930 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 2, APRIL 2007

Artificial Immune Network Classification Algorithmfor Fault Diagnosis of Power Transformer

Xiong Hao and Sun Cai-xin

AbstractDissolved gas analysis is an effective method forthe early detection of incipient fault in power transformers. Toimprove the capability of interpreting the result of dissolved gasanalysis, an artificial immune network classification algorithm(AINC), inspired by the natural immune system that is able torespond to an almost unlimited multitude of foreign pathogens,is proposed in this paper. The immune network system describesthe complex interaction of antibodies and antigens in virtue ofsome immune mechanisms, such as immune learning, immunememory, etc. AINC mimics these adaptive learning and defensemechanisms to respond to fault samples of power transformers.Consequently, AINC can find a limited number of antibodiesrepresenting all fault samples distributing structures and features,which helps to realize dynamic classification. This proposed AINCalgorithm has been tested by many real fault samples, and itsresults are compared with those of IEC ratio codes and artificialneural networks, which indicates that the proposed approachhas remarkable diagnosis accuracy, and with it multiple incipientfaults can be classified effectively.

Index TermsArtificial immune network, dissolved gas analysis,immune learning and memory, incipient fault, -nearest neighbormethod, power transformer.

I. INTRODUCTION

AS one of the key pieces of equipment in a transmissionand distribution system, the power transformer conditionhas a direct influence on the safety and reliability of a powersystem. Therefore, the online monitoring and offline test arevital for assessing power transformer conditions. Up to now,some technologies, such as dissolved gas analysis (DGA), par-tial discharge (PD), and moisture analysis in transformer oil[1][3] are widely used. Among these methods, DGA is a fastand economical method for detecting an incipient fault by utilityengineers. It is well known that transformer faults, mainly in theform of overheating, arcing, or partial discharge, develop cer-tain gaseous hydrocarbons, which are retained in the insulationoil as dissolved gases. The gas concentrations, generation rates,specific gas ratios, and the total combustible gas are importantparameters for interpreting the result of DGA. Presently, a con-ventional ratio method [4][6] and artificial-intelligence (AI)method [7][22] are the two major interpreting approaches.

Manuscript received December 22, 2005; revised August 14, 2006. Paper no.TPWRD-00724-2005.

The authors are with the Key Laboratory of High Voltage and ElectricalNew Technology of Ministry of Education, Chongqing University, Chongqing400044, China.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRD.2007.893182

The conventional ratio method mainly includes Rogers Ratios[4], Duval Triangle [5], and IEC Ratios [6], etc. Through calcu-lating several ratios of key gas concentrations, the fault type isdetermined by interpretation schemes defined in advance. How-ever, conventional ratios boundaries are sharp, and it is unableto provide interpretation for every possible combination of ratiovalues. Thus, fuzzy-logic technology is introduced into a con-ventional ratio method to make ratios boundaries vague. Thefuzzy ratio analysis method is used to diagnose multiple incip-ient faults in power transformers [7]. The deficiency is that itsmembership function is determined by practical experience ortrial-and-error tests.

There are many AI technologies, including expert system[9][11], fuzzy theory [7], neural network [12][20], evidentialreasoning theory [8], and Bayesian classifier [22], etc., whichare applied to the fault diagnosis of a power transformer. In anexpert system, diagnosis rules are determined by expert expe-rience and fuzzy-logic technology [11]. Therefore, diagnosisaccuracy depends upon whether expert rules are complete or not,and it is difficult to make use of fault data in the field. Neuralnetworks, including the backpropagation (BP) neural network[10], self-organizing map network [15], fuzzy learning vectorquantization network [16], wavelet networks [18], [19], etc., arewidely used in fault diagnosis. The neural network has the meritsof strong nonlinear and robust ability, resulting in the abilityto better depict the relationship between gas concentration andfault, but its demerits are that convergence speed is slow andthe network is easy to trap in local optimum. So the geneticalgorithm (GA) and evolving theory [17][19] are introducedto improve the deficiency of the neural network, which can tuneneural-network parameters and connecting weight, to yield theglobal optimum neural-network model. Since the relationshipbetween fault conditions and the gas data of neural networksis embedded in the networks structure, called the black box,a new rule table is obtained through mapping the knowledgeimplicitly captured by the neural network during the learningstage into a rule-based fuzzy inference system. It is easy for theutility engineer to interpret the result of DGA [20]. Evidentialreasoning theory is used to synthesize different diagnosis resultsfrom several conventional ratio methods, which results in abetter effect than any single ratio method [8]. In the light of thecapability of processing uncertain information of the Bayesiannetwork, a new fault diagnosis algorithm that integrates theBayesian network classifier with rough set is proposed to handlethe existing problem of incomplete and biased fault samples.Bayesian networks can combine prior knowledge with fault sam-ples, which is very important when samples are scarce or veryexpensive. Moreover, Bayesian networks can discover causal

0885-8977/$25.00 2007 IEEE

HAO AND CAI-XIN: ARTIFICIAL IMMUNE NETWORK CLASSIFICATION ALGORITHM 931

relationship among samples and handle incomplete samples,which other methods cannot do [22].

