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Proceedings of the 2012 International Conference on Wavelet Analysis and Pattern Recognition, Xian, 15-17 July, 2012 FAULT DIAGNOSIS USING NEURO-FUZZY NETWORK AND DEMPSTER-SHAFER THEORY XIN WANG 1,2, XIAO-BIN xu 3, YIN-DONG JI 1 ,2,. , XIN-YA SUN 1,2 "I'singhua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China 2Department of Automation, Tsinghua University, Beijing 100084, China 3Institute of Systems Science and Control Engineering, School of Automation, Hangzhou Dianzi Univeristy, Hangzhou,310018, China E-MAIL: [email protected]@163.com Abstract: This paper focuses on fault diagnosis using neuro-fuzzy network. It is shown that less reliable result may be derived as the network takes no consideration of previous state information in online fault diagnosis. To solve this problem, we combine a modified neuro-fuzzy network with the evidence update theory. Besides, a new updating rule that combining the Jeffery-like rule and linear combination rule is given. Simulation shows the effectiveness of this fault diagnosis method. Keywords: Fault diagnosis; Neuro-fuzzy network; Evidence update; Linear combination rule; Jeffery-like rule 1. Introduction Neuro-fuzzy network has been widely used in fault diagnosis in various fields. [1] used neuro-fuzzy methods in the fault diagnosis of the industrial gas turbine. [2] applied two neural fuzzy methods in motor fault detection and diagnosis. In chemical area, neural fuzzy network could also be used [3]. Using neuro-fuzzy network to diagnose faults in these systems achieves satisfactory results. When neuro-fuzzy network is used to do fault diagnosis, it transfers the system state into fuzzy expressions such as 'high', 'medium' and 'low'. Integrating some fuzzy if-then rules like "if voltage is very low, current is very low, then sensor is failure", neuro-fuzzy network outputs the diagnosis results. To derive what exactly these rules are and figure the parameters in the network such as parameters of the membership functions, sampled data of the fault is needed to train the network. Then in real-time diagnosis, the trained neuro-fuzzy network accepts current state of the system and outputs the diagnosis results. In this process, the online fault diagnosis result depends only on the current state of the system, and it does not taken into account the past state of the system. Generally speaking, the system state is continuous, and there is often some kind of relationship between the current state and the past states. However, current fault diagnosis method based on neuro-fuzzy network takes no consideration of this relationship, and their process assumes that past states has no impact on the current state. Apparently, this would lead the results less reliable. In fact, when dealing with faults in the system, we need to consider the following rules: a. When minor changes occur between the current state and past state of the system, the fault diagnosis result should basically keep consistent with the past, so as to reflect the stable state of the system. b. When there are progressive changes in the state of the system, the fault diagnosis result should reflect these changes sensitively. As the system are more likely transferring from a state to another, the result should converge quickly to this new state, thus the system can make early warnings to avoid bad damages. c. When great changes occur between the states, the fault diagnosis result should reflect these changes sensitively. The diagnosis should converge to the new fault state when the system transferred to a fault state, and on the other hand, it should also avoid the misdiagnosis from disturbance aroused by unreliable data. To make the fault diagnosis obey above rules, a new method combining evidence theory and neuro-fuzzy network is proposed. In the modified neuro-fuzzy network structure, the nodes in the normalization layer which represents the firing strength of the fuzzy rules construct a ·Corresponding author. Tel: +86 010 62780216; fax: +8601062785878. E-mail address:[email protected] 978·1-4673·1535·7/121$31.00 ©2012 IEEE 137

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Page 1: [IEEE 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR) - Xian, China (2012.07.15-2012.07.17)] 2012 International Conference on Wavelet Analysis and

Proceedings of the 2012 International Conference on Wavelet Analysis and Pattern Recognition, Xian, 15-17 July, 2012

FAULT DIAGNOSIS USING NEURO-FUZZY NETWORK ANDDEMPSTER-SHAFER THEORY

XIN WANG 1,2, XIAO-BIN xu 3, YIN-DONG JI 1,2,. , XIN-YA SUN 1,2

"I'singhua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China2Department ofAutomation, Tsinghua University, Beijing 100084, China

3Institute of Systems Science and Control Engineering, School ofAutomation,Hangzhou Dianzi Univeristy, Hangzhou,310018, China

E-MAIL: [email protected]@163.com

Abstract:This paper focuses on fault diagnosis using neuro-fuzzy

network. It is shown that less reliable result may be derived asthe network takes no consideration of previous stateinformation in online fault diagnosis. To solve this problem,we combine a modified neuro-fuzzy network with the evidenceupdate theory. Besides, a new updating rule that combiningthe Jeffery-like rule and linear combination rule is given.Simulation shows the effectiveness of this fault diagnosismethod.

