Research ArticlePower Transformer Partial Discharge Fault DiagnosisBased on Multidimensional Feature Region

Rong Jia1 Yongtao Xie1 Hua Wu1 Jian Dang1 and Kaisong Dong2

1Xirsquoan University of Technology Xirsquoan Shaanxi 710048 China2State Grid Gansu Province Electric Power Research Institute Gansu 730000 China

Correspondence should be addressed to Yongtao Xie 18792511340163com

Received 16 March 2016 Revised 7 June 2016 Accepted 3 July 2016

Academic Editor Wenyu Zhao

Copyright copy 2016 Rong Jia et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Effectively extracting power transformer partial discharge (PD) signals feature is of great significance for monitoring powertransformer insulation condition However there has been lack of practical and effective extraction methods For this reasonthis paper suggests a novel method for the PD signal feature extraction based on multidimensional feature region Firstly in orderto better describe differences in each frequency band of fault signals empirical mode decomposition (EMD) and Hilbert-Huangtransform (HHT) band-pass filter wave for raw signal is carried out And the component of raw signals on each frequency bandcan be obtained Secondly the sample entropy value and the energy value of each frequency band component are calculated Usingthe difference of each frequency band energy and complexity signals feature region is established by the multidimensional energyparameters and the multidimensional sample entropy parameters to describe PD signals multidimensional feature informationFinally partial discharge faults are classified by sphere-structured support vector machines algorithmThe result indicates that thismethod is able to identify and classify different partial discharge faults

1 Introduction

Power transformer is one of the most critical and expensiveelectrical pieces of equipment in power system whose safetyand reliability are closely related to the operation conditionof the whole system Furthermore in the process of actualoperation power transformer is unavoidable to subject tosuch outside factor influence as electricity machinery andheat and so forth further causing its winding insulationdeterioration to produce partial discharge (PD) phenomenathreatening the safety of operation of the whole systemTherefore it is essential to monitor the insulation conditionand provide a proper maintenance action for in-servicepower transformers [1ndash3] A CIGRE international surveyindicates that most of power transformers life is 30 years orso [4] However the majority of currently in-service powertransformers were installed prior to 1980 and as a result thebulk of the population is approaching or has already exceededits design life [5 6] which leads to a significant risk for power

system stakeholders Consequently monitoring and diagnos-tic techniques are of important significance for improvingoperational reliability of the in-service power transformers

At present variousmonitoring and diagnostic techniqueshave been adopted for power transformers such as visualinspection infrared scanning tan 120575 measurement PD mea-surement and oilmeteorologic chromatogram analysis [7 8]Among them PD measurement is considered as an effectivediagnostic tool to assess and monitor insulation conditionfor in-service power transformers PD is a type of slightfailure that does not usually lead to serious insulation damagebefore electrical tree occurs Therefore it is very critical forstakeholders to determine the insulation quality if PD activitycan be detected in its early stage

Accordingly this paper proposes a newmethod for powertransformer partial discharge fault diagnosis And this papercontent is arranged as such Section 2 summarizes relatedbackground information about how PD fault is diagnosedand states current challenges of PD signals feature extraction

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 4835694 11 pageshttpdxdoiorg10115520164835694

2 Mathematical Problems in Engineering

and diagnosis In Sections 3 and 4 this paper establishesa new feature extraction method to describe and classifydifferent PD patterns The sphere-structured support vectormachine algorithm is adopted to diagnose different partialdischarge faults in Section 5 The case study is presented inSection 6

2 Overview of PD Fault Diagnosis

Transformer PD signal is of strong nonlinearity and time-variation And in the in situ detection it is frequentlysubject to the overlap of many interference signals [9 10]Statistics [11] indicate that major interference signals are dis-crete spectral interferences stochastic shaped interferencesand periodic pulse shaped interferences which leads greatdifficulties to signals feature extraction and fault diagnosisTherefore how to accurately extract signals feature is the keyto PD faults identification

Up to now feature extraction methods mainly concen-trate on the analysis of statistic graphic spectrum and waveshapes [12 13] Among them methods based on statisticgraphic spectrum analysis require the high sampling rate anda large number of samples so it is unfavorable for onlinedetection of insulation whereas methods based on waveshape analysis require the low quantity of data samples Soit used to extract the time-variant signal feature whose mainmethods are time-frequency analysis Hilbert-Huang trans-form (HHT) wavelet theory fractal theory Chaos theoryand so forth [14ndash16] Frequency and time features are impor-tant character for signals Those can be obtained by usingfast Fourier transform algorithm (FFT) or short time Fouriertransform algorithm (STFT) However both FFT and STFTare not suitable for time-variation signals Because HHT hasbetter self-adaptability it is suitable for analyzing the partialdynamic feature of nonsmooth signals such as literatures [17]and [18] But HHT requires a priori knowledge about thesensitive frequency bands of fault signals Moreover there arethe end effects and themodemixing in HHT It is pointed outin literatures [19ndash21] that the frequency spectrum enveloptime-frequency energy entropy information and so forth areable to depict the features of nonstable time-varying signalsbut in practical use they are easy to be subjected to noiseinterference so that the effects are unrealistic

Unlike classical time-frequency analysis methods usinga series of sinusoidal functions to describe a signal wavelettransform decomposes a signal into wavelet coefficients ofvarious time scales And it is considered as one of the mostpowerful techniques for faults signal denoising and extractingtransient feature [22 23] For example the feature extrac-tion of PD signals is achieved based on the cross-wavelettransform and relevant coefficient matrix in literature [24]Unfortunately how to determine an optimal mother waveletis a big challenge for faults signal feature extraction In litera-ture [25ndash27] the fractal theory is successfully used to extractthe feature of GIS PD signals However how to select fractalelement shapes is unclear and fractal theory is still immature

Because different insulation defect faults have differentpartial discharge principle and there are strong randomnessand dispersion in its phase distribution feature frequencyand pulse magnitude those classical feature extractionmeth-ods are not well suitable for online PD faults diagnosisMoreover the same insulation defect fault has some similar-ities on its frequency spectrum envelop and the frequencyband energy distribution whose features have an obviousprobability distribution in certain frequency band So thisfrequency band can describe different faults signal featureThe magnitude of energy and the complexity of frequencycomponents are two different parameters which can repre-sent one frequency band from different angles And literature[28] points out that sample entropy value magnitude canreflect the complexity of the system Therefore this paperuses sample entropy and energy to establish one feature planeto describe the essential feature information of the fault Sothis paper proposes a new method for power transformerPD signal feature extraction and fault diagnosis based onmultidimensional feature region Firstly in order to obtaincomponents of raw signal on different frequency bands EMDand HHT band-pass filter wave for PD signal is carried outSecondly the sample entropy value and the energy value ofeach frequency band component are calculated And then thefeature region is established by using the sample entropy valueand the energy value of each frequency band componentto describe multidimensional features of PD signal Finallypartial discharge faults are classified by sphere-structuredsupport vector machines algorithm

3 Frequency Band Component Extraction

In order to better describe differences in each frequency bandof fault signals the frequency band component of raw signalshould be extracted Now EMDandHHTband-pass filter areused to extract frequency band component

31 EMD EMD is served as a kind of self-adaptive decompo-sition algorithm without obtaining a priori knowledge of rawsignals in advance And it avoids the optimum base functionselection problem of wavelet decomposition [29] the decom-position process of any signals 119904(119905) is shown in Figure 1

Analog signals given in literature [30] are shown inFigure 2 Taking these analog signals as the example theanalysis is carried out In the literature single exponentattenuation signal is shown as in formula (1) and singleexponent vibration signal is shown as in formula (2)

1199041(119905) = 119860119890

minus119905120591 (1)

1199042(119905) = 119860119890

minus119905120591 sin (2120587119891119888119905) (2)

It can be known from Figure 3 that after two types ofsignals are decomposed by EMD 7-order intrinsic modefunction (IMF) components (imf1 imf2 imf7) and 1residual component (res) are obtained Then Hilbert time-frequency distribution of the 2nd-order IMF component iscalculated The result is shown in Figure 4

Mathematical Problems in Engineering 3

Yes

No

Yes

Ending

No

Extracting signal details markingd(t) = s(t) minus m(t)

Letting s(t) = mi(t)

Letting s(t) = d(t)

Marking di(t) = d(t)

Letting mi(t) = s(t) minus di(t)

monotoneis

very smallfunction or mi(t) is

Judging whethermi(t)

whether to satisfy IMF two conditions or

not

Judging d(t)

m(t) =emax(t) + emin(t)

2

Calculating average value m(t) of the upper and lower envelopes

To seek for all the maximum and minimum value points and then bycubic spline interpolation to obtain upper and lower envelope

emax(t) and emin(t) of original signal

Signals s(t)

Figure 1 The algorithm flow process of EMD

It can be known from Figure 4 that the 2nd-order IMFfrequency band of single exponent attenuation PD signalsis 38ndash46MHz while the 2nd-order IMF frequency bandof single exponent vibration PD signals is 22ndash42MHzAccordingly the frequency band range of the same order IMFdecomposed by different signals is different

32 Extract Different Frequency Band Components of RawSignal The order of IMF obtained from PD signals throughEMD decomposition is closely related to partial dischargetype And even if they are at the same order of IMF theirfrequency band still has the obvious differences

Aiming at this phenomenon it is here that HHT bandpassing filter is adopted to solve the problem The concreteprocedures are as follows

(1) Sampling frequency of signals 119904(119905) is 119865119904 The numberof sampling points is 119899 After EMD decompositionthe 119898 pieces of IMF components are obtainedThe magnitude of each component Hilbert time-frequency spectrum is 119898 times 119899 which should be

classified as 119897 frequency bands and the set of instantamplitude values on the 119896 frequency band can bemarked as 119867(119896) (119896 = 1 2 119897)

(2) Zero set all the instant amplitude values on theHilberttime-frequency spectrum except for frequency band119896 and mark as 119867

lowast(119896)

(3) Zero set the IMF component point values which iscorresponding to the instant amplitude value beingset as zero in 119867

lowast(119896)

(4) Each IMF component treated using the filter can bereconstructed to obtain signals 119904(119905) component on thefrequency band

(5) As to the rest of frequency bands the above proce-dures are repeatedThat is signals 119904(119905) component onthe different frequency bands should be obtained

Signals 119904(119905) are treated through HHT band passing filterin order to obtain 119897 components Andmatrix119860 is constructed

4 Mathematical Problems in Engineering

Signal 1

Signal 2

times10minus3

times10minus3

01 02 03 04 05 06 07 08 09 10t (s)

minus02

0

02

04

06

Am

plitu

de (m

V)

minus02

minus01

0010203

Am

plitu

de (m

V)

01 02 03 04 05 06 07 08 09 10t (s)

Figure 2 The analog signals of PD

using 119897 components In other words matrix 119860 can cover theinformation of signal 119904(119905) under each frequency band

119860 =

[[[[[[[[

[

11988611

11988612

sdot sdot sdot 1198861119899

11988621

11988622

sdot sdot sdot 1198862119899

sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot

1198861198971

1198861198972

sdot sdot sdot 119886119897119899

]]]]]]]]

]

(3)

where 119886119894119895represents raw signals 119904(119905) data on each frequency

band

4 PD Signals Feature Region

41 Multidimensional Energy Parameters Different insula-tion defect faults have different partial discharge principleAnd their discharge pulse has obvious difference on the waveshape and the frequency band energy distribution while thesame insulation defect fault has strong similarity on the waveshape and the frequency band energy distribution [31] Forthis reason this paper suggests that multidimensional energyparameter is used to describe PD signals feature quantityThecalculation process of multidimensional energy parameter isgiven as follows

(1) Each row datum of time-frequency matrix 119860 ldquo1198861198941 1198861198942

119886119894119899rdquo stands for an independent frequency band

being marked as ldquo119883119896 119896 = 1 2 119897rdquo

(2) Energy value 119864(119896) of each frequency band is calcu-lated And then the normalization of 119864(119896) is carriedout

119864 (119896) = sum

119894=1119899

119883119896(119894)2

119864lowast(119896) =

119864 (119896)

sum119896=1119897

119864 (119896)

(4)

The multidimensional energy parameters of PD signalsobtained from the above steps are marked as 119864 = [119864

lowast

1 119864lowast

2

119864lowast

119897]

42 Multidimensional Sample Entropy Parameters Sampleentropy algorithm is a kind of theory originating fromnonlinear dynamics [28] whose value magnitude can reflectthe complexity of the system It is likely to provide a kind offresh solution for the nonstable signals analysis

Sample entropy of each row datum in time-frequencymatrix 119860 is calculated whose steps are as follows

(1) It is necessary to determine the dimensional number119898 and the threshold value 119903 How to choose theseparameters is discussed in [32] In this paper 119898 =

2 and 119903 = 02 Row data in the time-frequencymatrix 119860 is marked as ldquo119909

1 1199092 119909

119899rdquo And then ldquo119909

1

1199092 119909

119899rdquo should be converted into one group 119898

dimensional vectors see the following equation

119883(119894) = [119909 (119894) 119909 (119894 + 1) sdot sdot sdot 119909 (119894 + 119898 minus 1)] (5)

where 119894 = 1 2 119899 minus 119898 + 1(2) The maximum difference value between the corre-

sponding elements from 119883(119894) and 119883(119895) is defined asthe distance between 119883(119894) and 119883(119895) namely

119889 (119894 119895) = max119896

1003816100381610038161003816119909 (119894 + 119896) minus 119909 (119895 + 119896)1003816100381610038161003816

(119896 = 0 1 119898 minus 1)

(6)

(3) According to the given threshold 119903 count the numberof 119889(119894 119895) which make 119889(119894 119895) lt 119903 the ratio of thisnumber and the total vector 119899 minus 119898 + 1 is defined as119861119898

119894(119903)

119861119898

119894(119903) =

119873

119899 minus 119898 + 1 (7)

where 1 le 119895 le 119899 minus 119898 and 119895 = 119894(4) Take the average of119861119898

119894(119903) for every 119894 which is denoted

by 119861119898(119903)

119861119898

(119903) =1

119899 minus 119898 + 1

119899minus119898+1

sum

119894=1

119861119898

119894(119903) (8)

(5) Change the embedding dimension from 119898 to 119898 + 1repeating Step (1) to Step (4) and then 119861

119898+1(119903) is

obtained(6) The sample entropy of this row data in the time-

frequency matrix 119860 is obtained

SampEn (119898 119903 119899) = minus ln 119861119898+1

(119903)

119861119898 (119903) (9)

(7) Repeating Step (1) to Step (6) for the rest of other rowdata in the time-frequencymatrix119860 themultidimen-sional sample entropy parameters of PD signals can beobtained Then it is marked as follows

119875 = [1199011 1199012 119901

119897] (10)

Mathematical Problems in Engineering 5

Sign

alim

f1im

f2im

f3im

f4im

f5im

f6im

f7Empirical mode decomposition 1206012120587 = 1

times10minus3

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

minus40

100 150 200 250 300 350 400 450 50050com

pone

ntRe

sidua

l

(a) Analog signals served as single exponent attenuation type

Sign

alim

f1im

f2im

f3im

f4im

f5im

f6im

f7

Empirical mode decomposition 1206012120587 = 1

times10minus3

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050minus6

minus2

com

pone

ntRe

sidua

l

(b) Analog signals served as single exponent vibration type

Figure 3The PD analog signals of EMD decomposition results Note in the figure the scale of the vertical axis (imf1 imf2 imf7) is thesame as the raw signal the horizontal axis does not have unit the numerical meaning only on behalf of the sample points

0 02 04 06 08 1

0020406081Frequency (Hz)

002040608

1

Am

plitu

de (m

V)

t (s)times 10minus3

(a) Analog signals served as single exponent attenuation type

0020406081Frequency (Hz)

002040608

1

Am

plitu

de (m

V)

times 10minus3

0 02 04t (s)

06 08 1

(b) Analog signals served as single exponent vibration type

Figure 4 The 2nd-order IMF component 3D time-frequency spectrum

where 119901119894(119894 = 1 2 119897) represents the sample

entropy of the row 119894

43 PD Signal Feature Region A feature plane is establishedto describe the PD signals feature from different dimensionsThis feature plane consists of the multidimensional energyparameters and themultidimensional sample entropy param-eters

The energy parameter 119864(119896) and the sample entropyparameter 119901(119896) of the same frequency band would be definedas one feature point 119904

119896= (119901(119896) 119864(119896)) And then all the feature

points of PD signals are marked as one set 119878 namely

119878 = (119875 (1) 119864 (1)) (119875 (2) 119864 (2)) (119875 (119897) 119864 (119897)) (11)

Finding a minimum circle (119874 119877) on the feature planeincludes all elements of the feature point set 119878 And then

6 Mathematical Problems in Engineering

EMD decomposition

Frequency bands partition

Each frequency band component is calculatedby using HHT band-pass filter

Build the feature field and find a minimum circleon the feature field including all feature points

The sample entropy values of each frequency band component are calculated

The energy values of each frequency band component are calculated

Construct time-frequency matrix A

Row signals S(t)

Mark one feature point assk = (p(k) E(k))

P = [p1 p2 pl] E = [Elowast1 E

lowast2 E

lowastl ]

Figure 5 The calculation process of feature region

this circle (119874 119877) is defined as the feature region of PDsignals on the feature field It describes the PD signals featureinformation on the different frequency bands Its calculationprocess is shown in Figure 5 And the feature region of faultsignal is shown in Figure 6

5 Fault Diagnosis Based on Sphere-StructuredSupport Vector Machine

Support vector machine algorithm is a newmachine learningmethod developed on the statistical study theory It avoids thenetwork structure selection overlearning and underlearningand other problems in artificial neural network algorithmHowever standard SVM is a binary classifier so that it cannoteffectively solve multiclass classification [33] Therefore toovercome the shortages of standard SVM classifiers manyresearchers tried to modify and improve SVM such as ldquoone-against-onerdquo [34] ldquoone-against-allrdquo [35] and ldquodecision treerdquo[36] which is suitable for multiclass classification But theessences of these methods need to solve a large number ofquadratic programming problems [37] In order to reducecomputational complexity this paper suggests using sphere-structured SVM to deal with the multiclass classification

One multiclassification problem is expressed as follows119896 several 119899 dimensional space element set 119860119898 119898 = 1 119896

Sample parameters

Ener

gy p

aram

eter

s

OR

(p(1) E(1))

(p(2) E(2))

(p(l) E(l))

Figure 6 The feature region of signals

Each set 119860119898 stands for the one element including 119897 several

sample feature points 119909119894 119894 = 1 119897 As far as possible to find

a spherical surface includes all the elements of the set 119860119898

Mathematical Problems in Engineering 7

1

2

3

stands for class 1stands for class 2

stands for class 3

Figure 7 The sketch of spherical classification

In order to avoid some rough points impact on thealgorithm it is just here that a slack variable 120577

119898

119894is introduced

see the following equation1003817100381710038171003817119909119898

119894minus 11988611989810038171003817100381710038172

le 119877119898

+ 120577119898

119894120577119898

119894ge 0 119894 = 1 119897 (12)

where 119886119898 represents the center of sphere and 119877

119898 representsthe radius of sphere

The objective function of the above-mentioned problemsshould be defined as

min 119865 (119877119898 119886119898 120577119898

119894) = 119877119898

+ 119862119898sum

119894

120577119898

119894 (13)

where 119862119898 represents the penalty coefficient

Each classification can be described as similar to thequadratic programming problem Solving this quadratic pro-gramming problem can obtain one sphere And this sphererepresents this class Points on the spherical surface play a keyrole in spherical determination called the support vector asshown in Figure 7

One set 119883 = 1199091 1199092 119909

119897 represents one testing

sample 119909119894 119894 = 1 2 119897 represents one feature point of the

sample To judge which class sample119883 belongs to the processis as follows

Firstly it is necessary to calculatesum119894=1119897

119909119894minus 1198861198982 which

describes the quadratic sum of distance between 119909119894in the

sample 119883 with each spherical center And then to comparethe magnitude of sum

119894=1119897119909119894minus 1198861198982 with 119897 sdot 119877

119898 let 119889 representthe number of sum

119894=1119897119909119894minus 1198861198982le 119897 sdot 119877

119898

(1) For 119889 = 0 this means that most of feature pointsof sample 119883 are not located in any sphere So it isnecessary to find out one sphere which is the nearestto the sample 119883 If sum

119894=1119897119909119894minus 1198861199012

minus 119897 sdot 119877119901

=

minsum119894=1119897

119909119894minus 1198861198982minus 119897 sdot 119877

119898 the sample 119883 belongsto class 119901

(2) For 119889 = 1 the sample 119883 belongs to the class that thissphere represents

A

B

C D

xRi Rj

aiaj

Figure 8 The schematic diagram of spherical structure classifica-tion

(3) For 119889 gt 1 this means the sample 119883 is locatedin multiple spheres intersection area Then takingFigure 8 as the example consider the following

(1) All spheres including sample 119883 are marked asone set 119868

(2) forall119894 119895 isin 119868 calculate 119886119894119863 and 119886

119894119862 respectively

where 119886119894119863 represents the projection of

997888997888rarr119886119894119909 in

997888997888rarr119886119894119886119895 and 119886

119894119862 represents the projection of

997888997888rarr119886119894119860 in

997888997888rarr119886119894119886119895

119886119894119863 =

997888997888rarr119886119894119909 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

119886119894119862 =

997888997888rarr119886119894119860 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

(14)

(3) Compare the magnitude of 119886119894119863 with 119886

119894119862 for

119886119894119863 lt 119886

119894119862 the sample 119883 belongs to class 119894 or

else the sample 119883 belongs to class 119895

6 Experimental Analysis

Based on power transformer structure and the differentdischarge forms of the different insulation defect transformerpartial discharge forms can be divided into the followingthree types insulation internal defect (eg there are bubblesin insulating oil) surface discharge (eg the insulator surfaceflashover phenomenon) and electrode tip discharge (eg thewinding tip discharge)The in situ data of 330 kV transformerstations in Gansu province China are taken as a real examplefor carrying out the analysis Figure 9 shows the site conditionof the 330 kV transformer stations Figure 10 is a set of samplesignals of different faults

(1) Extract UHF PD Signal Feature Region EMD and HHTband-pass filters are carried out for different faults UHF PDsignals And then the PD signals components on different

8 Mathematical Problems in Engineering

UHFtransducer

Figure 9 The in situ condition Note power transformer (SSP-360MVA330 kV) and the UHF sensor parameters detection sensitivity(minus80 dBmsimminus35 dBm) working voltage (8Vsim15 V) working current (120mA) and output voltage (100mVsim3V)

Insulation internal defects

Surface discharge

Electrode tip discharge

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 10 Different defect UHF PD sample signals

frequency bands should be restructured Figure 11 shows thePD signals after filtering and reconstruction

Since the strongest noise in transformers station mainlyconcentrates into 10 kHz the transformers iron-core mag-netic noise mainly concentrates into the range of 10ndash70 kHz[38] so the paper chooses the subband over 1MHz to beserved as the feature subband The signals frequency bandenergy and sample entropy parameters on each subband arecalculated And then the feature filed is established to extractthe feature region PD signals Figure 12 shows the featureregion within 90 confidence interval of different UHF PDsignals Among them 1 represents the feature region ofthe surface discharge defect 2 represents the feature regionof the electrode tip discharge defect and 3 represents thefeature region of the insulation internal defect

Insulation internal defects

Surface discharge

Electrode tip discharge

times10minus3

minus005

0

005A

mpl

itude

(mV

)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus1

0

1

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus005

0

005

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 11 The PD signals after filtering and reconstruction

It can be seen from Figure 12 that there exist obviousdifferences in the feature region of the different defects Thedifferences mainly focus on the different frequency bandsenergy value and sample entropy value The sample entropyvalue of 2 and 3 is greater than 1 It indicates that thedischarge mechanism of 2 and 3 is more complicated andmore random than 1 The signals energy value of 1 and 2is greater than 3 It indicates that UHF PD signals amplitudeof 1 and 2 is bigger than 3 And their discharge processcan release more energy causing more serious damage to thepower transformer insulation

(2) Partial Discharge Fault Diagnosis The sphere-structuredsupport vectormachine algorithm is used to identify differentpartial discharge faults caused by different defects Accord-ingly 20 groups faults sample data are randomly selected to

Mathematical Problems in Engineering 9

Multidimensional characteristics region

0

02

04

06

08

1

12

14

16

18

2

Sign

al en

ergy

05 1 15 20Sample entropy

Feature pointsFeature pointsFeature points

1 characteristic region2 characteristic region3 characteristic region

Figure 12 The feature region within 90 confidence interval ofdifferent UHF PD signals

Table 1 Identification results

Types Maximumerror rate

Averageidentifying rate

Surface discharge 45 978Electrode tip discharge 6 953Insulation internal defect 43 961

carry out the training The rest of the faults sample data aremixed randomly Through many time testing experimentsthe final statistic results are shown in Table 1

It can be seen from Table 1 that the feature region of PDsignals is able to describe the feature information of differentpartial discharge faults And it is of better fault identificationresolutionThe average identification rate of different faults ismore than 95

Then two popular approaches of faults classification [39]PCA-SVM [40] and wavelet-SVM [41] are used to make acontrast analysis

As one can notice from Table 2 the fault classificationaccuracy of PCA-SVM is lower The fault classification accu-racy ofwavelet-SVMand the approach proposed in this paperis almost the same So PCA is unsuitable for feature extractionof time-variation signals The wavelet approach can betteranalyze time-variation signals but how to determine anoptimal mother wavelet is a big challenge for faults signalfeature extraction On the whole the method proposed inthis paper has more advantages in feature extraction of time-variation signals and faults classification

Table 2 The contrast analysis

Fault types

Fault classification accuracy ()

PCA-SVM Wavelet-SVMThe approachproposed inthis paper

Surface discharge 887 959 978Electrode tip discharge 881 971 953Insulation internal defect 90 942 961

7 Conclusion

Power transformer PD signals contain a large amount ofinsulation state information of power transformer Effectivelyextracting signals feature information is of great significancefor power transformer insulation onlinemonitoring In orderto effectively extract PD signals feature this paper suggestsa new method Firstly using UHF PD signals differentfrequency band components construct the time-frequencymatrix And then signals feature region is established bymultidimensional energy parameters and multidimensionalsample entropy parameters It is confirmed in Section 6 thatthis approach can describe PD signals feature informationFinally spherical structure support vectormachine algorithmis used to identify different partial discharge faults

Competing Interests

The authors declare there are no competing interests regard-ing the publication of this paper

Acknowledgments

This work was supported by the National Natural Sci-ence Foundation of China (no 51279161) Furthermore theauthors are grateful for the staff of China Electric PowerResearch Institute and State Grid Gansu Province ElectricPower Research Institute

