5

The time-frequency entropy of each state can be cal-culated based on the time-frequency matrices The time-frequency block was set as length = width = 64 and boththe lateral and longitudinal slip steps were 32 Then a six-dimensional time-frequency entropy was obtained for eachgroup which is one of the fault feature vectors All of the faultfeatures are listed in Table 1

(3) Feature Dimension Reduction Based on PCA To improvethe accuracy and robustness of the fault diagnosis dimensionreduction is necessary for the high dimensional fault featurevectors PCA which is an important and powerful methodsto extract the most significant information from data andcompress the size of the data [21] was used to acquire thethree-dimensional feature vectors in Table 2

The clustering result of the fault features is visuallydisplayed in Figure 6 which obviously shows a good perfor-mance of the hydraulic-pump fault mode classification

322 Fault Mode Classification Based on Multiclass SVMThe extracted fault feature sets were divided into trainingdata and testing data (the first ten groups were set as thetraining data and the remainder was set as the testing data forevery state) First the training multiclass SVM classifier was

6 Shock and Vibration

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

minus020

02

minus020

02

minus010

01

minus0050

005

minus010

01

04505

055

minus050

05

minus050

05

minus0050

005

minus0050

005

minus0020

002

minus0050

005

04505

055

minus050

05

minus0020

002

minus010

01

minus0020

002

minus0020

002

minus0020

002

046048

05

R(t)

minus050

05

R(t)

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

R(t)

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

Figure 4 First 6 IMFs of each state

Table 2 Feature vector set after dimension reduction

Fault pattern No Feature 1 Feature 2 Feature 3

Normal

1 41284 29741 564832 41327 29729 56553sdot sdot sdot

20 39954 29829 55353

Rotor wear

21 37289 20520 5258922 36789 20772 52629sdot sdot sdot

40 35266 21772 51467

Swash plate wear

41 32972 24613 5107842 33079 24822 51103sdot sdot sdot

60 33408 25041 51157

trained as previously proposed with the training data Thenthe trained classifier was used to classify the fault mode ofthe testing data and calculate the recognition accuracy Theclassification results of the testing data are shown in Table 3and Figure 7 These testing results verify that the recognition

performance is absolutely good and the multiclass SVMmethod is notably effective for mode classification

Combining the clustering figure and multiclass SVMclassification results the effectiveness and feasibility of thismethod for hydraulic-pump fault diagnosis were provenand a high classification performance was also obviouslyobtained

4 Conclusion

An effective method for the feature extraction and modeclassification of vibration signals has been performed in thispaper and this algorithm was successfully verified on practi-cal signals fromahydraulic pumpTheCEEMDmodel whichis an improvement of EMD and can solve the ldquomode mixingrdquoproblem was combined with the STFT analysis method andtime-frequency entropy calculation to extract the robust andsignificant fault feature Meanwhile the multiclass SVM clas-sifier was selected to process the small sample and multiple-fault situation and it obtained a perfect classification resultThen the accuracy and feasibility of this hydraulic-pumpfault diagnosis method were demonstrated Future work willconcentrate on the application of thismethod to other objectsor fields for signal analysis and fault diagnosis

Shock and Vibration 7

150 200 250 300 350

150 200 250 300 350

150 200 250 300 350

Freq

uenc

y (H

z)Fr

eque

ncy

(Hz)

Freq

uenc

y (H

z)

Time (ms)

Time (ms)

Time (ms)

minus40

minus60

minus80

minus100

minus120

minus140

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

050

100150200250300350400450500

050

100150200250300350400450500

050

100150200250300350400450500

minus100minus90minus80minus70minus60minus50minus40

minus100minus90minus80minus70minus60minus50minus40minus30minus20

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

Figure 5 Spectrograms of the first IMF of each state

Table 3 Classification results of the testing data

Fault pattern Actual label Index No Feature 1 Feature 2 Feature 3 Predicted label

Normal 1

1 11 40906 29178 55591 12 12 40961 29253 55036 1sdot sdot sdot sdot sdot sdot 110 20 39954 29829 55353 1

Rotor wear 2

11 31 37442 20107 51790 212 32 36416 21110 51027 2sdot sdot sdot sdot sdot sdot 220 40 35266 21772 51467 2

Swash plate wear 3

21 51 33093 25163 51968 322 52 33018 24982 52170 3sdot sdot sdot sdot sdot sdot 330 60 33408 25041 51157 3

8 Shock and Vibration

42414393837361st PC35343332182222nd PC

242628332

NormalRotor wear

Swash plate wear

5152535455565758

3rd

PC

Figure 6 Clustering result of the fault features

Index

Diagnosis results

Predicted labelsGround truth labels

1

2

3

Labe

l

1 2 3 4 5 6 7 8 910

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Figure 7 Classification results of the testing data

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This study was supported by the National Natural ScienceFoundation of China (Grant nos 51105019 and 51575021)as well as the Technology Foundation Program of NationalDefense (Grant no Z132013B002)

References

[1] Z Ruixiang L Tingqi H Jianding and Y Dongchao ldquoFaultdiagnosis of airplane hydraulic pumprdquo in Proceedings of the4th World Congress on Intelligent Control and AutomationShanghai China June 2002

[2] T Zhang and N Zhang ldquoVibration modes and the dynamicbehaviour of a hydraulic plunger pumprdquo Shock and Vibrationvol 2016 Article ID 9679542 7 pages 2016

[3] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciencesThe Royal Society vol 454 no 1971 pp 903ndash995 1998

[4] T Han D Jiang and N Wang ldquoThe fault feature extractionof rolling bearing based on EMD and difference spectrum

of singular valuerdquo Shock and Vibration vol 2016 Article ID5957179 14 pages 2016

[5] M E TorresMA Colominas G Schlotthauer and P FlandrinldquoA complete ensemble empirical mode decomposition withadaptive noiserdquo in Proceedings of the 36th IEEE InternationalConference on Acoustics Speech and Signal Processing (ICASSPrsquo11) pp 4144ndash4147 IEEE Prague Czech Republic May 2011

[6] L Zhao W Yu and R Yan ldquoGearbox fault diagnosis usingcomplementary ensemble empirical mode decomposition andpermutation entropyrdquo Shock and Vibration vol 2016 Article ID3891429 8 pages 2016

[7] J Han and M van der Baan ldquoEmpirical mode decompositionfor seismic time-frequency analysisrdquo Geophysics vol 78 no 2pp O9ndashO19 2013

[8] E Mayoraz and E Alpaydin ldquoSupport vector machines formulti-class classificationrdquo in Engineering Applications of Bio-Inspired Artificial Neural Networks pp 833ndash842 SpringerBerlin Germany 1999

[9] J Yang Y Zhang and Y Zhu ldquoIntelligent fault diagnosis ofrolling element bearing based on SVMs and fractal dimensionrdquoMechanical Systems and Signal Processing vol 21 no 5 pp2012ndash2024 2007

[10] M A Colominas G Schlotthauer andM E Torres ldquoImprovedcomplete ensemble EMD a suitable tool for biomedical signalprocessingrdquo Biomedical Signal Processing and Control vol 14no 1 pp 19ndash29 2014