Keywords:Fault diagnosis; Neuro-fuzzy network; Evidence update;

Linear combination rule; Jeffery-like rule

1. Introduction

Neuro-fuzzy network has been widely used in faultdiagnosis in various fields. [1] used neuro-fuzzy methods inthe fault diagnosis of the industrial gas turbine. [2] appliedtwo neural fuzzy methods in motor fault detection anddiagnosis. In chemical area, neural fuzzy network couldalso be used [3]. Using neuro-fuzzy network to diagnosefaults in these systems achieves satisfactory results.

When neuro-fuzzy network is used to do faultdiagnosis, it transfers the system state into fuzzyexpressions such as 'high', 'medium' and 'low'. Integratingsome fuzzy if-then rules like "ifvoltage is very low, currentis very low, then sensor is failure", neuro-fuzzy networkoutputs the diagnosis results. To derive what exactly theserules are and figure the parameters in the network such asparameters of the membership functions, sampled data ofthe fault is needed to train the network. Then in real-timediagnosis, the trained neuro-fuzzy network accepts current

state of the system and outputs the diagnosis results. In thisprocess, the online fault diagnosis result depends only onthe current state of the system, and it does not taken intoaccount the past state of the system. Generally speaking, thesystem state is continuous, and there is often some kind ofrelationship between the current state and the past states.However, current fault diagnosis method based onneuro-fuzzy network takes no consideration of thisrelationship, and their process assumes that past states hasno impact on the current state. Apparently, this would leadthe results less reliable.

In fact, when dealing with faults in the system, weneed to consider the following rules:

a. When minor changes occur between the currentstate and past state of the system, the fault diagnosis resultshould basically keep consistent with the past, so as toreflect the stable state of the system.

b. When there are progressive changes in the state ofthe system, the fault diagnosis result should reflect thesechanges sensitively. As the system are more likelytransferring from a state to another, the result shouldconverge quickly to this new state, thus the system canmake early warnings to avoid bad damages.

c. When great changes occur between the states, thefault diagnosis result should reflect these changessensitively. The diagnosis should converge to the new faultstate when the system transferred to a fault state, and on theother hand, it should also avoid the misdiagnosis fromdisturbance aroused by unreliable data.

To make the fault diagnosis obey above rules, a newmethod combining evidence theory and neuro-fuzzynetwork is proposed. In the modified neuro-fuzzy networkstructure, the nodes in the normalization layer whichrepresents the firing strength of the fuzzy rules construct a

·Corresponding author. Tel: +86 010 62780216; fax: +8601062785878.E-mail address:[email protected]

978·1-4673·1535·7/121$31.00 ©2012 IEEE137

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Proceedings of the 2012 International Conference on Wavelet Analysis and Pattern Recognition, Xian, 15-17 July, 2012

where a k and Pk are nonnegative and satisfy

a k +Pk =1, and

Given the frame of discernment e, B c e ,f(A) = {X E8:X =DuC,0 -:l:-D~B,0 -:I:- C ~ A~B}

, ek denotes the evidence deriving from the previous k

moment, and mk+1 denotes the evidence of the k+1th

moment, then the linear combination updating rule forupdating the mass ofB can be expressed as follows:

frame of discernment, and can be taken as evidence.Therefore, we can derive the evidence for the fuzzy rules ateach time k. Then we derive the global evidence from boththe current and the past evidence using the linearcombination of the available evidence and the conditionalevidence. Besides, we propose the method using the cosinesimilarity measure to determine the linear combinationweights, and combine the linear combination updating ruleand Jeffery-like updating rule to derive a new updating rule.After that, based on the evidence, the consequent anddefuzzification parts of the neuro-fuzzy network give thediagnosis results which can more reliable reflect the faultstate of the system. At last, we apply this new method in thefault diagnosis of the railway track circuit. Results showthat the new method is more reasonable and effectivecompared to neuro-fuzzy network in fault diagnosis.