In recent years, the natural immune system has providedmuch inspiration for solving some innovative problems. Thisis because the immune system exhibits the following strengths:immune recognition, reinforcement learning, feature extraction,immune memory, diversity and robustness, etc. The immunesystem combines these strengths to construct pattern classifierefficiently. Based on these underlying mechanisms, the artificialimmune network classification algorithm (AINC) mimickingthe bodys adaptive learning and defense mechanism in the faceof invading pathogens is used as a fault diagnosis method forpower transformers. Having been applied in a great deal of realDGA samples, the experimental results demonstrate that AINChas remarkable diagnosis accuracy and it provides effectiveclassification for multiple incipient faults.

II. ARTIFICIAL IMMUNE NETWORK

A. Brief Description of Natural Immune SystemThe natural immune system is a prime defense system of lim-

iting damage to the host organism by pathogens, which is com-posed of immune cells, molecules, and organs. Pathogens thatelicit an immune response are called antigens (Ag). The lym-phocyte is the main type of immune cells which detect and elim-inate pathogens through immune response. There are two majorclasses of lymphocytes in the immune system: B cells, whichgrow to maturity in bone marrow, and T cells, which maturein the thymus. The main function of B cells is to produce anti-bodies (Ab), which attach to foreign antigens to make them fordestruction by other immune cells. T cells play two major rolesin immune defense: alerting B cells to start making antibodiesand activating other T cells and immune system scavenger cellscalled macrophages. The match strength of interaction betweenAb and Ag is measured by the affinity.

The natural immune system basically works in this way: Whenan antigen invades the organisms, T cells, which have receptorsthat enable each of them to recognize a different epitope onthe surface of antigen, are activated and emit chemical signalsto other immune cells. B cells, which also have receptors of asingle specificity on their surface, then respond to those signals.However, these B cells can recognize parts of antigens. Whenactivated, the B cells divide and differentiate into plasma cellsthat secrete antibody proteins. By binding to the antigens theyfind, antibodies can neutralize them or precipitate their destruc-tion by complementing enzymes or by scavenging cells. Fig. 1depicts an antigen recognized by different B cells. Some T cellsand B cells become memory antibodies that are longer-lived.These memory antibodies in nature enable the immune systemto respond rapidly to the second invasion by a previouslyencountered threat, called secondary response.

Learning and memory are the main characteristics of immunesystem. They refer to the adaptability that the immune systemcan learn the structures of antigens and remember those struc-tures so that future response to the same or similar antigens willbe quick and effective by producing a large initial high affinityclone. This is an intrinsic scheme of a reinforcement learningstrategy in natural immune system.

Fig. 1. Antigen recognized by different B cells.

Fig. 2. Process of clonal selection.

B. Artificial Immune NetworkInspired by the immunological principles including the clonal

selection, affinity maturation, and immune network theory, theartificial immune network model (aiNet) is presented by Le-andro Nunes de Castro [23].

The clonal selection and affinity maturation principle describethe basic features of an adaptive immune response to an antigenicstimulus. It establishes the idea that only those high affinitycells are selected to proliferate (clone) and mutate, while lowaffinity ones do not. The selected cells are subject to an affinitymaturation process, which grow in concentration and affinity,while those that are not selected will undergo a process of clonaldeletion, clonal anergy, or receptor editing. When repeatedlyexposed to a given antigen, the immune system continues to learnthe structures of this antigen for enhancing its recognition ability[24]. The process of clonal selection is illustrated in Fig. 2.

Immune network theory is originally proposed by Jerne(1974) [25]. Unlike the clonal selection principle, the immunenetwork theory hypothesizes that the immune system maintainsa regulated network of cells and molecules which maintaininteractions between not only an antibody and an antigen,but also antibodies themselves. If an antigen is recognized byantibody Ab , then Ab may be recognized by Ab and, in turn,Ab may be recognized by Ab , which forms a network of anti-bodies interaction. Recognition among antibodies would elicita negative response and result in the tolerance and suppressionof antibodies. In this way, excessively similar antibodies of

932 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 2, APRIL 2007

the same types will be suppressed. In the end, the immunesystem will achieve the state of stabilization. It assures thatmemory antibodies can uniformly distribute in antigen space.In this way, although there are relatively smaller numbers ofantibodies in the immune system, they cover the whole antigensspace and recognize all antigens.