[11] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise-assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[12] J Li C Liu Z Zeng and L Chen ldquoGPR signal denoising andtarget extraction with the CEEMD methodrdquo IEEE Geoscienceand Remote Sensing Letters vol 12 no 8 pp 1615ndash1619 2015

[13] S H Nawab T F Quatieri and J S Lim ldquoSignal reconstructionfrom short-time fourier transform magnituderdquo IEEE Transac-tions on Acoustics Speech and Signal Processing vol 31 no 4pp 986ndash998 1983

[14] H K Kwok andD L Jones ldquoImproved instantaneous frequencyestimation using an adaptive short-time Fourier transformrdquoIEEE Transactions on Signal Processing vol 48 no 10 pp 2964ndash2972 2000

[15] L Mingliang W Keqi S Laijun and Z Jianju ldquoApplyingempiricalmode decomposition (EMD) and entropy to diagnosecircuit breaker faultsrdquo OptikmdashInternational Journal for Lightand Electron Optics vol 126 no 20 pp 2338ndash2342 2015

[16] X Zhang Y Liang J Zhou and Y Zang ldquoA novel bearing faultdiagnosis model integrated permutation entropy ensembleempirical mode decomposition and optimized SVMrdquoMeasure-ment vol 69 pp 164ndash179 2015

[17] D Yu Y Yang and J Cheng ldquoApplication of timendashfrequencyentropy method based on HilbertndashHuang transform to gearfault diagnosisrdquo Measurement vol 40 no 9-10 pp 823ndash8302007

[18] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

[19] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

[20] Z Cai Q Ding and M Wang ldquoStudy on automated incidentdetection algorithms based on PCA and SVM for freewayrdquo inProceedings of the International Conference on Optoelectronicsand Image Processing (ICOIP rsquo10) Haikou China November2010

[21] S Wold K Esbensen and P Geladi ldquoPrincipal componentanalysisrdquo Chemometrics and Intelligent Laboratory Systems vol2 no 1ndash3 pp 37ndash52 1987

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Shock and Vibration

Support vector

Support vector

Margin = 2120596

Figure 2 Illustration for data classification using a 2-class SVM

Let a time-frequency plane have 119873 blocks with equalareas where the information source for the entire plane is 119860and for each block is119882

119894(119894 = 1 119873) so the probability that

each information source appears in the entire system is

119873

sum119894=1

119902119894= 1 119902

119894=119882119894

119860 (119894 = 1 119873) (12)

According to the information entropy calculation [17] thetime-frequency entropy is defined as

119904 (119902) = minus

119873

sum119894=1

119902119894ln 119902119894 (13)

Now we can consider the time-frequency entropy of eachIMF as the extracted feature vectors which will be the inputof the mode classification

22 Mode Classification Based on the Multiclass SVM

221 Support Vector Machine (SVM) Support VectorMachine (SVM) which originated from the statisticallearning theory and an optimal separating hyper-plane in thecase of linear separation was developed by Cortes and hiscoworker [18] Through some nonlinear mapping functionsthe originalmode space ismapped into the high-dimensionalfeature space Z Then the optical separating hyper-plane isconstructed in the feature space Consequently the nonlinearproblem in the low-dimensional space corresponds to thelinear problem in the high-dimensional space

222 Two-Class SVM SVMs are primarily designed for 2-class classification problems To illustrate the basic principlea schematic diagram of 2-class SVM is shown in Figure 2where two different classes (circles and triangles) are classi-fied by a linear boundary 119867 and the distance between theboundary and the nearest data point in each class is maximal

Assume that the input vector is 119909 which is mapped intohigh-dimensional space Z through the nonlinear mappingfunction 120593(119909) and the linear function (120596 sdot 120593(119909)) + 119887 = 0 inthe high-dimensional feature space can be used to constructthe optimal classification hyper-plane The training data areset as 119909

119894 119910119894 119894 = 1 2 119897 119909

119894isin 119877119899 119910

119894isin minus1 +1 119910

119894is

the corresponding label of 119909119894 Then 120596 is a weight vector and

the margin is 1120596 The following constraint optimizationproblem is the solution of maximizing the margin 1120596

min 1

21205962+ 119862

119897

sum119894=1

120585119894

st 119910119894(120596 sdot 120593 (119909

119894) + 119887) ge 1 minus 120585

119894 119894 = 1 119897

120585119894ge 0 119894 = 1 119897

(14)

where coefficient 119862 is a penalty factor and 120585119894is a slack factor

[16]In addition using the duality theory of optimization

theory and Kernel function the final decision function isdescribed by

119891 (119909) = sgn( sum119909119894isin119878119881119904

119910119894120572119894(120593 (119909119894) sdot 120593 (119909)) + 119887)

= sgn( sum119909119894isin119878119881119904

119910119894120572119894119870(119909119894 119909) + 119887)

(15)

where 119870(119909119894 119909) is the kernel function which satisfies Mercer

condition the constants 120572119894are named Lagrange multipliers

and are determined in the optimization procedure The typ-ical kernel functions are the polynomial kernel Radial BasisFunction (RBF) kernel sigmoid kernel and linear kernel Inmany practical applications the RBF kernel has the highestclassification accuracy rate compared to the other kernelfunctions sowemainly consider the RBF kernel in this paper

The SVMwas originally designed for binary classificationand had good performance but it still faced many difficultiesin addressing multiclass classification problems The SVM isnot sufficient to handle a practical situation

223 Multiclass SVM Currently several methods based onthe SVM have been proposed for multiclass classificationsuch as ldquoone-against-allrdquo ldquoone-against-onerdquo and DirectedAcyclic Graph (DAG) Experiments indicate that the ldquoone-against-onerdquo and DAG-SVM methods are most suitablefor practical situation In this paper the ldquoone-against-onerdquomethod is selected for classification [19]

Let us suppose that the training data set is 119878 =

(1199091 1199101) (1199092 1199102) (119909

119897 119910119897) 119909119894isin 119877119899 and the ldquoone-against-

onerdquo method constructs 1198622119896= 119896(119896 minus 1)2 classifiers each of

which is trained using the data from two classes For examplewe should solve the following binary classification problemfor the training data from the 119894th and 119895th classes

min120596119894119895119887119894119895120585119894119895

1

2

1003817100381710038171003817100381712059611989411989510038171003817100381710038171003817

2

+ 119862[sum119894=1

120585119894119895

119905]

st [(120596119894119895sdot 119909119905) + 119887119894119895] minus 1 + 120585

119894119895

119905ge 0 if 119910

119905= 119894

[(120596119894119895sdot 119909119905) + 119887119894119895] + 1 minus 120585

119894119895

119905le 0

if 119910119905= 119895 120585

119894119895

119905ge 0

(16)

Shock and Vibration 5

Table 1 Six-dimensional fault features

Fault pattern No Feature 1 Feature 2 Feature 3 Feature 4 Feature 5 Feature 6

Normal

1 49681 39921 40155 36082 32670 265762 49732 39936 40145 36031 32395 26541sdot sdot sdot