References

[1] V P Darabad M Vakilian T R Blackburn and B T PhungldquoAn efficient PD data mining method for power transformerdefect models using SOM techniquerdquo International Journal ofElectrical Power amp Energy Systems vol 71 pp 373ndash382 2015

[2] M Yun K Park G Wang S Kim and G Kil ldquoAnalysisof propagation characteristics of acoustic signal in insulationoilrdquo Journal of the Korean Institute of Electrical and ElectronicMaterial Engineers vol 29 no 2 pp 114ndash119 2016

[3] X Zhang S Xiao N Shu J Tang and W Li ldquoGIS partialdischarge pattern recognition based on the chaos theoryrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 21 no2 pp 783ndash790 2014

[4] P B S M Gubanski G Csepes V Der Houhanessian etal ldquoDielectric response methods for diagnostics of powertransformersrdquo Tech Rep CIGRE Technical Brochure ParisFrance 2004

[5] A Abu-Siada and S Islam ldquoA new approach to identify powertransformer criticality and assetmanagement decision based on

10 Mathematical Problems in Engineering

dissolved gas-in-oil analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 19 no 3 pp 1007ndash1012 2012

[6] A Mikulecky and Z Stih ldquoInfluence of temperature moisturecontent and ageing on oil impregnated paper bushings insula-tionrdquo IEEE Transactions on Dielectrics and Electrical Insulationvol 20 no 4 pp 1421ndash1427 2013

[7] N Hashemnia A Abu-Siada and S Islam ldquoDetection ofpower transformer bushing faults and oil degradation usingfrequency response analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 23 no 1 pp 222ndash229 2016

[8] J A Almendros-Ibanez J C Burgos and B Garcia ldquoTrans-former field drying procedures a theoretical analysisrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 1978ndash19862009

[9] G-L Wang Y Zheng Y-P Hao and Y-M Li ldquoStudy onthe ultra-high-frequency sensor for PD detection in powertransformerrdquo Proceedings of the CSEE vol 22 no 4 pp 154ndash160 2002

[10] A A Bajwa S Habib and M Kamran ldquoAn investigationinto partial discharge pulse extraction methodsrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 964ndash982 2015

[11] L Satish and B Nazneen ldquoWavelet-based denoising of partialdischarge signals buried in excessive noise and interferencerdquoIEEE Transactions on Dielectrics and Electrical Insulation vol10 no 2 pp 354ndash367 2003

[12] W J K Raymond H A Illias A H A Bakar and H MokhlisldquoPartial discharge classifications review of recent progressrdquoMeasurement vol 68 pp 164ndash181 2015

[13] M Wu H Cao J Cao H-L Nguyen J B Gomes andS P Krishnaswamy ldquoAn overview of state-of-the-art partialdischarge analysis techniques for condition monitoringrdquo IEEEElectrical Insulation Magazine vol 31 no 6 pp 22ndash35 2015

[14] D Dey B Chatterjee S Chakravorti and S Munshi ldquoCross-wavelet transform as a new paradigm for feature extractionfrom noisy partial discharge pulsesrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 17 no 1 pp 157ndash1662010

[15] F-C Gu H-C Chang F-H Chen C-C Kuo and C-HHsu ldquoApplication of the Hilbert-Huang transform with fractalfeature enhancement on partial discharge recognition of powercable jointsrdquo IET Science Measurement and Technology vol 6no 6 pp 440ndash448 2012

[16] YGong Y Liu and LWu ldquoIdentification of partial discharge ingas insulated switchgears with fractal theory and support vectormachinerdquo Power System Technology vol 35 no 3 pp 135ndash1392011

[17] X-D Wang B Li Z Liu et al ldquoAnalysis of partial dischargesignal using the Hilbert-Huang transformrdquo IEEE Transactionson Power Delivery vol 21 no 3 pp 1063ndash1067 2006

[18] S-B Liu C Lu J-L Yu andL-XWang ldquoApplication of hilbert-huang transform in pattern recognition for partial dischargeof transformersrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 31 pp 114ndash119 2008

[19] L Shen F-C Yang X-J Zhou and L Liu ldquoGear fault featureextraction based on improved EMD and morphological filterrdquoJournal of Vibration and Shock vol 29 no 3 pp 154ndash157 2010

[20] J Huang X Hu and Y Gong ldquoMachinery fault diagnosisof high voltage circuit breaker based on empirical modedecompositionrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 31 no 12 pp 108ndash113 2011

[21] G Yong-gang H Yulong and Q Jiali ldquoAn overview onmechanical failure diagnosis technique for high voltage circuitbreaker based on vibration signalrdquo High Voltage Engineeringvol 26 no 3 pp 66ndash68 2000

[22] H-L Sun Z-J He Y-Y Zi and J Yuan ldquoMulti-wavelettransform and its applications in mechanical fault diagnosis-areviewrdquo Mechanical Systems and Signal Processing vol 43 no1-2 pp 1ndash24 2014

[23] D E Newland ldquoWavelet analysis of vibration part 1 theoryrdquoASME Transactions on Journal of Vibration and Acoustics vol116 pp 409ndash441 1994

[24] H Shang J Yuan Y Wang and S Jin ldquoFeature extraction forpartial discharge based on cross-wavelet transform and corre-lation coefficient matrixrdquo Transactions of China ElectrotechnicalSociety vol 29 no 4 pp 274ndash281 2014

[25] A Krivda E Gulski L Satish and W S Zaengl ldquoUse offractal features for recognition of 3-D discharge patternsrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 2 no5 pp 889ndash892 1995

[26] K Gao K-X Tan F-Q Li and C-Q Wu ldquoPattern recognitionof partial discharges based on fractal features of the scatter setrdquoProceedings of the Chinese Society of Electrical Engineering vol22 no 5 pp 22ndash26 2002

[27] Y Xiao C-J Huang W-Y Yu and X-C Jiang ldquoSignal charac-teristic extraction of partial discharge in gis based on waveletand fractal analysisrdquo Automation of Electric Power Systems vol30 no 6 pp 66ndash69 2006

[28] W Chen Z Wang H Xie and W Yu ldquoCharacterization ofsurface EMG signal based on fuzzy entropyrdquo IEEE Transactionson Neural Systems and Rehabilitation Engineering vol 15 no 2pp 266ndash272 2007

[29] N E Huang Z Shen S R Long et al ldquoThe empiricalmode decomposition and the Hilbert spectrum for nonlinearand non-stationary time series analysisrdquo Proceedings of theRoyal Society of London Series A Mathematical Physical andEngineering Sciences vol 454 no 1971 pp 903ndash995 1998

[30] R Jia Q Xu L Tian X Luo and W Liu ldquoExtractingpartial discharge signals of hydroelectric generating set basedon empirical mode decompositionrdquo Journal of HydroelectricEngineering vol 26 no 4 pp 146ndash150 2007

[31] J Tang L Fan X Zhang and X Liu ldquoMulti-scale featureparameters extraction of gis partial discharge signal withharmonic wavelet packet transformrdquo Transactions of ChinaElectrotechnical Society vol 30 no 3 pp 250ndash257 2015

[32] J S Richman and J Randall Moorman ldquoPhysiological time-series analysis using approximate entropy and sample entropyrdquoAmerican Journal of PhysiologymdashHeart and Circulatory Physiol-ogy vol 278 no 6 pp H2039ndashH2049 2000

[33] W-J Chen Y-H Shao C-N Li and N-Y Deng ldquoMLTSVMa novel twin support vector machine to multi-label learningrdquoPattern Recognition vol 52 pp 61ndash74 2016

[34] U Kreszligel ldquoPair-wise classification and support vectormachinesrdquo in Advances in Kernel Methods pp 255ndash268 MITPress Cambridge Mass USA 1999

[35] 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

[36] T Dietterich and G Bakiri ldquoSolving multiclass learning prob-lems via error-correcting output codesrdquo Journal of ArtificialIntelligence Research vol 2 pp 263ndash286 1995

Mathematical Problems in Engineering 11

[37] S Liu Y Liu BWang and X Feng ldquoAn improved hyper-spheresupport vector machinerdquo in Proceedings of the 3rd InternationalConference on Natural Computation (ICNC rsquo07) pp 497ndash500IEEE Haikou China August 2007

[38] J Seo H Ma and T Saha ldquoProbabilistic wavelet transform forpartial discharge measurement of transformerrdquo IEEE Transac-tions on Dielectrics and Electrical Insulation vol 22 no 2 pp1105ndash1117 2015

[39] J Singh Y R Sood R K Jarial and P Verma ldquoConditionmonitoring of power transformersmdashbibliography surveyrdquo IEEEElectrical Insulation Magazine vol 24 no 3 pp 11ndash25 2008

[40] E Gumus N Kilic A Sertbas and O N Ucan ldquoEvaluationof face recognition techniques using PCA wavelets and SVMrdquoExpert Systems with Applications vol 37 no 9 pp 6404ndash64082010

[41] Z Liu H Cao X Chen Z He and Z Shen ldquoMulti-faultclassification based on wavelet SVM with PSO algorithmto analyze vibration signals from rolling element bearingsrdquoNeurocomputing vol 99 pp 399ndash410 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

and diagnosis In Sections 3 and 4 this paper establishesa new feature extraction method to describe and classifydifferent PD patterns The sphere-structured support vectormachine algorithm is adopted to diagnose different partialdischarge faults in Section 5 The case study is presented inSection 6

2 Overview of PD Fault Diagnosis

Transformer PD signal is of strong nonlinearity and time-variation And in the in situ detection it is frequentlysubject to the overlap of many interference signals [9 10]Statistics [11] indicate that major interference signals are dis-crete spectral interferences stochastic shaped interferencesand periodic pulse shaped interferences which leads greatdifficulties to signals feature extraction and fault diagnosisTherefore how to accurately extract signals feature is the keyto PD faults identification

Up to now feature extraction methods mainly concen-trate on the analysis of statistic graphic spectrum and waveshapes [12 13] Among them methods based on statisticgraphic spectrum analysis require the high sampling rate anda large number of samples so it is unfavorable for onlinedetection of insulation whereas methods based on waveshape analysis require the low quantity of data samples Soit used to extract the time-variant signal feature whose mainmethods are time-frequency analysis Hilbert-Huang trans-form (HHT) wavelet theory fractal theory Chaos theoryand so forth [14ndash16] Frequency and time features are impor-tant character for signals Those can be obtained by usingfast Fourier transform algorithm (FFT) or short time Fouriertransform algorithm (STFT) However both FFT and STFTare not suitable for time-variation signals Because HHT hasbetter self-adaptability it is suitable for analyzing the partialdynamic feature of nonsmooth signals such as literatures [17]and [18] But HHT requires a priori knowledge about thesensitive frequency bands of fault signals Moreover there arethe end effects and themodemixing in HHT It is pointed outin literatures [19ndash21] that the frequency spectrum enveloptime-frequency energy entropy information and so forth areable to depict the features of nonstable time-varying signalsbut in practical use they are easy to be subjected to noiseinterference so that the effects are unrealistic

Unlike classical time-frequency analysis methods usinga series of sinusoidal functions to describe a signal wavelettransform decomposes a signal into wavelet coefficients ofvarious time scales And it is considered as one of the mostpowerful techniques for faults signal denoising and extractingtransient feature [22 23] For example the feature extrac-tion of PD signals is achieved based on the cross-wavelettransform and relevant coefficient matrix in literature [24]Unfortunately how to determine an optimal mother waveletis a big challenge for faults signal feature extraction In litera-ture [25ndash27] the fractal theory is successfully used to extractthe feature of GIS PD signals However how to select fractalelement shapes is unclear and fractal theory is still immature

Because different insulation defect faults have differentpartial discharge principle and there are strong randomnessand dispersion in its phase distribution feature frequencyand pulse magnitude those classical feature extractionmeth-ods are not well suitable for online PD faults diagnosisMoreover the same insulation defect fault has some similar-ities on its frequency spectrum envelop and the frequencyband energy distribution whose features have an obviousprobability distribution in certain frequency band So thisfrequency band can describe different faults signal featureThe magnitude of energy and the complexity of frequencycomponents are two different parameters which can repre-sent one frequency band from different angles And literature[28] points out that sample entropy value magnitude canreflect the complexity of the system Therefore this paperuses sample entropy and energy to establish one feature planeto describe the essential feature information of the fault Sothis paper proposes a new method for power transformerPD signal feature extraction and fault diagnosis based onmultidimensional feature region Firstly in order to obtaincomponents of raw signal on different frequency bands EMDand HHT band-pass filter wave for PD signal is carried outSecondly the sample entropy value and the energy value ofeach frequency band component are calculated And then thefeature region is established by using the sample entropy valueand the energy value of each frequency band componentto describe multidimensional features of PD signal Finallypartial discharge faults are classified by sphere-structuredsupport vector machines algorithm

3 Frequency Band Component Extraction

In order to better describe differences in each frequency bandof fault signals the frequency band component of raw signalshould be extracted Now EMDandHHTband-pass filter areused to extract frequency band component

31 EMD EMD is served as a kind of self-adaptive decompo-sition algorithm without obtaining a priori knowledge of rawsignals in advance And it avoids the optimum base functionselection problem of wavelet decomposition [29] the decom-position process of any signals 119904(119905) is shown in Figure 1

Analog signals given in literature [30] are shown inFigure 2 Taking these analog signals as the example theanalysis is carried out In the literature single exponentattenuation signal is shown as in formula (1) and singleexponent vibration signal is shown as in formula (2)

1199041(119905) = 119860119890

minus119905120591 (1)

1199042(119905) = 119860119890

minus119905120591 sin (2120587119891119888119905) (2)

It can be known from Figure 3 that after two types ofsignals are decomposed by EMD 7-order intrinsic modefunction (IMF) components (imf1 imf2 imf7) and 1residual component (res) are obtained Then Hilbert time-frequency distribution of the 2nd-order IMF component iscalculated The result is shown in Figure 4

Mathematical Problems in Engineering 3

Yes

No

Yes

Ending

No

Extracting signal details markingd(t) = s(t) minus m(t)

Letting s(t) = mi(t)

Letting s(t) = d(t)

Marking di(t) = d(t)

Letting mi(t) = s(t) minus di(t)

monotoneis

very smallfunction or mi(t) is

Judging whethermi(t)

whether to satisfy IMF two conditions or

not

Judging d(t)

m(t) =emax(t) + emin(t)

2

Calculating average value m(t) of the upper and lower envelopes

To seek for all the maximum and minimum value points and then bycubic spline interpolation to obtain upper and lower envelope

emax(t) and emin(t) of original signal

Signals s(t)

Figure 1 The algorithm flow process of EMD

It can be known from Figure 4 that the 2nd-order IMFfrequency band of single exponent attenuation PD signalsis 38ndash46MHz while the 2nd-order IMF frequency bandof single exponent vibration PD signals is 22ndash42MHzAccordingly the frequency band range of the same order IMFdecomposed by different signals is different

32 Extract Different Frequency Band Components of RawSignal The order of IMF obtained from PD signals throughEMD decomposition is closely related to partial dischargetype And even if they are at the same order of IMF theirfrequency band still has the obvious differences

Aiming at this phenomenon it is here that HHT bandpassing filter is adopted to solve the problem The concreteprocedures are as follows

(1) Sampling frequency of signals 119904(119905) is 119865119904 The numberof sampling points is 119899 After EMD decompositionthe 119898 pieces of IMF components are obtainedThe magnitude of each component Hilbert time-frequency spectrum is 119898 times 119899 which should be

classified as 119897 frequency bands and the set of instantamplitude values on the 119896 frequency band can bemarked as 119867(119896) (119896 = 1 2 119897)

(2) Zero set all the instant amplitude values on theHilberttime-frequency spectrum except for frequency band119896 and mark as 119867

lowast(119896)

(3) Zero set the IMF component point values which iscorresponding to the instant amplitude value beingset as zero in 119867

lowast(119896)

(4) Each IMF component treated using the filter can bereconstructed to obtain signals 119904(119905) component on thefrequency band

(5) As to the rest of frequency bands the above proce-dures are repeatedThat is signals 119904(119905) component onthe different frequency bands should be obtained

Signals 119904(119905) are treated through HHT band passing filterin order to obtain 119897 components Andmatrix119860 is constructed

4 Mathematical Problems in Engineering

Signal 1

Signal 2

times10minus3

times10minus3

01 02 03 04 05 06 07 08 09 10t (s)

minus02

0

02

04

06

Am

plitu

de (m

V)

minus02

minus01

0010203

Am

plitu

de (m

V)

01 02 03 04 05 06 07 08 09 10t (s)

Figure 2 The analog signals of PD

using 119897 components In other words matrix 119860 can cover theinformation of signal 119904(119905) under each frequency band

119860 =

[[[[[[[[

[

11988611

11988612

sdot sdot sdot 1198861119899

11988621

11988622

sdot sdot sdot 1198862119899

sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot

1198861198971

1198861198972

sdot sdot sdot 119886119897119899

]]]]]]]]

]

(3)

where 119886119894119895represents raw signals 119904(119905) data on each frequency

band

4 PD Signals Feature Region

41 Multidimensional Energy Parameters Different insula-tion defect faults have different partial discharge principleAnd their discharge pulse has obvious difference on the waveshape and the frequency band energy distribution while thesame insulation defect fault has strong similarity on the waveshape and the frequency band energy distribution [31] Forthis reason this paper suggests that multidimensional energyparameter is used to describe PD signals feature quantityThecalculation process of multidimensional energy parameter isgiven as follows

(1) Each row datum of time-frequency matrix 119860 ldquo1198861198941 1198861198942

119886119894119899rdquo stands for an independent frequency band

being marked as ldquo119883119896 119896 = 1 2 119897rdquo

(2) Energy value 119864(119896) of each frequency band is calcu-lated And then the normalization of 119864(119896) is carriedout

119864 (119896) = sum

119894=1119899

119883119896(119894)2

119864lowast(119896) =

119864 (119896)

sum119896=1119897

119864 (119896)

(4)

The multidimensional energy parameters of PD signalsobtained from the above steps are marked as 119864 = [119864

lowast

1 119864lowast

2

119864lowast

119897]

42 Multidimensional Sample Entropy Parameters Sampleentropy algorithm is a kind of theory originating fromnonlinear dynamics [28] whose value magnitude can reflectthe complexity of the system It is likely to provide a kind offresh solution for the nonstable signals analysis

Sample entropy of each row datum in time-frequencymatrix 119860 is calculated whose steps are as follows

(1) It is necessary to determine the dimensional number119898 and the threshold value 119903 How to choose theseparameters is discussed in [32] In this paper 119898 =

2 and 119903 = 02 Row data in the time-frequencymatrix 119860 is marked as ldquo119909

1 1199092 119909

119899rdquo And then ldquo119909

1

1199092 119909

119899rdquo should be converted into one group 119898

dimensional vectors see the following equation

119883(119894) = [119909 (119894) 119909 (119894 + 1) sdot sdot sdot 119909 (119894 + 119898 minus 1)] (5)

where 119894 = 1 2 119899 minus 119898 + 1(2) The maximum difference value between the corre-

sponding elements from 119883(119894) and 119883(119895) is defined asthe distance between 119883(119894) and 119883(119895) namely

119889 (119894 119895) = max119896

1003816100381610038161003816119909 (119894 + 119896) minus 119909 (119895 + 119896)1003816100381610038161003816

(119896 = 0 1 119898 minus 1)

(6)

(3) According to the given threshold 119903 count the numberof 119889(119894 119895) which make 119889(119894 119895) lt 119903 the ratio of thisnumber and the total vector 119899 minus 119898 + 1 is defined as119861119898

119894(119903)

119861119898

119894(119903) =

119873

119899 minus 119898 + 1 (7)

where 1 le 119895 le 119899 minus 119898 and 119895 = 119894(4) Take the average of119861119898

119894(119903) for every 119894 which is denoted

by 119861119898(119903)

119861119898

(119903) =1

119899 minus 119898 + 1

119899minus119898+1

sum

119894=1

119861119898

119894(119903) (8)

(5) Change the embedding dimension from 119898 to 119898 + 1repeating Step (1) to Step (4) and then 119861

119898+1(119903) is

obtained(6) The sample entropy of this row data in the time-

frequency matrix 119860 is obtained

SampEn (119898 119903 119899) = minus ln 119861119898+1

(119903)

119861119898 (119903) (9)

(7) Repeating Step (1) to Step (6) for the rest of other rowdata in the time-frequencymatrix119860 themultidimen-sional sample entropy parameters of PD signals can beobtained Then it is marked as follows

119875 = [1199011 1199012 119901

119897] (10)

Mathematical Problems in Engineering 5

Sign

alim

f1im

f2im

f3im

f4im

f5im

f6im

f7Empirical mode decomposition 1206012120587 = 1

times10minus3

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

minus40

100 150 200 250 300 350 400 450 50050com

pone

ntRe

sidua

l

(a) Analog signals served as single exponent attenuation type

Sign

alim

f1im

f2im

f3im

f4im

f5im

f6im

f7

Empirical mode decomposition 1206012120587 = 1

times10minus3

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050minus6

minus2

com

pone

ntRe

sidua

l

(b) Analog signals served as single exponent vibration type

Figure 3The PD analog signals of EMD decomposition results Note in the figure the scale of the vertical axis (imf1 imf2 imf7) is thesame as the raw signal the horizontal axis does not have unit the numerical meaning only on behalf of the sample points

0 02 04 06 08 1

0020406081Frequency (Hz)

002040608

1

Am

plitu

de (m

V)

t (s)times 10minus3

(a) Analog signals served as single exponent attenuation type

0020406081Frequency (Hz)

002040608

1

Am

plitu

de (m

V)

times 10minus3

0 02 04t (s)

06 08 1

(b) Analog signals served as single exponent vibration type

Figure 4 The 2nd-order IMF component 3D time-frequency spectrum

where 119901119894(119894 = 1 2 119897) represents the sample

entropy of the row 119894

43 PD Signal Feature Region A feature plane is establishedto describe the PD signals feature from different dimensionsThis feature plane consists of the multidimensional energyparameters and themultidimensional sample entropy param-eters

The energy parameter 119864(119896) and the sample entropyparameter 119901(119896) of the same frequency band would be definedas one feature point 119904

119896= (119901(119896) 119864(119896)) And then all the feature

points of PD signals are marked as one set 119878 namely

119878 = (119875 (1) 119864 (1)) (119875 (2) 119864 (2)) (119875 (119897) 119864 (119897)) (11)

Finding a minimum circle (119874 119877) on the feature planeincludes all elements of the feature point set 119878 And then

6 Mathematical Problems in Engineering

EMD decomposition

Frequency bands partition

Each frequency band component is calculatedby using HHT band-pass filter

Build the feature field and find a minimum circleon the feature field including all feature points

The sample entropy values of each frequency band component are calculated

The energy values of each frequency band component are calculated

Construct time-frequency matrix A

Row signals S(t)

Mark one feature point assk = (p(k) E(k))

P = [p1 p2 pl] E = [Elowast1 E

lowast2 E

lowastl ]

Figure 5 The calculation process of feature region

this circle (119874 119877) is defined as the feature region of PDsignals on the feature field It describes the PD signals featureinformation on the different frequency bands Its calculationprocess is shown in Figure 5 And the feature region of faultsignal is shown in Figure 6

5 Fault Diagnosis Based on Sphere-StructuredSupport Vector Machine

Support vector machine algorithm is a newmachine learningmethod developed on the statistical study theory It avoids thenetwork structure selection overlearning and underlearningand other problems in artificial neural network algorithmHowever standard SVM is a binary classifier so that it cannoteffectively solve multiclass classification [33] Therefore toovercome the shortages of standard SVM classifiers manyresearchers tried to modify and improve SVM such as ldquoone-against-onerdquo [34] ldquoone-against-allrdquo [35] and ldquodecision treerdquo[36] which is suitable for multiclass classification But theessences of these methods need to solve a large number ofquadratic programming problems [37] In order to reducecomputational complexity this paper suggests using sphere-structured SVM to deal with the multiclass classification

One multiclassification problem is expressed as follows119896 several 119899 dimensional space element set 119860119898 119898 = 1 119896

Sample parameters

Ener

gy p

aram

eter

s

OR

(p(1) E(1))

(p(2) E(2))

(p(l) E(l))

Figure 6 The feature region of signals

Each set 119860119898 stands for the one element including 119897 several

sample feature points 119909119894 119894 = 1 119897 As far as possible to find

a spherical surface includes all the elements of the set 119860119898

Mathematical Problems in Engineering 7

1

2

3

stands for class 1stands for class 2

stands for class 3

Figure 7 The sketch of spherical classification

In order to avoid some rough points impact on thealgorithm it is just here that a slack variable 120577

119898

119894is introduced

see the following equation1003817100381710038171003817119909119898

119894minus 11988611989810038171003817100381710038172

le 119877119898

+ 120577119898

119894120577119898

119894ge 0 119894 = 1 119897 (12)

where 119886119898 represents the center of sphere and 119877

119898 representsthe radius of sphere

The objective function of the above-mentioned problemsshould be defined as

min 119865 (119877119898 119886119898 120577119898

119894) = 119877119898

+ 119862119898sum

119894

120577119898

119894 (13)

where 119862119898 represents the penalty coefficient

Each classification can be described as similar to thequadratic programming problem Solving this quadratic pro-gramming problem can obtain one sphere And this sphererepresents this class Points on the spherical surface play a keyrole in spherical determination called the support vector asshown in Figure 7

One set 119883 = 1199091 1199092 119909

119897 represents one testing

sample 119909119894 119894 = 1 2 119897 represents one feature point of the

sample To judge which class sample119883 belongs to the processis as follows

Firstly it is necessary to calculatesum119894=1119897

119909119894minus 1198861198982 which

describes the quadratic sum of distance between 119909119894in the

sample 119883 with each spherical center And then to comparethe magnitude of sum

119894=1119897119909119894minus 1198861198982 with 119897 sdot 119877

119898 let 119889 representthe number of sum

119894=1119897119909119894minus 1198861198982le 119897 sdot 119877

119898

(1) For 119889 = 0 this means that most of feature pointsof sample 119883 are not located in any sphere So it isnecessary to find out one sphere which is the nearestto the sample 119883 If sum

119894=1119897119909119894minus 1198861199012

minus 119897 sdot 119877119901

=

minsum119894=1119897

119909119894minus 1198861198982minus 119897 sdot 119877

119898 the sample 119883 belongsto class 119901

(2) For 119889 = 1 the sample 119883 belongs to the class that thissphere represents

A

B

C D

xRi Rj

aiaj

Figure 8 The schematic diagram of spherical structure classifica-tion

(3) For 119889 gt 1 this means the sample 119883 is locatedin multiple spheres intersection area Then takingFigure 8 as the example consider the following

