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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
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Shock and Vibration
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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
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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
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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
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Navigation and Observation
International Journal of
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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
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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
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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
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