20 47565 39406 41075 36274 33763 26567

Rotor wear

21 38933 42478 35822 37066 32937 2596622 38923 41903 35846 37407 32990 25675sdot sdot sdot

40 38991 39456 35417 36743 33190 25426

Swash plate wear

41 41123 34824 34975 36294 32926 2533242 41285 34886 35151 36196 33310 25820sdot sdot sdot

60 41782 34949 35132 35932 33496 26182

When testing is performed for the unknown sample 119909we construct all 119896(119896 minus 1)2 classifiers to realize the classdiscrimination andmake decisions using the following votingstrategy if sgn((120596119894119895 sdot 119909

119905) + 119887119894119895) 119909 is in the 119894th class then the

vote for the 119894th class is increased by one otherwise the 119895thclass is increased by one Finally we predict that 119909 is in theclass with the largest vote [20]

3 Experimental Verification

31 Experiment Setup The plunger pump test-rig is shownin Figure 3 from this test-rig the original vibration signalswere obtained to verify the proposed method The vibrationdata were obtained from the front side of the hydraulic pumpwith a stabilized motor speed of 528 rmin and a samplingrate of 1000Hz In this experiment two commonly occurringfaults were set swash plate wear and rotor wear Under threeconditions (two faulty conditions and the normal state) 20groups of samples (1024 sampling points for each group) wereselected for the analysis

32 Model for Fault Diagnosis of Hydraulic Pumps

321 Feature Extraction Based on the CEEMD-STFTand Time-Frequency Entropy

(1) CEEMD Model The parameters of the CEEMD modelwere set as follows the noise standard deviation (Nstd) was02 the Number of Realizations (NR) was 600 and themaximumnumber of sifting iterations allowed (MaxIter) was5000The original signals of each state were decomposed intoa series of IMFs the first six IMFs were selected for furtheranalysis as shown in Figure 4

(2) Procedure of the STFT and Time-Frequency EntropyAcquisitionThe parameters of STFT were selected as followsthe length of the window number of overlaps and samplingfrequency (fs) were 256 254 and 1000 respectively andthe length of the discrete Fourier transforms was equal to

Figure 3 Plunger pump test-rig

the window length Then the time-frequency matrices orspectrograms of each state were obtained in Figure 5

The time-frequency entropy of each state can be cal-culated based on the time-frequency matrices The time-frequency block was set as length = width = 64 and boththe lateral and longitudinal slip steps were 32 Then a six-dimensional time-frequency entropy was obtained for eachgroup which is one of the fault feature vectors All of the faultfeatures are listed in Table 1

(3) Feature Dimension Reduction Based on PCA To improvethe accuracy and robustness of the fault diagnosis dimensionreduction is necessary for the high dimensional fault featurevectors PCA which is an important and powerful methodsto extract the most significant information from data andcompress the size of the data [21] was used to acquire thethree-dimensional feature vectors in Table 2

The clustering result of the fault features is visuallydisplayed in Figure 6 which obviously shows a good perfor-mance of the hydraulic-pump fault mode classification

322 Fault Mode Classification Based on Multiclass SVMThe extracted fault feature sets were divided into trainingdata and testing data (the first ten groups were set as thetraining data and the remainder was set as the testing data forevery state) First the training multiclass SVM classifier was

6 Shock and Vibration

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

minus020

02

minus020

02

minus010

01

minus0050

005

minus010

01

04505

055

minus050

05

minus050

05

minus0050

005

minus0050

005

minus0020

002

minus0050

005

04505

055

minus050

05

minus0020

002

minus010

01

minus0020

002

minus0020

002

minus0020

002

046048

05

R(t)

minus050

05

R(t)

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

R(t)

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

Figure 4 First 6 IMFs of each state

Table 2 Feature vector set after dimension reduction

Fault pattern No Feature 1 Feature 2 Feature 3

Normal

1 41284 29741 564832 41327 29729 56553sdot sdot sdot

20 39954 29829 55353

Rotor wear

21 37289 20520 5258922 36789 20772 52629sdot sdot sdot

40 35266 21772 51467

Swash plate wear

41 32972 24613 5107842 33079 24822 51103sdot sdot sdot

60 33408 25041 51157

trained as previously proposed with the training data Thenthe trained classifier was used to classify the fault mode ofthe testing data and calculate the recognition accuracy Theclassification results of the testing data are shown in Table 3and Figure 7 These testing results verify that the recognition

performance is absolutely good and the multiclass SVMmethod is notably effective for mode classification

Combining the clustering figure and multiclass SVMclassification results the effectiveness and feasibility of thismethod for hydraulic-pump fault diagnosis were provenand a high classification performance was also obviouslyobtained

4 Conclusion

An effective method for the feature extraction and modeclassification of vibration signals has been performed in thispaper and this algorithm was successfully verified on practi-cal signals fromahydraulic pumpTheCEEMDmodel whichis an improvement of EMD and can solve the ldquomode mixingrdquoproblem was combined with the STFT analysis method andtime-frequency entropy calculation to extract the robust andsignificant fault feature Meanwhile the multiclass SVM clas-sifier was selected to process the small sample and multiple-fault situation and it obtained a perfect classification resultThen the accuracy and feasibility of this hydraulic-pumpfault diagnosis method were demonstrated Future work willconcentrate on the application of thismethod to other objectsor fields for signal analysis and fault diagnosis

Shock and Vibration 7

150 200 250 300 350

150 200 250 300 350

150 200 250 300 350

Freq

uenc

y (H

z)Fr

eque

ncy

(Hz)

Freq

uenc

y (H

z)

Time (ms)

Time (ms)

Time (ms)

minus40

minus60

minus80

minus100

minus120

minus140

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

050

100150200250300350400450500

050

100150200250300350400450500

050

100150200250300350400450500

minus100minus90minus80minus70minus60minus50minus40

minus100minus90minus80minus70minus60minus50minus40minus30minus20

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

Figure 5 Spectrograms of the first IMF of each state

Table 3 Classification results of the testing data

Fault pattern Actual label Index No Feature 1 Feature 2 Feature 3 Predicted label

Normal 1

1 11 40906 29178 55591 12 12 40961 29253 55036 1sdot sdot sdot sdot sdot sdot 110 20 39954 29829 55353 1

Rotor wear 2

11 31 37442 20107 51790 212 32 36416 21110 51027 2sdot sdot sdot sdot sdot sdot 220 40 35266 21772 51467 2

Swash plate wear 3

21 51 33093 25163 51968 322 52 33018 24982 52170 3sdot sdot sdot sdot sdot sdot 330 60 33408 25041 51157 3

8 Shock and Vibration

42414393837361st PC35343332182222nd PC

242628332

NormalRotor wear

Swash plate wear

5152535455565758

3rd

PC

Figure 6 Clustering result of the fault features

Index

Diagnosis results

Predicted labelsGround truth labels

1

2

3

Labe

l

1 2 3 4 5 6 7 8 910

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Figure 7 Classification results of the testing data

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This study was supported by the National Natural ScienceFoundation of China (Grant nos 51105019 and 51575021)as well as the Technology Foundation Program of NationalDefense (Grant no Z132013B002)