To be brief, we only represent B cells in the immune net-work and make no difference between B cell and its surfacereceptor molecules. Therefore, we refer B cells to antibodies,which means that the immune network is composed of a numberof antibodies.

III. AINC ALGORITHM FOR FAULT DIAGNOSISOF POWER TRANSFORMER

Known from the introduction of aiNet, fault samples of thepower transformer can be regarded as antigens, and the memoryantibodies representing the characteristic of fault samples isgenerated through immune reinforcement learning, memory,and immune network suppression. So fault diagnosis of thepower transformer corresponds to the secondary responseof the immune system. Nevertheless, aiNet belongs to thenonsupervised clustering algorithm and its clustering centerscannot be exactly obtained [23]. In addition, because aiNetlacks fault-type information in the representation scheme ofantigens and memory antibodies, the ability to learn samplesof the same fault type is not strong. All of these might lead toinaccurate classification. Thus, AINC is proposed.

The AINC algorithm consists of three steps. First, fault sam-ples of the power transformer are classified as training antigensset and test antigens set. And both antigens and antibodies areinitialized. Second, we make use of the AINC to train the anti-gens set in order to obtain memory antibodies. Third, the Eu-clidean distance among the test antigens set and memory an-tibodies are calculated, and fault samples are classified by theimproved K-Nearest Neighbor (KNN) approach.

A. Initialization

In the initialization stage, fault samples of the power trans-former are mapped into the set of antigens in shape space.Then randomly generate antibodies and choose some anti-gens as memory antibodies . Finally, purify the antigensand antibodies.

The representation scheme of antigens and antibodies in theshape space determines a distance measure to be used to calcu-late the affinity between these molecules. In the original aiNet,the generalized shape of an antigen can be represented by a setof coordinates, which can be regarded as a point in a high-di-mensional real-valued shape space. For fault samples of thepower transformer in this paper, the representation scheme ofthe antigen is

, representing normalized concentrations of five oil-dis-solved gases H , CH , C H , C H , and C H , respectively.Normalization is calculated by (1)

(1)

Affinity between the antibody and antigen is shown as follows:

(2)

To enhance the learning capability of antibodies, fault-typeinformation was added in the antigen and memory anti-body. Thus, the improved representation scheme of is

. In it, representsthe fault type, which is the same as the representation schemeof the memory antibody. The function of the memory anti-bodys fault-type information lies in: first, the interaction of theantibody and antigen depends not only on its affinity but alsoon its type. Antigen is specifically recognized by antibodies ofthe same fault type. Second, both recognition and suppressionof the memory antibody should take its fault-type informationinto consideration. Third, the stopping criterion relies on boththe affinity and fault type of the memory antibody so as toretain the high-quality antibody.

The purification of the antigens is actually to eliminate thoseantigens whose Euclidean distance between the antigens is infe-rior to , which is used to measure the degree of similarity andis generally 0.01. The purification of antibodies is similar to thatof antigens. The only difference is that antigens are purified bydirectly eliminating those similar antigens in order to speed upthe convergence of the algorithm, while the purification of an-tibodies is required to supplement another antibody, which en-sures that the antibodies have better distributing features.

B. Learning Algorithm

After initialization, the learning algorithm of AINC aims atbuilding a memory set that recognizes and represents the datastructural organization. Only antibodies recognizing the antigenwith high affinity are activated to proliferate and mutate, accord-ingly, their affinities will increase. These antibodies can becomememory antibodies after immune suppression. The learning al-gorithm of AINC can be described as follows.

1) Affinity calculation: Calculate affinity betweenand antibodies and memory antibodies of the samefault type, respectively.

2) Clonal operator: select antibodies of the highest affinityto clone, and generate a clone set . The number of cloneis proportional to their antigenic affinity : the higher theaffinity, the larger the clonal scale for each of the selectedantibodies [see (3)]

round (3)

In (3), round is the operator that rounds the value inparentheses toward its closest integer and is theclonal scale.