(1) All spheres including sample 119883 are marked asone set 119868

(2) forall119894 119895 isin 119868 calculate 119886119894119863 and 119886

119894119862 respectively

where 119886119894119863 represents the projection of

997888997888rarr119886119894119909 in

997888997888rarr119886119894119886119895 and 119886

119894119862 represents the projection of

997888997888rarr119886119894119860 in

997888997888rarr119886119894119886119895

119886119894119863 =

997888997888rarr119886119894119909 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

119886119894119862 =

997888997888rarr119886119894119860 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

(14)

(3) Compare the magnitude of 119886119894119863 with 119886

119894119862 for

119886119894119863 lt 119886

119894119862 the sample 119883 belongs to class 119894 or

else the sample 119883 belongs to class 119895

6 Experimental Analysis

Based on power transformer structure and the differentdischarge forms of the different insulation defect transformerpartial discharge forms can be divided into the followingthree types insulation internal defect (eg there are bubblesin insulating oil) surface discharge (eg the insulator surfaceflashover phenomenon) and electrode tip discharge (eg thewinding tip discharge)The in situ data of 330 kV transformerstations in Gansu province China are taken as a real examplefor carrying out the analysis Figure 9 shows the site conditionof the 330 kV transformer stations Figure 10 is a set of samplesignals of different faults

(1) Extract UHF PD Signal Feature Region EMD and HHTband-pass filters are carried out for different faults UHF PDsignals And then the PD signals components on different

8 Mathematical Problems in Engineering

UHFtransducer

Figure 9 The in situ condition Note power transformer (SSP-360MVA330 kV) and the UHF sensor parameters detection sensitivity(minus80 dBmsimminus35 dBm) working voltage (8Vsim15 V) working current (120mA) and output voltage (100mVsim3V)

Insulation internal defects

Surface discharge

Electrode tip discharge

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 10 Different defect UHF PD sample signals

frequency bands should be restructured Figure 11 shows thePD signals after filtering and reconstruction

Since the strongest noise in transformers station mainlyconcentrates into 10 kHz the transformers iron-core mag-netic noise mainly concentrates into the range of 10ndash70 kHz[38] so the paper chooses the subband over 1MHz to beserved as the feature subband The signals frequency bandenergy and sample entropy parameters on each subband arecalculated And then the feature filed is established to extractthe feature region PD signals Figure 12 shows the featureregion within 90 confidence interval of different UHF PDsignals Among them 1 represents the feature region ofthe surface discharge defect 2 represents the feature regionof the electrode tip discharge defect and 3 represents thefeature region of the insulation internal defect

Insulation internal defects

Surface discharge

Electrode tip discharge

times10minus3

minus005

0

005A

mpl

itude

(mV

)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus1

0

1

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus005

0

005

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 11 The PD signals after filtering and reconstruction

It can be seen from Figure 12 that there exist obviousdifferences in the feature region of the different defects Thedifferences mainly focus on the different frequency bandsenergy value and sample entropy value The sample entropyvalue of 2 and 3 is greater than 1 It indicates that thedischarge mechanism of 2 and 3 is more complicated andmore random than 1 The signals energy value of 1 and 2is greater than 3 It indicates that UHF PD signals amplitudeof 1 and 2 is bigger than 3 And their discharge processcan release more energy causing more serious damage to thepower transformer insulation

(2) Partial Discharge Fault Diagnosis The sphere-structuredsupport vectormachine algorithm is used to identify differentpartial discharge faults caused by different defects Accord-ingly 20 groups faults sample data are randomly selected to

Mathematical Problems in Engineering 9

Multidimensional characteristics region

0

02

04

06

08

1

12

14

16

18

2

Sign

al en

ergy

05 1 15 20Sample entropy

Feature pointsFeature pointsFeature points

1 characteristic region2 characteristic region3 characteristic region

Figure 12 The feature region within 90 confidence interval ofdifferent UHF PD signals

Table 1 Identification results

Types Maximumerror rate

Averageidentifying rate

Surface discharge 45 978Electrode tip discharge 6 953Insulation internal defect 43 961

carry out the training The rest of the faults sample data aremixed randomly Through many time testing experimentsthe final statistic results are shown in Table 1

It can be seen from Table 1 that the feature region of PDsignals is able to describe the feature information of differentpartial discharge faults And it is of better fault identificationresolutionThe average identification rate of different faults ismore than 95

Then two popular approaches of faults classification [39]PCA-SVM [40] and wavelet-SVM [41] are used to make acontrast analysis

As one can notice from Table 2 the fault classificationaccuracy of PCA-SVM is lower The fault classification accu-racy ofwavelet-SVMand the approach proposed in this paperis almost the same So PCA is unsuitable for feature extractionof time-variation signals The wavelet approach can betteranalyze time-variation signals but how to determine anoptimal mother wavelet is a big challenge for faults signalfeature extraction On the whole the method proposed inthis paper has more advantages in feature extraction of time-variation signals and faults classification

Table 2 The contrast analysis

Fault types

Fault classification accuracy ()

PCA-SVM Wavelet-SVMThe approachproposed inthis paper

Surface discharge 887 959 978Electrode tip discharge 881 971 953Insulation internal defect 90 942 961

7 Conclusion

Power transformer PD signals contain a large amount ofinsulation state information of power transformer Effectivelyextracting signals feature information is of great significancefor power transformer insulation onlinemonitoring In orderto effectively extract PD signals feature this paper suggestsa new method Firstly using UHF PD signals differentfrequency band components construct the time-frequencymatrix And then signals feature region is established bymultidimensional energy parameters and multidimensionalsample entropy parameters It is confirmed in Section 6 thatthis approach can describe PD signals feature informationFinally spherical structure support vectormachine algorithmis used to identify different partial discharge faults

Competing Interests

The authors declare there are no competing interests regard-ing the publication of this paper

Acknowledgments

This work was supported by the National Natural Sci-ence Foundation of China (no 51279161) Furthermore theauthors are grateful for the staff of China Electric PowerResearch Institute and State Grid Gansu Province ElectricPower Research Institute

References

[1] V P Darabad M Vakilian T R Blackburn and B T PhungldquoAn efficient PD data mining method for power transformerdefect models using SOM techniquerdquo International Journal ofElectrical Power amp Energy Systems vol 71 pp 373ndash382 2015

[2] M Yun K Park G Wang S Kim and G Kil ldquoAnalysisof propagation characteristics of acoustic signal in insulationoilrdquo Journal of the Korean Institute of Electrical and ElectronicMaterial Engineers vol 29 no 2 pp 114ndash119 2016

[3] X Zhang S Xiao N Shu J Tang and W Li ldquoGIS partialdischarge pattern recognition based on the chaos theoryrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 21 no2 pp 783ndash790 2014

[4] P B S M Gubanski G Csepes V Der Houhanessian etal ldquoDielectric response methods for diagnostics of powertransformersrdquo Tech Rep CIGRE Technical Brochure ParisFrance 2004

[5] A Abu-Siada and S Islam ldquoA new approach to identify powertransformer criticality and assetmanagement decision based on

10 Mathematical Problems in Engineering

dissolved gas-in-oil analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 19 no 3 pp 1007ndash1012 2012

[6] A Mikulecky and Z Stih ldquoInfluence of temperature moisturecontent and ageing on oil impregnated paper bushings insula-tionrdquo IEEE Transactions on Dielectrics and Electrical Insulationvol 20 no 4 pp 1421ndash1427 2013

[7] N Hashemnia A Abu-Siada and S Islam ldquoDetection ofpower transformer bushing faults and oil degradation usingfrequency response analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 23 no 1 pp 222ndash229 2016

[8] J A Almendros-Ibanez J C Burgos and B Garcia ldquoTrans-former field drying procedures a theoretical analysisrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 1978ndash19862009

[9] G-L Wang Y Zheng Y-P Hao and Y-M Li ldquoStudy onthe ultra-high-frequency sensor for PD detection in powertransformerrdquo Proceedings of the CSEE vol 22 no 4 pp 154ndash160 2002

[10] A A Bajwa S Habib and M Kamran ldquoAn investigationinto partial discharge pulse extraction methodsrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 964ndash982 2015

[11] L Satish and B Nazneen ldquoWavelet-based denoising of partialdischarge signals buried in excessive noise and interferencerdquoIEEE Transactions on Dielectrics and Electrical Insulation vol10 no 2 pp 354ndash367 2003

[12] W J K Raymond H A Illias A H A Bakar and H MokhlisldquoPartial discharge classifications review of recent progressrdquoMeasurement vol 68 pp 164ndash181 2015

[13] M Wu H Cao J Cao H-L Nguyen J B Gomes andS P Krishnaswamy ldquoAn overview of state-of-the-art partialdischarge analysis techniques for condition monitoringrdquo IEEEElectrical Insulation Magazine vol 31 no 6 pp 22ndash35 2015

[14] D Dey B Chatterjee S Chakravorti and S Munshi ldquoCross-wavelet transform as a new paradigm for feature extractionfrom noisy partial discharge pulsesrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 17 no 1 pp 157ndash1662010

[15] F-C Gu H-C Chang F-H Chen C-C Kuo and C-HHsu ldquoApplication of the Hilbert-Huang transform with fractalfeature enhancement on partial discharge recognition of powercable jointsrdquo IET Science Measurement and Technology vol 6no 6 pp 440ndash448 2012

[16] YGong Y Liu and LWu ldquoIdentification of partial discharge ingas insulated switchgears with fractal theory and support vectormachinerdquo Power System Technology vol 35 no 3 pp 135ndash1392011

[17] X-D Wang B Li Z Liu et al ldquoAnalysis of partial dischargesignal using the Hilbert-Huang transformrdquo IEEE Transactionson Power Delivery vol 21 no 3 pp 1063ndash1067 2006

[18] S-B Liu C Lu J-L Yu andL-XWang ldquoApplication of hilbert-huang transform in pattern recognition for partial dischargeof transformersrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 31 pp 114ndash119 2008

[19] L Shen F-C Yang X-J Zhou and L Liu ldquoGear fault featureextraction based on improved EMD and morphological filterrdquoJournal of Vibration and Shock vol 29 no 3 pp 154ndash157 2010

[20] J Huang X Hu and Y Gong ldquoMachinery fault diagnosisof high voltage circuit breaker based on empirical modedecompositionrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 31 no 12 pp 108ndash113 2011

[21] G Yong-gang H Yulong and Q Jiali ldquoAn overview onmechanical failure diagnosis technique for high voltage circuitbreaker based on vibration signalrdquo High Voltage Engineeringvol 26 no 3 pp 66ndash68 2000

[22] H-L Sun Z-J He Y-Y Zi and J Yuan ldquoMulti-wavelettransform and its applications in mechanical fault diagnosis-areviewrdquo Mechanical Systems and Signal Processing vol 43 no1-2 pp 1ndash24 2014

[23] D E Newland ldquoWavelet analysis of vibration part 1 theoryrdquoASME Transactions on Journal of Vibration and Acoustics vol116 pp 409ndash441 1994

[24] H Shang J Yuan Y Wang and S Jin ldquoFeature extraction forpartial discharge based on cross-wavelet transform and corre-lation coefficient matrixrdquo Transactions of China ElectrotechnicalSociety vol 29 no 4 pp 274ndash281 2014

[25] A Krivda E Gulski L Satish and W S Zaengl ldquoUse offractal features for recognition of 3-D discharge patternsrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 2 no5 pp 889ndash892 1995

[26] K Gao K-X Tan F-Q Li and C-Q Wu ldquoPattern recognitionof partial discharges based on fractal features of the scatter setrdquoProceedings of the Chinese Society of Electrical Engineering vol22 no 5 pp 22ndash26 2002

[27] Y Xiao C-J Huang W-Y Yu and X-C Jiang ldquoSignal charac-teristic extraction of partial discharge in gis based on waveletand fractal analysisrdquo Automation of Electric Power Systems vol30 no 6 pp 66ndash69 2006

[28] W Chen Z Wang H Xie and W Yu ldquoCharacterization ofsurface EMG signal based on fuzzy entropyrdquo IEEE Transactionson Neural Systems and Rehabilitation Engineering vol 15 no 2pp 266ndash272 2007

[29] N E Huang Z Shen S R Long et al ldquoThe empiricalmode decomposition and the Hilbert spectrum for nonlinearand non-stationary time series analysisrdquo Proceedings of theRoyal Society of London Series A Mathematical Physical andEngineering Sciences vol 454 no 1971 pp 903ndash995 1998

[30] R Jia Q Xu L Tian X Luo and W Liu ldquoExtractingpartial discharge signals of hydroelectric generating set basedon empirical mode decompositionrdquo Journal of HydroelectricEngineering vol 26 no 4 pp 146ndash150 2007

[31] J Tang L Fan X Zhang and X Liu ldquoMulti-scale featureparameters extraction of gis partial discharge signal withharmonic wavelet packet transformrdquo Transactions of ChinaElectrotechnical Society vol 30 no 3 pp 250ndash257 2015

[32] J S Richman and J Randall Moorman ldquoPhysiological time-series analysis using approximate entropy and sample entropyrdquoAmerican Journal of PhysiologymdashHeart and Circulatory Physiol-ogy vol 278 no 6 pp H2039ndashH2049 2000

[33] W-J Chen Y-H Shao C-N Li and N-Y Deng ldquoMLTSVMa novel twin support vector machine to multi-label learningrdquoPattern Recognition vol 52 pp 61ndash74 2016

[34] U Kreszligel ldquoPair-wise classification and support vectormachinesrdquo in Advances in Kernel Methods pp 255ndash268 MITPress Cambridge Mass USA 1999

[35] 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

[36] T Dietterich and G Bakiri ldquoSolving multiclass learning prob-lems via error-correcting output codesrdquo Journal of ArtificialIntelligence Research vol 2 pp 263ndash286 1995

Mathematical Problems in Engineering 11

[37] S Liu Y Liu BWang and X Feng ldquoAn improved hyper-spheresupport vector machinerdquo in Proceedings of the 3rd InternationalConference on Natural Computation (ICNC rsquo07) pp 497ndash500IEEE Haikou China August 2007

[38] J Seo H Ma and T Saha ldquoProbabilistic wavelet transform forpartial discharge measurement of transformerrdquo IEEE Transac-tions on Dielectrics and Electrical Insulation vol 22 no 2 pp1105ndash1117 2015

[39] J Singh Y R Sood R K Jarial and P Verma ldquoConditionmonitoring of power transformersmdashbibliography surveyrdquo IEEEElectrical Insulation Magazine vol 24 no 3 pp 11ndash25 2008

[40] E Gumus N Kilic A Sertbas and O N Ucan ldquoEvaluationof face recognition techniques using PCA wavelets and SVMrdquoExpert Systems with Applications vol 37 no 9 pp 6404ndash64082010

[41] Z Liu H Cao X Chen Z He and Z Shen ldquoMulti-faultclassification based on wavelet SVM with PSO algorithmto analyze vibration signals from rolling element bearingsrdquoNeurocomputing vol 99 pp 399ndash410 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

Yes

No

Yes

Ending

No

Extracting signal details markingd(t) = s(t) minus m(t)

Letting s(t) = mi(t)

Letting s(t) = d(t)

Marking di(t) = d(t)

Letting mi(t) = s(t) minus di(t)

monotoneis

very smallfunction or mi(t) is

Judging whethermi(t)

whether to satisfy IMF two conditions or

not

Judging d(t)

m(t) =emax(t) + emin(t)

2

Calculating average value m(t) of the upper and lower envelopes

To seek for all the maximum and minimum value points and then bycubic spline interpolation to obtain upper and lower envelope

emax(t) and emin(t) of original signal

Signals s(t)

Figure 1 The algorithm flow process of EMD

It can be known from Figure 4 that the 2nd-order IMFfrequency band of single exponent attenuation PD signalsis 38ndash46MHz while the 2nd-order IMF frequency bandof single exponent vibration PD signals is 22ndash42MHzAccordingly the frequency band range of the same order IMFdecomposed by different signals is different

32 Extract Different Frequency Band Components of RawSignal The order of IMF obtained from PD signals throughEMD decomposition is closely related to partial dischargetype And even if they are at the same order of IMF theirfrequency band still has the obvious differences

Aiming at this phenomenon it is here that HHT bandpassing filter is adopted to solve the problem The concreteprocedures are as follows

(1) Sampling frequency of signals 119904(119905) is 119865119904 The numberof sampling points is 119899 After EMD decompositionthe 119898 pieces of IMF components are obtainedThe magnitude of each component Hilbert time-frequency spectrum is 119898 times 119899 which should be

classified as 119897 frequency bands and the set of instantamplitude values on the 119896 frequency band can bemarked as 119867(119896) (119896 = 1 2 119897)

(2) Zero set all the instant amplitude values on theHilberttime-frequency spectrum except for frequency band119896 and mark as 119867

lowast(119896)

(3) Zero set the IMF component point values which iscorresponding to the instant amplitude value beingset as zero in 119867

lowast(119896)

(4) Each IMF component treated using the filter can bereconstructed to obtain signals 119904(119905) component on thefrequency band

(5) As to the rest of frequency bands the above proce-dures are repeatedThat is signals 119904(119905) component onthe different frequency bands should be obtained

Signals 119904(119905) are treated through HHT band passing filterin order to obtain 119897 components Andmatrix119860 is constructed

4 Mathematical Problems in Engineering

Signal 1

Signal 2

times10minus3

times10minus3

01 02 03 04 05 06 07 08 09 10t (s)

minus02

0

02

04

06

Am

plitu

de (m

V)

minus02

minus01

0010203

Am

plitu

de (m

V)

01 02 03 04 05 06 07 08 09 10t (s)

Figure 2 The analog signals of PD

using 119897 components In other words matrix 119860 can cover theinformation of signal 119904(119905) under each frequency band

119860 =

[[[[[[[[

[

11988611

11988612

sdot sdot sdot 1198861119899

11988621

11988622

sdot sdot sdot 1198862119899

sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot

1198861198971

1198861198972

sdot sdot sdot 119886119897119899

]]]]]]]]

]

(3)

where 119886119894119895represents raw signals 119904(119905) data on each frequency

band

4 PD Signals Feature Region

41 Multidimensional Energy Parameters Different insula-tion defect faults have different partial discharge principleAnd their discharge pulse has obvious difference on the waveshape and the frequency band energy distribution while thesame insulation defect fault has strong similarity on the waveshape and the frequency band energy distribution [31] Forthis reason this paper suggests that multidimensional energyparameter is used to describe PD signals feature quantityThecalculation process of multidimensional energy parameter isgiven as follows

(1) Each row datum of time-frequency matrix 119860 ldquo1198861198941 1198861198942

119886119894119899rdquo stands for an independent frequency band

being marked as ldquo119883119896 119896 = 1 2 119897rdquo

(2) Energy value 119864(119896) of each frequency band is calcu-lated And then the normalization of 119864(119896) is carriedout

119864 (119896) = sum

119894=1119899

119883119896(119894)2

119864lowast(119896) =

119864 (119896)

sum119896=1119897

119864 (119896)

(4)

The multidimensional energy parameters of PD signalsobtained from the above steps are marked as 119864 = [119864

lowast

1 119864lowast

2

119864lowast

119897]

42 Multidimensional Sample Entropy Parameters Sampleentropy algorithm is a kind of theory originating fromnonlinear dynamics [28] whose value magnitude can reflectthe complexity of the system It is likely to provide a kind offresh solution for the nonstable signals analysis

Sample entropy of each row datum in time-frequencymatrix 119860 is calculated whose steps are as follows

(1) It is necessary to determine the dimensional number119898 and the threshold value 119903 How to choose theseparameters is discussed in [32] In this paper 119898 =

2 and 119903 = 02 Row data in the time-frequencymatrix 119860 is marked as ldquo119909

1 1199092 119909

119899rdquo And then ldquo119909

1

1199092 119909

119899rdquo should be converted into one group 119898

dimensional vectors see the following equation

119883(119894) = [119909 (119894) 119909 (119894 + 1) sdot sdot sdot 119909 (119894 + 119898 minus 1)] (5)

where 119894 = 1 2 119899 minus 119898 + 1(2) The maximum difference value between the corre-

sponding elements from 119883(119894) and 119883(119895) is defined asthe distance between 119883(119894) and 119883(119895) namely

119889 (119894 119895) = max119896

1003816100381610038161003816119909 (119894 + 119896) minus 119909 (119895 + 119896)1003816100381610038161003816

(119896 = 0 1 119898 minus 1)

(6)

(3) According to the given threshold 119903 count the numberof 119889(119894 119895) which make 119889(119894 119895) lt 119903 the ratio of thisnumber and the total vector 119899 minus 119898 + 1 is defined as119861119898

119894(119903)

119861119898

119894(119903) =

119873

119899 minus 119898 + 1 (7)

where 1 le 119895 le 119899 minus 119898 and 119895 = 119894(4) Take the average of119861119898

119894(119903) for every 119894 which is denoted

by 119861119898(119903)

119861119898

(119903) =1

119899 minus 119898 + 1

119899minus119898+1

sum

119894=1

119861119898

119894(119903) (8)

(5) Change the embedding dimension from 119898 to 119898 + 1repeating Step (1) to Step (4) and then 119861

119898+1(119903) is

obtained(6) The sample entropy of this row data in the time-

frequency matrix 119860 is obtained

SampEn (119898 119903 119899) = minus ln 119861119898+1

(119903)

119861119898 (119903) (9)

(7) Repeating Step (1) to Step (6) for the rest of other rowdata in the time-frequencymatrix119860 themultidimen-sional sample entropy parameters of PD signals can beobtained Then it is marked as follows

119875 = [1199011 1199012 119901

119897] (10)

Mathematical Problems in Engineering 5

Sign

alim

f1im

f2im

f3im

f4im

f5im

f6im

f7Empirical mode decomposition 1206012120587 = 1

times10minus3

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

minus40

100 150 200 250 300 350 400 450 50050com

pone

ntRe

sidua

l

(a) Analog signals served as single exponent attenuation type

Sign

alim

f1im

f2im

f3im

f4im

f5im

f6im

f7

Empirical mode decomposition 1206012120587 = 1

times10minus3

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050minus6

minus2

com

pone

ntRe

sidua

l

(b) Analog signals served as single exponent vibration type

Figure 3The PD analog signals of EMD decomposition results Note in the figure the scale of the vertical axis (imf1 imf2 imf7) is thesame as the raw signal the horizontal axis does not have unit the numerical meaning only on behalf of the sample points

0 02 04 06 08 1

0020406081Frequency (Hz)

002040608

1

Am

plitu

de (m

V)

t (s)times 10minus3

(a) Analog signals served as single exponent attenuation type

0020406081Frequency (Hz)

002040608

1

Am

plitu

de (m

V)

times 10minus3

0 02 04t (s)

06 08 1

(b) Analog signals served as single exponent vibration type

Figure 4 The 2nd-order IMF component 3D time-frequency spectrum

where 119901119894(119894 = 1 2 119897) represents the sample

entropy of the row 119894

43 PD Signal Feature Region A feature plane is establishedto describe the PD signals feature from different dimensionsThis feature plane consists of the multidimensional energyparameters and themultidimensional sample entropy param-eters

The energy parameter 119864(119896) and the sample entropyparameter 119901(119896) of the same frequency band would be definedas one feature point 119904

119896= (119901(119896) 119864(119896)) And then all the feature

points of PD signals are marked as one set 119878 namely

119878 = (119875 (1) 119864 (1)) (119875 (2) 119864 (2)) (119875 (119897) 119864 (119897)) (11)

Finding a minimum circle (119874 119877) on the feature planeincludes all elements of the feature point set 119878 And then

6 Mathematical Problems in Engineering

EMD decomposition

Frequency bands partition

Each frequency band component is calculatedby using HHT band-pass filter

Build the feature field and find a minimum circleon the feature field including all feature points

The sample entropy values of each frequency band component are calculated

The energy values of each frequency band component are calculated

Construct time-frequency matrix A

Row signals S(t)

Mark one feature point assk = (p(k) E(k))

P = [p1 p2 pl] E = [Elowast1 E

lowast2 E

lowastl ]

Figure 5 The calculation process of feature region

this circle (119874 119877) is defined as the feature region of PDsignals on the feature field It describes the PD signals featureinformation on the different frequency bands Its calculationprocess is shown in Figure 5 And the feature region of faultsignal is shown in Figure 6

5 Fault Diagnosis Based on Sphere-StructuredSupport Vector Machine

Support vector machine algorithm is a newmachine learningmethod developed on the statistical study theory It avoids thenetwork structure selection overlearning and underlearningand other problems in artificial neural network algorithmHowever standard SVM is a binary classifier so that it cannoteffectively solve multiclass classification [33] Therefore toovercome the shortages of standard SVM classifiers manyresearchers tried to modify and improve SVM such as ldquoone-against-onerdquo [34] ldquoone-against-allrdquo [35] and ldquodecision treerdquo[36] which is suitable for multiclass classification But theessences of these methods need to solve a large number ofquadratic programming problems [37] In order to reducecomputational complexity this paper suggests using sphere-structured SVM to deal with the multiclass classification

One multiclassification problem is expressed as follows119896 several 119899 dimensional space element set 119860119898 119898 = 1 119896

Sample parameters

Ener

gy p

aram

eter

s

OR

(p(1) E(1))

(p(2) E(2))

(p(l) E(l))

Figure 6 The feature region of signals

Each set 119860119898 stands for the one element including 119897 several

sample feature points 119909119894 119894 = 1 119897 As far as possible to find

a spherical surface includes all the elements of the set 119860119898

Mathematical Problems in Engineering 7

1

2

3

stands for class 1stands for class 2

stands for class 3

Figure 7 The sketch of spherical classification

In order to avoid some rough points impact on thealgorithm it is just here that a slack variable 120577

119898

119894is introduced

see the following equation1003817100381710038171003817119909119898

119894minus 11988611989810038171003817100381710038172

le 119877119898

+ 120577119898

119894120577119898

119894ge 0 119894 = 1 119897 (12)

where 119886119898 represents the center of sphere and 119877

119898 representsthe radius of sphere

The objective function of the above-mentioned problemsshould be defined as

min 119865 (119877119898 119886119898 120577119898

119894) = 119877119898

+ 119862119898sum

119894

120577119898

119894 (13)

where 119862119898 represents the penalty coefficient

Each classification can be described as similar to thequadratic programming problem Solving this quadratic pro-gramming problem can obtain one sphere And this sphererepresents this class Points on the spherical surface play a keyrole in spherical determination called the support vector asshown in Figure 7

