Power Transformer Fault Diagnosis Based on Integreted of Rough Set Theory and Evidence Theory

Zhou Ai-hua*�Yao yi�Song hong�Zeng xiao-hui ( Institute of Automation and Electronic Information Sichuan University of Science & Engineering

Zigong Sichuan 643000, China)

Abstract�When using chromatography data analysis in diagnosis of power transformer fault, fault information cannot be make full use , which can't effectively discover knowledge hidden in data. In this paper a method integreted of rough set theory and evidence theory for transformer fault diagnosis is presented. In this approach, in order to avoid subjectivity of basic probability assignment����rough set was induced to calculate the importance degree of condition attribute to decision attribute and act as basic probability assignment of recognition framework. Different evidence in the same reconginition framwork was combinated to obtain information on the fault types of decision classification information .A large number of examples analysis show that the rough set theory and evidence combination used in electric power transformer fault diagnosis, not only can effectively improve the single fault diagnosis accuracy, also give the information about compound fault analysis.

Keyword����Rough Set, Evidence Theory����Power Transformer����Fault Diagnosis

I INTRODUCTION

Power transformer is one of the most important devices in the electric power system, which operating condition is directly related to power system stability and the economy. Timely and accurately detect early latent fault in transformer has vital practical value. In recent years, chromatographic analysis data worked as analysis object, all kinds of classification algorithm and artificial intelligence were applied in early transformer latent fault, and developed from a single intelligent method gradually to a variety of intelligent method fusion. Evidence theory, as a kind of uncertainty reasoning method, has set up a file in the measurement control, fault diagnosis, computer engineering areas, recently it has been also applied in electric power transformer fault diagnosis field[1-3]. In Evidence theory, basic probability assignment is a very important factor when evidence combination, the asic probability assignment assigned by experts was too subjective, and not easy popularization and application. At present, some experts put the evidence theory combined with neural network, and serve the output of the neural network as the basic probability assignment, which obtains some effect. However�as we know�Neural network is sensitive to the selection of initial value ,and weighting method although solved the problem of evidence conflict, still can't avoid the basic probability assignment of subjectivity[4,5].�

� This work is being supported by artificial intelligence key laboratory of Sichuan province (Foundation number �2009RY006) *Corresponding author. E-mail address: :zahcc108@163.com

Rough set can describe incomplete and uncertainty data. Rough set objectively analysis data, discover patterns and relations underlying in the data[6,7]. In addition, data important degree were calculated to produce new rule from the data. Evidence theory has a lot of advantage in information fusion, but the evidence of the basic probability assignment is based on expert experience appointed, which is too subjectivity to cause difficult in practical application. This paper considered the rough sets theory and evidence theory reliability calculation, the relationship between the attribute importance through calculation, and obtain evidence of the basic probability assignment. Then, different evidence were combenated to mine more fault information in DGA . Example analysis shows that the proposed method is very favorable for transformer single fault and mixed fault diagnosis[8,9].

II ROUGH SET THEORY

Rough set regards information systems as an abstract object,which can be discribed as� >=<U,A,V,fS ,where U is the finite non-empty set consist of reseach object, called the domain; A is the finite non-empty set of attributes, DCA �= , where C is condition attribute, Dis the decision attribute; V is a set of attribute values,

aAaVV

∈= � ,where aV is the set of values of a ,called the

domain of attribute a . Define an information function VAUf →×: ,it gives each object information

for each property value. The relation between attribute and value constitutes a two-dimensional table, called the decision table.

2013 Third International Conference on Intelligent System Design and Engineering Applications

978-0-7695-4923-1/12 $26.00 © 2012 IEEE

DOI 10.1109/ISDEA.2012.247

1049

Definition 1. In information system >=<U,A,V,fS ,

AR ⊆ is attribute subset ,which decides an undistinguished binary relationship )(Rind , more

formally:

{ }),(),(,),()( ayfaxfRaUUyxRind =∈∀×∈=Obviously, )(Rind determined a division�expressed as

)(RindU or RU � [ ]Rx representing equivalence class

contains the Ux ∈ . Definition 2. In information system >=<U,A,V,fS ,

let X denotes the subset of element of universe U ( UX ⊆ ), the lower approximation of X in R( AR ⊆ ), denoted )(XR ,is defined as the union of all these elementary sets which is contained in X,more formally:

[ ]{ }XxUxXR R ⊆∈=)(

The above statement is to be read as: the lower approximation of the set X is a set of object x, which belong to the elementary sets contained in X.