3) Hypermutation: Each antibody in will undergo anaffinity maturation process, generating a mutated set . Itis important to note that mutation does not occur in fault-type information of the antibody but in attributes of the an-tibody. The mutated rate is inversely proportional to theantigenic affinity of its parent antibody: the higher the

HAO AND CAI-XIN: ARTIFICIAL IMMUNE NETWORK CLASSIFICATION ALGORITHM 933

affinity is, the smaller the mutation rate will be. Equation(4) is shown as follows:

(4)

4) Affinity calculation: Determine the affinity among andall the elements of . From , reselect % of the anti-bodies with the highest affinity as the set of partial anti-bodies . At the same time, eliminate all of the memoryantibodies from whose affinities are smaller than thenatural death threshold .

5) Clonal suppression: Eliminate those memory clones of thesame fault type from , whose affinity is superior tothe suppression threshold and generate the set of partialmemory antibodies . The total memory antibody poolcan be obtained as follows: .

6) Antigen presentation: Select the next antigen and returnto (1). This process continues until all antigens have beenpresented to the network.

7) Network suppression: From , eliminate those memoryantibodies of the same fault type whose affinity is su-perior to until the discrepancy of the average affinity isinferior to a prescribed threshold in four consecutive itera-tions. If the stopping criterion has not been met, then turnto (8).

8) Randomly generating antibody: Randomly generate an-tibodies and add them to , so antibodies set isequal to , then turn to (1) to repeat the entireprocess.

C. Improved KNN ClassifierThe KNN is a simple but effective classification method.

It assigns an input pattern to the majority class according toEuclidean distances between the pattern and its nearestneighbors in the training data space. After fulfilling the artifi-cial immune network training, the evolved memory antibodiesare available for KNN classification. Through calculating theEuclidean distance between test antigen and memory anti-bodies, the fault type of the test antigen is determined byusing a majority vote of the outputs of the most stimulatedmemory antibodies. But that is only applicable to single faultdiagnosis. Since multiple faults antigens have almost equaldistances among several fault types of memory antibodies, onlythe nearest memory antibody votes would result in an incorrectdiagnosis. After many tests, we can draw the conclusion thatthe fault type of the test antigen is determined by both memoryantibodies if the discrepancy of the Euclidean distance betweentest antigen and two nearest memory antibodies is inferior to10% of their average distance. If the test antigen obtains thesame votes, multiple incipient faults are considered to occursimultaneously.

IV. PARAMETERS ANALYSIS

In this section, we intend to discuss and analyze how sensitivethe algorithm is to some user-defined parameters. In particular,we will study the influence of the parameters and to the con-vergence speed, final network size, and recognition accuracy.

Fig. 3. Relationship of n and cycle times.

1) The best number of chosen antibodies : where is thenumber of antibodies chosen from the set of antibodies,which are used to proliferate. The larger the value of is,the larger the set of clones will be. Under such condi-tions, the searching space can be enlarged, but calculationcomplexity will also be increased. On the other hand, thesmaller the value of is, the smaller the set of memory an-tibodies generated at each iteration will be. Consequently,cycle times will be increased. Fig. 3 shows the paradigmof and cycle times. The value of is 4 in this paper.

2) Suppression threshold : The suppression thresholdcontrols the specificity level of the antibodies, the final net-work size, and is responsible for the network plasticity.Larger values of indicate more generalized antibodies,while smaller values result in highly specific antibodies.This parameter is critical, because the choice of a highvalue for might yield a misleading classification. There-fore, if fault samples of the power transformer distributerelatively densely, can be properly diminished. If faultsamples distribute sparsely, we can make the value oflarger. After many experiments, we find that 0.15 forcan preferably represent the features of the original sam-ples, and the size of memory antibodies set is moderate.

Other parameters in AINC are defined as follows: Thenumber of initial antibody 20, purification threshold ofantigens and antibodies 0.01, clonal scale of antibody

5, ratio of reselection % 10%, natural deaththreshold 1, the number of new generated antibody10, and the number of vote 5.

V. EXPERIMENT RESULTS AND DISCUSSIONSIn many cases, there is mostly a single incipient fault in the

power transformer, occasionally along with multiple incipientfaults. Common single incipient faults are as follows: 300thermal fault (T1), 300 700 thermal fault (T2),700 thermal fault (T3), partial discharge (PD), low energy dis-charge (D1), and high energy discharge (D2), etc. Multiple in-cipient faults comprise high energy discharge and thermal fault(MF1), low energy discharge and thermal fault (MF2), and high-temperature and medium-temperature thermal fault (MF3), etc.