2. Preliminaries

L m(C)m(A IB) = C:CcA

Pl(A)- LX:XEl(A)m(X)L m(CIB)

C:C~A(4)

2.1. Introduction to DS theory

2.2. Updating evidence

K is the mass assigned to <D, and represents conflict inevidence.

In this section, we introduce two rules for updatingevidences: the linear combination updating rule[4] and theJeffery-like rule[5].

(6)

(5)

and for all A c B ,s.t. m(A) =Bel(A) ,

m(A IB) = m(A) m(A)Pl(B)- ~X:XEl(A)m(X) m(A)+Pl(B-A)

for all A c B ,s.t. A E f(B)

meA IB) = meA)Pl(B)

where f(B) = {A c B c e :f(A) =0} .

Three choices of {a k , Pk } are:

(1) The choice {ak,Pk} ={I,O}. This perceives the

incoming evidence to be completely unreliable, and accountfor the complete inflexibility of the available evidencetowards changes.

(2) The choice {ak,Pk} ={O,I}. This perceives the

incoming evidence to be completely reliable, and accountfor the complete flexibility of the available evidencetowards changes.

N 1(3) The choice {ak,Pk} ={--,--}. This takes

N+I N+Ithe incoming evidence and the already gathered evidence asequal.

[5] proposes Jeffery-like rule. In the frame ofdiscernment we mentioned above, the Jeffery-like rule forupdating the mass ofB can be expressed as follows:

(2)

(1)

K = L ~(B)m2(C)BnC=(J)

m(A) = LBnc=A"'t (B)m2 (C)l-K

where

In Dempster-Shafer evidence theory, the frame ofdiscernment, e, contains a set of mutually exclusive andexhaustive hypotheses. 29 denotes the power set of . ABasic Belief Assignment function (BBA), also called themass function, is defined as m: 29---+[0,1], m satisfies m( cP)

= 0 and LAeem(A) =1where cP is the empty set.

The mass function represents the degree to which theevidence supports A. Each element A satisfying m(A) > 0 iscalled focal element. A body of evidence is the pair (R, m),where R is the set ofall focal elements.

Now consider two independent bodies of evidence m,and mu they can be combined using Dempster's rule ofcombination:

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centroid as the defuzzifier, we have the following afterthese fuzzy control rules:

z;Y~II JlAf (x )Yj = S i (10)

Ll=lIIJlAf (x )i

where IiAI is the membership function of the fuzzy set

AJ ' and Y~ is the output ofthejthrule.

The purpose of such system is to apply neural learningtechniques to identify and tune the parameters and/orstructure ofneuro-fuzzy systems[7].

(9)

(8)

(7)

where

ek+1(B I(k,ek)) = L mk+1(A)ek(B IA)A~8

2.3. Neuro-fuzzy inference systems

Neuro-fuzzy inference systems generally are neuralsystems realizing the following fuzzy control rules:

R1: IFx1isA; ,.....xn is A~,

THEN Y1 is B; ,....Ym isB~where 1=1,2... ,S and S denotes the sum of fuzzy controlrules [6]. If we use the multiplication operator and the

Figure 1 CANFIS structure with two inputs and three outputs

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Proceedings of the 2012 International Conference on Wavelet Analysis and Pattern Recognition, Xian, 15-17 July, 2012

2.4. Structure of the fuzzy neural networkby mk+1(A),mk+1(B),mk+1(C). Then we can update

evidence using linear combination updating rule:

3. Combining the neuro-fuzzy network with updateevidence theory

From section 2.4, we can see that the output of layer 4,which is normalization layer, is actually the extent to whatthe premise of the rule is supported by the input. If we labelthe premise part of the rules which nodes in layer 4 represents

in Fig.l as A, B and C, for output ,the system can bebriefly described by

Here we briefly introduce the structure of onecommonly used neuro-fuzzy network: CANFIS (coactiveadaptive neuro-fuzzy inference system) [8], [9]. Fig.lillustrates the CANFIS structure with two inputs and threeoutputs.

The function ofeach layer is:• Fuzzification: convert the input variable into

linguistic values through membership functions.Multiplication: multiply all the incoming signals to get thefiring strength ofeach fuzzy rule.

• Normalization: normalize the firing strength.• Defuzzification: perform defuzzification through

fuzzy rule operations.• Summation: compute the overall output as the

summation of all incoming signals.