One set 119883 = 1199091 1199092 119909

119897 represents one testing

sample 119909119894 119894 = 1 2 119897 represents one feature point of the

sample To judge which class sample119883 belongs to the processis as follows

Firstly it is necessary to calculatesum119894=1119897

119909119894minus 1198861198982 which

describes the quadratic sum of distance between 119909119894in the

sample 119883 with each spherical center And then to comparethe magnitude of sum

119894=1119897119909119894minus 1198861198982 with 119897 sdot 119877

119898 let 119889 representthe number of sum

119894=1119897119909119894minus 1198861198982le 119897 sdot 119877

119898

(1) For 119889 = 0 this means that most of feature pointsof sample 119883 are not located in any sphere So it isnecessary to find out one sphere which is the nearestto the sample 119883 If sum

119894=1119897119909119894minus 1198861199012

minus 119897 sdot 119877119901

=

minsum119894=1119897

119909119894minus 1198861198982minus 119897 sdot 119877

119898 the sample 119883 belongsto class 119901

(2) For 119889 = 1 the sample 119883 belongs to the class that thissphere represents

A

B

C D

xRi Rj

aiaj

Figure 8 The schematic diagram of spherical structure classifica-tion

(3) For 119889 gt 1 this means the sample 119883 is locatedin multiple spheres intersection area Then takingFigure 8 as the example consider the following

(1) All spheres including sample 119883 are marked asone set 119868

(2) forall119894 119895 isin 119868 calculate 119886119894119863 and 119886

119894119862 respectively

where 119886119894119863 represents the projection of

997888997888rarr119886119894119909 in

997888997888rarr119886119894119886119895 and 119886

119894119862 represents the projection of

997888997888rarr119886119894119860 in

997888997888rarr119886119894119886119895

119886119894119863 =

997888997888rarr119886119894119909 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

119886119894119862 =

997888997888rarr119886119894119860 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

(14)

(3) Compare the magnitude of 119886119894119863 with 119886

119894119862 for

119886119894119863 lt 119886

119894119862 the sample 119883 belongs to class 119894 or

else the sample 119883 belongs to class 119895

6 Experimental Analysis

Based on power transformer structure and the differentdischarge forms of the different insulation defect transformerpartial discharge forms can be divided into the followingthree types insulation internal defect (eg there are bubblesin insulating oil) surface discharge (eg the insulator surfaceflashover phenomenon) and electrode tip discharge (eg thewinding tip discharge)The in situ data of 330 kV transformerstations in Gansu province China are taken as a real examplefor carrying out the analysis Figure 9 shows the site conditionof the 330 kV transformer stations Figure 10 is a set of samplesignals of different faults

(1) Extract UHF PD Signal Feature Region EMD and HHTband-pass filters are carried out for different faults UHF PDsignals And then the PD signals components on different

8 Mathematical Problems in Engineering

UHFtransducer

Figure 9 The in situ condition Note power transformer (SSP-360MVA330 kV) and the UHF sensor parameters detection sensitivity(minus80 dBmsimminus35 dBm) working voltage (8Vsim15 V) working current (120mA) and output voltage (100mVsim3V)

Insulation internal defects

Surface discharge

Electrode tip discharge

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 10 Different defect UHF PD sample signals

frequency bands should be restructured Figure 11 shows thePD signals after filtering and reconstruction

Since the strongest noise in transformers station mainlyconcentrates into 10 kHz the transformers iron-core mag-netic noise mainly concentrates into the range of 10ndash70 kHz[38] so the paper chooses the subband over 1MHz to beserved as the feature subband The signals frequency bandenergy and sample entropy parameters on each subband arecalculated And then the feature filed is established to extractthe feature region PD signals Figure 12 shows the featureregion within 90 confidence interval of different UHF PDsignals Among them 1 represents the feature region ofthe surface discharge defect 2 represents the feature regionof the electrode tip discharge defect and 3 represents thefeature region of the insulation internal defect

Insulation internal defects

Surface discharge

Electrode tip discharge

times10minus3

minus005

0

005A

mpl

itude

(mV

)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus1

0

1

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus005

0

005

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 11 The PD signals after filtering and reconstruction

It can be seen from Figure 12 that there exist obviousdifferences in the feature region of the different defects Thedifferences mainly focus on the different frequency bandsenergy value and sample entropy value The sample entropyvalue of 2 and 3 is greater than 1 It indicates that thedischarge mechanism of 2 and 3 is more complicated andmore random than 1 The signals energy value of 1 and 2is greater than 3 It indicates that UHF PD signals amplitudeof 1 and 2 is bigger than 3 And their discharge processcan release more energy causing more serious damage to thepower transformer insulation

(2) Partial Discharge Fault Diagnosis The sphere-structuredsupport vectormachine algorithm is used to identify differentpartial discharge faults caused by different defects Accord-ingly 20 groups faults sample data are randomly selected to

Mathematical Problems in Engineering 9

Multidimensional characteristics region

0

02

04

06

08

1

12

14

16

18

2

Sign

al en

ergy

05 1 15 20Sample entropy

Feature pointsFeature pointsFeature points

1 characteristic region2 characteristic region3 characteristic region

Figure 12 The feature region within 90 confidence interval ofdifferent UHF PD signals

Table 1 Identification results

Types Maximumerror rate

Averageidentifying rate

Surface discharge 45 978Electrode tip discharge 6 953Insulation internal defect 43 961

carry out the training The rest of the faults sample data aremixed randomly Through many time testing experimentsthe final statistic results are shown in Table 1

It can be seen from Table 1 that the feature region of PDsignals is able to describe the feature information of differentpartial discharge faults And it is of better fault identificationresolutionThe average identification rate of different faults ismore than 95

Then two popular approaches of faults classification [39]PCA-SVM [40] and wavelet-SVM [41] are used to make acontrast analysis

As one can notice from Table 2 the fault classificationaccuracy of PCA-SVM is lower The fault classification accu-racy ofwavelet-SVMand the approach proposed in this paperis almost the same So PCA is unsuitable for feature extractionof time-variation signals The wavelet approach can betteranalyze time-variation signals but how to determine anoptimal mother wavelet is a big challenge for faults signalfeature extraction On the whole the method proposed inthis paper has more advantages in feature extraction of time-variation signals and faults classification

Table 2 The contrast analysis

Fault types

Fault classification accuracy ()

PCA-SVM Wavelet-SVMThe approachproposed inthis paper

Surface discharge 887 959 978Electrode tip discharge 881 971 953Insulation internal defect 90 942 961

7 Conclusion

Power transformer PD signals contain a large amount ofinsulation state information of power transformer Effectivelyextracting signals feature information is of great significancefor power transformer insulation onlinemonitoring In orderto effectively extract PD signals feature this paper suggestsa new method Firstly using UHF PD signals differentfrequency band components construct the time-frequencymatrix And then signals feature region is established bymultidimensional energy parameters and multidimensionalsample entropy parameters It is confirmed in Section 6 thatthis approach can describe PD signals feature informationFinally spherical structure support vectormachine algorithmis used to identify different partial discharge faults

Competing Interests

The authors declare there are no competing interests regard-ing the publication of this paper

Acknowledgments

This work was supported by the National Natural Sci-ence Foundation of China (no 51279161) Furthermore theauthors are grateful for the staff of China Electric PowerResearch Institute and State Grid Gansu Province ElectricPower Research Institute

References

[1] V P Darabad M Vakilian T R Blackburn and B T PhungldquoAn efficient PD data mining method for power transformerdefect models using SOM techniquerdquo International Journal ofElectrical Power amp Energy Systems vol 71 pp 373ndash382 2015

[2] M Yun K Park G Wang S Kim and G Kil ldquoAnalysisof propagation characteristics of acoustic signal in insulationoilrdquo Journal of the Korean Institute of Electrical and ElectronicMaterial Engineers vol 29 no 2 pp 114ndash119 2016

[3] X Zhang S Xiao N Shu J Tang and W Li ldquoGIS partialdischarge pattern recognition based on the chaos theoryrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 21 no2 pp 783ndash790 2014

[4] P B S M Gubanski G Csepes V Der Houhanessian etal ldquoDielectric response methods for diagnostics of powertransformersrdquo Tech Rep CIGRE Technical Brochure ParisFrance 2004

[5] A Abu-Siada and S Islam ldquoA new approach to identify powertransformer criticality and assetmanagement decision based on

10 Mathematical Problems in Engineering

dissolved gas-in-oil analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 19 no 3 pp 1007ndash1012 2012

[6] A Mikulecky and Z Stih ldquoInfluence of temperature moisturecontent and ageing on oil impregnated paper bushings insula-tionrdquo IEEE Transactions on Dielectrics and Electrical Insulationvol 20 no 4 pp 1421ndash1427 2013

[7] N Hashemnia A Abu-Siada and S Islam ldquoDetection ofpower transformer bushing faults and oil degradation usingfrequency response analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 23 no 1 pp 222ndash229 2016

[8] J A Almendros-Ibanez J C Burgos and B Garcia ldquoTrans-former field drying procedures a theoretical analysisrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 1978ndash19862009

[9] G-L Wang Y Zheng Y-P Hao and Y-M Li ldquoStudy onthe ultra-high-frequency sensor for PD detection in powertransformerrdquo Proceedings of the CSEE vol 22 no 4 pp 154ndash160 2002

[10] A A Bajwa S Habib and M Kamran ldquoAn investigationinto partial discharge pulse extraction methodsrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 964ndash982 2015

[11] L Satish and B Nazneen ldquoWavelet-based denoising of partialdischarge signals buried in excessive noise and interferencerdquoIEEE Transactions on Dielectrics and Electrical Insulation vol10 no 2 pp 354ndash367 2003

[12] W J K Raymond H A Illias A H A Bakar and H MokhlisldquoPartial discharge classifications review of recent progressrdquoMeasurement vol 68 pp 164ndash181 2015

[13] M Wu H Cao J Cao H-L Nguyen J B Gomes andS P Krishnaswamy ldquoAn overview of state-of-the-art partialdischarge analysis techniques for condition monitoringrdquo IEEEElectrical Insulation Magazine vol 31 no 6 pp 22ndash35 2015

[14] D Dey B Chatterjee S Chakravorti and S Munshi ldquoCross-wavelet transform as a new paradigm for feature extractionfrom noisy partial discharge pulsesrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 17 no 1 pp 157ndash1662010

[15] F-C Gu H-C Chang F-H Chen C-C Kuo and C-HHsu ldquoApplication of the Hilbert-Huang transform with fractalfeature enhancement on partial discharge recognition of powercable jointsrdquo IET Science Measurement and Technology vol 6no 6 pp 440ndash448 2012

[16] YGong Y Liu and LWu ldquoIdentification of partial discharge ingas insulated switchgears with fractal theory and support vectormachinerdquo Power System Technology vol 35 no 3 pp 135ndash1392011

[17] X-D Wang B Li Z Liu et al ldquoAnalysis of partial dischargesignal using the Hilbert-Huang transformrdquo IEEE Transactionson Power Delivery vol 21 no 3 pp 1063ndash1067 2006

[18] S-B Liu C Lu J-L Yu andL-XWang ldquoApplication of hilbert-huang transform in pattern recognition for partial dischargeof transformersrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 31 pp 114ndash119 2008

[19] L Shen F-C Yang X-J Zhou and L Liu ldquoGear fault featureextraction based on improved EMD and morphological filterrdquoJournal of Vibration and Shock vol 29 no 3 pp 154ndash157 2010

[20] J Huang X Hu and Y Gong ldquoMachinery fault diagnosisof high voltage circuit breaker based on empirical modedecompositionrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 31 no 12 pp 108ndash113 2011

[21] G Yong-gang H Yulong and Q Jiali ldquoAn overview onmechanical failure diagnosis technique for high voltage circuitbreaker based on vibration signalrdquo High Voltage Engineeringvol 26 no 3 pp 66ndash68 2000

[22] H-L Sun Z-J He Y-Y Zi and J Yuan ldquoMulti-wavelettransform and its applications in mechanical fault diagnosis-areviewrdquo Mechanical Systems and Signal Processing vol 43 no1-2 pp 1ndash24 2014

[23] D E Newland ldquoWavelet analysis of vibration part 1 theoryrdquoASME Transactions on Journal of Vibration and Acoustics vol116 pp 409ndash441 1994

[24] H Shang J Yuan Y Wang and S Jin ldquoFeature extraction forpartial discharge based on cross-wavelet transform and corre-lation coefficient matrixrdquo Transactions of China ElectrotechnicalSociety vol 29 no 4 pp 274ndash281 2014

[25] A Krivda E Gulski L Satish and W S Zaengl ldquoUse offractal features for recognition of 3-D discharge patternsrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 2 no5 pp 889ndash892 1995

[26] K Gao K-X Tan F-Q Li and C-Q Wu ldquoPattern recognitionof partial discharges based on fractal features of the scatter setrdquoProceedings of the Chinese Society of Electrical Engineering vol22 no 5 pp 22ndash26 2002

[27] Y Xiao C-J Huang W-Y Yu and X-C Jiang ldquoSignal charac-teristic extraction of partial discharge in gis based on waveletand fractal analysisrdquo Automation of Electric Power Systems vol30 no 6 pp 66ndash69 2006

[28] W Chen Z Wang H Xie and W Yu ldquoCharacterization ofsurface EMG signal based on fuzzy entropyrdquo IEEE Transactionson Neural Systems and Rehabilitation Engineering vol 15 no 2pp 266ndash272 2007

[29] N E Huang Z Shen S R Long et al ldquoThe empiricalmode decomposition and the Hilbert spectrum for nonlinearand non-stationary time series analysisrdquo Proceedings of theRoyal Society of London Series A Mathematical Physical andEngineering Sciences vol 454 no 1971 pp 903ndash995 1998

[30] R Jia Q Xu L Tian X Luo and W Liu ldquoExtractingpartial discharge signals of hydroelectric generating set basedon empirical mode decompositionrdquo Journal of HydroelectricEngineering vol 26 no 4 pp 146ndash150 2007

[31] J Tang L Fan X Zhang and X Liu ldquoMulti-scale featureparameters extraction of gis partial discharge signal withharmonic wavelet packet transformrdquo Transactions of ChinaElectrotechnical Society vol 30 no 3 pp 250ndash257 2015

[32] J S Richman and J Randall Moorman ldquoPhysiological time-series analysis using approximate entropy and sample entropyrdquoAmerican Journal of PhysiologymdashHeart and Circulatory Physiol-ogy vol 278 no 6 pp H2039ndashH2049 2000

[33] W-J Chen Y-H Shao C-N Li and N-Y Deng ldquoMLTSVMa novel twin support vector machine to multi-label learningrdquoPattern Recognition vol 52 pp 61ndash74 2016

[34] U Kreszligel ldquoPair-wise classification and support vectormachinesrdquo in Advances in Kernel Methods pp 255ndash268 MITPress Cambridge Mass USA 1999

[35] 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

[36] T Dietterich and G Bakiri ldquoSolving multiclass learning prob-lems via error-correcting output codesrdquo Journal of ArtificialIntelligence Research vol 2 pp 263ndash286 1995

Mathematical Problems in Engineering 11

[37] S Liu Y Liu BWang and X Feng ldquoAn improved hyper-spheresupport vector machinerdquo in Proceedings of the 3rd InternationalConference on Natural Computation (ICNC rsquo07) pp 497ndash500IEEE Haikou China August 2007

[38] J Seo H Ma and T Saha ldquoProbabilistic wavelet transform forpartial discharge measurement of transformerrdquo IEEE Transac-tions on Dielectrics and Electrical Insulation vol 22 no 2 pp1105ndash1117 2015

[39] J Singh Y R Sood R K Jarial and P Verma ldquoConditionmonitoring of power transformersmdashbibliography surveyrdquo IEEEElectrical Insulation Magazine vol 24 no 3 pp 11ndash25 2008

[40] E Gumus N Kilic A Sertbas and O N Ucan ldquoEvaluationof face recognition techniques using PCA wavelets and SVMrdquoExpert Systems with Applications vol 37 no 9 pp 6404ndash64082010

[41] Z Liu H Cao X Chen Z He and Z Shen ldquoMulti-faultclassification based on wavelet SVM with PSO algorithmto analyze vibration signals from rolling element bearingsrdquoNeurocomputing vol 99 pp 399ndash410 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

Signal 1

Signal 2

times10minus3

times10minus3

01 02 03 04 05 06 07 08 09 10t (s)

minus02

0

02

04

06

Am

plitu

de (m

V)

minus02

minus01

0010203

Am

plitu

de (m

V)

01 02 03 04 05 06 07 08 09 10t (s)

Figure 2 The analog signals of PD

using 119897 components In other words matrix 119860 can cover theinformation of signal 119904(119905) under each frequency band

119860 =

[[[[[[[[

[

11988611

11988612

sdot sdot sdot 1198861119899

11988621

11988622

sdot sdot sdot 1198862119899

sdot sdot sdot sdot sdot sdot

sdot sdot sdot sdot sdot sdot

1198861198971

1198861198972

sdot sdot sdot 119886119897119899

]]]]]]]]

]

(3)

where 119886119894119895represents raw signals 119904(119905) data on each frequency

band

4 PD Signals Feature Region

41 Multidimensional Energy Parameters Different insula-tion defect faults have different partial discharge principleAnd their discharge pulse has obvious difference on the waveshape and the frequency band energy distribution while thesame insulation defect fault has strong similarity on the waveshape and the frequency band energy distribution [31] Forthis reason this paper suggests that multidimensional energyparameter is used to describe PD signals feature quantityThecalculation process of multidimensional energy parameter isgiven as follows

(1) Each row datum of time-frequency matrix 119860 ldquo1198861198941 1198861198942

119886119894119899rdquo stands for an independent frequency band

being marked as ldquo119883119896 119896 = 1 2 119897rdquo

(2) Energy value 119864(119896) of each frequency band is calcu-lated And then the normalization of 119864(119896) is carriedout

119864 (119896) = sum

119894=1119899

119883119896(119894)2

119864lowast(119896) =

119864 (119896)

sum119896=1119897

119864 (119896)

(4)

The multidimensional energy parameters of PD signalsobtained from the above steps are marked as 119864 = [119864

lowast

1 119864lowast

2

119864lowast

119897]

42 Multidimensional Sample Entropy Parameters Sampleentropy algorithm is a kind of theory originating fromnonlinear dynamics [28] whose value magnitude can reflectthe complexity of the system It is likely to provide a kind offresh solution for the nonstable signals analysis

Sample entropy of each row datum in time-frequencymatrix 119860 is calculated whose steps are as follows

(1) It is necessary to determine the dimensional number119898 and the threshold value 119903 How to choose theseparameters is discussed in [32] In this paper 119898 =

2 and 119903 = 02 Row data in the time-frequencymatrix 119860 is marked as ldquo119909

1 1199092 119909

119899rdquo And then ldquo119909

1

1199092 119909

119899rdquo should be converted into one group 119898

dimensional vectors see the following equation

119883(119894) = [119909 (119894) 119909 (119894 + 1) sdot sdot sdot 119909 (119894 + 119898 minus 1)] (5)

where 119894 = 1 2 119899 minus 119898 + 1(2) The maximum difference value between the corre-

sponding elements from 119883(119894) and 119883(119895) is defined asthe distance between 119883(119894) and 119883(119895) namely

119889 (119894 119895) = max119896

1003816100381610038161003816119909 (119894 + 119896) minus 119909 (119895 + 119896)1003816100381610038161003816

(119896 = 0 1 119898 minus 1)

(6)

(3) According to the given threshold 119903 count the numberof 119889(119894 119895) which make 119889(119894 119895) lt 119903 the ratio of thisnumber and the total vector 119899 minus 119898 + 1 is defined as119861119898

119894(119903)

119861119898

119894(119903) =

119873

119899 minus 119898 + 1 (7)

where 1 le 119895 le 119899 minus 119898 and 119895 = 119894(4) Take the average of119861119898

119894(119903) for every 119894 which is denoted

by 119861119898(119903)

119861119898

(119903) =1

119899 minus 119898 + 1

119899minus119898+1

sum

119894=1

119861119898

119894(119903) (8)

(5) Change the embedding dimension from 119898 to 119898 + 1repeating Step (1) to Step (4) and then 119861

119898+1(119903) is

obtained(6) The sample entropy of this row data in the time-

frequency matrix 119860 is obtained

SampEn (119898 119903 119899) = minus ln 119861119898+1

(119903)

119861119898 (119903) (9)

(7) Repeating Step (1) to Step (6) for the rest of other rowdata in the time-frequencymatrix119860 themultidimen-sional sample entropy parameters of PD signals can beobtained Then it is marked as follows

119875 = [1199011 1199012 119901

119897] (10)

Mathematical Problems in Engineering 5

Sign

alim

f1im

f2im

f3im

f4im

f5im

f6im

f7Empirical mode decomposition 1206012120587 = 1

times10minus3

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

minus40

100 150 200 250 300 350 400 450 50050com

pone

ntRe

sidua

l

(a) Analog signals served as single exponent attenuation type

Sign

alim

f1im

f2im

f3im

f4im

f5im

f6im

f7

Empirical mode decomposition 1206012120587 = 1

times10minus3

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050minus6

minus2

com

pone

ntRe

sidua

l

(b) Analog signals served as single exponent vibration type

Figure 3The PD analog signals of EMD decomposition results Note in the figure the scale of the vertical axis (imf1 imf2 imf7) is thesame as the raw signal the horizontal axis does not have unit the numerical meaning only on behalf of the sample points

0 02 04 06 08 1

0020406081Frequency (Hz)

002040608

1

Am

plitu

de (m

V)

t (s)times 10minus3

(a) Analog signals served as single exponent attenuation type

0020406081Frequency (Hz)

002040608

1

Am

plitu

de (m

V)

times 10minus3

0 02 04t (s)

06 08 1

(b) Analog signals served as single exponent vibration type

Figure 4 The 2nd-order IMF component 3D time-frequency spectrum

where 119901119894(119894 = 1 2 119897) represents the sample

entropy of the row 119894

43 PD Signal Feature Region A feature plane is establishedto describe the PD signals feature from different dimensionsThis feature plane consists of the multidimensional energyparameters and themultidimensional sample entropy param-eters

The energy parameter 119864(119896) and the sample entropyparameter 119901(119896) of the same frequency band would be definedas one feature point 119904

119896= (119901(119896) 119864(119896)) And then all the feature

points of PD signals are marked as one set 119878 namely

119878 = (119875 (1) 119864 (1)) (119875 (2) 119864 (2)) (119875 (119897) 119864 (119897)) (11)

Finding a minimum circle (119874 119877) on the feature planeincludes all elements of the feature point set 119878 And then

6 Mathematical Problems in Engineering

EMD decomposition

Frequency bands partition

Each frequency band component is calculatedby using HHT band-pass filter

Build the feature field and find a minimum circleon the feature field including all feature points

The sample entropy values of each frequency band component are calculated

The energy values of each frequency band component are calculated

Construct time-frequency matrix A

Row signals S(t)

Mark one feature point assk = (p(k) E(k))

P = [p1 p2 pl] E = [Elowast1 E

lowast2 E

lowastl ]

Figure 5 The calculation process of feature region

this circle (119874 119877) is defined as the feature region of PDsignals on the feature field It describes the PD signals featureinformation on the different frequency bands Its calculationprocess is shown in Figure 5 And the feature region of faultsignal is shown in Figure 6

5 Fault Diagnosis Based on Sphere-StructuredSupport Vector Machine

Support vector machine algorithm is a newmachine learningmethod developed on the statistical study theory It avoids thenetwork structure selection overlearning and underlearningand other problems in artificial neural network algorithmHowever standard SVM is a binary classifier so that it cannoteffectively solve multiclass classification [33] Therefore toovercome the shortages of standard SVM classifiers manyresearchers tried to modify and improve SVM such as ldquoone-against-onerdquo [34] ldquoone-against-allrdquo [35] and ldquodecision treerdquo[36] which is suitable for multiclass classification But theessences of these methods need to solve a large number ofquadratic programming problems [37] In order to reducecomputational complexity this paper suggests using sphere-structured SVM to deal with the multiclass classification

One multiclassification problem is expressed as follows119896 several 119899 dimensional space element set 119860119898 119898 = 1 119896

Sample parameters

Ener

gy p

aram

eter

s

OR

(p(1) E(1))

(p(2) E(2))

(p(l) E(l))

Figure 6 The feature region of signals

Each set 119860119898 stands for the one element including 119897 several

sample feature points 119909119894 119894 = 1 119897 As far as possible to find

a spherical surface includes all the elements of the set 119860119898

Mathematical Problems in Engineering 7

1

2

3

stands for class 1stands for class 2

stands for class 3

Figure 7 The sketch of spherical classification

In order to avoid some rough points impact on thealgorithm it is just here that a slack variable 120577

119898

119894is introduced

see the following equation1003817100381710038171003817119909119898

119894minus 11988611989810038171003817100381710038172

le 119877119898

+ 120577119898

119894120577119898

119894ge 0 119894 = 1 119897 (12)

where 119886119898 represents the center of sphere and 119877

119898 representsthe radius of sphere

The objective function of the above-mentioned problemsshould be defined as

min 119865 (119877119898 119886119898 120577119898

119894) = 119877119898

+ 119862119898sum

119894

120577119898

119894 (13)

where 119862119898 represents the penalty coefficient

Each classification can be described as similar to thequadratic programming problem Solving this quadratic pro-gramming problem can obtain one sphere And this sphererepresents this class Points on the spherical surface play a keyrole in spherical determination called the support vector asshown in Figure 7

One set 119883 = 1199091 1199092 119909

119897 represents one testing

sample 119909119894 119894 = 1 2 119897 represents one feature point of the

sample To judge which class sample119883 belongs to the processis as follows

Firstly it is necessary to calculatesum119894=1119897

119909119894minus 1198861198982 which

describes the quadratic sum of distance between 119909119894in the

sample 119883 with each spherical center And then to comparethe magnitude of sum

119894=1119897119909119894minus 1198861198982 with 119897 sdot 119877

119898 let 119889 representthe number of sum

119894=1119897119909119894minus 1198861198982le 119897 sdot 119877

119898

(1) For 119889 = 0 this means that most of feature pointsof sample 119883 are not located in any sphere So it isnecessary to find out one sphere which is the nearestto the sample 119883 If sum

119894=1119897119909119894minus 1198861199012

minus 119897 sdot 119877119901

=

minsum119894=1119897

119909119894minus 1198861198982minus 119897 sdot 119877

119898 the sample 119883 belongsto class 119901

(2) For 119889 = 1 the sample 119883 belongs to the class that thissphere represents

A

B

C D

xRi Rj

aiaj

Figure 8 The schematic diagram of spherical structure classifica-tion

(3) For 119889 gt 1 this means the sample 119883 is locatedin multiple spheres intersection area Then takingFigure 8 as the example consider the following