We collected 720 fault samples from about 450 220-kV500-kV power transformers in China, whose fault types are

confirmed by expert experience according to various DGA

934 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 2, APRIL 2007

TABLE ICOLLECTED FAULT SAMPLES OF VARIOUS TYPES

Fig. 4. Shape space of high energy discharge and its memory antibodies.

analysis methods and an internal examination of the suspectedtransformer. Among these samples, there are 652 single incip-ient fault samples and 68 multiple incipient faults samples. Wedivided the 720 fault samples as the training antigens set andtest antigens set. The composition of the samples can be seenin Table I.

1) Diagnosis of single incipient fault.Using the learning algorithm above, the training process was

repeated 20 times. The immune networks can lead to conver-gence each time. The number of memory antibodies was 42 onthe average, and the data suppression ratio of training antigensset was 86%. Fig. 4 shows the distribution of high energy dis-charge fault samples and its memory antibodies by the coordi-nate of C H /C H , CH /H , and C H /C H . We can seefrom Fig. 4 that memory antibodies can cover the whole shapespace and represent different features of training antigens verywell. For a given affinity, some fault mode can be conduced formthe memory antibodies, as shown in Table II.

It has been obtained that the total diagnosis accuracy was93.2% by computing the Euclidean distances between test anti-gens and memory antibodies, and selecting five nearest memoryantibodies. The fault type of the test antigen was determined bya majority vote of the same type. One of the processing resultsof single incipient fault samples based on AINC and the diag-nosis accuracy were seen in Table III. To compare AINC, theBPNN and IEC ratio method were also used in the same faultsamples. The structure of BPNN is 5-12-6. After approximately9500 iteration times, BPNN converged and the total diagnosis

TABLE IISOME FAULT MODES OF HIGH ENERGY DISCHARGE. (AFFINITY 0.8)

TABLE IIIPROCESSING OF SINGLE-FAULT SAMPLES BASED ON AINC AND ITS

DIAGNOSIS ACCURACY FOR THE POWER TRANSFORMER

Fig. 5. Shape space of MF1 and its memory antibodies of T3 and D2.

accuracy rate of the test samples was 85.8%. The accuracy ofthe IEC ratios method was 71%. The diagnosis results of theBPNN and IEC ratios method were also shown in Table III. It isobviously indicated that the diagnosis accuracy and rate of theAINC algorithm presented in this paper is higher than that ofthe IEC ratios method and BPNN.

2) Diagnosis of multiple incipient faults.Memory antibodies of the single incipient fault can also be

effective classifiers of multiple faults. We can determine thatmultiple faults occur simultaneously in a power transformer ifthe votes are equal. Fig. 5 describes the distribution of MF1samples and its memory antibodies of T3 and D2.

With the approach, the diagnosis accuracy rate of multipleincipient faults was 88.2%. Table IV shows the diagnosis accu-

HAO AND CAI-XIN: ARTIFICIAL IMMUNE NETWORK CLASSIFICATION ALGORITHM 935

TABLE IVMULTIPLE INCIPIENT FAULTS DIAGNOSISACCURACY OF THE POWER TRANSFORMER

TABLE VFAULT DIAGNOSIS OF EIGHT REPRESENTATIVE SAMPLES USING AINC

racy of BPNN and AINC methods for multiple incipient faults.And the results of 8 representative fault samples using AINCare listed in Table V.

VI. CONCLUSIONIn this paper, we have presented the AINC algorithm for fault

diagnosis of the power transformer, based upon metaphors fromthe artificial immune system paradigm. This algorithm makesuse of the learning, memory, and network suppression mecha-nism of the artificial immune network to train and optimize faultsamples. At the same time, with a view to adequately reveal theinteraction of antigens and memory antibodies, we add infor-mation of fault type to memory antibodies. Thus, memory an-tibodies can preferably learn and memorize the features of thesame type of antigens; hence, classification accuracy of the al-gorithm can be improved. Moreover, experimental results showthat the diagnosis accuracy of this algorithm is higher than thatof the IEC ratios method and BP neural network. It is provedthat our algorithm is very feasible and useful in the multiplefaults diagnosis of power transformers.

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Xiong Hao was born in Nanchang, China, on May 6, 1979. He received the M.S.degree in power engineering from Chongqing University, Chongqing, China, in2003, where he is currently pursuing the Ph.D. degree in the key lab of highvoltage and new electrical technology.

His research area is online monitoring and fault diagnosis for high-voltage(HV) apparatus.

Sun Cai-xin is a Professor of electrical engineering at Chongqing University,Chongqing, China. He is an Academician of the Chinese Academy of Engi-neering. His research includes online monitoring and fault diagnosis for high-voltage (HV) apparatus, discharge mechanism in a complicated environment,and power geography information systems.