Definition 3. In information system >=< U,A,V,fS ,

let c represent one of condition attributes ,C represent condition attribute set , D is decision attribute set, the importance of c relative to D denoted as )(cSIG , more

formally:

{ } )()()( DDcSIG cCc −−= γγ

Where )(Dcγ is the support degree of condition

attribute c relative decision attribute D, more formally

U

XRD

n

ii

c

�== 1)(γ

III EVIDENCE THEORY

Evidence theory is firstly proposed by Dempster in 1967, then improved by Shafer, after decades of development, it has formed a relatively complete theoretical system. In evidence theory, different evidence coming from different channels can be fusion, thus giving rise to a new rules. The combining rule of the Dempster- theory is well suiable for solving the problem of incomplete knowledge. In evidence theory, the union of all hypothesis called a recognition framework, denoted as

Θ2 , which is a set, contains the all uncertain answers to the hypothesis, but only one of them is correct. If each evidence in Θ2 satisfy incompatible conditions, let A represent the element of Θ2 �then basic probability

assignment function can be denoted )(Am : ]1,0[2 →Θ , a

basic probability assignment function is a generalization of the traditional probability density function. Actrually , basic probability assignment(bpa) describe the impact of each distinct piece of evidence on the subset of Θ2 . The belief function, denoted Bel, corresponding to a specific bpa, m, assigns to every subset A of Θ2 the sum of the beliefs committed exactly to every subset of A by m. Thus )(ABel is a measure of tatal amount of belief in

A and not of the amount conmmitted to A by the evidence giving rise to m. Evidence combination rule is the core of evidence theory. Given two belief functions, based on two observations but with the same frame of dicernment, Dempster’s combination rule, shown below ,computes a new belief function that represents the impact of the combined evidence[10].

1)()( 21 <� jBA

i BmAmji�

Where m1 and m2 denote bpa of two belief functions ,denoted 21 mm ⊕ .

IV POWER TRANSFORMER FAULT DIAGNOSIS BASED ON

ROUGH SET AND EVIDENCE THEORY

A. Establish decision tablebBased on rough set and evidence theory, the

relationship between the different evidence as rough

concentration of condition attributes subset, the

importance degree of evidence condition attributes subset

relative to decision attribute is the basic probability

assignment. Evidence combination can mine the

information in the data. In electric power transformer

fault diagnosis, chromatographic analysis data can be

constitute two evidence � the proportion of

62422242 H��H��H�����H works as an evidence ,

and discreted according to the characteristic gas method,

the other evidence is consist of )HC(/)HC( 4222 ϕϕ �

)H(/)HC( 24 ϕϕ � )HC(/)CH( 624 ϕϕ �discreted according

to IEC-60599. The decision table contains 60 samples,

including 6 types fault for decision attribute, respectively

high temperature fault(T3), medium temperature fault(T2),

lower temperature fault(T1), high energy discharges(D2),

lower energy discharges(D1) and partial discharges(PD).

1050

Somewhere in the listed in table 1 ,only 12 of these samples, table 2 is the decision table after discretization.

Tab 1. Original Decision Table

Condition Attribute U

H2 CH4 C2H4 C2H6 C2H2 )H(C)HC(

42

22

ϕϕ

)(H)CH(

2

4

ϕϕ

)H(C)CH(

62

4

ϕϕ

Decision Attribute

1 0.01 0.12 0.74 0.14 0.00 0.00 14.23 0.86 T32 0.12 0.22 0.54 0.11 0.01 0.02 1.78 2.02 T33 0.09 0.26 0.43 0.22 0.00 0.00 2.82 1.19 T24 0.06 0.37 0.39 0.18 0.00 0.00 6.14 2.00 T25 0.19 0.16 0.32 0.33 0.00 0.01 0.89 0.50 T16 0.17 0.18 0.28 0.36 0.00 0.01 1.04 0.49 T1 7 0.13 0.13 0.55 0.06 0.13 0.24 1.03 2.37 D28 0.07 0.01 0.04 0.00 0.88 22.46 0.21 12.38 D29 0.28 0.24 0.08 0.05 0.35 4.33 0.85 5.15 D110 0.87 0.07 0.01 0.05 0.00 0.00 0.07 1.26 D111 0.74 0.04 0.04 0.10 0.08 1.83 0.05 0.36 PD 12 0.12 0.10 0.43 0.31 0.05 0.11 0.84 0.33 PD