(1) All spheres including sample 119883 are marked asone set 119868

(2) forall119894 119895 isin 119868 calculate 119886119894119863 and 119886

119894119862 respectively

where 119886119894119863 represents the projection of

997888997888rarr119886119894119909 in

997888997888rarr119886119894119886119895 and 119886

119894119862 represents the projection of

997888997888rarr119886119894119860 in

997888997888rarr119886119894119886119895

119886119894119863 =

997888997888rarr119886119894119909 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

119886119894119862 =

997888997888rarr119886119894119860 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

(14)

(3) Compare the magnitude of 119886119894119863 with 119886

119894119862 for

119886119894119863 lt 119886

119894119862 the sample 119883 belongs to class 119894 or

else the sample 119883 belongs to class 119895

6 Experimental Analysis

Based on power transformer structure and the differentdischarge forms of the different insulation defect transformerpartial discharge forms can be divided into the followingthree types insulation internal defect (eg there are bubblesin insulating oil) surface discharge (eg the insulator surfaceflashover phenomenon) and electrode tip discharge (eg thewinding tip discharge)The in situ data of 330 kV transformerstations in Gansu province China are taken as a real examplefor carrying out the analysis Figure 9 shows the site conditionof the 330 kV transformer stations Figure 10 is a set of samplesignals of different faults

(1) Extract UHF PD Signal Feature Region EMD and HHTband-pass filters are carried out for different faults UHF PDsignals And then the PD signals components on different

8 Mathematical Problems in Engineering

UHFtransducer

Figure 9 The in situ condition Note power transformer (SSP-360MVA330 kV) and the UHF sensor parameters detection sensitivity(minus80 dBmsimminus35 dBm) working voltage (8Vsim15 V) working current (120mA) and output voltage (100mVsim3V)

Insulation internal defects

Surface discharge

Electrode tip discharge

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 10 Different defect UHF PD sample signals

frequency bands should be restructured Figure 11 shows thePD signals after filtering and reconstruction

Since the strongest noise in transformers station mainlyconcentrates into 10 kHz the transformers iron-core mag-netic noise mainly concentrates into the range of 10ndash70 kHz[38] so the paper chooses the subband over 1MHz to beserved as the feature subband The signals frequency bandenergy and sample entropy parameters on each subband arecalculated And then the feature filed is established to extractthe feature region PD signals Figure 12 shows the featureregion within 90 confidence interval of different UHF PDsignals Among them 1 represents the feature region ofthe surface discharge defect 2 represents the feature regionof the electrode tip discharge defect and 3 represents thefeature region of the insulation internal defect

Insulation internal defects

Surface discharge

Electrode tip discharge

times10minus3

minus005

0

005A

mpl

itude

(mV

)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus1

0

1

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus005

0

005

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 11 The PD signals after filtering and reconstruction

It can be seen from Figure 12 that there exist obviousdifferences in the feature region of the different defects Thedifferences mainly focus on the different frequency bandsenergy value and sample entropy value The sample entropyvalue of 2 and 3 is greater than 1 It indicates that thedischarge mechanism of 2 and 3 is more complicated andmore random than 1 The signals energy value of 1 and 2is greater than 3 It indicates that UHF PD signals amplitudeof 1 and 2 is bigger than 3 And their discharge processcan release more energy causing more serious damage to thepower transformer insulation

(2) Partial Discharge Fault Diagnosis The sphere-structuredsupport vectormachine algorithm is used to identify differentpartial discharge faults caused by different defects Accord-ingly 20 groups faults sample data are randomly selected to

Mathematical Problems in Engineering 9

Multidimensional characteristics region

0

02

04

06

08

1

12

14

16

18

2

Sign

al en

ergy

05 1 15 20Sample entropy

Feature pointsFeature pointsFeature points

1 characteristic region2 characteristic region3 characteristic region

Figure 12 The feature region within 90 confidence interval ofdifferent UHF PD signals

Table 1 Identification results

Types Maximumerror rate

Averageidentifying rate

Surface discharge 45 978Electrode tip discharge 6 953Insulation internal defect 43 961

carry out the training The rest of the faults sample data aremixed randomly Through many time testing experimentsthe final statistic results are shown in Table 1

It can be seen from Table 1 that the feature region of PDsignals is able to describe the feature information of differentpartial discharge faults And it is of better fault identificationresolutionThe average identification rate of different faults ismore than 95

Then two popular approaches of faults classification [39]PCA-SVM [40] and wavelet-SVM [41] are used to make acontrast analysis

As one can notice from Table 2 the fault classificationaccuracy of PCA-SVM is lower The fault classification accu-racy ofwavelet-SVMand the approach proposed in this paperis almost the same So PCA is unsuitable for feature extractionof time-variation signals The wavelet approach can betteranalyze time-variation signals but how to determine anoptimal mother wavelet is a big challenge for faults signalfeature extraction On the whole the method proposed inthis paper has more advantages in feature extraction of time-variation signals and faults classification

Table 2 The contrast analysis

Fault types

Fault classification accuracy ()

PCA-SVM Wavelet-SVMThe approachproposed inthis paper

Surface discharge 887 959 978Electrode tip discharge 881 971 953Insulation internal defect 90 942 961

7 Conclusion

Power transformer PD signals contain a large amount ofinsulation state information of power transformer Effectivelyextracting signals feature information is of great significancefor power transformer insulation onlinemonitoring In orderto effectively extract PD signals feature this paper suggestsa new method Firstly using UHF PD signals differentfrequency band components construct the time-frequencymatrix And then signals feature region is established bymultidimensional energy parameters and multidimensionalsample entropy parameters It is confirmed in Section 6 thatthis approach can describe PD signals feature informationFinally spherical structure support vectormachine algorithmis used to identify different partial discharge faults

Competing Interests

The authors declare there are no competing interests regard-ing the publication of this paper

Acknowledgments

This work was supported by the National Natural Sci-ence Foundation of China (no 51279161) Furthermore theauthors are grateful for the staff of China Electric PowerResearch Institute and State Grid Gansu Province ElectricPower Research Institute

References

[1] V P Darabad M Vakilian T R Blackburn and B T PhungldquoAn efficient PD data mining method for power transformerdefect models using SOM techniquerdquo International Journal ofElectrical Power amp Energy Systems vol 71 pp 373ndash382 2015

[2] M Yun K Park G Wang S Kim and G Kil ldquoAnalysisof propagation characteristics of acoustic signal in insulationoilrdquo Journal of the Korean Institute of Electrical and ElectronicMaterial Engineers vol 29 no 2 pp 114ndash119 2016

[3] X Zhang S Xiao N Shu J Tang and W Li ldquoGIS partialdischarge pattern recognition based on the chaos theoryrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 21 no2 pp 783ndash790 2014

[4] P B S M Gubanski G Csepes V Der Houhanessian etal ldquoDielectric response methods for diagnostics of powertransformersrdquo Tech Rep CIGRE Technical Brochure ParisFrance 2004

[5] A Abu-Siada and S Islam ldquoA new approach to identify powertransformer criticality and assetmanagement decision based on

10 Mathematical Problems in Engineering

dissolved gas-in-oil analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 19 no 3 pp 1007ndash1012 2012

[6] A Mikulecky and Z Stih ldquoInfluence of temperature moisturecontent and ageing on oil impregnated paper bushings insula-tionrdquo IEEE Transactions on Dielectrics and Electrical Insulationvol 20 no 4 pp 1421ndash1427 2013

[7] N Hashemnia A Abu-Siada and S Islam ldquoDetection ofpower transformer bushing faults and oil degradation usingfrequency response analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 23 no 1 pp 222ndash229 2016

[8] J A Almendros-Ibanez J C Burgos and B Garcia ldquoTrans-former field drying procedures a theoretical analysisrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 1978ndash19862009

[9] G-L Wang Y Zheng Y-P Hao and Y-M Li ldquoStudy onthe ultra-high-frequency sensor for PD detection in powertransformerrdquo Proceedings of the CSEE vol 22 no 4 pp 154ndash160 2002

[10] A A Bajwa S Habib and M Kamran ldquoAn investigationinto partial discharge pulse extraction methodsrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 964ndash982 2015

[11] L Satish and B Nazneen ldquoWavelet-based denoising of partialdischarge signals buried in excessive noise and interferencerdquoIEEE Transactions on Dielectrics and Electrical Insulation vol10 no 2 pp 354ndash367 2003

[12] W J K Raymond H A Illias A H A Bakar and H MokhlisldquoPartial discharge classifications review of recent progressrdquoMeasurement vol 68 pp 164ndash181 2015

[13] M Wu H Cao J Cao H-L Nguyen J B Gomes andS P Krishnaswamy ldquoAn overview of state-of-the-art partialdischarge analysis techniques for condition monitoringrdquo IEEEElectrical Insulation Magazine vol 31 no 6 pp 22ndash35 2015

[14] D Dey B Chatterjee S Chakravorti and S Munshi ldquoCross-wavelet transform as a new paradigm for feature extractionfrom noisy partial discharge pulsesrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 17 no 1 pp 157ndash1662010

[15] F-C Gu H-C Chang F-H Chen C-C Kuo and C-HHsu ldquoApplication of the Hilbert-Huang transform with fractalfeature enhancement on partial discharge recognition of powercable jointsrdquo IET Science Measurement and Technology vol 6no 6 pp 440ndash448 2012

[16] YGong Y Liu and LWu ldquoIdentification of partial discharge ingas insulated switchgears with fractal theory and support vectormachinerdquo Power System Technology vol 35 no 3 pp 135ndash1392011

[17] X-D Wang B Li Z Liu et al ldquoAnalysis of partial dischargesignal using the Hilbert-Huang transformrdquo IEEE Transactionson Power Delivery vol 21 no 3 pp 1063ndash1067 2006

[18] S-B Liu C Lu J-L Yu andL-XWang ldquoApplication of hilbert-huang transform in pattern recognition for partial dischargeof transformersrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 31 pp 114ndash119 2008

[19] L Shen F-C Yang X-J Zhou and L Liu ldquoGear fault featureextraction based on improved EMD and morphological filterrdquoJournal of Vibration and Shock vol 29 no 3 pp 154ndash157 2010

[20] J Huang X Hu and Y Gong ldquoMachinery fault diagnosisof high voltage circuit breaker based on empirical modedecompositionrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 31 no 12 pp 108ndash113 2011

[21] G Yong-gang H Yulong and Q Jiali ldquoAn overview onmechanical failure diagnosis technique for high voltage circuitbreaker based on vibration signalrdquo High Voltage Engineeringvol 26 no 3 pp 66ndash68 2000

[22] H-L Sun Z-J He Y-Y Zi and J Yuan ldquoMulti-wavelettransform and its applications in mechanical fault diagnosis-areviewrdquo Mechanical Systems and Signal Processing vol 43 no1-2 pp 1ndash24 2014

[23] D E Newland ldquoWavelet analysis of vibration part 1 theoryrdquoASME Transactions on Journal of Vibration and Acoustics vol116 pp 409ndash441 1994

[24] H Shang J Yuan Y Wang and S Jin ldquoFeature extraction forpartial discharge based on cross-wavelet transform and corre-lation coefficient matrixrdquo Transactions of China ElectrotechnicalSociety vol 29 no 4 pp 274ndash281 2014

[25] A Krivda E Gulski L Satish and W S Zaengl ldquoUse offractal features for recognition of 3-D discharge patternsrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 2 no5 pp 889ndash892 1995

[26] K Gao K-X Tan F-Q Li and C-Q Wu ldquoPattern recognitionof partial discharges based on fractal features of the scatter setrdquoProceedings of the Chinese Society of Electrical Engineering vol22 no 5 pp 22ndash26 2002

[27] Y Xiao C-J Huang W-Y Yu and X-C Jiang ldquoSignal charac-teristic extraction of partial discharge in gis based on waveletand fractal analysisrdquo Automation of Electric Power Systems vol30 no 6 pp 66ndash69 2006

[28] W Chen Z Wang H Xie and W Yu ldquoCharacterization ofsurface EMG signal based on fuzzy entropyrdquo IEEE Transactionson Neural Systems and Rehabilitation Engineering vol 15 no 2pp 266ndash272 2007

[29] N E Huang Z Shen S R Long et al ldquoThe empiricalmode decomposition and the Hilbert spectrum for nonlinearand non-stationary time series analysisrdquo Proceedings of theRoyal Society of London Series A Mathematical Physical andEngineering Sciences vol 454 no 1971 pp 903ndash995 1998

[30] R Jia Q Xu L Tian X Luo and W Liu ldquoExtractingpartial discharge signals of hydroelectric generating set basedon empirical mode decompositionrdquo Journal of HydroelectricEngineering vol 26 no 4 pp 146ndash150 2007

[31] J Tang L Fan X Zhang and X Liu ldquoMulti-scale featureparameters extraction of gis partial discharge signal withharmonic wavelet packet transformrdquo Transactions of ChinaElectrotechnical Society vol 30 no 3 pp 250ndash257 2015

[32] J S Richman and J Randall Moorman ldquoPhysiological time-series analysis using approximate entropy and sample entropyrdquoAmerican Journal of PhysiologymdashHeart and Circulatory Physiol-ogy vol 278 no 6 pp H2039ndashH2049 2000

[33] W-J Chen Y-H Shao C-N Li and N-Y Deng ldquoMLTSVMa novel twin support vector machine to multi-label learningrdquoPattern Recognition vol 52 pp 61ndash74 2016

[34] U Kreszligel ldquoPair-wise classification and support vectormachinesrdquo in Advances in Kernel Methods pp 255ndash268 MITPress Cambridge Mass USA 1999

[35] 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

[36] T Dietterich and G Bakiri ldquoSolving multiclass learning prob-lems via error-correcting output codesrdquo Journal of ArtificialIntelligence Research vol 2 pp 263ndash286 1995

Mathematical Problems in Engineering 11

[37] S Liu Y Liu BWang and X Feng ldquoAn improved hyper-spheresupport vector machinerdquo in Proceedings of the 3rd InternationalConference on Natural Computation (ICNC rsquo07) pp 497ndash500IEEE Haikou China August 2007

[38] J Seo H Ma and T Saha ldquoProbabilistic wavelet transform forpartial discharge measurement of transformerrdquo IEEE Transac-tions on Dielectrics and Electrical Insulation vol 22 no 2 pp1105ndash1117 2015

[39] J Singh Y R Sood R K Jarial and P Verma ldquoConditionmonitoring of power transformersmdashbibliography surveyrdquo IEEEElectrical Insulation Magazine vol 24 no 3 pp 11ndash25 2008

[40] E Gumus N Kilic A Sertbas and O N Ucan ldquoEvaluationof face recognition techniques using PCA wavelets and SVMrdquoExpert Systems with Applications vol 37 no 9 pp 6404ndash64082010

[41] Z Liu H Cao X Chen Z He and Z Shen ldquoMulti-faultclassification based on wavelet SVM with PSO algorithmto analyze vibration signals from rolling element bearingsrdquoNeurocomputing vol 99 pp 399ndash410 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

Sign

alim

f1im

f2im

f3im

f4im

f5im

f6im

f7Empirical mode decomposition 1206012120587 = 1

times10minus3

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

minus40

100 150 200 250 300 350 400 450 50050com

pone

ntRe

sidua

l

(a) Analog signals served as single exponent attenuation type

Sign

alim

f1im

f2im

f3im

f4im

f5im

f6im

f7

Empirical mode decomposition 1206012120587 = 1

times10minus3

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050

100 150 200 250 300 350 400 450 50050minus6

minus2

com

pone

ntRe

sidua

l

(b) Analog signals served as single exponent vibration type

Figure 3The PD analog signals of EMD decomposition results Note in the figure the scale of the vertical axis (imf1 imf2 imf7) is thesame as the raw signal the horizontal axis does not have unit the numerical meaning only on behalf of the sample points

0 02 04 06 08 1

0020406081Frequency (Hz)

002040608

1

Am

plitu

de (m

V)

t (s)times 10minus3

(a) Analog signals served as single exponent attenuation type

0020406081Frequency (Hz)

002040608

1

Am

plitu

de (m

V)

times 10minus3

0 02 04t (s)

06 08 1

(b) Analog signals served as single exponent vibration type

Figure 4 The 2nd-order IMF component 3D time-frequency spectrum

where 119901119894(119894 = 1 2 119897) represents the sample

entropy of the row 119894

43 PD Signal Feature Region A feature plane is establishedto describe the PD signals feature from different dimensionsThis feature plane consists of the multidimensional energyparameters and themultidimensional sample entropy param-eters

The energy parameter 119864(119896) and the sample entropyparameter 119901(119896) of the same frequency band would be definedas one feature point 119904

119896= (119901(119896) 119864(119896)) And then all the feature

points of PD signals are marked as one set 119878 namely

119878 = (119875 (1) 119864 (1)) (119875 (2) 119864 (2)) (119875 (119897) 119864 (119897)) (11)

Finding a minimum circle (119874 119877) on the feature planeincludes all elements of the feature point set 119878 And then

6 Mathematical Problems in Engineering

EMD decomposition

Frequency bands partition

Each frequency band component is calculatedby using HHT band-pass filter

Build the feature field and find a minimum circleon the feature field including all feature points

The sample entropy values of each frequency band component are calculated

The energy values of each frequency band component are calculated

Construct time-frequency matrix A

Row signals S(t)

Mark one feature point assk = (p(k) E(k))

P = [p1 p2 pl] E = [Elowast1 E

lowast2 E

lowastl ]

Figure 5 The calculation process of feature region

this circle (119874 119877) is defined as the feature region of PDsignals on the feature field It describes the PD signals featureinformation on the different frequency bands Its calculationprocess is shown in Figure 5 And the feature region of faultsignal is shown in Figure 6

5 Fault Diagnosis Based on Sphere-StructuredSupport Vector Machine

Support vector machine algorithm is a newmachine learningmethod developed on the statistical study theory It avoids thenetwork structure selection overlearning and underlearningand other problems in artificial neural network algorithmHowever standard SVM is a binary classifier so that it cannoteffectively solve multiclass classification [33] Therefore toovercome the shortages of standard SVM classifiers manyresearchers tried to modify and improve SVM such as ldquoone-against-onerdquo [34] ldquoone-against-allrdquo [35] and ldquodecision treerdquo[36] which is suitable for multiclass classification But theessences of these methods need to solve a large number ofquadratic programming problems [37] In order to reducecomputational complexity this paper suggests using sphere-structured SVM to deal with the multiclass classification

One multiclassification problem is expressed as follows119896 several 119899 dimensional space element set 119860119898 119898 = 1 119896

Sample parameters

Ener

gy p

aram

eter

s

OR

(p(1) E(1))

(p(2) E(2))

(p(l) E(l))

Figure 6 The feature region of signals

Each set 119860119898 stands for the one element including 119897 several

sample feature points 119909119894 119894 = 1 119897 As far as possible to find

a spherical surface includes all the elements of the set 119860119898

Mathematical Problems in Engineering 7

1

2

3

stands for class 1stands for class 2

stands for class 3

Figure 7 The sketch of spherical classification

In order to avoid some rough points impact on thealgorithm it is just here that a slack variable 120577

119898

119894is introduced

see the following equation1003817100381710038171003817119909119898

119894minus 11988611989810038171003817100381710038172

le 119877119898

+ 120577119898

119894120577119898

119894ge 0 119894 = 1 119897 (12)

where 119886119898 represents the center of sphere and 119877

119898 representsthe radius of sphere

The objective function of the above-mentioned problemsshould be defined as

min 119865 (119877119898 119886119898 120577119898

119894) = 119877119898

+ 119862119898sum

119894

120577119898

119894 (13)

where 119862119898 represents the penalty coefficient

Each classification can be described as similar to thequadratic programming problem Solving this quadratic pro-gramming problem can obtain one sphere And this sphererepresents this class Points on the spherical surface play a keyrole in spherical determination called the support vector asshown in Figure 7

One set 119883 = 1199091 1199092 119909

119897 represents one testing

sample 119909119894 119894 = 1 2 119897 represents one feature point of the

sample To judge which class sample119883 belongs to the processis as follows

Firstly it is necessary to calculatesum119894=1119897

119909119894minus 1198861198982 which

describes the quadratic sum of distance between 119909119894in the

sample 119883 with each spherical center And then to comparethe magnitude of sum

119894=1119897119909119894minus 1198861198982 with 119897 sdot 119877

119898 let 119889 representthe number of sum

119894=1119897119909119894minus 1198861198982le 119897 sdot 119877

119898

(1) For 119889 = 0 this means that most of feature pointsof sample 119883 are not located in any sphere So it isnecessary to find out one sphere which is the nearestto the sample 119883 If sum

119894=1119897119909119894minus 1198861199012

minus 119897 sdot 119877119901

=

minsum119894=1119897

119909119894minus 1198861198982minus 119897 sdot 119877

119898 the sample 119883 belongsto class 119901

(2) For 119889 = 1 the sample 119883 belongs to the class that thissphere represents

A

B

C D

xRi Rj

aiaj

Figure 8 The schematic diagram of spherical structure classifica-tion

(3) For 119889 gt 1 this means the sample 119883 is locatedin multiple spheres intersection area Then takingFigure 8 as the example consider the following

(1) All spheres including sample 119883 are marked asone set 119868

(2) forall119894 119895 isin 119868 calculate 119886119894119863 and 119886

119894119862 respectively

where 119886119894119863 represents the projection of

997888997888rarr119886119894119909 in

997888997888rarr119886119894119886119895 and 119886

119894119862 represents the projection of

997888997888rarr119886119894119860 in

997888997888rarr119886119894119886119895

119886119894119863 =

997888997888rarr119886119894119909 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

119886119894119862 =

997888997888rarr119886119894119860 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

(14)

(3) Compare the magnitude of 119886119894119863 with 119886

119894119862 for

119886119894119863 lt 119886

119894119862 the sample 119883 belongs to class 119894 or

else the sample 119883 belongs to class 119895

6 Experimental Analysis

Based on power transformer structure and the differentdischarge forms of the different insulation defect transformerpartial discharge forms can be divided into the followingthree types insulation internal defect (eg there are bubblesin insulating oil) surface discharge (eg the insulator surfaceflashover phenomenon) and electrode tip discharge (eg thewinding tip discharge)The in situ data of 330 kV transformerstations in Gansu province China are taken as a real examplefor carrying out the analysis Figure 9 shows the site conditionof the 330 kV transformer stations Figure 10 is a set of samplesignals of different faults

(1) Extract UHF PD Signal Feature Region EMD and HHTband-pass filters are carried out for different faults UHF PDsignals And then the PD signals components on different

8 Mathematical Problems in Engineering

UHFtransducer

Figure 9 The in situ condition Note power transformer (SSP-360MVA330 kV) and the UHF sensor parameters detection sensitivity(minus80 dBmsimminus35 dBm) working voltage (8Vsim15 V) working current (120mA) and output voltage (100mVsim3V)

Insulation internal defects

Surface discharge

Electrode tip discharge

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 10 Different defect UHF PD sample signals

frequency bands should be restructured Figure 11 shows thePD signals after filtering and reconstruction

Since the strongest noise in transformers station mainlyconcentrates into 10 kHz the transformers iron-core mag-netic noise mainly concentrates into the range of 10ndash70 kHz[38] so the paper chooses the subband over 1MHz to beserved as the feature subband The signals frequency bandenergy and sample entropy parameters on each subband arecalculated And then the feature filed is established to extractthe feature region PD signals Figure 12 shows the featureregion within 90 confidence interval of different UHF PDsignals Among them 1 represents the feature region ofthe surface discharge defect 2 represents the feature regionof the electrode tip discharge defect and 3 represents thefeature region of the insulation internal defect

Insulation internal defects

Surface discharge

Electrode tip discharge

times10minus3

minus005

0

005A

mpl

itude

(mV

)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus1

0

1

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus005

0

005

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 11 The PD signals after filtering and reconstruction

It can be seen from Figure 12 that there exist obviousdifferences in the feature region of the different defects Thedifferences mainly focus on the different frequency bandsenergy value and sample entropy value The sample entropyvalue of 2 and 3 is greater than 1 It indicates that thedischarge mechanism of 2 and 3 is more complicated andmore random than 1 The signals energy value of 1 and 2is greater than 3 It indicates that UHF PD signals amplitudeof 1 and 2 is bigger than 3 And their discharge processcan release more energy causing more serious damage to thepower transformer insulation

(2) Partial Discharge Fault Diagnosis The sphere-structuredsupport vectormachine algorithm is used to identify differentpartial discharge faults caused by different defects Accord-ingly 20 groups faults sample data are randomly selected to

Mathematical Problems in Engineering 9

Multidimensional characteristics region

0

02

04

06

08

1

12

14

16

18

2

Sign

al en

ergy

05 1 15 20Sample entropy

Feature pointsFeature pointsFeature points

1 characteristic region2 characteristic region3 characteristic region

Figure 12 The feature region within 90 confidence interval ofdifferent UHF PD signals

Table 1 Identification results

Types Maximumerror rate

Averageidentifying rate

Surface discharge 45 978Electrode tip discharge 6 953Insulation internal defect 43 961

carry out the training The rest of the faults sample data aremixed randomly Through many time testing experimentsthe final statistic results are shown in Table 1

It can be seen from Table 1 that the feature region of PDsignals is able to describe the feature information of differentpartial discharge faults And it is of better fault identificationresolutionThe average identification rate of different faults ismore than 95

Then two popular approaches of faults classification [39]PCA-SVM [40] and wavelet-SVM [41] are used to make acontrast analysis

As one can notice from Table 2 the fault classificationaccuracy of PCA-SVM is lower The fault classification accu-racy ofwavelet-SVMand the approach proposed in this paperis almost the same So PCA is unsuitable for feature extractionof time-variation signals The wavelet approach can betteranalyze time-variation signals but how to determine anoptimal mother wavelet is a big challenge for faults signalfeature extraction On the whole the method proposed inthis paper has more advantages in feature extraction of time-variation signals and faults classification

Table 2 The contrast analysis

Fault types

Fault classification accuracy ()

PCA-SVM Wavelet-SVMThe approachproposed inthis paper

Surface discharge 887 959 978Electrode tip discharge 881 971 953Insulation internal defect 90 942 961

7 Conclusion

Power transformer PD signals contain a large amount ofinsulation state information of power transformer Effectivelyextracting signals feature information is of great significancefor power transformer insulation onlinemonitoring In orderto effectively extract PD signals feature this paper suggestsa new method Firstly using UHF PD signals differentfrequency band components construct the time-frequencymatrix And then signals feature region is established bymultidimensional energy parameters and multidimensionalsample entropy parameters It is confirmed in Section 6 thatthis approach can describe PD signals feature informationFinally spherical structure support vectormachine algorithmis used to identify different partial discharge faults

Competing Interests

The authors declare there are no competing interests regard-ing the publication of this paper

