Research Article Fault Diagnosis of Oil-Immersed Transformers...

Research ArticleFault Diagnosis of Oil-Immersed Transformers UsingSelf-Organization Antibody Network and Immune Operator

Liwei Zhang

School of Electrical Engineering Northeast Dianli University Jilin 132012 China

Correspondence should be addressed to Liwei Zhang zlwbd126com

Received 2 July 2014 Accepted 18 August 2014 Published 16 November 2014

Academic Editor Yoshinori Hayafuji

Copyright copy 2014 Liwei Zhang This 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

There are some drawbacks when diagnosis techniques based on one intelligent method are applied to identify incipient faultsin power transformers In this paper a hybrid immune algorithm is proposed to improve the reliability of fault diagnosis Theproposed algorithm is a hybridization of self-organization antibody network (soAbNet) and immune operatorThere are two phasesin immune operator One is vaccination and the other is immune selection In the process of vaccination vaccines were obtainedfrom training dataset by using consistency-preserving K-means algorithm (K-means-CP algorithm) and were taken as the initialantibodies for soAbNet After the soAbNet was trained immune selection was applied to optimize the memory antibodies inthe trained soAbNet The effectiveness of the proposed algorithm is verified using benchmark classification dataset and real-worldtransformer fault dataset For comparison purpose three transformer diagnosis methods such as the IEC criteria back propagationneural network (BPNN) and soAbNet are utilized The experimental results indicate that the proposed approach can extract thedataset characteristics efficiently and the diagnostic accuracy is higher than that obtained with other individual methods

1 Introduction

Power transformers are considered as highly essential equip-ment of electric power transmission systems and often themost expensive devices in a substation Failures of largepower transformers can cause operational problems to thetransmission system [1]

Dissolved gas analysis (DGA) is one of the most widelyused tools to diagnose the condition of oil-immersed trans-formers in service The ratios of certain dissolved gases inthe insulating oil can be used for qualitative determination offault types Several criteria have been established to interpretresults from laboratory analysis of dissolved gases such asIEC 60599 [2] and IEEE Std C57104-2008 [3] Howeveranalysis of these gases generated in mineral-oil-filled trans-formers is often complicated for fault interpretation which isdependent on equipment variables

With the development of artificial intelligence variousintelligent methods have been applied to improve the DGAreliability for oil-immersed transformers Based on DGA

technique an expert system was proposed for transformerfault diagnosis and corresponding maintenance actions andthe test results showed that it was effective [4] By usingfuzzy information approach Tomsovic et al [5] developeda framework that combined several transformer diagnosticmethods to provide the ldquobestrdquo conclusion Based on artificialneural network (ANN) Zhang et al presented a two-stepmethod for fault detection in oil-filled transformer and theproposed approach achieved good diagnostic accuracy [6]Lin et al proposed a novel fault diagnosis method for powertransformer based on Cerebellar Model Articulation Con-troller (CMAC) and the new scheme was shown with highaccuracy [7] Huang presented a fault detection approach ofoil-immersed power transformers based on genetic algorithmtuned wavelet networks (GAWNs) demonstrating remark-able diagnosis accuracy [8] Chen et al studied the efficiencyof wavelet networks (WNs) for transformer fault detectionusing gases-in-oil samples and the diagnostic accuracy andefficiency were proved better than these derived from BPNN[9] A fault classifier for power transformer was proposed by

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 847623 8 pageshttpdxdoiorg1011552014847623

2 Mathematical Problems in Engineering

Zheng et al based on multiclass least square support vectormachines (LS-SVM) [10] Hao and Cai-Xin developed anartificial immune algorithm for transformer fault detection[11]These novel diagnosis methods overcome the drawbacksof IECmethod and improve the diagnosis accuracyHowevereach intelligentmethod has its own advantages and disadvan-tages and there are limitations when one method is appliedto transformer fault diagnosis [12ndash14]

At present hybridization of two or more intelligentmethods becomes one of the most intensively growing areasas well as a new way for transformer fault diagnosis [1516] A multilevel decision-making model was proposed forincipient fault detection of oil-immersed transformer byusing K-nearest neighbor (K-NN) to improve the classifi-cation results of SVM [17] Morais and Rolim developedan integrated method to detect incipient faults in powertransformers combining some traditional criteria and othertwo intelligent techniques [18] Shintemirov et al utilizedbootstrap to preprocess DGA samples and extract featurewith genetic programming (GP) and the combined approachcould improve the fault diagnosis accuracy [19] A hybridneural fuzzy method was presented for dissolved gas analysiscombining neural fuzzymodel and competitive learning [20]Du and Wang provided a priori knowledge for artificialimmune network using adaptive resonance network (ART)[21] It provides inspiration for the combination of artificialimmune network and other intelligent methodsThe existingliteratures show that making full use of a priori knowledgeand combination with multiple algorithms can effectivelyimprove the diagnosis reliability for dissolved gas analysis

As an artificial intelligence (AI) technique artificialimmune system (AIS) is inspired by biological immunologyaiming at solving engineering or complex computationalproblems [22] Numerous studies have been done on AISfor machine learning and shown tremendous potential indata classification pattern recognition and function opti-mization [23ndash25] As a novel artificial immune system self-organization antibody network (soAbNet) learns and mem-orizes the characters of antigens effectively by three differentstrategies [26] In general the initial antibodies in soAbNetare randomly selected from training dataset However thelearning process of the immune algorithm is sensitive toinitial antibodies On the other hand there is no networksuppression mechanism to control the specificity level of thememory antibodies As a result redundant antibodies wouldexist in the trained network