If rule A, thenY1 is 0S,l

If rule Bithen y, »o.,If rule C, thenY1 is O, 3

defuzzification ) Y1 (11)

RuleA :ek+1(A) =akek(A) +Pkmk(AIA)

RuleB :ek+1(B) =akek(B) +Pkmk(B IB) (12)

RuleC: ek+1(C) =akek(C)+Pkmk(CIC)

However, due to the following reasons, this rule is notquite fit for the updating of the evidence in our situation:

(1) The linear combination updating rule concernsonly the proposition of the current evidence without takinginto account how the current evidence perceive thisproposition, i.e. the mass value of focal elements. In our case,the updating rule cares that the new evidence supports {A, B,C}, but the mass value assigned to each focal element isneglected.

(2) In the linear combination updating rule, thereal-time evidence plays a minor role while the historicevidence plays the main role. However, in fault diagnosis, wehope that enough emphasis is placed on the real-timeevidence so as to get a real-time diagnosis result, and thehistoric evidence should be emphasized but notover-emphasized.

(3) The three choices for the weight in the rule(described in section 2.2) is not appropriate as they don't takethe relationship of the evidences into consideration.

Therefore, in the next two sections, to settle theseproblems, we combine the linear combination rules andJeffery-like rules, and propose a method to dynamicallycalculate the weight based on similarities of evidences.

3.2. Combine the two updating rules

Furthermore, if we denote the output value of layer 4 as

m(A), m(B) and m(C), then we get the e = {A, B, C} as

the frame of discernment, and m(A), m(B), and m(C) arerespectively, the value of the mass function of A, Band C,and satisfies m(A) +m(B) +m(C) =1. Therefore, input

in the system can be transferred to evidence.

3.1. Update the evidence

Now suppose we use the neuro-fuzzy network in Fig.lto diagnose the faults in a system. We use the trained networkto diagnose the faults. Suppose at time k, the input of the

system is denoted by {~,k' X2,k} , and the evidence by

ek(A), ek(B), ek(c) . At time k+1, the evidence is denoted

In linear combination rule, the second part of the

formula (3), mk (A IB) , is actually the degree to which the

proposition of the evidence at (k+l)th moment supports theproposition in previous k moment. So this rule can be viewedas the combination of the history evidence and the degree thatthe proposition of real-time evidence supports the historyevidence. On the other hand, in Jeffery-like rule,

ek(B IA) in formula (7) can be viewed as the degree that

history proposition supports the real-time evidence. The

multiplication of ek(B IA) and mk+1(A) represents the

real-time evidence under support of the history proposition.So, if we replace the second part of the linear

combination rule with the Jeffery-like rule, the new rulewould be constituted of the history evidence and the real-timeevidence under history support. In other words, the mass

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value of the real-time evidence is considered, and the role ofreal-time evidence can be tuned by the weight. Thecombining rule is as follows:

Sup(mp ) = LSpqop,q = 1,2,ooo,np-:t:q

(17)

(18)

j=l(14)

(13) The credibility ofevidence can be defmed as

Crd(i) = NSup(m)

LSup(mj )ek+1(B I(k,ek)) = L mk+1(A)ek(B IA)A~8

where

Thenweset a k+1 = Crd(k + l)'Pk+l =1-ak+1 •

3.4. The overall fault diagnosis procedure

3.3. Calculate the weights based on similarities ofevidences

In this section, we give the method of calculating theweights based on similarities ofevidences so that relationshipamong the evidences can be considered. First, we give thedefmition of the cosine similarity of evidence. Then we usethat to determine the pair wise similarities between the(k+ l)th, J(h, (k-l)th, (k-2)th evidence, as these evidences allrepresent the recent state of the system. Thus we get thecredibility of the (k+ 1)th evidence, denoted by Crd(k+1). Set

a k+1 = Crd(k+ l),Pk+l = l-ak+1 •

In evidence theory, let m1 and m2 are two mass

functions, then the similarity between them is

~.mTSim(~,m2) = cosO = 2 (15)

11~11·llm211

where mI. m2T ='" ~ m1 · • m2 · is inner product of~}=1'} ,}

m1 and m2 , and k is the dimension of vector; II-II represents

the norm of the vector. Then for n-sources fusion system,similarity measure matrix is denoted as

SII S12 SIn

SIM=S21 S22 S2n

(16)