References

[1] Z Ruixiang L Tingqi H Jianding and Y Dongchao ldquoFaultdiagnosis of airplane hydraulic pumprdquo in Proceedings of the4th World Congress on Intelligent Control and AutomationShanghai China June 2002

[2] T Zhang and N Zhang ldquoVibration modes and the dynamicbehaviour of a hydraulic plunger pumprdquo Shock and Vibrationvol 2016 Article ID 9679542 7 pages 2016

[3] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciencesThe Royal Society vol 454 no 1971 pp 903ndash995 1998

[4] T Han D Jiang and N Wang ldquoThe fault feature extractionof rolling bearing based on EMD and difference spectrum

of singular valuerdquo Shock and Vibration vol 2016 Article ID5957179 14 pages 2016

[5] M E TorresMA Colominas G Schlotthauer and P FlandrinldquoA complete ensemble empirical mode decomposition withadaptive noiserdquo in Proceedings of the 36th IEEE InternationalConference on Acoustics Speech and Signal Processing (ICASSPrsquo11) pp 4144ndash4147 IEEE Prague Czech Republic May 2011

[6] L Zhao W Yu and R Yan ldquoGearbox fault diagnosis usingcomplementary ensemble empirical mode decomposition andpermutation entropyrdquo Shock and Vibration vol 2016 Article ID3891429 8 pages 2016

[7] J Han and M van der Baan ldquoEmpirical mode decompositionfor seismic time-frequency analysisrdquo Geophysics vol 78 no 2pp O9ndashO19 2013

[8] E Mayoraz and E Alpaydin ldquoSupport vector machines formulti-class classificationrdquo in Engineering Applications of Bio-Inspired Artificial Neural Networks pp 833ndash842 SpringerBerlin Germany 1999

[9] J Yang Y Zhang and Y Zhu ldquoIntelligent fault diagnosis ofrolling element bearing based on SVMs and fractal dimensionrdquoMechanical Systems and Signal Processing vol 21 no 5 pp2012ndash2024 2007

[10] M A Colominas G Schlotthauer andM E Torres ldquoImprovedcomplete ensemble EMD a suitable tool for biomedical signalprocessingrdquo Biomedical Signal Processing and Control vol 14no 1 pp 19ndash29 2014

[11] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise-assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[12] J Li C Liu Z Zeng and L Chen ldquoGPR signal denoising andtarget extraction with the CEEMD methodrdquo IEEE Geoscienceand Remote Sensing Letters vol 12 no 8 pp 1615ndash1619 2015

[13] S H Nawab T F Quatieri and J S Lim ldquoSignal reconstructionfrom short-time fourier transform magnituderdquo IEEE Transac-tions on Acoustics Speech and Signal Processing vol 31 no 4pp 986ndash998 1983

[14] H K Kwok andD L Jones ldquoImproved instantaneous frequencyestimation using an adaptive short-time Fourier transformrdquoIEEE Transactions on Signal Processing vol 48 no 10 pp 2964ndash2972 2000

[15] L Mingliang W Keqi S Laijun and Z Jianju ldquoApplyingempiricalmode decomposition (EMD) and entropy to diagnosecircuit breaker faultsrdquo OptikmdashInternational Journal for Lightand Electron Optics vol 126 no 20 pp 2338ndash2342 2015

[16] X Zhang Y Liang J Zhou and Y Zang ldquoA novel bearing faultdiagnosis model integrated permutation entropy ensembleempirical mode decomposition and optimized SVMrdquoMeasure-ment vol 69 pp 164ndash179 2015

[17] D Yu Y Yang and J Cheng ldquoApplication of timendashfrequencyentropy method based on HilbertndashHuang transform to gearfault diagnosisrdquo Measurement vol 40 no 9-10 pp 823ndash8302007

[18] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

[19] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

[20] Z Cai Q Ding and M Wang ldquoStudy on automated incidentdetection algorithms based on PCA and SVM for freewayrdquo inProceedings of the International Conference on Optoelectronicsand Image Processing (ICOIP rsquo10) Haikou China November2010

[21] S Wold K Esbensen and P Geladi ldquoPrincipal componentanalysisrdquo Chemometrics and Intelligent Laboratory Systems vol2 no 1ndash3 pp 37ndash52 1987

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 5

Table 1 Six-dimensional fault features

Fault pattern No Feature 1 Feature 2 Feature 3 Feature 4 Feature 5 Feature 6

Normal

1 49681 39921 40155 36082 32670 265762 49732 39936 40145 36031 32395 26541sdot sdot sdot

20 47565 39406 41075 36274 33763 26567

Rotor wear

21 38933 42478 35822 37066 32937 2596622 38923 41903 35846 37407 32990 25675sdot sdot sdot

40 38991 39456 35417 36743 33190 25426

Swash plate wear

41 41123 34824 34975 36294 32926 2533242 41285 34886 35151 36196 33310 25820sdot sdot sdot

60 41782 34949 35132 35932 33496 26182

When testing is performed for the unknown sample 119909we construct all 119896(119896 minus 1)2 classifiers to realize the classdiscrimination andmake decisions using the following votingstrategy if sgn((120596119894119895 sdot 119909

119905) + 119887119894119895) 119909 is in the 119894th class then the

vote for the 119894th class is increased by one otherwise the 119895thclass is increased by one Finally we predict that 119909 is in theclass with the largest vote [20]

3 Experimental Verification

31 Experiment Setup The plunger pump test-rig is shownin Figure 3 from this test-rig the original vibration signalswere obtained to verify the proposed method The vibrationdata were obtained from the front side of the hydraulic pumpwith a stabilized motor speed of 528 rmin and a samplingrate of 1000Hz In this experiment two commonly occurringfaults were set swash plate wear and rotor wear Under threeconditions (two faulty conditions and the normal state) 20groups of samples (1024 sampling points for each group) wereselected for the analysis

32 Model for Fault Diagnosis of Hydraulic Pumps

321 Feature Extraction Based on the CEEMD-STFTand Time-Frequency Entropy

(1) CEEMD Model The parameters of the CEEMD modelwere set as follows the noise standard deviation (Nstd) was02 the Number of Realizations (NR) was 600 and themaximumnumber of sifting iterations allowed (MaxIter) was5000The original signals of each state were decomposed intoa series of IMFs the first six IMFs were selected for furtheranalysis as shown in Figure 4

(2) Procedure of the STFT and Time-Frequency EntropyAcquisitionThe parameters of STFT were selected as followsthe length of the window number of overlaps and samplingfrequency (fs) were 256 254 and 1000 respectively andthe length of the discrete Fourier transforms was equal to

Figure 3 Plunger pump test-rig

the window length Then the time-frequency matrices orspectrograms of each state were obtained in Figure 5

The time-frequency entropy of each state can be cal-culated based on the time-frequency matrices The time-frequency block was set as length = width = 64 and boththe lateral and longitudinal slip steps were 32 Then a six-dimensional time-frequency entropy was obtained for eachgroup which is one of the fault feature vectors All of the faultfeatures are listed in Table 1