Based on the works above this paper proposes a hybridimmune algorithm combining immune operator and self-organization antibody network for transformer fault diagno-sis There are two phases in immune operator The first stepis vaccination and the other one is immune selection Inimmune operator vaccination preprocesses transformer faultsamples by using cluster K-means-CP algorithm and thenthe obtained cluster centers are taken as initial antibodies insoAbNet During the training of soAbNet memory antibod-ies were suppressed by immune selection of immune operatorto enhance the antibody quality In order to show the validityof the proposed algorithm experiments are performed andthe results are illustrated

c

c

c

c

c c

c

c

c

1

2

2 2 3

3

Figure 1 Architecture of self-organization antibody network

2 Self-Organization Antibody Network

21 Brief Description of soAbNet In soAbNet antibodies andT-cells are abstracted as antibodies ignoring their difference[26] Antibodies of different class are regarded as vertices inthe immune network and antibodies of the same class areconnected to form a semiconnected graph Each antibodyhas concentration as its weight representing its recognitioncapability The whole network is expressed as an incompleteconnected graph with weighted verticesThus each antibodyhas abilities of recognition response and memory for anti-gens Antibodies learn memorize and recognize antigens byantigen-antibody and antibody-antibody interactions

Figure 1 shows a soAbNet consisting of three classesof antibody Numbers 1 2 and 3 represent the type ofeach antibody respectively Antibodies of the same typeare connected via class information and 119888 is the antibodyconcentration

22 Antigen and Antibody Coding In self-organization anti-body network antigen (Ag) and antibody (Ab) are encodedin real value and their coding structures are different fromeach other

(1) Antigen Coding Each antigen is regarded as a point in itsshape space and is represented by an 119899-dimensional vectorAg119895 as

Ag119895 = (Ag1198951Ag1198952 Ag119895119899) (1)

Each attribute of vectorAg119895 is supposed to represent a featureof the corresponding antigen

(2) Antibody Coding Antibody coding consists of antibodybasic information and its attribute informationThe antibodyconstruction can be defined as

Ab119894 = (119879119894 119862119894Ab1198941Ab1198942 Ab119894119899) (2)

Here 119879119894 is the class antibody Ab119894 belongs to 119862119894 is its con-centration and Ab1198951 sim Ab119895119899 are the dimensional attributesrepresenting the feature of Ab119894

Mathematical Problems in Engineering 3

23 Learning andMemory Strategies There are three learningstrategies in soAbNet as follows

(1) Antibody EvolutionAntibodyAb119894 in the immune networklearns and memorizes the characteristic of input antigen Ag119895by concentration adjustment and attribute value adjustmentThe antibody evolution is executed according to the followingupdating equation

1198621015840119894 = 119862119894 + 1

Ab1015840119894119896 =(119862119894 times Ab119894119896 + Ag119895119896)

1198621015840119894

119896 = 1 2 119899

Ab119894 = (119879119894 1198621015840119894 Ab10158401198941Ab10158401198942 Ab

1015840119894119899)

(3)

(2) Antibody Combination In soAbNet two antibodies ofthe same class combine into one antibody to eliminateredundancy by concentration adjustment and attribute valueadjustment when their affinity is less than a given thresholdAntibodiesAb119894 andAb119895 combine into one antibodyAb119896 andthe original antibodies Ab119894 and Ab119895 would be removed frommemory antibody set Ab119896 can be calculated by

119862119896 = 119862119894 + 119862119895

Ab119896119898 =(119862119894 times Ab119894119898 + 119862119895 times Ab119895119898)

119862119896

119898 = 1 2 119899

Ab119896 = (119879119894 119862119896Ab1198961Ab1198962 Ab119894119899)

(4)

(3) Antibody Generation In soAbNet when the memoryantibodies cannot identify the input antigen during trainingprocess new antibody is added to the network to learnand memorize the input antigen Whereas Ag119895 is the inputantigen new antibody Ab119894 can be added to the memoryantibody set by

Ab119894 = (119879119895 1Ag1198951Ag1198952 Ag119895119899) (5)

24 Learning Algorithm The learning algorithm of soAbNetcan be described as follows

Step 1 (initialization) Randomly select 119896 samples from train-ing dataset as initial antibodies

Step 2 For each input antigen Ag119895 do the following

Step 21Calculate the affinity betweenAg119895 and each antibodyAb119894 in the network

Step 22 Select the antibody Ab119903 where the affinity betweenAb119903 and Ag119895 is the highest

Step 23 If type 119879119903 of Ab119903 is different from type 119879119895 of Ag119895execute antibody generation and go to Step 3

Step 24 If type 119879119903 of Ab119903 is the same as type 119879119895 Ab119903 isregarded as the best recognition antibody Ab119887

Step 25 Calculate the affinities between Ab119887 and eachantibody of the same class Select Ab119896 where the affinitybetween Ab119887 and Ag119896 is the highest

Step 26 If the affinity betweenAb119887 andAb119896 is higher than theaffinity between Ab119887 andAg119895 execute antibody combinationbetween Ab119887 and Ab119896 and antibody generation according tothe input antigen Ag119895 and go to Step 3