Snl Sn,2 Snn

where Spq =Sim(mp,mq) is the similarity of mp and

m . The support degree of evidence is defmed asq

In this section, we first give the structure of the modifiedneuro-fuzzy network. The main difference between this newnetwork and the network in section 2.4 is that it has adifferent consequent part and a different defuzzifier. Then weuse samples in the real system to train this network. After that,in real-time fault diagnosis, we combine it with the evidenceupdate.

i. The structure of the modified neuro-fuzzy networkThe structure of fuzzy neural network with two input

nodes and three rules for each output is shown in Fig.2. Thereare 7 layers in this system. The first layer represents the inputlayer, and it accepts input states. The last layer is the outputlayer, it outputs results such as control signals or faultdiagnosis results. The hidden layers in the system realize thefunctions of formula (9). Nodes in layer 2 is the membershipfunction, it represents the degree to which the input statebelongs to a linguistic variable. Layer 3 is the multiplicationlayer. Layer 4 performs normalization of layer 3. Layer 5 isthe then part of the fuzzy rules, and layer 6 is thedefuzzification layer. Details ofeach layer are as follows.

Layer 1: Input layer. Each node in this layer correspondsto an input variable. This layer directly transfers the inputvariable to the next layer, i.e. each node is connected to somenodes in layer 2, which represents the membership function.

Layer 2: Fuzzyfication layer. Node in this layer acts asmembership function of a linguistic variable. Commonlyused membership functions are trapezoidal, triangular-shaped,or bell-shaped membership functions. In this paper,bell-shaped membership function defined in the following isused:

f1A (x) = e-((X-C)2tu2)

(19)

where parameters c and a are, respectively, the centerand the width of the bell-shaped membership function.Different values of c and a represents different linguisticlabels. Parameters in this layer are referred to as premiseparameters.

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(21)

(22)

Layer 3: Multiplication layer. Node in this layerperforms the AND operation. It multiplies the incomingsignals from layer 2. This layer functions as the IF-part of thefuzzy rule, and outputs the firing strength of each rule. Thefunctions of this layer are

(20)

Layer 4: Normalization layer. Node in this layercalculates the ratio of the firing strength of each rule to thesum ofall rules' firing strengths:

°3 "o = ,I

4,i ~Q"L...J 3,j

j

Layer 5: Consequent layer. This layer functions as theTHEN-part of the fuzzy rule. Each node in this layer has two

parameters US,k and CS,k' and they are respectively, the

centroid and width of the membership function of the outputlinguistic value of the rule. The output of this layer is the

multiplication of the firing strength coming from layer 4 andthe membership functions of layer 5.

Layer 6: Defuzzification layer. Node in this layercomputes a crisp value using the Center ofArea method

L °4,k0"5,kC5,k

06,i = kLO ,k Eli

4kUSk

k

where Ii is the set of indices of the nodes in layer 5 that

connected to node i in layer 6, 0 4 k is the firing strength of

the rule, US,k and CS,k are parameters in layer 5.

Layer 7: Output layer. This layer outputs the valuecoming from layer 6 as control signals or fault diagnosisresults.

We can see that the parameters need to be tuned in thesystem is membership functions in layer 2 and layer 5.

Figure 2 Structure of the modified neuro-fuzzy network

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(25)

ii. Train the networkSuppose we have P training examples of the fault data in

a system, and they are used to train the network. To tune theparameters in the system, we use the gradient descentlearning algorithm to minimize the cost function:

E,p = .!.(y; -07 ;)2 ,i = 1, 2....m,p = 1, 2...P (23), 2 '

where m is the sum of nodes of output layer, Y i is the target

output of the ith node of the output layer, 07 i is the actual

output.According to gradient descent algorithm, parameters in

layer 5 can be updated by

BE BEUS . = Us . -TJ--,Cs . = Cs .-TJ-- (24)

,j ,j Da.: ,j ,j Dc.:S,j S,j

BE BEwhere B and -B- can be determined by the chain

US,j CS,j

rule. In the same way, parameters in layer 2 can be updated.iii. Do the real-time fault diagnosis with evidence

updateBy now, we've got a trained neuro-fuzzy network for the

system. Then we use network in Fig.3 to do real-time faultdiagnosis, and we use the parameters in the trained network

to set the parameters in this network.Suppose at the JCh moment in the real-time fault

diagnosis, we get the evidence of the rules from the

normalization layer in the network, denoted by mk • The

global evidences of previous k and k-l moment are denoted

by ek and ek- 1 respectively. Evidences at (k-l )th, (k-2)th

and (k-3)th moment are denoted by mk- 1 , mk- 2 ,

mk - 3 respectively.