(3) Feature Dimension Reduction Based on PCA To improvethe accuracy and robustness of the fault diagnosis dimensionreduction is necessary for the high dimensional fault featurevectors PCA which is an important and powerful methodsto extract the most significant information from data andcompress the size of the data [21] was used to acquire thethree-dimensional feature vectors in Table 2

The clustering result of the fault features is visuallydisplayed in Figure 6 which obviously shows a good perfor-mance of the hydraulic-pump fault mode classification

322 Fault Mode Classification Based on Multiclass SVMThe extracted fault feature sets were divided into trainingdata and testing data (the first ten groups were set as thetraining data and the remainder was set as the testing data forevery state) First the training multiclass SVM classifier was

6 Shock and Vibration

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

minus020

02

minus020

02

minus010

01

minus0050

005

minus010

01

04505

055

minus050

05

minus050

05

minus0050

005

minus0050

005

minus0020

002

minus0050

005

04505

055

minus050

05

minus0020

002

minus010

01

minus0020

002

minus0020

002

minus0020

002

046048

05

R(t)

minus050

05

R(t)

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

R(t)

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

Figure 4 First 6 IMFs of each state

Table 2 Feature vector set after dimension reduction

Fault pattern No Feature 1 Feature 2 Feature 3

Normal

1 41284 29741 564832 41327 29729 56553sdot sdot sdot

20 39954 29829 55353

Rotor wear

21 37289 20520 5258922 36789 20772 52629sdot sdot sdot

40 35266 21772 51467

Swash plate wear

41 32972 24613 5107842 33079 24822 51103sdot sdot sdot

60 33408 25041 51157

trained as previously proposed with the training data Thenthe trained classifier was used to classify the fault mode ofthe testing data and calculate the recognition accuracy Theclassification results of the testing data are shown in Table 3and Figure 7 These testing results verify that the recognition

performance is absolutely good and the multiclass SVMmethod is notably effective for mode classification

Combining the clustering figure and multiclass SVMclassification results the effectiveness and feasibility of thismethod for hydraulic-pump fault diagnosis were provenand a high classification performance was also obviouslyobtained

4 Conclusion

An effective method for the feature extraction and modeclassification of vibration signals has been performed in thispaper and this algorithm was successfully verified on practi-cal signals fromahydraulic pumpTheCEEMDmodel whichis an improvement of EMD and can solve the ldquomode mixingrdquoproblem was combined with the STFT analysis method andtime-frequency entropy calculation to extract the robust andsignificant fault feature Meanwhile the multiclass SVM clas-sifier was selected to process the small sample and multiple-fault situation and it obtained a perfect classification resultThen the accuracy and feasibility of this hydraulic-pumpfault diagnosis method were demonstrated Future work willconcentrate on the application of thismethod to other objectsor fields for signal analysis and fault diagnosis

Shock and Vibration 7

150 200 250 300 350

150 200 250 300 350

150 200 250 300 350

Freq

uenc

y (H

z)Fr

eque

ncy

(Hz)

Freq

uenc

y (H

z)

Time (ms)

Time (ms)

Time (ms)

minus40

minus60

minus80

minus100

minus120

minus140

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

050

100150200250300350400450500

050

100150200250300350400450500

050

100150200250300350400450500

minus100minus90minus80minus70minus60minus50minus40

minus100minus90minus80minus70minus60minus50minus40minus30minus20

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

Figure 5 Spectrograms of the first IMF of each state

Table 3 Classification results of the testing data

Fault pattern Actual label Index No Feature 1 Feature 2 Feature 3 Predicted label

Normal 1

1 11 40906 29178 55591 12 12 40961 29253 55036 1sdot sdot sdot sdot sdot sdot 110 20 39954 29829 55353 1

Rotor wear 2

11 31 37442 20107 51790 212 32 36416 21110 51027 2sdot sdot sdot sdot sdot sdot 220 40 35266 21772 51467 2

Swash plate wear 3

21 51 33093 25163 51968 322 52 33018 24982 52170 3sdot sdot sdot sdot sdot sdot 330 60 33408 25041 51157 3

8 Shock and Vibration

42414393837361st PC35343332182222nd PC

242628332

NormalRotor wear

Swash plate wear

5152535455565758

3rd

PC

Figure 6 Clustering result of the fault features

Index

Diagnosis results

Predicted labelsGround truth labels

1

2

3

Labe

l

1 2 3 4 5 6 7 8 910

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Figure 7 Classification results of the testing data

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This study was supported by the National Natural ScienceFoundation of China (Grant nos 51105019 and 51575021)as well as the Technology Foundation Program of NationalDefense (Grant no Z132013B002)

References

[1] Z Ruixiang L Tingqi H Jianding and Y Dongchao ldquoFaultdiagnosis of airplane hydraulic pumprdquo in Proceedings of the4th World Congress on Intelligent Control and AutomationShanghai China June 2002

[2] T Zhang and N Zhang ldquoVibration modes and the dynamicbehaviour of a hydraulic plunger pumprdquo Shock and Vibrationvol 2016 Article ID 9679542 7 pages 2016

[3] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciencesThe Royal Society vol 454 no 1971 pp 903ndash995 1998

[4] T Han D Jiang and N Wang ldquoThe fault feature extractionof rolling bearing based on EMD and difference spectrum

of singular valuerdquo Shock and Vibration vol 2016 Article ID5957179 14 pages 2016

[5] M E TorresMA Colominas G Schlotthauer and P FlandrinldquoA complete ensemble empirical mode decomposition withadaptive noiserdquo in Proceedings of the 36th IEEE InternationalConference on Acoustics Speech and Signal Processing (ICASSPrsquo11) pp 4144ndash4147 IEEE Prague Czech Republic May 2011

[6] L Zhao W Yu and R Yan ldquoGearbox fault diagnosis usingcomplementary ensemble empirical mode decomposition andpermutation entropyrdquo Shock and Vibration vol 2016 Article ID3891429 8 pages 2016

[7] J Han and M van der Baan ldquoEmpirical mode decompositionfor seismic time-frequency analysisrdquo Geophysics vol 78 no 2pp O9ndashO19 2013

[8] E Mayoraz and E Alpaydin ldquoSupport vector machines formulti-class classificationrdquo in Engineering Applications of Bio-Inspired Artificial Neural Networks pp 833ndash842 SpringerBerlin Germany 1999

[9] J Yang Y Zhang and Y Zhu ldquoIntelligent fault diagnosis ofrolling element bearing based on SVMs and fractal dimensionrdquoMechanical Systems and Signal Processing vol 21 no 5 pp2012ndash2024 2007

[10] M A Colominas G Schlotthauer andM E Torres ldquoImprovedcomplete ensemble EMD a suitable tool for biomedical signalprocessingrdquo Biomedical Signal Processing and Control vol 14no 1 pp 19ndash29 2014

[11] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise-assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[12] J Li C Liu Z Zeng and L Chen ldquoGPR signal denoising andtarget extraction with the CEEMD methodrdquo IEEE Geoscienceand Remote Sensing Letters vol 12 no 8 pp 1615ndash1619 2015