Tab 2. Discrete Decision Table

Condition Attribute U

H2 CH4 C2H4 C2H6 C2H2 )H(C)HC(

42

22

ϕϕ

)(H)CH(

2

4

ϕϕ

)H(C)CH(

62

4

ϕϕ

Decision Attribute

1 0 0 1 0 0 0 2 2 T32 0 1 1 0 1 0 2 2 T33 0 1 1 1 0 0 2 1 T24 0 1 1 1 0 0 2 1 T25 1 1 1 1 1 0 0 0 T16 1 1 1 1 0 0 2 0 T17 1 0 1 0 1 1 2 2 D28 0 0 0 0 1 2 0 2 D29 1 1 0 0 1 2 0 1 D110 1 0 0 0 0 0 1 0 D111 1 0 0 0 1 1 1 0 PD 12 0 0 1 1 1 1 0 1 PD

B. Examples

The chromatogram analysis data of a main transformer list in table 3

Tab.3 The DGA Data of One Main Transformer ����L/L

H2 CH4 C2H4 C2H6 C2H2 Total Hydrocarbon

19 147 319 547 176 1208

According to the calculation table 2, the weights of attributes is evidence of the basic probability assignment, so we can get the DGA data probability assignment, such as shown in table 4. Tab.4 probability assignment Diagnostic Results by Combination of

Evidence Evidence T3 T2 T1 D2 D1 PD

1 0.3465 0.2376 0.0245 0.3521 0.0031 0.03622 0.2346 0.1576 0.1356 0.4321 0.0041 0.0360

1+2 0.5357 0.0124 0.0021 0.4321 0.0011 0.0166

As shown in table 3 and 4, Evidence before Combinated , the three ratio coding of chromatographic data of is 122, without corresponding fault code. In addition, gas characteristics method cannot be sure is high temperature fault or high energy fault, although the two fault's approval rating higher, but is not very outstanding characteristics. However, after fusion of evidence 1 and 2

evidence , the approval rating of high temperature fault and high energy discharge fault's is obviously higher than other fault types, it is obvious that both high temperature of transformer fault and high energy discharge fault. The more detailed analysis though hanging core inspection proved the correctness of the judgment. There are two evidence,first, the insulation space distance of upper core grounding copper to core is not wide enough, which cause multipoint earthing and high temperature fault. Second low voltage winding of A phase badly burned burns, which suggests that high energy discharge fault in A winding. More example analysis show that the evidence fusion method, not only can improve the precision of the single fault diagnosis, but also gives the possibility of compound fault analysis.

V CONCLUTION

In this paper, a method Integreted rough set and evidence theory was proposed. Fault sample was first descreted before structuring decision table, then the importence of condition attribute to decision was calculated to work as basic possibility assignment. The

1051

above approach to ensure that the basic probability distribution of objectivity. At last, different evidence was combinated to gain information about fault. The proposed approach are effective for single fault and mixed fault and easy to spread.

REFERENCE

[1] Zhu Cheng-zhi, Guo Chuang-xin�Sun Min�Xin Jian-bo.Power transformer condition assessment Based on improved evidential reasoning[J].High Voltage Engineering, 2008�35(11)�2332-2337(in Chinese) [2] Xie Hong-ling, Lu Fang-cheng. Transformer condition evaluation based on information fusion[J]. Journal of North China Electric Power University, 2006, 33(2) : 8-11(in Chinese) [3] Fu Hua, Li Bo, Xue Yong-cun. Analysis of underground monitor method based on D-S decision-making data fusion,2007�26(1)�27-293(in Chinese) [4] Liao Rui-jin, Liao Yu-xiang, Yang Li-jun, Wang You-yuan.Study on

synthetic diagnosis method of transformer fault using multi-neural network and Evidence Theory[J]. Proceedings of the CSEE�2006�26(3)�119-124 [5] Tan Qing, Xiang Yang-hui. Application of weighted evidential theory and its information fusion method in fault diagnosis[J]. Journal of Vibrationand Shock ,2008�7(4)�112-116 [6] Paw Lak Z.Rough sets approach to knowledge-based decision support[J].European J of Operational Research,1977,99(1)�48-57. [7]Zhang Wen-xiu.Rough set theory and method. [M]. Beijing: Science Press�2001(in Chinese) [8]Skowron A,Grzymalfa-Busse J.From Rough set theory to evidence theory advances in the Dempster-Shafer theory of evidence[M].New York:John Wiley & Sons,inc�1994�193-236 [9]Yao Y Y,Lingras P J.Interpretation of belief functions in the theory of rough sets[J].Information Sciences�1998�104(1/2)�81-106 [10] Dempster A.P. Upper and lower probabilities induced by a multivalued mapping[J]. Annals of Mathmatical Statistics, 1967,38(2):325:339

1052