We can calculate the weights a k and Pk by calculating

the credibility through the similarities among mk '

mk - 1, mk - 2 , and mk - 3 • Then we update the evidence using

formula (13), i.e.

ek(B)= akek-1(B) +Pkek(B I(k-l,ek_1»= akek-1(B) +Pk LA£;(') mk(A)ek(B IA)

Then we deliver the global evidence ek to layer 5.

After the consequent and defuzzification layer, we get theoutput, which indicates the fault diagnosis result of thesystem.

Figure 3 Neuro-fuzzy network for real-time fault diagnosis

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receiving end demodulates the currents signal transmittedalong two rails and control the track relay. The short trackcircuit is an electric insulating section composed of twotuning units (BA) and a track air-core inductor (SVA), whichcan achieves good signal insulation between adjacent trackcircuits through itself resonance characteristic.

Track circuits in railway system are usually exposedoutside, and their components are much influenced by theweather such as temperature or humidity variations, humaninterference, etc. These factors can often lead to faults intrack circuits, and make them work improperly, bringingsafety hazards to running trains.

Faults in the track circuits can be classified into twocategories: the hard faults and the soft faults. Hard faults referto the short circuit and open circuit faults, and they can bediagnosed using fault dictionary method. Soft faults refer tofaults caused by the parameter drifts, or abnormal function ofsome components. Most faults occurred in track circuits aresoft faults. To detect these faults, the fault diagnosis systemshould keep up with the state of track circuit, and reflect thestate change of the circuit sensitively.

Railway track circuit

Application in the fault diagnosis of railway trackcircuit

4.1.

Railway track circuit is an essential component ofinformation transmission system between track and vehicle,and the automatic train control system[10, 11]. It uses aspecific carrier frequency to transmit coded data to the train,for example the maximum authorized speed on a givensection on the basis of safety constraints. The applicationconsidered in this paper concerns the soft fault of theinsulating section of a new jointless track circuit named asZPW 2000A which will be widely laid on Chinese high-speedrailway lines. This device will first be described and theproblem addressed will be exposed.

The railway track is divided into different sections. Eachone of them has a specific ZPW 2000A consisting of maintrack circuit and short track circuit [10] (Fig.4). In main trackcircuit, a transmitter in sending end delivers an alternatingcurrent with the specific modulation frequency, a receiver in

Track circuit G2 The adjacent track circuit Gl....------ The carrier frequencyJ;=2300Hz --------.~ The carrier frequency.f2=1700Hz

4.

Main track circuit

JI Trimming capacitors

DirectionIt

Sending end... _----

Track circuits can be modeled as an electrical networkthat combines distributed and lumped-parameter components[12, 13]. Distributed components represent a railway tracksection using the transmission line model. Lumped-parametercomponents represent track circuit components. In thesimulation, we replace the transmission line model by

Track circuits simulation with Simulink4.2.

Figure 4 System structure of ZPW 2000A

cascaded identical subsections. The simulation system for asingle track section in Simulink is shown in Fig.5, an? th~

system is verified by data collected from the real track CIrCUitsystem.

To illustrate the way to build this system, Fig.6 showsthe model of the matching transformer. Fig.? shows theparameters for the matching transformer. In this case theparameter resistance is set by the variable TAD_S_R, whosevalue is set in a program. The inductance is set by the

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variable TAD_S_L in the same way.

Figure S Simulation of a track circuit in Simulink

Series RLC Branchl

Series RLC Branch94 Linear Transformerl TABLE 1 MEASUREMENTS OF THE S SENSORSConn1

<I>.-~ t----~~---------<:I>Conn2Series RLC Branch95 1 2 Seri~<; RI r. Rr,:mch61 Conn4

<I>.-~ t---- ~-----....@Conn3

Figure 6 Model of the matching transformer in Simulink

Sensor CodeSensor 1 (VAl)Sensor 2 (IB1)Sensor 3 (VA2)Sensor 4 (VB2)Sensor 5 (VB3)

MeasurementThe transmitter output voltageThe transmitter currentThe receiver cable voltage in the sending endThe receiver voltageThe receiver cable voltage in the receiving end

TABLE 2 FAULTS CONSIDERED IN THE DIAGNOSIS SYSTEM

4.3. Fault diagnosis of simulated track circuits

Figure 7 Parameters set of the matching transformer

Using the system in Fig.5, we can collect faults data bysetting different configurations. Considering that in the realrailway system there are some practical constraints withsetting sensors to the system, therefore we set 5 sensors inreasonable places in the simulation system to collect faultdata. Measurements of these 5 sensors are shown in Table.l.