Step 27 Execute antibody evolution between Ab119887 and Ag119895

Step 3 If stopping criterion is met end training otherwisego to Step 2

The affinity is measured by Euclidean distance betweentwo vectors The smaller the distance value is the higher theaffinity will be The stopping criterion is that the amounts ofmemory antibodies in the network are the same between twosuccessive training processes The network output is maturememory antibody set representing the antigen characteristicof each class which can be used for pattern recognitiondirectly

3 Proposed Hybrid Immune Algorithm

As most immune algorithms the initial antibodies in soAb-Net are randomly selected from training set which does notmake full use of prior knowledge of training set Whereaslearning process of the immune algorithm is sensitive toinitial antibodies the randomly selected initial antibodies areof different distribution in shape-space resulting in differentconvergence rate of the network during learning process andthe quality of memory antibodies is variable As a resultthe network performance is unstable and the recognitioncapability of antigen is affected to some extent

On the other hand there is no network compressionmechanism to simplify network structure The network sizewould increase with the increasing of initial antibodies andtraining times As a result a number of redundant antibodieswould exist in the trained network

To improve the performance of soAbNet a hybridimmune algorithm combining immune operator and soAb-Net is proposed in this section

31 Immune Operator The immune operator is a two-stepprocess that is vaccination and immune selection Vaccina-tion is used to provide initial antibodies whereas immune


selection is used to optimize memory antibodies [27] Thequality of vaccine affects the convergence rate of learningprocess but does not affect the convergence of the algorithmwhich is guaranteed by the immune selection in the learningprocess In the next two sections vaccination and immuneselection were constructed in accordance with soAbNetrespectively

32 Vaccination As an advantage biological immune systemcan learn how to identify a new infection by using vaccinesVaccines make the body produce antibodies by specificpathogens in order to speed up the response to infections

In artificial immune systems vaccines would be obtainedfrom the known information of the problem to be solved inorder to guide the learning process In practice vaccines canbe obtained by using optimization algorithms

In this study consistency-preserving K-means algorithm(K-means-CP) was used to obtain vaccines for each classfrom training set respectively Then the vaccines that isthe cluster centers were taken as the initial antibodies insoAbNet

The number of vaccines that is the cluster number 119870is assigned according to the complexity of training datasetSince there have been many papers to study on determiningoptimal cluster number of a dataset [28ndash30] estimating thecluster number would not be discussed in this section

K-means-CP algorithm can be described as follow [31]

Step 1 Initialize cluster centers (1198881 1198881 119888119870)

Step 2 Assign cluster membership Assign one closed-neighbor-set 119878 at a time Assign all objects of the closed-neighbor-set 119878 to the closest cluster 119862119901 where the closenessis defined in average sense that is

119901 = argmin119896

sum

119894isin119878

(119909119894 minus 119888119896) (6)

Step 3 Update centers

119888119896 = sum

119894isin119862119896

119909119894

119899119896

(7)

Here 119888119896 is the centroid of cluster 119862119896 and 119899119896 = |119862119896|

Step 4 Iterate Steps 2 and 3 until convergeThe objective function is the sum of error squared

119869119870119898 =

119870

sum

119896=1

sum

119894isin119862119896

(119909119894 minus 119888119896)2 (8)

K-means-CP algorithm and the standard K-means havethe same efficiency and convergence property [31] But thereis still some difference between the two algorithms Each unitof the cluster is assigned to an object in K-means algorithmwhile in K-means-CP algorithm each unit of the cluster isassigned to the closed-neighbor-set in order to enforce stricttransitivity

Given dataset

Data preprocessing

soAbNet

Immune selection

Training dataset

Memory antibodies

Testing dataset

Classification

Outputs

Vaccination

Initial antibodies

Immune operator

Figure 2 Flowchart of the proposed hybrid immune algorithm

33 Immune Selection The immune selection correspondsto immune regulation mechanism in biological immunesystem It is accomplished by the following two steps immunedetection and antibody selection During the training processof soAbNet immune detection firstly calculates the affinitiesbetween pairwise antibodies of the memory antibodiesThenantibody selection combines the two antibodies into onethrough antibody combination between which the affinity isless than a preset affinity threshold 120590

The value of affinity threshold 120590 has important effectsupon the amount and the distribution of memory antibodiesGenerally affinity threshold 120590 can be initially preset at asmaller value (such as 120590 ⩽ 01) and then 120590 could be assignedappropriate value finally after analyzing the results with itsvalue increase

The immune selection has the robustness in enhancingthe positive function of the vaccination and eliminating itsnegative influence

34 Procedure of Hybrid Immune Algorithm The process ofthe proposed hybrid algorithm is illustrated as in Figure 2

The proposed hybrid immune algorithm is trainedaccording the steps as follows

(1) Data Preprocessing In order to improve the generalizationperformance of the proposed immune algorithm the givendataset is normalized Then training dataset is selected atrandom and the rest is taken as testing dataset

(2) Vaccination As the first phase of immune operatorvaccination obtains antibodies from the training datasetusingK-means-CP algorithmThen the obtained vaccines are


1

0

minus1

minus1 0 1

Figure 3 Distribution of memory antibodies in soAbNet

taken as the initial antibodies in the soAbNet and encodedaccording to antibody coding

(3) Training soAbNet Train the soAbNet with the initialantibodies on the training dataset and get antibody set

(4) Immune Selection The antibody set in soAbNet canbecome memory antibodies after immune detection andantibody selection

(5) Classification Testing dataset is encoded according toantigen coding and classified with memory antibodies tovalidate the trained classifier