Acknowledgments

This work was supported by the National Natural Sci-ence Foundation of China (no 51279161) Furthermore theauthors are grateful for the staff of China Electric PowerResearch Institute and State Grid Gansu Province ElectricPower Research Institute

References

[1] V P Darabad M Vakilian T R Blackburn and B T PhungldquoAn efficient PD data mining method for power transformerdefect models using SOM techniquerdquo International Journal ofElectrical Power amp Energy Systems vol 71 pp 373ndash382 2015

[2] M Yun K Park G Wang S Kim and G Kil ldquoAnalysisof propagation characteristics of acoustic signal in insulationoilrdquo Journal of the Korean Institute of Electrical and ElectronicMaterial Engineers vol 29 no 2 pp 114ndash119 2016

[3] X Zhang S Xiao N Shu J Tang and W Li ldquoGIS partialdischarge pattern recognition based on the chaos theoryrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 21 no2 pp 783ndash790 2014

[4] P B S M Gubanski G Csepes V Der Houhanessian etal ldquoDielectric response methods for diagnostics of powertransformersrdquo Tech Rep CIGRE Technical Brochure ParisFrance 2004

[5] A Abu-Siada and S Islam ldquoA new approach to identify powertransformer criticality and assetmanagement decision based on

10 Mathematical Problems in Engineering

dissolved gas-in-oil analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 19 no 3 pp 1007ndash1012 2012

[6] A Mikulecky and Z Stih ldquoInfluence of temperature moisturecontent and ageing on oil impregnated paper bushings insula-tionrdquo IEEE Transactions on Dielectrics and Electrical Insulationvol 20 no 4 pp 1421ndash1427 2013

[7] N Hashemnia A Abu-Siada and S Islam ldquoDetection ofpower transformer bushing faults and oil degradation usingfrequency response analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 23 no 1 pp 222ndash229 2016

[8] J A Almendros-Ibanez J C Burgos and B Garcia ldquoTrans-former field drying procedures a theoretical analysisrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 1978ndash19862009

[9] G-L Wang Y Zheng Y-P Hao and Y-M Li ldquoStudy onthe ultra-high-frequency sensor for PD detection in powertransformerrdquo Proceedings of the CSEE vol 22 no 4 pp 154ndash160 2002

[10] A A Bajwa S Habib and M Kamran ldquoAn investigationinto partial discharge pulse extraction methodsrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 964ndash982 2015

[11] L Satish and B Nazneen ldquoWavelet-based denoising of partialdischarge signals buried in excessive noise and interferencerdquoIEEE Transactions on Dielectrics and Electrical Insulation vol10 no 2 pp 354ndash367 2003

[12] W J K Raymond H A Illias A H A Bakar and H MokhlisldquoPartial discharge classifications review of recent progressrdquoMeasurement vol 68 pp 164ndash181 2015

[13] M Wu H Cao J Cao H-L Nguyen J B Gomes andS P Krishnaswamy ldquoAn overview of state-of-the-art partialdischarge analysis techniques for condition monitoringrdquo IEEEElectrical Insulation Magazine vol 31 no 6 pp 22ndash35 2015

[14] D Dey B Chatterjee S Chakravorti and S Munshi ldquoCross-wavelet transform as a new paradigm for feature extractionfrom noisy partial discharge pulsesrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 17 no 1 pp 157ndash1662010

[15] F-C Gu H-C Chang F-H Chen C-C Kuo and C-HHsu ldquoApplication of the Hilbert-Huang transform with fractalfeature enhancement on partial discharge recognition of powercable jointsrdquo IET Science Measurement and Technology vol 6no 6 pp 440ndash448 2012

[16] YGong Y Liu and LWu ldquoIdentification of partial discharge ingas insulated switchgears with fractal theory and support vectormachinerdquo Power System Technology vol 35 no 3 pp 135ndash1392011

[17] X-D Wang B Li Z Liu et al ldquoAnalysis of partial dischargesignal using the Hilbert-Huang transformrdquo IEEE Transactionson Power Delivery vol 21 no 3 pp 1063ndash1067 2006

[18] S-B Liu C Lu J-L Yu andL-XWang ldquoApplication of hilbert-huang transform in pattern recognition for partial dischargeof transformersrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 31 pp 114ndash119 2008

[19] L Shen F-C Yang X-J Zhou and L Liu ldquoGear fault featureextraction based on improved EMD and morphological filterrdquoJournal of Vibration and Shock vol 29 no 3 pp 154ndash157 2010

[20] J Huang X Hu and Y Gong ldquoMachinery fault diagnosisof high voltage circuit breaker based on empirical modedecompositionrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 31 no 12 pp 108ndash113 2011

[21] G Yong-gang H Yulong and Q Jiali ldquoAn overview onmechanical failure diagnosis technique for high voltage circuitbreaker based on vibration signalrdquo High Voltage Engineeringvol 26 no 3 pp 66ndash68 2000

[22] H-L Sun Z-J He Y-Y Zi and J Yuan ldquoMulti-wavelettransform and its applications in mechanical fault diagnosis-areviewrdquo Mechanical Systems and Signal Processing vol 43 no1-2 pp 1ndash24 2014

[23] D E Newland ldquoWavelet analysis of vibration part 1 theoryrdquoASME Transactions on Journal of Vibration and Acoustics vol116 pp 409ndash441 1994

[24] H Shang J Yuan Y Wang and S Jin ldquoFeature extraction forpartial discharge based on cross-wavelet transform and corre-lation coefficient matrixrdquo Transactions of China ElectrotechnicalSociety vol 29 no 4 pp 274ndash281 2014

[25] A Krivda E Gulski L Satish and W S Zaengl ldquoUse offractal features for recognition of 3-D discharge patternsrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 2 no5 pp 889ndash892 1995

[26] K Gao K-X Tan F-Q Li and C-Q Wu ldquoPattern recognitionof partial discharges based on fractal features of the scatter setrdquoProceedings of the Chinese Society of Electrical Engineering vol22 no 5 pp 22ndash26 2002

[27] Y Xiao C-J Huang W-Y Yu and X-C Jiang ldquoSignal charac-teristic extraction of partial discharge in gis based on waveletand fractal analysisrdquo Automation of Electric Power Systems vol30 no 6 pp 66ndash69 2006

[28] W Chen Z Wang H Xie and W Yu ldquoCharacterization ofsurface EMG signal based on fuzzy entropyrdquo IEEE Transactionson Neural Systems and Rehabilitation Engineering vol 15 no 2pp 266ndash272 2007

[29] N E Huang Z Shen S R Long et al ldquoThe empiricalmode decomposition and the Hilbert spectrum for nonlinearand non-stationary time series analysisrdquo Proceedings of theRoyal Society of London Series A Mathematical Physical andEngineering Sciences vol 454 no 1971 pp 903ndash995 1998

[30] R Jia Q Xu L Tian X Luo and W Liu ldquoExtractingpartial discharge signals of hydroelectric generating set basedon empirical mode decompositionrdquo Journal of HydroelectricEngineering vol 26 no 4 pp 146ndash150 2007

[31] J Tang L Fan X Zhang and X Liu ldquoMulti-scale featureparameters extraction of gis partial discharge signal withharmonic wavelet packet transformrdquo Transactions of ChinaElectrotechnical Society vol 30 no 3 pp 250ndash257 2015

[32] J S Richman and J Randall Moorman ldquoPhysiological time-series analysis using approximate entropy and sample entropyrdquoAmerican Journal of PhysiologymdashHeart and Circulatory Physiol-ogy vol 278 no 6 pp H2039ndashH2049 2000

[33] W-J Chen Y-H Shao C-N Li and N-Y Deng ldquoMLTSVMa novel twin support vector machine to multi-label learningrdquoPattern Recognition vol 52 pp 61ndash74 2016

[34] U Kreszligel ldquoPair-wise classification and support vectormachinesrdquo in Advances in Kernel Methods pp 255ndash268 MITPress Cambridge Mass USA 1999

[35] 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

[36] T Dietterich and G Bakiri ldquoSolving multiclass learning prob-lems via error-correcting output codesrdquo Journal of ArtificialIntelligence Research vol 2 pp 263ndash286 1995

Mathematical Problems in Engineering 11

[37] S Liu Y Liu BWang and X Feng ldquoAn improved hyper-spheresupport vector machinerdquo in Proceedings of the 3rd InternationalConference on Natural Computation (ICNC rsquo07) pp 497ndash500IEEE Haikou China August 2007

[38] J Seo H Ma and T Saha ldquoProbabilistic wavelet transform forpartial discharge measurement of transformerrdquo IEEE Transac-tions on Dielectrics and Electrical Insulation vol 22 no 2 pp1105ndash1117 2015

[39] J Singh Y R Sood R K Jarial and P Verma ldquoConditionmonitoring of power transformersmdashbibliography surveyrdquo IEEEElectrical Insulation Magazine vol 24 no 3 pp 11ndash25 2008

[40] E Gumus N Kilic A Sertbas and O N Ucan ldquoEvaluationof face recognition techniques using PCA wavelets and SVMrdquoExpert Systems with Applications vol 37 no 9 pp 6404ndash64082010

[41] Z Liu H Cao X Chen Z He and Z Shen ldquoMulti-faultclassification based on wavelet SVM with PSO algorithmto analyze vibration signals from rolling element bearingsrdquoNeurocomputing vol 99 pp 399ndash410 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

EMD decomposition

Frequency bands partition

Each frequency band component is calculatedby using HHT band-pass filter

Build the feature field and find a minimum circleon the feature field including all feature points

The sample entropy values of each frequency band component are calculated

The energy values of each frequency band component are calculated

Construct time-frequency matrix A

Row signals S(t)

Mark one feature point assk = (p(k) E(k))

P = [p1 p2 pl] E = [Elowast1 E

lowast2 E

lowastl ]

Figure 5 The calculation process of feature region

this circle (119874 119877) is defined as the feature region of PDsignals on the feature field It describes the PD signals featureinformation on the different frequency bands Its calculationprocess is shown in Figure 5 And the feature region of faultsignal is shown in Figure 6

5 Fault Diagnosis Based on Sphere-StructuredSupport Vector Machine

Support vector machine algorithm is a newmachine learningmethod developed on the statistical study theory It avoids thenetwork structure selection overlearning and underlearningand other problems in artificial neural network algorithmHowever standard SVM is a binary classifier so that it cannoteffectively solve multiclass classification [33] Therefore toovercome the shortages of standard SVM classifiers manyresearchers tried to modify and improve SVM such as ldquoone-against-onerdquo [34] ldquoone-against-allrdquo [35] and ldquodecision treerdquo[36] which is suitable for multiclass classification But theessences of these methods need to solve a large number ofquadratic programming problems [37] In order to reducecomputational complexity this paper suggests using sphere-structured SVM to deal with the multiclass classification

One multiclassification problem is expressed as follows119896 several 119899 dimensional space element set 119860119898 119898 = 1 119896

Sample parameters

Ener

gy p

aram

eter

s

OR

(p(1) E(1))

(p(2) E(2))

(p(l) E(l))

Figure 6 The feature region of signals

Each set 119860119898 stands for the one element including 119897 several

sample feature points 119909119894 119894 = 1 119897 As far as possible to find

a spherical surface includes all the elements of the set 119860119898

Mathematical Problems in Engineering 7

1

2

3

stands for class 1stands for class 2

stands for class 3

Figure 7 The sketch of spherical classification

In order to avoid some rough points impact on thealgorithm it is just here that a slack variable 120577

119898

119894is introduced

see the following equation1003817100381710038171003817119909119898

119894minus 11988611989810038171003817100381710038172

le 119877119898

+ 120577119898

119894120577119898

119894ge 0 119894 = 1 119897 (12)

where 119886119898 represents the center of sphere and 119877

119898 representsthe radius of sphere

The objective function of the above-mentioned problemsshould be defined as

min 119865 (119877119898 119886119898 120577119898

119894) = 119877119898

+ 119862119898sum

119894

120577119898

119894 (13)

where 119862119898 represents the penalty coefficient

Each classification can be described as similar to thequadratic programming problem Solving this quadratic pro-gramming problem can obtain one sphere And this sphererepresents this class Points on the spherical surface play a keyrole in spherical determination called the support vector asshown in Figure 7

One set 119883 = 1199091 1199092 119909

119897 represents one testing

sample 119909119894 119894 = 1 2 119897 represents one feature point of the

sample To judge which class sample119883 belongs to the processis as follows

Firstly it is necessary to calculatesum119894=1119897

119909119894minus 1198861198982 which

describes the quadratic sum of distance between 119909119894in the

sample 119883 with each spherical center And then to comparethe magnitude of sum

119894=1119897119909119894minus 1198861198982 with 119897 sdot 119877

119898 let 119889 representthe number of sum

119894=1119897119909119894minus 1198861198982le 119897 sdot 119877

119898

(1) For 119889 = 0 this means that most of feature pointsof sample 119883 are not located in any sphere So it isnecessary to find out one sphere which is the nearestto the sample 119883 If sum

119894=1119897119909119894minus 1198861199012

minus 119897 sdot 119877119901

=

minsum119894=1119897

119909119894minus 1198861198982minus 119897 sdot 119877

119898 the sample 119883 belongsto class 119901

(2) For 119889 = 1 the sample 119883 belongs to the class that thissphere represents

A

B

C D

xRi Rj

aiaj

Figure 8 The schematic diagram of spherical structure classifica-tion

(3) For 119889 gt 1 this means the sample 119883 is locatedin multiple spheres intersection area Then takingFigure 8 as the example consider the following

(1) All spheres including sample 119883 are marked asone set 119868

(2) forall119894 119895 isin 119868 calculate 119886119894119863 and 119886

119894119862 respectively

where 119886119894119863 represents the projection of

997888997888rarr119886119894119909 in

997888997888rarr119886119894119886119895 and 119886

119894119862 represents the projection of

997888997888rarr119886119894119860 in

997888997888rarr119886119894119886119895

119886119894119863 =

997888997888rarr119886119894119909 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

119886119894119862 =

997888997888rarr119886119894119860 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

(14)

(3) Compare the magnitude of 119886119894119863 with 119886

119894119862 for

119886119894119863 lt 119886

119894119862 the sample 119883 belongs to class 119894 or

else the sample 119883 belongs to class 119895

6 Experimental Analysis

Based on power transformer structure and the differentdischarge forms of the different insulation defect transformerpartial discharge forms can be divided into the followingthree types insulation internal defect (eg there are bubblesin insulating oil) surface discharge (eg the insulator surfaceflashover phenomenon) and electrode tip discharge (eg thewinding tip discharge)The in situ data of 330 kV transformerstations in Gansu province China are taken as a real examplefor carrying out the analysis Figure 9 shows the site conditionof the 330 kV transformer stations Figure 10 is a set of samplesignals of different faults

(1) Extract UHF PD Signal Feature Region EMD and HHTband-pass filters are carried out for different faults UHF PDsignals And then the PD signals components on different

8 Mathematical Problems in Engineering

UHFtransducer

Figure 9 The in situ condition Note power transformer (SSP-360MVA330 kV) and the UHF sensor parameters detection sensitivity(minus80 dBmsimminus35 dBm) working voltage (8Vsim15 V) working current (120mA) and output voltage (100mVsim3V)

Insulation internal defects

Surface discharge

Electrode tip discharge

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 10 Different defect UHF PD sample signals

frequency bands should be restructured Figure 11 shows thePD signals after filtering and reconstruction

Since the strongest noise in transformers station mainlyconcentrates into 10 kHz the transformers iron-core mag-netic noise mainly concentrates into the range of 10ndash70 kHz[38] so the paper chooses the subband over 1MHz to beserved as the feature subband The signals frequency bandenergy and sample entropy parameters on each subband arecalculated And then the feature filed is established to extractthe feature region PD signals Figure 12 shows the featureregion within 90 confidence interval of different UHF PDsignals Among them 1 represents the feature region ofthe surface discharge defect 2 represents the feature regionof the electrode tip discharge defect and 3 represents thefeature region of the insulation internal defect

Insulation internal defects

Surface discharge

Electrode tip discharge

times10minus3

minus005

0

005A

mpl

itude

(mV

)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus1

0

1

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus005

0

005

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 11 The PD signals after filtering and reconstruction

It can be seen from Figure 12 that there exist obviousdifferences in the feature region of the different defects Thedifferences mainly focus on the different frequency bandsenergy value and sample entropy value The sample entropyvalue of 2 and 3 is greater than 1 It indicates that thedischarge mechanism of 2 and 3 is more complicated andmore random than 1 The signals energy value of 1 and 2is greater than 3 It indicates that UHF PD signals amplitudeof 1 and 2 is bigger than 3 And their discharge processcan release more energy causing more serious damage to thepower transformer insulation

(2) Partial Discharge Fault Diagnosis The sphere-structuredsupport vectormachine algorithm is used to identify differentpartial discharge faults caused by different defects Accord-ingly 20 groups faults sample data are randomly selected to

Mathematical Problems in Engineering 9

Multidimensional characteristics region

0

02

04

06

08

1

12

14

16

18

2

Sign

al en

ergy

05 1 15 20Sample entropy

Feature pointsFeature pointsFeature points

1 characteristic region2 characteristic region3 characteristic region

Figure 12 The feature region within 90 confidence interval ofdifferent UHF PD signals

Table 1 Identification results

Types Maximumerror rate

Averageidentifying rate

Surface discharge 45 978Electrode tip discharge 6 953Insulation internal defect 43 961

carry out the training The rest of the faults sample data aremixed randomly Through many time testing experimentsthe final statistic results are shown in Table 1

It can be seen from Table 1 that the feature region of PDsignals is able to describe the feature information of differentpartial discharge faults And it is of better fault identificationresolutionThe average identification rate of different faults ismore than 95

Then two popular approaches of faults classification [39]PCA-SVM [40] and wavelet-SVM [41] are used to make acontrast analysis

As one can notice from Table 2 the fault classificationaccuracy of PCA-SVM is lower The fault classification accu-racy ofwavelet-SVMand the approach proposed in this paperis almost the same So PCA is unsuitable for feature extractionof time-variation signals The wavelet approach can betteranalyze time-variation signals but how to determine anoptimal mother wavelet is a big challenge for faults signalfeature extraction On the whole the method proposed inthis paper has more advantages in feature extraction of time-variation signals and faults classification

Table 2 The contrast analysis

Fault types

Fault classification accuracy ()

PCA-SVM Wavelet-SVMThe approachproposed inthis paper

Surface discharge 887 959 978Electrode tip discharge 881 971 953Insulation internal defect 90 942 961

7 Conclusion

Power transformer PD signals contain a large amount ofinsulation state information of power transformer Effectivelyextracting signals feature information is of great significancefor power transformer insulation onlinemonitoring In orderto effectively extract PD signals feature this paper suggestsa new method Firstly using UHF PD signals differentfrequency band components construct the time-frequencymatrix And then signals feature region is established bymultidimensional energy parameters and multidimensionalsample entropy parameters It is confirmed in Section 6 thatthis approach can describe PD signals feature informationFinally spherical structure support vectormachine algorithmis used to identify different partial discharge faults

Competing Interests

The authors declare there are no competing interests regard-ing the publication of this paper

Acknowledgments

This work was supported by the National Natural Sci-ence Foundation of China (no 51279161) Furthermore theauthors are grateful for the staff of China Electric PowerResearch Institute and State Grid Gansu Province ElectricPower Research Institute

References

[1] V P Darabad M Vakilian T R Blackburn and B T PhungldquoAn efficient PD data mining method for power transformerdefect models using SOM techniquerdquo International Journal ofElectrical Power amp Energy Systems vol 71 pp 373ndash382 2015

[2] M Yun K Park G Wang S Kim and G Kil ldquoAnalysisof propagation characteristics of acoustic signal in insulationoilrdquo Journal of the Korean Institute of Electrical and ElectronicMaterial Engineers vol 29 no 2 pp 114ndash119 2016

[3] X Zhang S Xiao N Shu J Tang and W Li ldquoGIS partialdischarge pattern recognition based on the chaos theoryrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 21 no2 pp 783ndash790 2014

[4] P B S M Gubanski G Csepes V Der Houhanessian etal ldquoDielectric response methods for diagnostics of powertransformersrdquo Tech Rep CIGRE Technical Brochure ParisFrance 2004

[5] A Abu-Siada and S Islam ldquoA new approach to identify powertransformer criticality and assetmanagement decision based on

10 Mathematical Problems in Engineering

dissolved gas-in-oil analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 19 no 3 pp 1007ndash1012 2012

[6] A Mikulecky and Z Stih ldquoInfluence of temperature moisturecontent and ageing on oil impregnated paper bushings insula-tionrdquo IEEE Transactions on Dielectrics and Electrical Insulationvol 20 no 4 pp 1421ndash1427 2013

[7] N Hashemnia A Abu-Siada and S Islam ldquoDetection ofpower transformer bushing faults and oil degradation usingfrequency response analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 23 no 1 pp 222ndash229 2016

[8] J A Almendros-Ibanez J C Burgos and B Garcia ldquoTrans-former field drying procedures a theoretical analysisrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 1978ndash19862009

[9] G-L Wang Y Zheng Y-P Hao and Y-M Li ldquoStudy onthe ultra-high-frequency sensor for PD detection in powertransformerrdquo Proceedings of the CSEE vol 22 no 4 pp 154ndash160 2002

[10] A A Bajwa S Habib and M Kamran ldquoAn investigationinto partial discharge pulse extraction methodsrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 964ndash982 2015

[11] L Satish and B Nazneen ldquoWavelet-based denoising of partialdischarge signals buried in excessive noise and interferencerdquoIEEE Transactions on Dielectrics and Electrical Insulation vol10 no 2 pp 354ndash367 2003

[12] W J K Raymond H A Illias A H A Bakar and H MokhlisldquoPartial discharge classifications review of recent progressrdquoMeasurement vol 68 pp 164ndash181 2015

[13] M Wu H Cao J Cao H-L Nguyen J B Gomes andS P Krishnaswamy ldquoAn overview of state-of-the-art partialdischarge analysis techniques for condition monitoringrdquo IEEEElectrical Insulation Magazine vol 31 no 6 pp 22ndash35 2015

[14] D Dey B Chatterjee S Chakravorti and S Munshi ldquoCross-wavelet transform as a new paradigm for feature extractionfrom noisy partial discharge pulsesrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 17 no 1 pp 157ndash1662010

[15] F-C Gu H-C Chang F-H Chen C-C Kuo and C-HHsu ldquoApplication of the Hilbert-Huang transform with fractalfeature enhancement on partial discharge recognition of powercable jointsrdquo IET Science Measurement and Technology vol 6no 6 pp 440ndash448 2012

[16] YGong Y Liu and LWu ldquoIdentification of partial discharge ingas insulated switchgears with fractal theory and support vectormachinerdquo Power System Technology vol 35 no 3 pp 135ndash1392011

[17] X-D Wang B Li Z Liu et al ldquoAnalysis of partial dischargesignal using the Hilbert-Huang transformrdquo IEEE Transactionson Power Delivery vol 21 no 3 pp 1063ndash1067 2006

[18] S-B Liu C Lu J-L Yu andL-XWang ldquoApplication of hilbert-huang transform in pattern recognition for partial dischargeof transformersrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 31 pp 114ndash119 2008

[19] L Shen F-C Yang X-J Zhou and L Liu ldquoGear fault featureextraction based on improved EMD and morphological filterrdquoJournal of Vibration and Shock vol 29 no 3 pp 154ndash157 2010

[20] J Huang X Hu and Y Gong ldquoMachinery fault diagnosisof high voltage circuit breaker based on empirical modedecompositionrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 31 no 12 pp 108ndash113 2011

[21] G Yong-gang H Yulong and Q Jiali ldquoAn overview onmechanical failure diagnosis technique for high voltage circuitbreaker based on vibration signalrdquo High Voltage Engineeringvol 26 no 3 pp 66ndash68 2000

[22] H-L Sun Z-J He Y-Y Zi and J Yuan ldquoMulti-wavelettransform and its applications in mechanical fault diagnosis-areviewrdquo Mechanical Systems and Signal Processing vol 43 no1-2 pp 1ndash24 2014

[23] D E Newland ldquoWavelet analysis of vibration part 1 theoryrdquoASME Transactions on Journal of Vibration and Acoustics vol116 pp 409ndash441 1994

[24] H Shang J Yuan Y Wang and S Jin ldquoFeature extraction forpartial discharge based on cross-wavelet transform and corre-lation coefficient matrixrdquo Transactions of China ElectrotechnicalSociety vol 29 no 4 pp 274ndash281 2014

[25] A Krivda E Gulski L Satish and W S Zaengl ldquoUse offractal features for recognition of 3-D discharge patternsrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 2 no5 pp 889ndash892 1995

[26] K Gao K-X Tan F-Q Li and C-Q Wu ldquoPattern recognitionof partial discharges based on fractal features of the scatter setrdquoProceedings of the Chinese Society of Electrical Engineering vol22 no 5 pp 22ndash26 2002

[27] Y Xiao C-J Huang W-Y Yu and X-C Jiang ldquoSignal charac-teristic extraction of partial discharge in gis based on waveletand fractal analysisrdquo Automation of Electric Power Systems vol30 no 6 pp 66ndash69 2006

[28] W Chen Z Wang H Xie and W Yu ldquoCharacterization ofsurface EMG signal based on fuzzy entropyrdquo IEEE Transactionson Neural Systems and Rehabilitation Engineering vol 15 no 2pp 266ndash272 2007

[29] N E Huang Z Shen S R Long et al ldquoThe empiricalmode decomposition and the Hilbert spectrum for nonlinearand non-stationary time series analysisrdquo Proceedings of theRoyal Society of London Series A Mathematical Physical andEngineering Sciences vol 454 no 1971 pp 903ndash995 1998

[30] R Jia Q Xu L Tian X Luo and W Liu ldquoExtractingpartial discharge signals of hydroelectric generating set basedon empirical mode decompositionrdquo Journal of HydroelectricEngineering vol 26 no 4 pp 146ndash150 2007

[31] J Tang L Fan X Zhang and X Liu ldquoMulti-scale featureparameters extraction of gis partial discharge signal withharmonic wavelet packet transformrdquo Transactions of ChinaElectrotechnical Society vol 30 no 3 pp 250ndash257 2015

[32] J S Richman and J Randall Moorman ldquoPhysiological time-series analysis using approximate entropy and sample entropyrdquoAmerican Journal of PhysiologymdashHeart and Circulatory Physiol-ogy vol 278 no 6 pp H2039ndashH2049 2000

[33] W-J Chen Y-H Shao C-N Li and N-Y Deng ldquoMLTSVMa novel twin support vector machine to multi-label learningrdquoPattern Recognition vol 52 pp 61ndash74 2016