Eight commonly occurred soft faults together with thehealthy state are considered dealing with the fault diagnosisof the system. These faults are listed in Table.2.

Fault codeF1F2

F3

F4

F5

F6

F7

F8

F9

Fault descriptionHealthy stateLead wire resistance in tune units in sender end

increases to 2......5 timesLead wire resistance in air-core inductor in sender end

increases to 20......50 timesLead wire resistance in receiver cable in sender end

increases to 20......5OtimesLead wire resistance in matching transformer in

receiver end increases to 100-200 timesLead wire resistance in tune units in receiver end

increases to 1......3 timesLead wire resistance in air-core inductor in receiver

end increases to 20......50 timesLead wire resistance in receiver cable in receiver end

increases to 20......5OtimesLead wire resistance in matching transformer in

receiver end increases to 100-300 times

As it is shown previously, five current and voltagemeasurements can be used as the input variables to ourneuro-fuzzy network. The neuro-fuzzy network is constructedwith five inputs, corresponding to five sensors, and nineoutputs, corresponding to the nine faults mentioned above.

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After some trials, the number of the membership functions isset to 12 to each input. The initial values are estimated usingthe k-means algorithm. The initial neuro-fuzzy network istrained using 3600 data points with each fault 400 samplescollected from the simulation system. The test data points are2205 points with each fault 245 samples. The result of theneuro-fuzzy network performance is shown in Fig.8. TheRMS (root mean square) error is satisfactory after about 100epochs, reaching approximately 0.09. Then the trainednetwork is applied to the test data samples, and 2077 of2205fault samples are correctly identified, i.e. more than 95%correct.

Figure 8 RMS error for each epoch of training of the network

Then we use different simulations with changingparameters to simulate the real-time soft faults that caused byparameter drift. We here take the track circuit statetransferring between the Fl (health state) and the F4 state asexample.

i. Track circuit in health state

The track circuit runs in health state, except for somefluctuations. In this case, data points collected from sensorsin the simulation system and the diagnosis results are shownin Table.3. In the Diagnosis result column, method 1 is usingthe modified neuro-fuzzy network, and method 2 is using thecombined evidence update and the neuro-fuzzy network. Theresult indicates the fault mode and the closing degreebetween the sample data and the fault.

From the results in the table, we can see that both themethods can reflect the real state of the track circuits.However, the combined method performs better dealing withthe 5th and the 10th sample as they are more inclined to thehealth state. Therefore, the combination of evidence updateand neuro-fuzzy network can make the diagnosis results morestable when fluctuations happen.

ii. Track circuit fault caused by dramatic parameter change

The track circuit runs in health state first. Suppose bysome unknown interference, parameters in the lead wireresistance in receiver cable dramatically changed, leading to

fault mode 4. In this case, data points collected from sensorsin the simulation system and the diagnosis results are shownin Table.4.

TABLE 3 TRACK CIRCUIT IN HEALTH STATE

TimeSensor data Diagnosis result

VAl (V) mI(A) VA2(V) VB2(V) VB 3(V) Method I Method 21 135.85 0.269 42.02 10.75 1.23 F1(0.95) F1 (0.95)2 135.55 0.276 42.20 10.50 1.30 F1 (1.00) F1 (1.00)3 135.56 0.271 41.51 10.68 1.27 F1 (0.94) F1 (0.94)4 135.75 0.270 41.91 10.66 1.24 F1 (0.93) F1 (0.97)5 135.85 0.278 41.94 10.62 1.20 F1 (1.00) F1 (1.00)6 135.77 0.270 42.04 10.78 1.20 F1 (0.84) F1 (0.96)7 135.50 0.275 42.39 10.87 1.19 F1 (0.75) F1 (0.89)8 135.51 0.277 42.72 10.53 1.29 F1 (1.00) F1 (1.00)9 135.54 0.271 41.76 10.74 1.29 F1 (0.99) F1 (0.96)10 135.62 0.273 41.41 10.82 1.19 F1 (0.71) F1 (0.87)