4 Experiment Results and Discussion

41 Experiment on Four-Class Dataset In order to validatethe antibody optimization of the hybrid algorithm four-classdataset was chosen from UCI machine learning dataset foralgorithm test compared with soAbNet

Four-class dataset is a typical classification dataset pro-vided by Ho and Kleinberg [32] It was obtained by prepro-cessing 4 kinds of two-dimensional samples into 2 classesThe dataset consists of 2 class datasets 862 instances in totalEach instance includes 2 feature attributes The range of eachattribute is [minus1 1]

In this section 684 instances were randomly selected astraining dataset and the rest of the 172 instances as testingdataset The vaccine number was set as 10 the vaccinenumber of each class was 5 Each type instances from thetraining dataset were clustered by K-means-CP algorithmthe obtained 10 cluster centerswere taken as initial antibodiesAffinity threshold 120590 was set as 025 In order to comparethe test results the initial antibody number of each type insoAbNet was set as 5 After being trained the classificationaccuracy on test dataset was 100 for the two immunealgorithms Memory antibody distributions are illustrated asFigures 3 and 4 respectively

1

0

minus1

minus1 0 1

Figure 4 Distribution of memory antibodies in the proposedmethod

Through the comparison and analysis between Figures3 and 4 it can be observed that the developed algorithmgets lesser memory antibodies than soAbNet with the samenumbers of initial antibodies whereas with the same correctrecognition rate The memory antibody distribution of theproposed algorithm is more reasonable The number of anti-bodies is less in the simple classification space the number ofantibodies increases in the cross-space of two classes

42 Experiments on Three Other Data Sets To validatethe classification capacity of the hybrid immune algorithmexperiments are performed on three other benchmarkdatasets which are from the UCI databases [33] The threereal-world data sets are described as in Table 1

In this section the experimental comparisons are madeamong the proposed hybrid immune algorithm soAbNet andback propagation neural network (BPNN) with 10-fold cross-validation on the three different datasets For comparisonpurpose the number of initial antibodies in soAbNet andthe number of vaccines in the proposed algorithm were setto be the same as 8 14 and 12 for iris wine and breasttissue datasets respectively The affinity threshold 120590 was setas 016 02 and 011 for iris wine and breast tissue datasetsrespectively The number of hidden layer nodes was set as 1015 and 8 for iris wine and breast tissue datasets respectivelyExperimental results including the average training accuracyand the average testing accuracy are given in Table 2

From the results shown in Table 2 we can conclude thatthe proposed algorithm demonstrates excellent classificationperformance Besides it gains good training accuracy andmeanwhile maintains good generalization ability

43 Transformer Fault Diagnosis There are five dissolvedgases in oil-immersed transformers hydrogen (H2) ethy-lene (C2H4) methane (CH4) ethane (C2H6) and acetylene(C2H2) which are the byproducts caused by internal faults[3] The technique of dissolved gas analysis (DGA) is effec-tive in detecting incipient fault of power transformers To


Table 1 The datasets used

datasets Number of classes Number of attributes Number of instances Number of training Number of testingIris 3 4 150 120 30Wine 3 13 178 148 30Breast tissue 4 9 106 85 21

Table 2 Training and testing accuracy comparison ()

Datasets Proposed algorithm soAbNet BPNNTraining Testing Training Testing Training Testing

Iris 975 976 9667 9733 9667 9628Wine 9837 9857 9848 9763 9847 9763Breasttissue 8975 9235 9005 8906 8975 898

accelerate the convergence of artificial immune algorithmnormalized concentrations H2T CH4T C2H6T C2H4TC2H2T are taken as the characteristic vector where Trepresents the total gas

The two main reasons of oil deterioration in operatingtransformers are thermal and electrical failures Detectablefaults in IEC of Publication 60599 by using dissolved gasanalysis (DGA) are discharges of low energy (D1) dischargesof high energy (D2) partial discharges (PD) thermal faultsbelow 300∘C (T1) thermal faults above 300∘C (T2) andthermal faults above 700∘C (T3)

In this study 350 DGA samples from fault transformersare chosen as experimental data These samples were dividedinto two parts 213 samples were taken as training dataset andthe rest of the 137 samples as test dataset

Through analysis of transformer fault samples it can beobserved that the key gases of thermal faults are CH4 andC2H4 whereas among the electrical faults the key gases oflow intensity discharges and high intensity discharges areC2H2 and H2 H2 is the principal gas of partial dischargesThermal faults and electrical faults are relatively easy todistinguish The fault type of thermal faults is closely relatedto the temperature of fault location the boundaries are tooobscure to distinguish fault typeThe initial antibody numbershould be increased appropriately when training the immunenetwork

According to the above analysis each class of trainingsamples was clustered using K-means-CP algorithm Theobtained cluster centers were used as initial antibodies forthe training of soAbNetThe training sample distribution andmemory antibodies after training are shown as in Table 3Here affinity threshold 120590 was set as 01

The affinities between test samples and memory antibod-ies are calculated respectively According to nearest neighborrule memory antibody with the highest affinity is selected toidentify the type of antigen Using the proposed transformerfault diagnosis method the total diagnostic accuracy on 137samples is 8467 Diagnosis results in detail are shown as inTable 4

The diagnostic accuracy on the testing fault datasetusing the proposed hybrid immune algorithm was compared