[13] S H Nawab T F Quatieri and J S Lim ldquoSignal reconstructionfrom short-time fourier transform magnituderdquo IEEE Transac-tions on Acoustics Speech and Signal Processing vol 31 no 4pp 986ndash998 1983

[14] H K Kwok andD L Jones ldquoImproved instantaneous frequencyestimation using an adaptive short-time Fourier transformrdquoIEEE Transactions on Signal Processing vol 48 no 10 pp 2964ndash2972 2000

[15] L Mingliang W Keqi S Laijun and Z Jianju ldquoApplyingempiricalmode decomposition (EMD) and entropy to diagnosecircuit breaker faultsrdquo OptikmdashInternational Journal for Lightand Electron Optics vol 126 no 20 pp 2338ndash2342 2015

[16] X Zhang Y Liang J Zhou and Y Zang ldquoA novel bearing faultdiagnosis model integrated permutation entropy ensembleempirical mode decomposition and optimized SVMrdquoMeasure-ment vol 69 pp 164ndash179 2015

[17] D Yu Y Yang and J Cheng ldquoApplication of timendashfrequencyentropy method based on HilbertndashHuang transform to gearfault diagnosisrdquo Measurement vol 40 no 9-10 pp 823ndash8302007

[18] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

[19] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

[20] Z Cai Q Ding and M Wang ldquoStudy on automated incidentdetection algorithms based on PCA and SVM for freewayrdquo inProceedings of the International Conference on Optoelectronicsand Image Processing (ICOIP rsquo10) Haikou China November2010

[21] S Wold K Esbensen and P Geladi ldquoPrincipal componentanalysisrdquo Chemometrics and Intelligent Laboratory Systems vol2 no 1ndash3 pp 37ndash52 1987

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Shock and Vibration

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

minus020

02

minus020

02

minus010

01

minus0050

005

minus010

01

04505

055

minus050

05

minus050

05

minus0050

005

minus0050

005

minus0020

002

minus0050

005

04505

055

minus050

05

minus0020

002

minus010

01

minus0020

002

minus0020

002

minus0020

002

046048

05

R(t)

minus050

05

R(t)

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

0 50 100 150 200 250 300 350 400 450 500

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

R(t)

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

IMF1

IMF2

IMF3

IMF4

IMF5

IMF6

Figure 4 First 6 IMFs of each state

Table 2 Feature vector set after dimension reduction

Fault pattern No Feature 1 Feature 2 Feature 3

Normal

1 41284 29741 564832 41327 29729 56553sdot sdot sdot

20 39954 29829 55353

Rotor wear

21 37289 20520 5258922 36789 20772 52629sdot sdot sdot

40 35266 21772 51467

Swash plate wear

41 32972 24613 5107842 33079 24822 51103sdot sdot sdot

60 33408 25041 51157

trained as previously proposed with the training data Thenthe trained classifier was used to classify the fault mode ofthe testing data and calculate the recognition accuracy Theclassification results of the testing data are shown in Table 3and Figure 7 These testing results verify that the recognition

performance is absolutely good and the multiclass SVMmethod is notably effective for mode classification

Combining the clustering figure and multiclass SVMclassification results the effectiveness and feasibility of thismethod for hydraulic-pump fault diagnosis were provenand a high classification performance was also obviouslyobtained

4 Conclusion

An effective method for the feature extraction and modeclassification of vibration signals has been performed in thispaper and this algorithm was successfully verified on practi-cal signals fromahydraulic pumpTheCEEMDmodel whichis an improvement of EMD and can solve the ldquomode mixingrdquoproblem was combined with the STFT analysis method andtime-frequency entropy calculation to extract the robust andsignificant fault feature Meanwhile the multiclass SVM clas-sifier was selected to process the small sample and multiple-fault situation and it obtained a perfect classification resultThen the accuracy and feasibility of this hydraulic-pumpfault diagnosis method were demonstrated Future work willconcentrate on the application of thismethod to other objectsor fields for signal analysis and fault diagnosis

Shock and Vibration 7

150 200 250 300 350

150 200 250 300 350

150 200 250 300 350

Freq

uenc

y (H

z)Fr

eque

ncy

(Hz)

Freq

uenc

y (H

z)

Time (ms)

Time (ms)

Time (ms)

minus40

minus60

minus80

minus100

minus120

minus140

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

050

100150200250300350400450500

050

100150200250300350400450500

050

100150200250300350400450500

minus100minus90minus80minus70minus60minus50minus40

minus100minus90minus80minus70minus60minus50minus40minus30minus20

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

Figure 5 Spectrograms of the first IMF of each state

Table 3 Classification results of the testing data

Fault pattern Actual label Index No Feature 1 Feature 2 Feature 3 Predicted label

Normal 1

1 11 40906 29178 55591 12 12 40961 29253 55036 1sdot sdot sdot sdot sdot sdot 110 20 39954 29829 55353 1

Rotor wear 2

11 31 37442 20107 51790 212 32 36416 21110 51027 2sdot sdot sdot sdot sdot sdot 220 40 35266 21772 51467 2

Swash plate wear 3

21 51 33093 25163 51968 322 52 33018 24982 52170 3sdot sdot sdot sdot sdot sdot 330 60 33408 25041 51157 3

8 Shock and Vibration

42414393837361st PC35343332182222nd PC

242628332

NormalRotor wear

Swash plate wear

5152535455565758

3rd

PC

Figure 6 Clustering result of the fault features

Index

Diagnosis results

Predicted labelsGround truth labels

1

2

3

Labe

l

1 2 3 4 5 6 7 8 910

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Figure 7 Classification results of the testing data

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This study was supported by the National Natural ScienceFoundation of China (Grant nos 51105019 and 51575021)as well as the Technology Foundation Program of NationalDefense (Grant no Z132013B002)

References

[1] Z Ruixiang L Tingqi H Jianding and Y Dongchao ldquoFaultdiagnosis of airplane hydraulic pumprdquo in Proceedings of the4th World Congress on Intelligent Control and AutomationShanghai China June 2002

[2] T Zhang and N Zhang ldquoVibration modes and the dynamicbehaviour of a hydraulic plunger pumprdquo Shock and Vibrationvol 2016 Article ID 9679542 7 pages 2016

[3] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciencesThe Royal Society vol 454 no 1971 pp 903ndash995 1998

[4] T Han D Jiang and N Wang ldquoThe fault feature extractionof rolling bearing based on EMD and difference spectrum

of singular valuerdquo Shock and Vibration vol 2016 Article ID5957179 14 pages 2016

[5] M E TorresMA Colominas G Schlotthauer and P FlandrinldquoA complete ensemble empirical mode decomposition withadaptive noiserdquo in Proceedings of the 36th IEEE InternationalConference on Acoustics Speech and Signal Processing (ICASSPrsquo11) pp 4144ndash4147 IEEE Prague Czech Republic May 2011

[6] L Zhao W Yu and R Yan ldquoGearbox fault diagnosis usingcomplementary ensemble empirical mode decomposition andpermutation entropyrdquo Shock and Vibration vol 2016 Article ID3891429 8 pages 2016

[7] J Han and M van der Baan ldquoEmpirical mode decompositionfor seismic time-frequency analysisrdquo Geophysics vol 78 no 2pp O9ndashO19 2013