TABLE 4 FAULTS CAUSED BY DRAMATIC PARAMETER CHANGE

Time Sensor data Diagnosis resultVAIM mI(A) VA2M VB2M VB3M Method 1 Method 2

135.88 0.274 41.46 10.80 1.21F1(1.00) F1(1.00)

F4(0) F4(0)

2 135.49 0.276 41.53 10.70 1.25F1(0.86) F1(0.86)

F4(0) F4(0)

3 135.44 0.274 41.61 10.74 1.24F1(0.71) F1(0.71)

F4(0) F4(0)

4 135.45 0.274 41.61 10.74 1.24F1(0.92) F1(0.88)

F4(0) F4(0)

5 136.55 0.289 38.25 9.71 1.13F1(0) F1(0.88)

F4(0.52) F4(0)

6 138.51 0.319 31.46 8.08 0.93F1(0) F1(0.52)

F4(1.00) F4(0.48)

7 138.52 0.321 31.98 7.96 0.94F1(0) F1(0.21)

F4(1.00) F4(0.79)

8 138.53 0.322 32.24 8.15 0.96F1(0) F1(0.16)

F4(1.00) F4(0.84)

9 138.52 0.318 32.21 8.16 0.93F1(0) F1(0.11)

F4(1.00) F4(0.89)

10 138.47 0.319 32.32 8.09 0.94F1(0) F1(0.07)

F4(1.00) F4(0.93)

It is shown in the table that results from both the twomethods converge to the F4 fault quickly. In this case,performances of the two methods are pretty much the same.However, out of the reason that in reality the dramatic changein the sensors may be caused by some unstable factors in thesystem, not by the fault, the method using evidence updatedoes not converge to the new fault immediately. And as moreand more coming evidence supports the new fault state, theresults converge to the new fault.

iii. Sensor influenced by external interference

The circuit runs in health state. Suppose sensors areinfluenced by some external interference, such as poorcontact to the circuits, and this leads to the inaccurate data intime 4. This case is shown in Table 5.

From Table 5 we can see that the combining method

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5

678910

holds the fault state as a sudden change in the sensor data forthe reason that this change vanishes in the coming data. Ityields a more accurate fault state than the method 1.

TABLE S FAULT DATA WITH SENSOR INFLUENCED BY EXTERNAL

INTERFERENCE

. Sensor data Diagnosis resultTIme VA1(V) m1(A) VA2(V) VB2(V) VB 3(V) Method 1 Method 2

1 135.40 0.273 42.63 10.53 1.22 F1(0.77) F1(0.77)2 135.81 0.270 42.24 10.68 1.23 F1(1.00) F1(0.99)3 135.71 0.276 42.64 10.85 1.20 F1(0.96) F1(0.96)4 135.77 0.270 41.90 10.74 1.30 F1(1.00) F1(0.96)

F1(0.00)137.25 0.287 42.70 10.76 1.24 F5(1.00) F1(0.96)

135.51 0.276 41.47 10.82 1.27 F1(0.84) F1(0.90)135.88 0.275 42.78 10.78 1.20 F1(1.00) F1(1.00)135.40 0.276 42.63 10.79 1.23 F1(0.79) F1(0.88)135.49 0.272 41.97 10.85 1.27 F1(0.77) F1(0.85)135.40 0.273 42.63 10.53 1.22 F1(0.77) F1(0.77)

Let's make a short conclusion. From the test of theneuro-fuzzy network and the three experiments in this section,we can see that:

1. For a single state of the track circuit, theneuro-fuzzy network can achieve an accurate diagnosis result.The test of the network shows that more than 95% samplesare correctly identified.

2. In the simulated real-time diagnosis, the methodcombining neuro-fuzzy network and evidence update can notonly yield a relatively stable and sensitive result, but alsokeeps the interference to the system away to a degree.

5. Conclusion

In this paper, a new evidence update rule is combinedwith neuro-fuzzy network to do the real-time fault diagnosis.Fault diagnosis using the neuro-fuzzy network does not takethe history information in the system into account, so theresults can not reflect the fault state of the system accurately.A new evidence update rule is proposed to solve this problem.Applications show that the new combined fault diagnosismethod can sensitively reflect the real fault state of thesystem, and at the same the diagnosis results become morerobust to fluctuation or sensor interference.

Acknowledgements

This research is supported by National Key TechnologyR&D Program Project (2009BAGI2A08), National ScienceFoundation of China (61004070,61104019), and TsinghuaUniversity Initiative Scientific Research Program.

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