Table 3 Sample distribution and memory antibodies

Faulttype

Sampleamount

Trainingsampleamount

Initialantibodyamount

Memoryantibodyamount

T1 43 26 11 16T2 64 39 14 21T3 86 52 17 25D1 67 41 13 19D2 52 32 9 14PD 38 23 12 16Total 350 213 76 111

with that using soAbNet back-propagation neural network(BPNN) and IEC method The diagnostic accuracy of eachfault type is shown in Table 5 As shown in Table 5 the pro-posed immune algorithm is with higher diagnosis accuracycompared to soAbNet BPNN and IEC method

5 Conclusions

This paper has presented a hybrid immune algorithm toimprove the classification accuracy for transformer faultdiagnosis which is a hybridization of soAbNet and immuneoperator Immune operator obtained vaccines from trainingdataset to provide initial antibodies for soAbNet Moreoverimmune operator accelerates convergence and enhancesthe quality of memory antibodies in soAbNet by immuneselection

The experimental results on four-class dataset show thatthe proposed algorithm can enhance the quality of memoryantibodies The experimental results on the other threedatasets demonstrate the excellent classification performanceof the proposed algorithm The experimental results onreal-world transformer fault dataset show that the proposedimmune algorithm obtained very promising abilities in faultclassification for power transformers Furthermore throughthe comparison with three other transformer diagnosisapproaches such as soAbNet IEC method and BPNN theresults highlight the superiority of the proposed approach intesting diagnosis accuracy

It is worthwhile pointing that the affinity threshold 120590 inimmune selection has an important effect on the performanceof the proposed algorithm The value of 120590 is selected byanalyzing experimental results on training dataset in thispaper To enhance the solution optimization algorithms canbe used for parameter optimization such as particle swarmoptimization (PSO) and genetic algorithm (GA)


Table 4 Diagnosis results of test samples

Fault type Number of testing samples Classification results Diagnostic accuracyT1 T2 T3 D1 D2 PD

T1 17 14 1 2 0 0 0 8235T2 25 1 21 2 1 0 0 8400T3 34 2 2 28 1 1 0 8235D1 26 0 0 1 22 2 1 8462D2 20 0 0 0 1 18 1 9000PD 15 0 0 0 2 0 13 8667

Table 5 Diagnosis accuracy comparison among different methods()

Fault type Proposedalgorithm soAbNet IEC method BPNN

T1 8235 8235 7647 7647T2 8400 7600 7600 8000T3 8235 7941 7941 8235D1 8462 8462 8077 8077D2 9000 8500 8000 8500PD 8667 7333 6667 8667

Finally hybridization of two or more intelligent methodswould improve the diagnosis reliability for incipient faultin oil-immersed transformers which is helpful to practicalengineering application

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This paper was supported by the Fundamental ResearchFunds for the Central Universities (no 13MS69) and theDoctoral Scientific Research Foundation of Northeast DianliUniversity (no BSJXM-201401) China

References

[1] W H Tang and Q H Wu Condition Monitoring and Assess-ment of Power Transformers Using Computational IntelligenceSpringer London UK 2011

[2] Mineral Oil-Impregnated Electrical Equipment in ServicemdashGuide to the Interpretation of Dissolved and Free Gases AnalysisIEC Publication 2007

[3] ldquoGuide for the interpretation of gases generated in oil-immersedtransformersrdquo Tech Rep IEEE Std C57104-2008 2009

[4] C E Lin J M Ling and C L Huang ldquoAn expert system fortransformer fault diagnosis using dissolved gas analysisrdquo IEEETransactions on Power Delivery vol 8 no 1 pp 231ndash238 1993

[5] K Tomsovic M Tapper and T Ingvarsson ldquoA fuzzy informa-tion approach to integrating different transformer diagnostic

methodsrdquo IEEE Transactions on Power Delivery vol 8 no 3pp 1638ndash1645 1993

[6] Y Zhang X Ding Y Liu and P J Griffin ldquoAn artificialneural network approach to transformer fault diagnosisrdquo IEEETransactions on Power Delivery vol 11 no 4 pp 1836ndash18411996

[7] W S Lin C P Hung and M H Wang ldquoCMAC basedfault diagnosis of power transformersrdquo in Proceedings of theInternational Joint Conference on Neural Networks (IJCNN rsquo02)pp 986ndash991 May 2002

[8] Y-C Huang ldquoA new data mining approach to dissolved gasanalysis of oil-insulated power apparatusrdquo IEEE Transactions onPower Delivery vol 18 no 4 pp 1257ndash1261 2003

[9] W Chen C Pan Y Yun and Y Liu ldquoWavelet networks inpower transformers diagnosis using dissolved gas analysisrdquoIEEE Transactions on Power Delivery vol 24 no 1 pp 187ndash1942009

[10] H B Zheng R J Liao S Grzybowski and L J YangldquoFault diagnosis of power transformers using multi-class leastsquare support vector machines classifiers with particle swarmoptimisationrdquo IET Electric Power Applications vol 5 no 9 pp691ndash696 2011

[11] X Hao and S Cai-Xin ldquoArtificial immune network classifica-tion algorithm for fault diagnosis of power transformerrdquo IEEETransactions on Power Delivery vol 22 no 2 pp 930ndash935 2007

[12] N Liu W Gao and K Tan ldquoFault diagnosis of power trans-former using a combinatorial neural networkrdquo Transactions ofChina Electrotechnical Society vol 18 no 2 pp 83ndash86 2003

[13] LWu Y Zhu and J Yuan ldquoNovelmethod for transformer faultsintegrated diagnosis based on Bayesian network classifierrdquoTransactions of China Electrotechnical Society vol 20 no 4 pp45ndash51 2005