[34] U Kreszligel ldquoPair-wise classification and support vectormachinesrdquo in Advances in Kernel Methods pp 255ndash268 MITPress Cambridge Mass USA 1999

[35] 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

[36] T Dietterich and G Bakiri ldquoSolving multiclass learning prob-lems via error-correcting output codesrdquo Journal of ArtificialIntelligence Research vol 2 pp 263ndash286 1995

Mathematical Problems in Engineering 11

[37] S Liu Y Liu BWang and X Feng ldquoAn improved hyper-spheresupport vector machinerdquo in Proceedings of the 3rd InternationalConference on Natural Computation (ICNC rsquo07) pp 497ndash500IEEE Haikou China August 2007

[38] J Seo H Ma and T Saha ldquoProbabilistic wavelet transform forpartial discharge measurement of transformerrdquo IEEE Transac-tions on Dielectrics and Electrical Insulation vol 22 no 2 pp1105ndash1117 2015

[39] J Singh Y R Sood R K Jarial and P Verma ldquoConditionmonitoring of power transformersmdashbibliography surveyrdquo IEEEElectrical Insulation Magazine vol 24 no 3 pp 11ndash25 2008

[40] E Gumus N Kilic A Sertbas and O N Ucan ldquoEvaluationof face recognition techniques using PCA wavelets and SVMrdquoExpert Systems with Applications vol 37 no 9 pp 6404ndash64082010

[41] Z Liu H Cao X Chen Z He and Z Shen ldquoMulti-faultclassification based on wavelet SVM with PSO algorithmto analyze vibration signals from rolling element bearingsrdquoNeurocomputing vol 99 pp 399ndash410 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

1

2

3

stands for class 1stands for class 2

stands for class 3

Figure 7 The sketch of spherical classification

In order to avoid some rough points impact on thealgorithm it is just here that a slack variable 120577

119898

119894is introduced

see the following equation1003817100381710038171003817119909119898

119894minus 11988611989810038171003817100381710038172

le 119877119898

+ 120577119898

119894120577119898

119894ge 0 119894 = 1 119897 (12)

where 119886119898 represents the center of sphere and 119877

119898 representsthe radius of sphere

The objective function of the above-mentioned problemsshould be defined as

min 119865 (119877119898 119886119898 120577119898

119894) = 119877119898

+ 119862119898sum

119894

120577119898

119894 (13)

where 119862119898 represents the penalty coefficient

Each classification can be described as similar to thequadratic programming problem Solving this quadratic pro-gramming problem can obtain one sphere And this sphererepresents this class Points on the spherical surface play a keyrole in spherical determination called the support vector asshown in Figure 7

One set 119883 = 1199091 1199092 119909

119897 represents one testing

sample 119909119894 119894 = 1 2 119897 represents one feature point of the

sample To judge which class sample119883 belongs to the processis as follows

Firstly it is necessary to calculatesum119894=1119897

119909119894minus 1198861198982 which

describes the quadratic sum of distance between 119909119894in the

sample 119883 with each spherical center And then to comparethe magnitude of sum

119894=1119897119909119894minus 1198861198982 with 119897 sdot 119877

119898 let 119889 representthe number of sum

119894=1119897119909119894minus 1198861198982le 119897 sdot 119877

119898

(1) For 119889 = 0 this means that most of feature pointsof sample 119883 are not located in any sphere So it isnecessary to find out one sphere which is the nearestto the sample 119883 If sum

119894=1119897119909119894minus 1198861199012

minus 119897 sdot 119877119901

=

minsum119894=1119897

119909119894minus 1198861198982minus 119897 sdot 119877

119898 the sample 119883 belongsto class 119901

(2) For 119889 = 1 the sample 119883 belongs to the class that thissphere represents

A

B

C D

xRi Rj

aiaj

Figure 8 The schematic diagram of spherical structure classifica-tion

(3) For 119889 gt 1 this means the sample 119883 is locatedin multiple spheres intersection area Then takingFigure 8 as the example consider the following

(1) All spheres including sample 119883 are marked asone set 119868

(2) forall119894 119895 isin 119868 calculate 119886119894119863 and 119886

119894119862 respectively

where 119886119894119863 represents the projection of

997888997888rarr119886119894119909 in

997888997888rarr119886119894119886119895 and 119886

119894119862 represents the projection of

997888997888rarr119886119894119860 in

997888997888rarr119886119894119886119895

119886119894119863 =

997888997888rarr119886119894119909 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

119886119894119862 =

997888997888rarr119886119894119860 sdot

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

997888997888rarr119886119894119886119895

10038171003817100381710038171003817100381710038171003817

(14)

(3) Compare the magnitude of 119886119894119863 with 119886

119894119862 for

119886119894119863 lt 119886

119894119862 the sample 119883 belongs to class 119894 or

else the sample 119883 belongs to class 119895

6 Experimental Analysis

Based on power transformer structure and the differentdischarge forms of the different insulation defect transformerpartial discharge forms can be divided into the followingthree types insulation internal defect (eg there are bubblesin insulating oil) surface discharge (eg the insulator surfaceflashover phenomenon) and electrode tip discharge (eg thewinding tip discharge)The in situ data of 330 kV transformerstations in Gansu province China are taken as a real examplefor carrying out the analysis Figure 9 shows the site conditionof the 330 kV transformer stations Figure 10 is a set of samplesignals of different faults

(1) Extract UHF PD Signal Feature Region EMD and HHTband-pass filters are carried out for different faults UHF PDsignals And then the PD signals components on different

8 Mathematical Problems in Engineering

UHFtransducer

Figure 9 The in situ condition Note power transformer (SSP-360MVA330 kV) and the UHF sensor parameters detection sensitivity(minus80 dBmsimminus35 dBm) working voltage (8Vsim15 V) working current (120mA) and output voltage (100mVsim3V)

Insulation internal defects

Surface discharge

Electrode tip discharge

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 10 Different defect UHF PD sample signals

frequency bands should be restructured Figure 11 shows thePD signals after filtering and reconstruction

Since the strongest noise in transformers station mainlyconcentrates into 10 kHz the transformers iron-core mag-netic noise mainly concentrates into the range of 10ndash70 kHz[38] so the paper chooses the subband over 1MHz to beserved as the feature subband The signals frequency bandenergy and sample entropy parameters on each subband arecalculated And then the feature filed is established to extractthe feature region PD signals Figure 12 shows the featureregion within 90 confidence interval of different UHF PDsignals Among them 1 represents the feature region ofthe surface discharge defect 2 represents the feature regionof the electrode tip discharge defect and 3 represents thefeature region of the insulation internal defect

Insulation internal defects

Surface discharge

Electrode tip discharge

times10minus3

minus005

0

005A

mpl

itude

(mV

)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus1

0

1

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus005

0

005

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 11 The PD signals after filtering and reconstruction

It can be seen from Figure 12 that there exist obviousdifferences in the feature region of the different defects Thedifferences mainly focus on the different frequency bandsenergy value and sample entropy value The sample entropyvalue of 2 and 3 is greater than 1 It indicates that thedischarge mechanism of 2 and 3 is more complicated andmore random than 1 The signals energy value of 1 and 2is greater than 3 It indicates that UHF PD signals amplitudeof 1 and 2 is bigger than 3 And their discharge processcan release more energy causing more serious damage to thepower transformer insulation

(2) Partial Discharge Fault Diagnosis The sphere-structuredsupport vectormachine algorithm is used to identify differentpartial discharge faults caused by different defects Accord-ingly 20 groups faults sample data are randomly selected to

Mathematical Problems in Engineering 9

Multidimensional characteristics region

0

02

04

06

08

1

12

14

16

18

2

Sign

al en

ergy

05 1 15 20Sample entropy

Feature pointsFeature pointsFeature points

1 characteristic region2 characteristic region3 characteristic region

Figure 12 The feature region within 90 confidence interval ofdifferent UHF PD signals

Table 1 Identification results

Types Maximumerror rate

Averageidentifying rate

Surface discharge 45 978Electrode tip discharge 6 953Insulation internal defect 43 961

carry out the training The rest of the faults sample data aremixed randomly Through many time testing experimentsthe final statistic results are shown in Table 1

It can be seen from Table 1 that the feature region of PDsignals is able to describe the feature information of differentpartial discharge faults And it is of better fault identificationresolutionThe average identification rate of different faults ismore than 95

Then two popular approaches of faults classification [39]PCA-SVM [40] and wavelet-SVM [41] are used to make acontrast analysis

As one can notice from Table 2 the fault classificationaccuracy of PCA-SVM is lower The fault classification accu-racy ofwavelet-SVMand the approach proposed in this paperis almost the same So PCA is unsuitable for feature extractionof time-variation signals The wavelet approach can betteranalyze time-variation signals but how to determine anoptimal mother wavelet is a big challenge for faults signalfeature extraction On the whole the method proposed inthis paper has more advantages in feature extraction of time-variation signals and faults classification

Table 2 The contrast analysis

Fault types

Fault classification accuracy ()

PCA-SVM Wavelet-SVMThe approachproposed inthis paper

Surface discharge 887 959 978Electrode tip discharge 881 971 953Insulation internal defect 90 942 961

7 Conclusion

Power transformer PD signals contain a large amount ofinsulation state information of power transformer Effectivelyextracting signals feature information is of great significancefor power transformer insulation onlinemonitoring In orderto effectively extract PD signals feature this paper suggestsa new method Firstly using UHF PD signals differentfrequency band components construct the time-frequencymatrix And then signals feature region is established bymultidimensional energy parameters and multidimensionalsample entropy parameters It is confirmed in Section 6 thatthis approach can describe PD signals feature informationFinally spherical structure support vectormachine algorithmis used to identify different partial discharge faults

Competing Interests

The authors declare there are no competing interests regard-ing the publication of this paper

Acknowledgments

This work was supported by the National Natural Sci-ence Foundation of China (no 51279161) Furthermore theauthors are grateful for the staff of China Electric PowerResearch Institute and State Grid Gansu Province ElectricPower Research Institute

References

[1] V P Darabad M Vakilian T R Blackburn and B T PhungldquoAn efficient PD data mining method for power transformerdefect models using SOM techniquerdquo International Journal ofElectrical Power amp Energy Systems vol 71 pp 373ndash382 2015

[2] M Yun K Park G Wang S Kim and G Kil ldquoAnalysisof propagation characteristics of acoustic signal in insulationoilrdquo Journal of the Korean Institute of Electrical and ElectronicMaterial Engineers vol 29 no 2 pp 114ndash119 2016

[3] X Zhang S Xiao N Shu J Tang and W Li ldquoGIS partialdischarge pattern recognition based on the chaos theoryrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 21 no2 pp 783ndash790 2014

[4] P B S M Gubanski G Csepes V Der Houhanessian etal ldquoDielectric response methods for diagnostics of powertransformersrdquo Tech Rep CIGRE Technical Brochure ParisFrance 2004

[5] A Abu-Siada and S Islam ldquoA new approach to identify powertransformer criticality and assetmanagement decision based on

10 Mathematical Problems in Engineering

dissolved gas-in-oil analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 19 no 3 pp 1007ndash1012 2012

[6] A Mikulecky and Z Stih ldquoInfluence of temperature moisturecontent and ageing on oil impregnated paper bushings insula-tionrdquo IEEE Transactions on Dielectrics and Electrical Insulationvol 20 no 4 pp 1421ndash1427 2013

[7] N Hashemnia A Abu-Siada and S Islam ldquoDetection ofpower transformer bushing faults and oil degradation usingfrequency response analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 23 no 1 pp 222ndash229 2016

[8] J A Almendros-Ibanez J C Burgos and B Garcia ldquoTrans-former field drying procedures a theoretical analysisrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 1978ndash19862009

[9] G-L Wang Y Zheng Y-P Hao and Y-M Li ldquoStudy onthe ultra-high-frequency sensor for PD detection in powertransformerrdquo Proceedings of the CSEE vol 22 no 4 pp 154ndash160 2002

[10] A A Bajwa S Habib and M Kamran ldquoAn investigationinto partial discharge pulse extraction methodsrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 964ndash982 2015

[11] L Satish and B Nazneen ldquoWavelet-based denoising of partialdischarge signals buried in excessive noise and interferencerdquoIEEE Transactions on Dielectrics and Electrical Insulation vol10 no 2 pp 354ndash367 2003

[12] W J K Raymond H A Illias A H A Bakar and H MokhlisldquoPartial discharge classifications review of recent progressrdquoMeasurement vol 68 pp 164ndash181 2015

[13] M Wu H Cao J Cao H-L Nguyen J B Gomes andS P Krishnaswamy ldquoAn overview of state-of-the-art partialdischarge analysis techniques for condition monitoringrdquo IEEEElectrical Insulation Magazine vol 31 no 6 pp 22ndash35 2015

[14] D Dey B Chatterjee S Chakravorti and S Munshi ldquoCross-wavelet transform as a new paradigm for feature extractionfrom noisy partial discharge pulsesrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 17 no 1 pp 157ndash1662010

[15] F-C Gu H-C Chang F-H Chen C-C Kuo and C-HHsu ldquoApplication of the Hilbert-Huang transform with fractalfeature enhancement on partial discharge recognition of powercable jointsrdquo IET Science Measurement and Technology vol 6no 6 pp 440ndash448 2012

[16] YGong Y Liu and LWu ldquoIdentification of partial discharge ingas insulated switchgears with fractal theory and support vectormachinerdquo Power System Technology vol 35 no 3 pp 135ndash1392011

[17] X-D Wang B Li Z Liu et al ldquoAnalysis of partial dischargesignal using the Hilbert-Huang transformrdquo IEEE Transactionson Power Delivery vol 21 no 3 pp 1063ndash1067 2006

[18] S-B Liu C Lu J-L Yu andL-XWang ldquoApplication of hilbert-huang transform in pattern recognition for partial dischargeof transformersrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 31 pp 114ndash119 2008

[19] L Shen F-C Yang X-J Zhou and L Liu ldquoGear fault featureextraction based on improved EMD and morphological filterrdquoJournal of Vibration and Shock vol 29 no 3 pp 154ndash157 2010

[20] J Huang X Hu and Y Gong ldquoMachinery fault diagnosisof high voltage circuit breaker based on empirical modedecompositionrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 31 no 12 pp 108ndash113 2011

[21] G Yong-gang H Yulong and Q Jiali ldquoAn overview onmechanical failure diagnosis technique for high voltage circuitbreaker based on vibration signalrdquo High Voltage Engineeringvol 26 no 3 pp 66ndash68 2000

[22] H-L Sun Z-J He Y-Y Zi and J Yuan ldquoMulti-wavelettransform and its applications in mechanical fault diagnosis-areviewrdquo Mechanical Systems and Signal Processing vol 43 no1-2 pp 1ndash24 2014

[23] D E Newland ldquoWavelet analysis of vibration part 1 theoryrdquoASME Transactions on Journal of Vibration and Acoustics vol116 pp 409ndash441 1994

[24] H Shang J Yuan Y Wang and S Jin ldquoFeature extraction forpartial discharge based on cross-wavelet transform and corre-lation coefficient matrixrdquo Transactions of China ElectrotechnicalSociety vol 29 no 4 pp 274ndash281 2014

[25] A Krivda E Gulski L Satish and W S Zaengl ldquoUse offractal features for recognition of 3-D discharge patternsrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 2 no5 pp 889ndash892 1995

[26] K Gao K-X Tan F-Q Li and C-Q Wu ldquoPattern recognitionof partial discharges based on fractal features of the scatter setrdquoProceedings of the Chinese Society of Electrical Engineering vol22 no 5 pp 22ndash26 2002

[27] Y Xiao C-J Huang W-Y Yu and X-C Jiang ldquoSignal charac-teristic extraction of partial discharge in gis based on waveletand fractal analysisrdquo Automation of Electric Power Systems vol30 no 6 pp 66ndash69 2006

[28] W Chen Z Wang H Xie and W Yu ldquoCharacterization ofsurface EMG signal based on fuzzy entropyrdquo IEEE Transactionson Neural Systems and Rehabilitation Engineering vol 15 no 2pp 266ndash272 2007

[29] N E Huang Z Shen S R Long et al ldquoThe empiricalmode decomposition and the Hilbert spectrum for nonlinearand non-stationary time series analysisrdquo Proceedings of theRoyal Society of London Series A Mathematical Physical andEngineering Sciences vol 454 no 1971 pp 903ndash995 1998

[30] R Jia Q Xu L Tian X Luo and W Liu ldquoExtractingpartial discharge signals of hydroelectric generating set basedon empirical mode decompositionrdquo Journal of HydroelectricEngineering vol 26 no 4 pp 146ndash150 2007

[31] J Tang L Fan X Zhang and X Liu ldquoMulti-scale featureparameters extraction of gis partial discharge signal withharmonic wavelet packet transformrdquo Transactions of ChinaElectrotechnical Society vol 30 no 3 pp 250ndash257 2015

[32] J S Richman and J Randall Moorman ldquoPhysiological time-series analysis using approximate entropy and sample entropyrdquoAmerican Journal of PhysiologymdashHeart and Circulatory Physiol-ogy vol 278 no 6 pp H2039ndashH2049 2000

[33] W-J Chen Y-H Shao C-N Li and N-Y Deng ldquoMLTSVMa novel twin support vector machine to multi-label learningrdquoPattern Recognition vol 52 pp 61ndash74 2016

[34] U Kreszligel ldquoPair-wise classification and support vectormachinesrdquo in Advances in Kernel Methods pp 255ndash268 MITPress Cambridge Mass USA 1999

[35] 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

[36] T Dietterich and G Bakiri ldquoSolving multiclass learning prob-lems via error-correcting output codesrdquo Journal of ArtificialIntelligence Research vol 2 pp 263ndash286 1995

Mathematical Problems in Engineering 11

[37] S Liu Y Liu BWang and X Feng ldquoAn improved hyper-spheresupport vector machinerdquo in Proceedings of the 3rd InternationalConference on Natural Computation (ICNC rsquo07) pp 497ndash500IEEE Haikou China August 2007

[38] J Seo H Ma and T Saha ldquoProbabilistic wavelet transform forpartial discharge measurement of transformerrdquo IEEE Transac-tions on Dielectrics and Electrical Insulation vol 22 no 2 pp1105ndash1117 2015

[39] J Singh Y R Sood R K Jarial and P Verma ldquoConditionmonitoring of power transformersmdashbibliography surveyrdquo IEEEElectrical Insulation Magazine vol 24 no 3 pp 11ndash25 2008

[40] E Gumus N Kilic A Sertbas and O N Ucan ldquoEvaluationof face recognition techniques using PCA wavelets and SVMrdquoExpert Systems with Applications vol 37 no 9 pp 6404ndash64082010

[41] Z Liu H Cao X Chen Z He and Z Shen ldquoMulti-faultclassification based on wavelet SVM with PSO algorithmto analyze vibration signals from rolling element bearingsrdquoNeurocomputing vol 99 pp 399ndash410 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

UHFtransducer

Figure 9 The in situ condition Note power transformer (SSP-360MVA330 kV) and the UHF sensor parameters detection sensitivity(minus80 dBmsimminus35 dBm) working voltage (8Vsim15 V) working current (120mA) and output voltage (100mVsim3V)

Insulation internal defects

Surface discharge

Electrode tip discharge

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

minus01

0

01

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 10 Different defect UHF PD sample signals

frequency bands should be restructured Figure 11 shows thePD signals after filtering and reconstruction

Since the strongest noise in transformers station mainlyconcentrates into 10 kHz the transformers iron-core mag-netic noise mainly concentrates into the range of 10ndash70 kHz[38] so the paper chooses the subband over 1MHz to beserved as the feature subband The signals frequency bandenergy and sample entropy parameters on each subband arecalculated And then the feature filed is established to extractthe feature region PD signals Figure 12 shows the featureregion within 90 confidence interval of different UHF PDsignals Among them 1 represents the feature region ofthe surface discharge defect 2 represents the feature regionof the electrode tip discharge defect and 3 represents thefeature region of the insulation internal defect

Insulation internal defects

Surface discharge

Electrode tip discharge

times10minus3

minus005

0

005A

mpl

itude

(mV

)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus1

0

1

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

minus005

0

005

Am

plitu

de (m

V)

500 1000 1500 2000 2500 3000 3500 4000 4500 50000Sampling number

Figure 11 The PD signals after filtering and reconstruction

It can be seen from Figure 12 that there exist obviousdifferences in the feature region of the different defects Thedifferences mainly focus on the different frequency bandsenergy value and sample entropy value The sample entropyvalue of 2 and 3 is greater than 1 It indicates that thedischarge mechanism of 2 and 3 is more complicated andmore random than 1 The signals energy value of 1 and 2is greater than 3 It indicates that UHF PD signals amplitudeof 1 and 2 is bigger than 3 And their discharge processcan release more energy causing more serious damage to thepower transformer insulation

(2) Partial Discharge Fault Diagnosis The sphere-structuredsupport vectormachine algorithm is used to identify differentpartial discharge faults caused by different defects Accord-ingly 20 groups faults sample data are randomly selected to

Mathematical Problems in Engineering 9

Multidimensional characteristics region

0

02

04

06

08

1

12

14

16

18

2

Sign

al en

ergy

05 1 15 20Sample entropy

Feature pointsFeature pointsFeature points

1 characteristic region2 characteristic region3 characteristic region

Figure 12 The feature region within 90 confidence interval ofdifferent UHF PD signals

Table 1 Identification results

Types Maximumerror rate

Averageidentifying rate

Surface discharge 45 978Electrode tip discharge 6 953Insulation internal defect 43 961

carry out the training The rest of the faults sample data aremixed randomly Through many time testing experimentsthe final statistic results are shown in Table 1

It can be seen from Table 1 that the feature region of PDsignals is able to describe the feature information of differentpartial discharge faults And it is of better fault identificationresolutionThe average identification rate of different faults ismore than 95

Then two popular approaches of faults classification [39]PCA-SVM [40] and wavelet-SVM [41] are used to make acontrast analysis

As one can notice from Table 2 the fault classificationaccuracy of PCA-SVM is lower The fault classification accu-racy ofwavelet-SVMand the approach proposed in this paperis almost the same So PCA is unsuitable for feature extractionof time-variation signals The wavelet approach can betteranalyze time-variation signals but how to determine anoptimal mother wavelet is a big challenge for faults signalfeature extraction On the whole the method proposed inthis paper has more advantages in feature extraction of time-variation signals and faults classification

Table 2 The contrast analysis

Fault types

Fault classification accuracy ()

PCA-SVM Wavelet-SVMThe approachproposed inthis paper

Surface discharge 887 959 978Electrode tip discharge 881 971 953Insulation internal defect 90 942 961

7 Conclusion

Power transformer PD signals contain a large amount ofinsulation state information of power transformer Effectivelyextracting signals feature information is of great significancefor power transformer insulation onlinemonitoring In orderto effectively extract PD signals feature this paper suggestsa new method Firstly using UHF PD signals differentfrequency band components construct the time-frequencymatrix And then signals feature region is established bymultidimensional energy parameters and multidimensionalsample entropy parameters It is confirmed in Section 6 thatthis approach can describe PD signals feature informationFinally spherical structure support vectormachine algorithmis used to identify different partial discharge faults

Competing Interests

The authors declare there are no competing interests regard-ing the publication of this paper

Acknowledgments

This work was supported by the National Natural Sci-ence Foundation of China (no 51279161) Furthermore theauthors are grateful for the staff of China Electric PowerResearch Institute and State Grid Gansu Province ElectricPower Research Institute

References

[1] V P Darabad M Vakilian T R Blackburn and B T PhungldquoAn efficient PD data mining method for power transformerdefect models using SOM techniquerdquo International Journal ofElectrical Power amp Energy Systems vol 71 pp 373ndash382 2015

[2] M Yun K Park G Wang S Kim and G Kil ldquoAnalysisof propagation characteristics of acoustic signal in insulationoilrdquo Journal of the Korean Institute of Electrical and ElectronicMaterial Engineers vol 29 no 2 pp 114ndash119 2016

[3] X Zhang S Xiao N Shu J Tang and W Li ldquoGIS partialdischarge pattern recognition based on the chaos theoryrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 21 no2 pp 783ndash790 2014

[4] P B S M Gubanski G Csepes V Der Houhanessian etal ldquoDielectric response methods for diagnostics of powertransformersrdquo Tech Rep CIGRE Technical Brochure ParisFrance 2004

[5] A Abu-Siada and S Islam ldquoA new approach to identify powertransformer criticality and assetmanagement decision based on

10 Mathematical Problems in Engineering

dissolved gas-in-oil analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 19 no 3 pp 1007ndash1012 2012

[6] A Mikulecky and Z Stih ldquoInfluence of temperature moisturecontent and ageing on oil impregnated paper bushings insula-tionrdquo IEEE Transactions on Dielectrics and Electrical Insulationvol 20 no 4 pp 1421ndash1427 2013

[7] N Hashemnia A Abu-Siada and S Islam ldquoDetection ofpower transformer bushing faults and oil degradation usingfrequency response analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 23 no 1 pp 222ndash229 2016

[8] J A Almendros-Ibanez J C Burgos and B Garcia ldquoTrans-former field drying procedures a theoretical analysisrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 1978ndash19862009

[9] G-L Wang Y Zheng Y-P Hao and Y-M Li ldquoStudy onthe ultra-high-frequency sensor for PD detection in powertransformerrdquo Proceedings of the CSEE vol 22 no 4 pp 154ndash160 2002

[10] A A Bajwa S Habib and M Kamran ldquoAn investigationinto partial discharge pulse extraction methodsrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 964ndash982 2015

[11] L Satish and B Nazneen ldquoWavelet-based denoising of partialdischarge signals buried in excessive noise and interferencerdquoIEEE Transactions on Dielectrics and Electrical Insulation vol10 no 2 pp 354ndash367 2003

[12] W J K Raymond H A Illias A H A Bakar and H MokhlisldquoPartial discharge classifications review of recent progressrdquoMeasurement vol 68 pp 164ndash181 2015

[13] M Wu H Cao J Cao H-L Nguyen J B Gomes andS P Krishnaswamy ldquoAn overview of state-of-the-art partialdischarge analysis techniques for condition monitoringrdquo IEEEElectrical Insulation Magazine vol 31 no 6 pp 22ndash35 2015

[14] D Dey B Chatterjee S Chakravorti and S Munshi ldquoCross-wavelet transform as a new paradigm for feature extractionfrom noisy partial discharge pulsesrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 17 no 1 pp 157ndash1662010

[15] F-C Gu H-C Chang F-H Chen C-C Kuo and C-HHsu ldquoApplication of the Hilbert-Huang transform with fractalfeature enhancement on partial discharge recognition of powercable jointsrdquo IET Science Measurement and Technology vol 6no 6 pp 440ndash448 2012