[8] E Mayoraz and E Alpaydin ldquoSupport vector machines formulti-class classificationrdquo in Engineering Applications of Bio-Inspired Artificial Neural Networks pp 833ndash842 SpringerBerlin Germany 1999

[9] J Yang Y Zhang and Y Zhu ldquoIntelligent fault diagnosis ofrolling element bearing based on SVMs and fractal dimensionrdquoMechanical Systems and Signal Processing vol 21 no 5 pp2012ndash2024 2007

[10] M A Colominas G Schlotthauer andM E Torres ldquoImprovedcomplete ensemble EMD a suitable tool for biomedical signalprocessingrdquo Biomedical Signal Processing and Control vol 14no 1 pp 19ndash29 2014

[11] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise-assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[12] J Li C Liu Z Zeng and L Chen ldquoGPR signal denoising andtarget extraction with the CEEMD methodrdquo IEEE Geoscienceand Remote Sensing Letters vol 12 no 8 pp 1615ndash1619 2015

[13] S H Nawab T F Quatieri and J S Lim ldquoSignal reconstructionfrom short-time fourier transform magnituderdquo IEEE Transac-tions on Acoustics Speech and Signal Processing vol 31 no 4pp 986ndash998 1983

[14] H K Kwok andD L Jones ldquoImproved instantaneous frequencyestimation using an adaptive short-time Fourier transformrdquoIEEE Transactions on Signal Processing vol 48 no 10 pp 2964ndash2972 2000

[15] L Mingliang W Keqi S Laijun and Z Jianju ldquoApplyingempiricalmode decomposition (EMD) and entropy to diagnosecircuit breaker faultsrdquo OptikmdashInternational Journal for Lightand Electron Optics vol 126 no 20 pp 2338ndash2342 2015

[16] X Zhang Y Liang J Zhou and Y Zang ldquoA novel bearing faultdiagnosis model integrated permutation entropy ensembleempirical mode decomposition and optimized SVMrdquoMeasure-ment vol 69 pp 164ndash179 2015

[17] D Yu Y Yang and J Cheng ldquoApplication of timendashfrequencyentropy method based on HilbertndashHuang transform to gearfault diagnosisrdquo Measurement vol 40 no 9-10 pp 823ndash8302007

[18] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

[19] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

[20] Z Cai Q Ding and M Wang ldquoStudy on automated incidentdetection algorithms based on PCA and SVM for freewayrdquo inProceedings of the International Conference on Optoelectronicsand Image Processing (ICOIP rsquo10) Haikou China November2010

[21] S Wold K Esbensen and P Geladi ldquoPrincipal componentanalysisrdquo Chemometrics and Intelligent Laboratory Systems vol2 no 1ndash3 pp 37ndash52 1987

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Shock and Vibration 7

150 200 250 300 350

150 200 250 300 350

150 200 250 300 350

Freq

uenc

y (H

z)Fr

eque

ncy

(Hz)

Freq

uenc

y (H

z)

Time (ms)

Time (ms)

Time (ms)

minus40

minus60

minus80

minus100

minus120

minus140

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

Pow

erfr

eque

ncy

(dB

Hz)

050

100150200250300350400450500

050

100150200250300350400450500

050

100150200250300350400450500

minus100minus90minus80minus70minus60minus50minus40

minus100minus90minus80minus70minus60minus50minus40minus30minus20

(1) State 1 normal

(3) State 3 swash plate wear

(2) State 2 rotor wear

Figure 5 Spectrograms of the first IMF of each state

Table 3 Classification results of the testing data

Fault pattern Actual label Index No Feature 1 Feature 2 Feature 3 Predicted label

Normal 1

1 11 40906 29178 55591 12 12 40961 29253 55036 1sdot sdot sdot sdot sdot sdot 110 20 39954 29829 55353 1

Rotor wear 2

11 31 37442 20107 51790 212 32 36416 21110 51027 2sdot sdot sdot sdot sdot sdot 220 40 35266 21772 51467 2

Swash plate wear 3

21 51 33093 25163 51968 322 52 33018 24982 52170 3sdot sdot sdot sdot sdot sdot 330 60 33408 25041 51157 3

8 Shock and Vibration

42414393837361st PC35343332182222nd PC

242628332

NormalRotor wear

Swash plate wear

5152535455565758

3rd

PC

Figure 6 Clustering result of the fault features

Index

Diagnosis results

Predicted labelsGround truth labels

1

2

3

Labe

l

1 2 3 4 5 6 7 8 910

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Figure 7 Classification results of the testing data

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This study was supported by the National Natural ScienceFoundation of China (Grant nos 51105019 and 51575021)as well as the Technology Foundation Program of NationalDefense (Grant no Z132013B002)

References

[1] Z Ruixiang L Tingqi H Jianding and Y Dongchao ldquoFaultdiagnosis of airplane hydraulic pumprdquo in Proceedings of the4th World Congress on Intelligent Control and AutomationShanghai China June 2002

[2] T Zhang and N Zhang ldquoVibration modes and the dynamicbehaviour of a hydraulic plunger pumprdquo Shock and Vibrationvol 2016 Article ID 9679542 7 pages 2016

[3] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciencesThe Royal Society vol 454 no 1971 pp 903ndash995 1998

[4] T Han D Jiang and N Wang ldquoThe fault feature extractionof rolling bearing based on EMD and difference spectrum

of singular valuerdquo Shock and Vibration vol 2016 Article ID5957179 14 pages 2016

[5] M E TorresMA Colominas G Schlotthauer and P FlandrinldquoA complete ensemble empirical mode decomposition withadaptive noiserdquo in Proceedings of the 36th IEEE InternationalConference on Acoustics Speech and Signal Processing (ICASSPrsquo11) pp 4144ndash4147 IEEE Prague Czech Republic May 2011

[6] L Zhao W Yu and R Yan ldquoGearbox fault diagnosis usingcomplementary ensemble empirical mode decomposition andpermutation entropyrdquo Shock and Vibration vol 2016 Article ID3891429 8 pages 2016

[7] J Han and M van der Baan ldquoEmpirical mode decompositionfor seismic time-frequency analysisrdquo Geophysics vol 78 no 2pp O9ndashO19 2013

[8] E Mayoraz and E Alpaydin ldquoSupport vector machines formulti-class classificationrdquo in Engineering Applications of Bio-Inspired Artificial Neural Networks pp 833ndash842 SpringerBerlin Germany 1999

[9] J Yang Y Zhang and Y Zhu ldquoIntelligent fault diagnosis ofrolling element bearing based on SVMs and fractal dimensionrdquoMechanical Systems and Signal Processing vol 21 no 5 pp2012ndash2024 2007

[10] M A Colominas G Schlotthauer andM E Torres ldquoImprovedcomplete ensemble EMD a suitable tool for biomedical signalprocessingrdquo Biomedical Signal Processing and Control vol 14no 1 pp 19ndash29 2014