[14] J Zhang H Zhou and C Xiang ldquoApplication of super SABANN model for transformer fault diagnosisrdquo Transactions ofChina Electrotechnical Society vol 19 no 7 pp 49ndash58 2004

[15] Y-Q Wang F-C Lu and H-M Li ldquoSynthetic fault diagnosismethod of power transformer based on rough set theoryand bayesian networkrdquo Proceedings of the Chinese Society ofElectrical Engineering vol 26 no 8 pp 137ndash141 2006

[16] D B Zhang Y Xu and Y N Wang ldquoNeural network ensemblemethod and its application in DGA fault diagnosis of powertransformer on the basis of active diverse learningrdquo Proceedingsof the Chinese Society of Electrical Engineering vol 30 no 22pp 64ndash70 2010

[17] M Dong D K XuMH Li and Z Yan ldquoFault diagnosismodelfor power transformer based on statistical learning theory anddissolved gas analysisrdquo in Proceedings of the Conference Recordof the IEEE International Symposium on Electrical Insulation pp85ndash88 September 2004


[18] D R Morais and J G Rolim ldquoA hybrid tool for detectionof incipient faults in transformers based on the dissolved gasanalysis of insulating oilrdquo IEEE Transactions on Power Deliveryvol 21 no 2 pp 673ndash680 2006

[19] A Shintemirov W Tang and Q H Wu ldquoPower transformerfault classification based on dissolved gas analysis by imple-menting bootstrap and genetic programmingrdquo IEEE Transac-tions on Systems Man and Cybernetics vol 39 no 1 pp 69ndash792009

[20] R Naresh V Sharma and M Vashisth ldquoAn integrated neuralfuzzy approach for fault diagnosis of transformersrdquo IEEETransactions on Power Delivery vol 23 no 4 pp 2017ndash20242008

[21] H Du and S Wang ldquoData enriching based on art-artificialimmune networkrdquo Pattern Recognition and Artificial Intelli-gence vol 14 no 4 pp 401ndash405 2001

[22] L N de Castro and J Timmis Artificial Immune Systems ANew Computational Intelligence Approach Springer LondonUK 2002

[23] J Timmis M Neal and J Hunt ldquoAn artificial immune systemfor data analysisrdquo BioSystems vol 55 no 1ndash3 pp 143ndash150 2000

[24] A Watkins J Timmis and L Boggess ldquoArtificial immunerecognition system (AIRS) an immune-inspired supervisedlearning algorithmrdquo Genetic Programming and EvolvableMachines vol 5 no 3 pp 291ndash317 2004

[25] L N de Castro and J Timmis ldquoAn artificial immune networkfor multimodal function optimizationrdquo in Proceedings of theIEEE Congress on Evolutionary Computation (CEC rsquo02) pp699ndash704 May 2002

[26] Z Li J Yuan and L Zhang ldquoFault diagnosis for powertransformer based on the self-organization antibody netrdquoTransactions of China Electrotechnical Society vol 25 no 10 pp200ndash206 2010

[27] W Lei and J Licheng ldquoImmune evolutionary algorithmrdquo inProceedings of the 3rd International Conference on Knowledge-Based Intelligent Information Engineering Systems (KES rsquo99) pp99ndash102 September 1999

[28] T Calinski and J Harabasz ldquoA dendrite method for clusteranalysisrdquo Communications in Statistics vol 3 pp 1ndash27 1974

[29] R Tibshirani G Walther and T Hastie ldquoEstimating thenumber of clusters in a data set via the gap statisticrdquo Journalof the Royal Statistical Society B Statistical Methodology vol 63no 2 pp 411ndash423 2001

[30] S Dudoit and J Fridlyand ldquoA prediction-based resamplingmethod for estimating the number of clusters in a datasetrdquoGenome Biology vol 3 no 7 pp 1ndash21 2002

[31] C Ding and X He ldquoK-nearest-neighbor consistency in dataclustering incorporating local information into global opti-mizationrdquo in Proceedings of the ACM Symposium on AppliedComputing pp 584ndash589 Nicosia Cyprus March 2004

[32] T K Ho and E M Kleinberg ldquoBuilding projectable classifiersof arbitrary complexityrdquo in Proceedings of the 13th InternationalConference on Pattern Recognition (ICPR rsquo96) pp 880ndash885August 1996

[33] K Bache and M Lichman UCI Machine Learning RepositoryUniversity of California School of Information and ComputerScience Irvine Calif USA 2013

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Stochastic AnalysisInternational Journal of


Zheng et al based on multiclass least square support vectormachines (LS-SVM) [10] Hao and Cai-Xin developed anartificial immune algorithm for transformer fault detection[11]These novel diagnosis methods overcome the drawbacksof IECmethod and improve the diagnosis accuracyHowevereach intelligentmethod has its own advantages and disadvan-tages and there are limitations when one method is appliedto transformer fault diagnosis [12ndash14]