[16] YGong Y Liu and LWu ldquoIdentification of partial discharge ingas insulated switchgears with fractal theory and support vectormachinerdquo Power System Technology vol 35 no 3 pp 135ndash1392011

[17] X-D Wang B Li Z Liu et al ldquoAnalysis of partial dischargesignal using the Hilbert-Huang transformrdquo IEEE Transactionson Power Delivery vol 21 no 3 pp 1063ndash1067 2006

[18] S-B Liu C Lu J-L Yu andL-XWang ldquoApplication of hilbert-huang transform in pattern recognition for partial dischargeof transformersrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 31 pp 114ndash119 2008

[19] L Shen F-C Yang X-J Zhou and L Liu ldquoGear fault featureextraction based on improved EMD and morphological filterrdquoJournal of Vibration and Shock vol 29 no 3 pp 154ndash157 2010

[20] J Huang X Hu and Y Gong ldquoMachinery fault diagnosisof high voltage circuit breaker based on empirical modedecompositionrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 31 no 12 pp 108ndash113 2011

[21] G Yong-gang H Yulong and Q Jiali ldquoAn overview onmechanical failure diagnosis technique for high voltage circuitbreaker based on vibration signalrdquo High Voltage Engineeringvol 26 no 3 pp 66ndash68 2000

[22] H-L Sun Z-J He Y-Y Zi and J Yuan ldquoMulti-wavelettransform and its applications in mechanical fault diagnosis-areviewrdquo Mechanical Systems and Signal Processing vol 43 no1-2 pp 1ndash24 2014

[23] D E Newland ldquoWavelet analysis of vibration part 1 theoryrdquoASME Transactions on Journal of Vibration and Acoustics vol116 pp 409ndash441 1994

[24] H Shang J Yuan Y Wang and S Jin ldquoFeature extraction forpartial discharge based on cross-wavelet transform and corre-lation coefficient matrixrdquo Transactions of China ElectrotechnicalSociety vol 29 no 4 pp 274ndash281 2014

[25] A Krivda E Gulski L Satish and W S Zaengl ldquoUse offractal features for recognition of 3-D discharge patternsrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 2 no5 pp 889ndash892 1995

[26] K Gao K-X Tan F-Q Li and C-Q Wu ldquoPattern recognitionof partial discharges based on fractal features of the scatter setrdquoProceedings of the Chinese Society of Electrical Engineering vol22 no 5 pp 22ndash26 2002

[27] Y Xiao C-J Huang W-Y Yu and X-C Jiang ldquoSignal charac-teristic extraction of partial discharge in gis based on waveletand fractal analysisrdquo Automation of Electric Power Systems vol30 no 6 pp 66ndash69 2006

[28] W Chen Z Wang H Xie and W Yu ldquoCharacterization ofsurface EMG signal based on fuzzy entropyrdquo IEEE Transactionson Neural Systems and Rehabilitation Engineering vol 15 no 2pp 266ndash272 2007

[29] N E Huang Z Shen S R Long et al ldquoThe empiricalmode decomposition and the Hilbert spectrum for nonlinearand non-stationary time series analysisrdquo Proceedings of theRoyal Society of London Series A Mathematical Physical andEngineering Sciences vol 454 no 1971 pp 903ndash995 1998

[30] R Jia Q Xu L Tian X Luo and W Liu ldquoExtractingpartial discharge signals of hydroelectric generating set basedon empirical mode decompositionrdquo Journal of HydroelectricEngineering vol 26 no 4 pp 146ndash150 2007

[31] J Tang L Fan X Zhang and X Liu ldquoMulti-scale featureparameters extraction of gis partial discharge signal withharmonic wavelet packet transformrdquo Transactions of ChinaElectrotechnical Society vol 30 no 3 pp 250ndash257 2015

[32] J S Richman and J Randall Moorman ldquoPhysiological time-series analysis using approximate entropy and sample entropyrdquoAmerican Journal of PhysiologymdashHeart and Circulatory Physiol-ogy vol 278 no 6 pp H2039ndashH2049 2000

[33] W-J Chen Y-H Shao C-N Li and N-Y Deng ldquoMLTSVMa novel twin support vector machine to multi-label learningrdquoPattern Recognition vol 52 pp 61ndash74 2016

[34] U Kreszligel ldquoPair-wise classification and support vectormachinesrdquo in Advances in Kernel Methods pp 255ndash268 MITPress Cambridge Mass USA 1999

[35] 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

[36] T Dietterich and G Bakiri ldquoSolving multiclass learning prob-lems via error-correcting output codesrdquo Journal of ArtificialIntelligence Research vol 2 pp 263ndash286 1995

Mathematical Problems in Engineering 11

[37] S Liu Y Liu BWang and X Feng ldquoAn improved hyper-spheresupport vector machinerdquo in Proceedings of the 3rd InternationalConference on Natural Computation (ICNC rsquo07) pp 497ndash500IEEE Haikou China August 2007

[38] J Seo H Ma and T Saha ldquoProbabilistic wavelet transform forpartial discharge measurement of transformerrdquo IEEE Transac-tions on Dielectrics and Electrical Insulation vol 22 no 2 pp1105ndash1117 2015

[39] J Singh Y R Sood R K Jarial and P Verma ldquoConditionmonitoring of power transformersmdashbibliography surveyrdquo IEEEElectrical Insulation Magazine vol 24 no 3 pp 11ndash25 2008

[40] E Gumus N Kilic A Sertbas and O N Ucan ldquoEvaluationof face recognition techniques using PCA wavelets and SVMrdquoExpert Systems with Applications vol 37 no 9 pp 6404ndash64082010

[41] Z Liu H Cao X Chen Z He and Z Shen ldquoMulti-faultclassification based on wavelet SVM with PSO algorithmto analyze vibration signals from rolling element bearingsrdquoNeurocomputing vol 99 pp 399ndash410 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

Multidimensional characteristics region

0

02

04

06

08

1

12

14

16

18

2

Sign

al en

ergy

05 1 15 20Sample entropy

Feature pointsFeature pointsFeature points

1 characteristic region2 characteristic region3 characteristic region

Figure 12 The feature region within 90 confidence interval ofdifferent UHF PD signals

Table 1 Identification results

Types Maximumerror rate

Averageidentifying rate

Surface discharge 45 978Electrode tip discharge 6 953Insulation internal defect 43 961

carry out the training The rest of the faults sample data aremixed randomly Through many time testing experimentsthe final statistic results are shown in Table 1

It can be seen from Table 1 that the feature region of PDsignals is able to describe the feature information of differentpartial discharge faults And it is of better fault identificationresolutionThe average identification rate of different faults ismore than 95

Then two popular approaches of faults classification [39]PCA-SVM [40] and wavelet-SVM [41] are used to make acontrast analysis

As one can notice from Table 2 the fault classificationaccuracy of PCA-SVM is lower The fault classification accu-racy ofwavelet-SVMand the approach proposed in this paperis almost the same So PCA is unsuitable for feature extractionof time-variation signals The wavelet approach can betteranalyze time-variation signals but how to determine anoptimal mother wavelet is a big challenge for faults signalfeature extraction On the whole the method proposed inthis paper has more advantages in feature extraction of time-variation signals and faults classification

Table 2 The contrast analysis

Fault types

Fault classification accuracy ()

PCA-SVM Wavelet-SVMThe approachproposed inthis paper

Surface discharge 887 959 978Electrode tip discharge 881 971 953Insulation internal defect 90 942 961

7 Conclusion

Power transformer PD signals contain a large amount ofinsulation state information of power transformer Effectivelyextracting signals feature information is of great significancefor power transformer insulation onlinemonitoring In orderto effectively extract PD signals feature this paper suggestsa new method Firstly using UHF PD signals differentfrequency band components construct the time-frequencymatrix And then signals feature region is established bymultidimensional energy parameters and multidimensionalsample entropy parameters It is confirmed in Section 6 thatthis approach can describe PD signals feature informationFinally spherical structure support vectormachine algorithmis used to identify different partial discharge faults

Competing Interests

The authors declare there are no competing interests regard-ing the publication of this paper

Acknowledgments

This work was supported by the National Natural Sci-ence Foundation of China (no 51279161) Furthermore theauthors are grateful for the staff of China Electric PowerResearch Institute and State Grid Gansu Province ElectricPower Research Institute

References

[1] V P Darabad M Vakilian T R Blackburn and B T PhungldquoAn efficient PD data mining method for power transformerdefect models using SOM techniquerdquo International Journal ofElectrical Power amp Energy Systems vol 71 pp 373ndash382 2015

[2] M Yun K Park G Wang S Kim and G Kil ldquoAnalysisof propagation characteristics of acoustic signal in insulationoilrdquo Journal of the Korean Institute of Electrical and ElectronicMaterial Engineers vol 29 no 2 pp 114ndash119 2016

[3] X Zhang S Xiao N Shu J Tang and W Li ldquoGIS partialdischarge pattern recognition based on the chaos theoryrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 21 no2 pp 783ndash790 2014

[4] P B S M Gubanski G Csepes V Der Houhanessian etal ldquoDielectric response methods for diagnostics of powertransformersrdquo Tech Rep CIGRE Technical Brochure ParisFrance 2004

[5] A Abu-Siada and S Islam ldquoA new approach to identify powertransformer criticality and assetmanagement decision based on

10 Mathematical Problems in Engineering

dissolved gas-in-oil analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 19 no 3 pp 1007ndash1012 2012

[6] A Mikulecky and Z Stih ldquoInfluence of temperature moisturecontent and ageing on oil impregnated paper bushings insula-tionrdquo IEEE Transactions on Dielectrics and Electrical Insulationvol 20 no 4 pp 1421ndash1427 2013

[7] N Hashemnia A Abu-Siada and S Islam ldquoDetection ofpower transformer bushing faults and oil degradation usingfrequency response analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 23 no 1 pp 222ndash229 2016

[8] J A Almendros-Ibanez J C Burgos and B Garcia ldquoTrans-former field drying procedures a theoretical analysisrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 1978ndash19862009

[9] G-L Wang Y Zheng Y-P Hao and Y-M Li ldquoStudy onthe ultra-high-frequency sensor for PD detection in powertransformerrdquo Proceedings of the CSEE vol 22 no 4 pp 154ndash160 2002

[10] A A Bajwa S Habib and M Kamran ldquoAn investigationinto partial discharge pulse extraction methodsrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 964ndash982 2015

[11] L Satish and B Nazneen ldquoWavelet-based denoising of partialdischarge signals buried in excessive noise and interferencerdquoIEEE Transactions on Dielectrics and Electrical Insulation vol10 no 2 pp 354ndash367 2003

[12] W J K Raymond H A Illias A H A Bakar and H MokhlisldquoPartial discharge classifications review of recent progressrdquoMeasurement vol 68 pp 164ndash181 2015

[13] M Wu H Cao J Cao H-L Nguyen J B Gomes andS P Krishnaswamy ldquoAn overview of state-of-the-art partialdischarge analysis techniques for condition monitoringrdquo IEEEElectrical Insulation Magazine vol 31 no 6 pp 22ndash35 2015

[14] D Dey B Chatterjee S Chakravorti and S Munshi ldquoCross-wavelet transform as a new paradigm for feature extractionfrom noisy partial discharge pulsesrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 17 no 1 pp 157ndash1662010

[15] F-C Gu H-C Chang F-H Chen C-C Kuo and C-HHsu ldquoApplication of the Hilbert-Huang transform with fractalfeature enhancement on partial discharge recognition of powercable jointsrdquo IET Science Measurement and Technology vol 6no 6 pp 440ndash448 2012

[16] YGong Y Liu and LWu ldquoIdentification of partial discharge ingas insulated switchgears with fractal theory and support vectormachinerdquo Power System Technology vol 35 no 3 pp 135ndash1392011

[17] X-D Wang B Li Z Liu et al ldquoAnalysis of partial dischargesignal using the Hilbert-Huang transformrdquo IEEE Transactionson Power Delivery vol 21 no 3 pp 1063ndash1067 2006

[18] S-B Liu C Lu J-L Yu andL-XWang ldquoApplication of hilbert-huang transform in pattern recognition for partial dischargeof transformersrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 31 pp 114ndash119 2008

[19] L Shen F-C Yang X-J Zhou and L Liu ldquoGear fault featureextraction based on improved EMD and morphological filterrdquoJournal of Vibration and Shock vol 29 no 3 pp 154ndash157 2010

[20] J Huang X Hu and Y Gong ldquoMachinery fault diagnosisof high voltage circuit breaker based on empirical modedecompositionrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 31 no 12 pp 108ndash113 2011

[21] G Yong-gang H Yulong and Q Jiali ldquoAn overview onmechanical failure diagnosis technique for high voltage circuitbreaker based on vibration signalrdquo High Voltage Engineeringvol 26 no 3 pp 66ndash68 2000

[22] H-L Sun Z-J He Y-Y Zi and J Yuan ldquoMulti-wavelettransform and its applications in mechanical fault diagnosis-areviewrdquo Mechanical Systems and Signal Processing vol 43 no1-2 pp 1ndash24 2014

[23] D E Newland ldquoWavelet analysis of vibration part 1 theoryrdquoASME Transactions on Journal of Vibration and Acoustics vol116 pp 409ndash441 1994

[24] H Shang J Yuan Y Wang and S Jin ldquoFeature extraction forpartial discharge based on cross-wavelet transform and corre-lation coefficient matrixrdquo Transactions of China ElectrotechnicalSociety vol 29 no 4 pp 274ndash281 2014

[25] A Krivda E Gulski L Satish and W S Zaengl ldquoUse offractal features for recognition of 3-D discharge patternsrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 2 no5 pp 889ndash892 1995

[26] K Gao K-X Tan F-Q Li and C-Q Wu ldquoPattern recognitionof partial discharges based on fractal features of the scatter setrdquoProceedings of the Chinese Society of Electrical Engineering vol22 no 5 pp 22ndash26 2002

[27] Y Xiao C-J Huang W-Y Yu and X-C Jiang ldquoSignal charac-teristic extraction of partial discharge in gis based on waveletand fractal analysisrdquo Automation of Electric Power Systems vol30 no 6 pp 66ndash69 2006

[28] W Chen Z Wang H Xie and W Yu ldquoCharacterization ofsurface EMG signal based on fuzzy entropyrdquo IEEE Transactionson Neural Systems and Rehabilitation Engineering vol 15 no 2pp 266ndash272 2007

[29] N E Huang Z Shen S R Long et al ldquoThe empiricalmode decomposition and the Hilbert spectrum for nonlinearand non-stationary time series analysisrdquo Proceedings of theRoyal Society of London Series A Mathematical Physical andEngineering Sciences vol 454 no 1971 pp 903ndash995 1998

[30] R Jia Q Xu L Tian X Luo and W Liu ldquoExtractingpartial discharge signals of hydroelectric generating set basedon empirical mode decompositionrdquo Journal of HydroelectricEngineering vol 26 no 4 pp 146ndash150 2007

[31] J Tang L Fan X Zhang and X Liu ldquoMulti-scale featureparameters extraction of gis partial discharge signal withharmonic wavelet packet transformrdquo Transactions of ChinaElectrotechnical Society vol 30 no 3 pp 250ndash257 2015

[32] J S Richman and J Randall Moorman ldquoPhysiological time-series analysis using approximate entropy and sample entropyrdquoAmerican Journal of PhysiologymdashHeart and Circulatory Physiol-ogy vol 278 no 6 pp H2039ndashH2049 2000

[33] W-J Chen Y-H Shao C-N Li and N-Y Deng ldquoMLTSVMa novel twin support vector machine to multi-label learningrdquoPattern Recognition vol 52 pp 61ndash74 2016

[34] U Kreszligel ldquoPair-wise classification and support vectormachinesrdquo in Advances in Kernel Methods pp 255ndash268 MITPress Cambridge Mass USA 1999

[35] 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

[36] T Dietterich and G Bakiri ldquoSolving multiclass learning prob-lems via error-correcting output codesrdquo Journal of ArtificialIntelligence Research vol 2 pp 263ndash286 1995

Mathematical Problems in Engineering 11

[37] S Liu Y Liu BWang and X Feng ldquoAn improved hyper-spheresupport vector machinerdquo in Proceedings of the 3rd InternationalConference on Natural Computation (ICNC rsquo07) pp 497ndash500IEEE Haikou China August 2007

[38] J Seo H Ma and T Saha ldquoProbabilistic wavelet transform forpartial discharge measurement of transformerrdquo IEEE Transac-tions on Dielectrics and Electrical Insulation vol 22 no 2 pp1105ndash1117 2015

[39] J Singh Y R Sood R K Jarial and P Verma ldquoConditionmonitoring of power transformersmdashbibliography surveyrdquo IEEEElectrical Insulation Magazine vol 24 no 3 pp 11ndash25 2008

[40] E Gumus N Kilic A Sertbas and O N Ucan ldquoEvaluationof face recognition techniques using PCA wavelets and SVMrdquoExpert Systems with Applications vol 37 no 9 pp 6404ndash64082010

[41] Z Liu H Cao X Chen Z He and Z Shen ldquoMulti-faultclassification based on wavelet SVM with PSO algorithmto analyze vibration signals from rolling element bearingsrdquoNeurocomputing vol 99 pp 399ndash410 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

10 Mathematical Problems in Engineering

dissolved gas-in-oil analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 19 no 3 pp 1007ndash1012 2012

[6] A Mikulecky and Z Stih ldquoInfluence of temperature moisturecontent and ageing on oil impregnated paper bushings insula-tionrdquo IEEE Transactions on Dielectrics and Electrical Insulationvol 20 no 4 pp 1421ndash1427 2013

[7] N Hashemnia A Abu-Siada and S Islam ldquoDetection ofpower transformer bushing faults and oil degradation usingfrequency response analysisrdquo IEEE Transactions on Dielectricsand Electrical Insulation vol 23 no 1 pp 222ndash229 2016

[8] J A Almendros-Ibanez J C Burgos and B Garcia ldquoTrans-former field drying procedures a theoretical analysisrdquo IEEETransactions on Power Delivery vol 24 no 4 pp 1978ndash19862009

[9] G-L Wang Y Zheng Y-P Hao and Y-M Li ldquoStudy onthe ultra-high-frequency sensor for PD detection in powertransformerrdquo Proceedings of the CSEE vol 22 no 4 pp 154ndash160 2002

[10] A A Bajwa S Habib and M Kamran ldquoAn investigationinto partial discharge pulse extraction methodsrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 964ndash982 2015

[11] L Satish and B Nazneen ldquoWavelet-based denoising of partialdischarge signals buried in excessive noise and interferencerdquoIEEE Transactions on Dielectrics and Electrical Insulation vol10 no 2 pp 354ndash367 2003

[12] W J K Raymond H A Illias A H A Bakar and H MokhlisldquoPartial discharge classifications review of recent progressrdquoMeasurement vol 68 pp 164ndash181 2015

[13] M Wu H Cao J Cao H-L Nguyen J B Gomes andS P Krishnaswamy ldquoAn overview of state-of-the-art partialdischarge analysis techniques for condition monitoringrdquo IEEEElectrical Insulation Magazine vol 31 no 6 pp 22ndash35 2015

[14] D Dey B Chatterjee S Chakravorti and S Munshi ldquoCross-wavelet transform as a new paradigm for feature extractionfrom noisy partial discharge pulsesrdquo IEEE Transactions onDielectrics and Electrical Insulation vol 17 no 1 pp 157ndash1662010

[15] F-C Gu H-C Chang F-H Chen C-C Kuo and C-HHsu ldquoApplication of the Hilbert-Huang transform with fractalfeature enhancement on partial discharge recognition of powercable jointsrdquo IET Science Measurement and Technology vol 6no 6 pp 440ndash448 2012

[16] YGong Y Liu and LWu ldquoIdentification of partial discharge ingas insulated switchgears with fractal theory and support vectormachinerdquo Power System Technology vol 35 no 3 pp 135ndash1392011

[17] X-D Wang B Li Z Liu et al ldquoAnalysis of partial dischargesignal using the Hilbert-Huang transformrdquo IEEE Transactionson Power Delivery vol 21 no 3 pp 1063ndash1067 2006

[18] S-B Liu C Lu J-L Yu andL-XWang ldquoApplication of hilbert-huang transform in pattern recognition for partial dischargeof transformersrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 28 no 31 pp 114ndash119 2008

[19] L Shen F-C Yang X-J Zhou and L Liu ldquoGear fault featureextraction based on improved EMD and morphological filterrdquoJournal of Vibration and Shock vol 29 no 3 pp 154ndash157 2010

[20] J Huang X Hu and Y Gong ldquoMachinery fault diagnosisof high voltage circuit breaker based on empirical modedecompositionrdquo Proceedings of the Chinese Society of ElectricalEngineering vol 31 no 12 pp 108ndash113 2011

[21] G Yong-gang H Yulong and Q Jiali ldquoAn overview onmechanical failure diagnosis technique for high voltage circuitbreaker based on vibration signalrdquo High Voltage Engineeringvol 26 no 3 pp 66ndash68 2000

[22] H-L Sun Z-J He Y-Y Zi and J Yuan ldquoMulti-wavelettransform and its applications in mechanical fault diagnosis-areviewrdquo Mechanical Systems and Signal Processing vol 43 no1-2 pp 1ndash24 2014

[23] D E Newland ldquoWavelet analysis of vibration part 1 theoryrdquoASME Transactions on Journal of Vibration and Acoustics vol116 pp 409ndash441 1994

[24] H Shang J Yuan Y Wang and S Jin ldquoFeature extraction forpartial discharge based on cross-wavelet transform and corre-lation coefficient matrixrdquo Transactions of China ElectrotechnicalSociety vol 29 no 4 pp 274ndash281 2014

[25] A Krivda E Gulski L Satish and W S Zaengl ldquoUse offractal features for recognition of 3-D discharge patternsrdquo IEEETransactions on Dielectrics and Electrical Insulation vol 2 no5 pp 889ndash892 1995

[26] K Gao K-X Tan F-Q Li and C-Q Wu ldquoPattern recognitionof partial discharges based on fractal features of the scatter setrdquoProceedings of the Chinese Society of Electrical Engineering vol22 no 5 pp 22ndash26 2002

[27] Y Xiao C-J Huang W-Y Yu and X-C Jiang ldquoSignal charac-teristic extraction of partial discharge in gis based on waveletand fractal analysisrdquo Automation of Electric Power Systems vol30 no 6 pp 66ndash69 2006

[28] W Chen Z Wang H Xie and W Yu ldquoCharacterization ofsurface EMG signal based on fuzzy entropyrdquo IEEE Transactionson Neural Systems and Rehabilitation Engineering vol 15 no 2pp 266ndash272 2007

[29] N E Huang Z Shen S R Long et al ldquoThe empiricalmode decomposition and the Hilbert spectrum for nonlinearand non-stationary time series analysisrdquo Proceedings of theRoyal Society of London Series A Mathematical Physical andEngineering Sciences vol 454 no 1971 pp 903ndash995 1998

[30] R Jia Q Xu L Tian X Luo and W Liu ldquoExtractingpartial discharge signals of hydroelectric generating set basedon empirical mode decompositionrdquo Journal of HydroelectricEngineering vol 26 no 4 pp 146ndash150 2007

[31] J Tang L Fan X Zhang and X Liu ldquoMulti-scale featureparameters extraction of gis partial discharge signal withharmonic wavelet packet transformrdquo Transactions of ChinaElectrotechnical Society vol 30 no 3 pp 250ndash257 2015

[32] J S Richman and J Randall Moorman ldquoPhysiological time-series analysis using approximate entropy and sample entropyrdquoAmerican Journal of PhysiologymdashHeart and Circulatory Physiol-ogy vol 278 no 6 pp H2039ndashH2049 2000

[33] W-J Chen Y-H Shao C-N Li and N-Y Deng ldquoMLTSVMa novel twin support vector machine to multi-label learningrdquoPattern Recognition vol 52 pp 61ndash74 2016

[34] U Kreszligel ldquoPair-wise classification and support vectormachinesrdquo in Advances in Kernel Methods pp 255ndash268 MITPress Cambridge Mass USA 1999

[35] 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

[36] T Dietterich and G Bakiri ldquoSolving multiclass learning prob-lems via error-correcting output codesrdquo Journal of ArtificialIntelligence Research vol 2 pp 263ndash286 1995

Mathematical Problems in Engineering 11

[37] S Liu Y Liu BWang and X Feng ldquoAn improved hyper-spheresupport vector machinerdquo in Proceedings of the 3rd InternationalConference on Natural Computation (ICNC rsquo07) pp 497ndash500IEEE Haikou China August 2007

[38] J Seo H Ma and T Saha ldquoProbabilistic wavelet transform forpartial discharge measurement of transformerrdquo IEEE Transac-tions on Dielectrics and Electrical Insulation vol 22 no 2 pp1105ndash1117 2015

[39] J Singh Y R Sood R K Jarial and P Verma ldquoConditionmonitoring of power transformersmdashbibliography surveyrdquo IEEEElectrical Insulation Magazine vol 24 no 3 pp 11ndash25 2008

[40] E Gumus N Kilic A Sertbas and O N Ucan ldquoEvaluationof face recognition techniques using PCA wavelets and SVMrdquoExpert Systems with Applications vol 37 no 9 pp 6404ndash64082010

[41] Z Liu H Cao X Chen Z He and Z Shen ldquoMulti-faultclassification based on wavelet SVM with PSO algorithmto analyze vibration signals from rolling element bearingsrdquoNeurocomputing vol 99 pp 399ndash410 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 11

[37] S Liu Y Liu BWang and X Feng ldquoAn improved hyper-spheresupport vector machinerdquo in Proceedings of the 3rd InternationalConference on Natural Computation (ICNC rsquo07) pp 497ndash500IEEE Haikou China August 2007

[38] J Seo H Ma and T Saha ldquoProbabilistic wavelet transform forpartial discharge measurement of transformerrdquo IEEE Transac-tions on Dielectrics and Electrical Insulation vol 22 no 2 pp1105ndash1117 2015

[39] J Singh Y R Sood R K Jarial and P Verma ldquoConditionmonitoring of power transformersmdashbibliography surveyrdquo IEEEElectrical Insulation Magazine vol 24 no 3 pp 11ndash25 2008

[40] E Gumus N Kilic A Sertbas and O N Ucan ldquoEvaluationof face recognition techniques using PCA wavelets and SVMrdquoExpert Systems with Applications vol 37 no 9 pp 6404ndash64082010

[41] Z Liu H Cao X Chen Z He and Z Shen ldquoMulti-faultclassification based on wavelet SVM with PSO algorithmto analyze vibration signals from rolling element bearingsrdquoNeurocomputing vol 99 pp 399ndash410 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of