[11] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise-assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[12] J Li C Liu Z Zeng and L Chen ldquoGPR signal denoising andtarget extraction with the CEEMD methodrdquo IEEE Geoscienceand Remote Sensing Letters vol 12 no 8 pp 1615ndash1619 2015

[13] S H Nawab T F Quatieri and J S Lim ldquoSignal reconstructionfrom short-time fourier transform magnituderdquo IEEE Transac-tions on Acoustics Speech and Signal Processing vol 31 no 4pp 986ndash998 1983

[14] H K Kwok andD L Jones ldquoImproved instantaneous frequencyestimation using an adaptive short-time Fourier transformrdquoIEEE Transactions on Signal Processing vol 48 no 10 pp 2964ndash2972 2000

[15] L Mingliang W Keqi S Laijun and Z Jianju ldquoApplyingempiricalmode decomposition (EMD) and entropy to diagnosecircuit breaker faultsrdquo OptikmdashInternational Journal for Lightand Electron Optics vol 126 no 20 pp 2338ndash2342 2015

[16] X Zhang Y Liang J Zhou and Y Zang ldquoA novel bearing faultdiagnosis model integrated permutation entropy ensembleempirical mode decomposition and optimized SVMrdquoMeasure-ment vol 69 pp 164ndash179 2015

[17] D Yu Y Yang and J Cheng ldquoApplication of timendashfrequencyentropy method based on HilbertndashHuang transform to gearfault diagnosisrdquo Measurement vol 40 no 9-10 pp 823ndash8302007

[18] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

[19] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

[20] Z Cai Q Ding and M Wang ldquoStudy on automated incidentdetection algorithms based on PCA and SVM for freewayrdquo inProceedings of the International Conference on Optoelectronicsand Image Processing (ICOIP rsquo10) Haikou China November2010

[21] S Wold K Esbensen and P Geladi ldquoPrincipal componentanalysisrdquo Chemometrics and Intelligent Laboratory Systems vol2 no 1ndash3 pp 37ndash52 1987

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Shock and Vibration

42414393837361st PC35343332182222nd PC

242628332

NormalRotor wear

Swash plate wear

5152535455565758

3rd

PC

Figure 6 Clustering result of the fault features

Index

Diagnosis results

Predicted labelsGround truth labels

1

2

3

Labe

l

1 2 3 4 5 6 7 8 910

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Figure 7 Classification results of the testing data

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This study was supported by the National Natural ScienceFoundation of China (Grant nos 51105019 and 51575021)as well as the Technology Foundation Program of NationalDefense (Grant no Z132013B002)

References

[1] Z Ruixiang L Tingqi H Jianding and Y Dongchao ldquoFaultdiagnosis of airplane hydraulic pumprdquo in Proceedings of the4th World Congress on Intelligent Control and AutomationShanghai China June 2002

[2] T Zhang and N Zhang ldquoVibration modes and the dynamicbehaviour of a hydraulic plunger pumprdquo Shock and Vibrationvol 2016 Article ID 9679542 7 pages 2016

[3] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo Proceedings of the RoyalSociety of London A Mathematical Physical and EngineeringSciencesThe Royal Society vol 454 no 1971 pp 903ndash995 1998

[4] T Han D Jiang and N Wang ldquoThe fault feature extractionof rolling bearing based on EMD and difference spectrum

of singular valuerdquo Shock and Vibration vol 2016 Article ID5957179 14 pages 2016

[5] M E TorresMA Colominas G Schlotthauer and P FlandrinldquoA complete ensemble empirical mode decomposition withadaptive noiserdquo in Proceedings of the 36th IEEE InternationalConference on Acoustics Speech and Signal Processing (ICASSPrsquo11) pp 4144ndash4147 IEEE Prague Czech Republic May 2011

[6] L Zhao W Yu and R Yan ldquoGearbox fault diagnosis usingcomplementary ensemble empirical mode decomposition andpermutation entropyrdquo Shock and Vibration vol 2016 Article ID3891429 8 pages 2016

[7] J Han and M van der Baan ldquoEmpirical mode decompositionfor seismic time-frequency analysisrdquo Geophysics vol 78 no 2pp O9ndashO19 2013

[8] E Mayoraz and E Alpaydin ldquoSupport vector machines formulti-class classificationrdquo in Engineering Applications of Bio-Inspired Artificial Neural Networks pp 833ndash842 SpringerBerlin Germany 1999

[9] J Yang Y Zhang and Y Zhu ldquoIntelligent fault diagnosis ofrolling element bearing based on SVMs and fractal dimensionrdquoMechanical Systems and Signal Processing vol 21 no 5 pp2012ndash2024 2007

[10] M A Colominas G Schlotthauer andM E Torres ldquoImprovedcomplete ensemble EMD a suitable tool for biomedical signalprocessingrdquo Biomedical Signal Processing and Control vol 14no 1 pp 19ndash29 2014

[11] Z Wu and N E Huang ldquoEnsemble empirical mode decom-position a noise-assisted data analysis methodrdquo Advances inAdaptive Data Analysis vol 1 no 1 pp 1ndash41 2009

[12] J Li C Liu Z Zeng and L Chen ldquoGPR signal denoising andtarget extraction with the CEEMD methodrdquo IEEE Geoscienceand Remote Sensing Letters vol 12 no 8 pp 1615ndash1619 2015

[13] S H Nawab T F Quatieri and J S Lim ldquoSignal reconstructionfrom short-time fourier transform magnituderdquo IEEE Transac-tions on Acoustics Speech and Signal Processing vol 31 no 4pp 986ndash998 1983

[14] H K Kwok andD L Jones ldquoImproved instantaneous frequencyestimation using an adaptive short-time Fourier transformrdquoIEEE Transactions on Signal Processing vol 48 no 10 pp 2964ndash2972 2000

[15] L Mingliang W Keqi S Laijun and Z Jianju ldquoApplyingempiricalmode decomposition (EMD) and entropy to diagnosecircuit breaker faultsrdquo OptikmdashInternational Journal for Lightand Electron Optics vol 126 no 20 pp 2338ndash2342 2015

[16] X Zhang Y Liang J Zhou and Y Zang ldquoA novel bearing faultdiagnosis model integrated permutation entropy ensembleempirical mode decomposition and optimized SVMrdquoMeasure-ment vol 69 pp 164ndash179 2015

[17] D Yu Y Yang and J Cheng ldquoApplication of timendashfrequencyentropy method based on HilbertndashHuang transform to gearfault diagnosisrdquo Measurement vol 40 no 9-10 pp 823ndash8302007

[18] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

[19] C-W Hsu and C-J Lin ldquoA comparison of methods for mul-ticlass support vector machinesrdquo IEEE Transactions on NeuralNetworks vol 13 no 2 pp 415ndash425 2002

[20] Z Cai Q Ding and M Wang ldquoStudy on automated incidentdetection algorithms based on PCA and SVM for freewayrdquo inProceedings of the International Conference on Optoelectronicsand Image Processing (ICOIP rsquo10) Haikou China November2010

[21] S Wold K Esbensen and P Geladi ldquoPrincipal componentanalysisrdquo Chemometrics and Intelligent Laboratory Systems vol2 no 1ndash3 pp 37ndash52 1987

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of