At present hybridization of two or more intelligentmethods becomes one of the most intensively growing areasas well as a new way for transformer fault diagnosis [1516] A multilevel decision-making model was proposed forincipient fault detection of oil-immersed transformer byusing K-nearest neighbor (K-NN) to improve the classifi-cation results of SVM [17] Morais and Rolim developedan integrated method to detect incipient faults in powertransformers combining some traditional criteria and othertwo intelligent techniques [18] Shintemirov et al utilizedbootstrap to preprocess DGA samples and extract featurewith genetic programming (GP) and the combined approachcould improve the fault diagnosis accuracy [19] A hybridneural fuzzy method was presented for dissolved gas analysiscombining neural fuzzymodel and competitive learning [20]Du and Wang provided a priori knowledge for artificialimmune network using adaptive resonance network (ART)[21] It provides inspiration for the combination of artificialimmune network and other intelligent methodsThe existingliteratures show that making full use of a priori knowledgeand combination with multiple algorithms can effectivelyimprove the diagnosis reliability for dissolved gas analysis

As an artificial intelligence (AI) technique artificialimmune system (AIS) is inspired by biological immunologyaiming at solving engineering or complex computationalproblems [22] Numerous studies have been done on AISfor machine learning and shown tremendous potential indata classification pattern recognition and function opti-mization [23ndash25] As a novel artificial immune system self-organization antibody network (soAbNet) learns and mem-orizes the characters of antigens effectively by three differentstrategies [26] In general the initial antibodies in soAbNetare randomly selected from training dataset However thelearning process of the immune algorithm is sensitive toinitial antibodies On the other hand there is no networksuppression mechanism to control the specificity level of thememory antibodies As a result redundant antibodies wouldexist in the trained network

Based on the works above this paper proposes a hybridimmune algorithm combining immune operator and self-organization antibody network for transformer fault diagno-sis There are two phases in immune operator The first stepis vaccination and the other one is immune selection Inimmune operator vaccination preprocesses transformer faultsamples by using cluster K-means-CP algorithm and thenthe obtained cluster centers are taken as initial antibodies insoAbNet During the training of soAbNet memory antibod-ies were suppressed by immune selection of immune operatorto enhance the antibody quality In order to show the validityof the proposed algorithm experiments are performed andthe results are illustrated

c

c

c

c

c c

c

c

c

1

2

2 2 3

3

Figure 1 Architecture of self-organization antibody network

2 Self-Organization Antibody Network

21 Brief Description of soAbNet In soAbNet antibodies andT-cells are abstracted as antibodies ignoring their difference[26] Antibodies of different class are regarded as vertices inthe immune network and antibodies of the same class areconnected to form a semiconnected graph Each antibodyhas concentration as its weight representing its recognitioncapability The whole network is expressed as an incompleteconnected graph with weighted verticesThus each antibodyhas abilities of recognition response and memory for anti-gens Antibodies learn memorize and recognize antigens byantigen-antibody and antibody-antibody interactions

Figure 1 shows a soAbNet consisting of three classesof antibody Numbers 1 2 and 3 represent the type ofeach antibody respectively Antibodies of the same typeare connected via class information and 119888 is the antibodyconcentration

22 Antigen and Antibody Coding In self-organization anti-body network antigen (Ag) and antibody (Ab) are encodedin real value and their coding structures are different fromeach other

(1) Antigen Coding Each antigen is regarded as a point in itsshape space and is represented by an 119899-dimensional vectorAg119895 as

Ag119895 = (Ag1198951Ag1198952 Ag119895119899) (1)

Each attribute of vectorAg119895 is supposed to represent a featureof the corresponding antigen

(2) Antibody Coding Antibody coding consists of antibodybasic information and its attribute informationThe antibodyconstruction can be defined as

Ab119894 = (119879119894 119862119894Ab1198941Ab1198942 Ab119894119899) (2)

Here 119879119894 is the class antibody Ab119894 belongs to 119862119894 is its con-centration and Ab1198951 sim Ab119895119899 are the dimensional attributesrepresenting the feature of Ab119894




1198621015840119894 = 119862119894 + 1

Ab1015840119894119896 =(119862119894 times Ab119894119896 + Ag119895119896)

1198621015840119894

119896 = 1 2 119899

Ab119894 = (119879119894 1198621015840119894 Ab10158401198941Ab10158401198942 Ab

1015840119894119899)

(3)


119862119896 = 119862119894 + 119862119895


119862119896

119898 = 1 2 119899

Ab119896 = (119879119894 119862119896Ab1198961Ab1198962 Ab119894119899)

(4)


Ab119894 = (119879119895 1Ag1198951Ag1198952 Ag119895119899) (5)



























119901 = argmin119896

sum

119894isin119878

(119909119894 minus 119888119896) (6)


119888119896 = sum

119894isin119862119896

119909119894

119899119896

(7)



119869119870119898 =

119870

sum

119896=1

sum

119894isin119862119896

(119909119894 minus 119888119896)2 (8)


Given dataset

Data preprocessing

soAbNet

Immune selection

Training dataset

Memory antibodies

Testing dataset

Classification

Outputs

Vaccination

Initial antibodies

Immune operator










1

0

minus1

minus1 0 1










1

0

minus1

minus1 0 1





















Faulttype

Sampleamount




T1 43 26 11 16T2 64 39 14 21T3 86 52 17 25D1 67 41 13 19D2 52 32 9 14PD 38 23 12 16Total 350 213 76 111


5 Conclusions







T1 17 14 1 2 0 0 0 8235T2 25 1 21 2 1 0 0 8400T3 34 2 2 28 1 1 0 8235D1 26 0 0 1 22 2 1 8462D2 20 0 0 0 1 18 1 9000PD 15 0 0 0 2 0 13 8667



T1 8235 8235 7647 7647T2 8400 7600 7600 8000T3 8235 7941 7941 8235D1 8462 8462 8077 8077D2 9000 8500 8000 8500PD 8667 7333 6667 8667




Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












1198621015840119894 = 119862119894 + 1

Ab1015840119894119896 =(119862119894 times Ab119894119896 + Ag119895119896)

1198621015840119894

119896 = 1 2 119899

Ab119894 = (119879119894 1198621015840119894 Ab10158401198941Ab10158401198942 Ab

1015840119894119899)

(3)


119862119896 = 119862119894 + 119862119895


119862119896

119898 = 1 2 119899

Ab119896 = (119879119894 119862119896Ab1198961Ab1198962 Ab119894119899)

(4)


Ab119894 = (119879119895 1Ag1198951Ag1198952 Ag119895119899) (5)



























119901 = argmin119896

sum

119894isin119878

(119909119894 minus 119888119896) (6)


119888119896 = sum

119894isin119862119896

119909119894

119899119896

(7)



119869119870119898 =

119870

sum

119896=1

sum

119894isin119862119896

(119909119894 minus 119888119896)2 (8)


Given dataset

Data preprocessing

soAbNet

Immune selection

Training dataset

Memory antibodies

Testing dataset

Classification

Outputs

Vaccination

Initial antibodies

Immune operator










1

0

minus1

minus1 0 1










1

0

minus1

minus1 0 1





















Faulttype

Sampleamount




T1 43 26 11 16T2 64 39 14 21T3 86 52 17 25D1 67 41 13 19D2 52 32 9 14PD 38 23 12 16Total 350 213 76 111


5 Conclusions







T1 17 14 1 2 0 0 0 8235T2 25 1 21 2 1 0 0 8400T3 34 2 2 28 1 1 0 8235D1 26 0 0 1 22 2 1 8462D2 20 0 0 0 1 18 1 9000PD 15 0 0 0 2 0 13 8667



T1 8235 8235 7647 7647T2 8400 7600 7600 8000T3 8235 7941 7941 8235D1 8462 8462 8077 8077D2 9000 8500 8000 8500PD 8667 7333 6667 8667




Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















119901 = argmin119896

sum

119894isin119878

(119909119894 minus 119888119896) (6)


119888119896 = sum

119894isin119862119896

119909119894

119899119896

(7)



119869119870119898 =

119870

sum

119896=1

sum

119894isin119862119896

(119909119894 minus 119888119896)2 (8)


Given dataset

Data preprocessing

soAbNet

Immune selection

Training dataset

Memory antibodies

Testing dataset

Classification

Outputs

Vaccination

Initial antibodies

Immune operator










1

0

minus1

minus1 0 1










1

0

minus1

minus1 0 1





















Faulttype

Sampleamount




T1 43 26 11 16T2 64 39 14 21T3 86 52 17 25D1 67 41 13 19D2 52 32 9 14PD 38 23 12 16Total 350 213 76 111


5 Conclusions







T1 17 14 1 2 0 0 0 8235T2 25 1 21 2 1 0 0 8400T3 34 2 2 28 1 1 0 8235D1 26 0 0 1 22 2 1 8462D2 20 0 0 0 1 18 1 9000PD 15 0 0 0 2 0 13 8667



T1 8235 8235 7647 7647T2 8400 7600 7600 8000T3 8235 7941 7941 8235D1 8462 8462 8077 8077D2 9000 8500 8000 8500PD 8667 7333 6667 8667




Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1

0

minus1

minus1 0 1










1

0

minus1

minus1 0 1





















Faulttype

Sampleamount




T1 43 26 11 16T2 64 39 14 21T3 86 52 17 25D1 67 41 13 19D2 52 32 9 14PD 38 23 12 16Total 350 213 76 111


5 Conclusions







T1 17 14 1 2 0 0 0 8235T2 25 1 21 2 1 0 0 8400T3 34 2 2 28 1 1 0 8235D1 26 0 0 1 22 2 1 8462D2 20 0 0 0 1 18 1 9000PD 15 0 0 0 2 0 13 8667



T1 8235 8235 7647 7647T2 8400 7600 7600 8000T3 8235 7941 7941 8235D1 8462 8462 8077 8077D2 9000 8500 8000 8500PD 8667 7333 6667 8667




Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra























Faulttype

Sampleamount




T1 43 26 11 16T2 64 39 14 21T3 86 52 17 25D1 67 41 13 19D2 52 32 9 14PD 38 23 12 16Total 350 213 76 111


5 Conclusions







T1 17 14 1 2 0 0 0 8235T2 25 1 21 2 1 0 0 8400T3 34 2 2 28 1 1 0 8235D1 26 0 0 1 22 2 1 8462D2 20 0 0 0 1 18 1 9000PD 15 0 0 0 2 0 13 8667



T1 8235 8235 7647 7647T2 8400 7600 7600 8000T3 8235 7941 7941 8235D1 8462 8462 8077 8077D2 9000 8500 8000 8500PD 8667 7333 6667 8667




Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












T1 17 14 1 2 0 0 0 8235T2 25 1 21 2 1 0 0 8400T3 34 2 2 28 1 1 0 8235D1 26 0 0 1 22 2 1 8462D2 20 0 0 0 1 18 1 9000PD 15 0 0 0 2 0 13 8667



T1 8235 8235 7647 7647T2 8400 7600 7600 8000T3 8235 7941 7941 8235D1 8462 8462 8077 8077D2 9000 8500 8000 8500PD 8667 7333 6667 8667




Acknowledgments


References











































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Research Article Fault Diagnosis of Oil-Immersed Transformers...

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