IMACS Multiconference on "Computational Engineering in Systems Applications"(CESA), October 4-6, 2006, Beijing, China.

Fault Diagnosis of TV TransmittersBased on Fuzzy Petri Nets

Chunlai Zhou and Zhongcheng Jiang

Abstract-TV transmitters are complicated electronicequipment and the fault diagnosis of such equipment is difficult.This paper presents a novel fault diagnosis approach basedupon fuzzy Petri net. First of all the knowledge of fault diagnosisis summarized into fuzzy rules; secondly the fuzzy rules aretranslated into fuzzy Petri net by an algorithm; thirdly the faultdiagnosis is implemented by a parallel reasoning algorithmbased on fuzzy Petri net. The paper studied the algorithm toconstruct a fuzzy Petri net by fuzzy rules and the algorithm toaccomplish the fault reasoning. A case of TV transmitter faultdiagnosis is discussed to explain the approach presented in thispaper.

I. INTRODUCTION

Petri nets (PN) are a well-known graphical and modelingtool for concurrent and distributed systems proposed by C. A.Petri in 1962 [1], and there have been extended in variousdirections such as: timed Petri nets, colored Petri nets, fuzzyPetri nets, hybrid Petri nets etc.

Fuzzy Petri Net (FPN) is a combination of Petri Net andFuzzy set. There are many results about Fuzzy Petri Net (FPN)for knowledge representation and reasoning [2] [3] [4] [5]. Therelated works about reasoning approaches with Fuzzy PetriNets focus on Petri denotations of generic reasoning rules,while reasoning methods in available works follow classicalserial computing methods, in other words, during reasoning,the rules are used one by one till reaching a conclusion. Inrelated works, the Petri Nets are just graphic denotations,there isn't correlation between graphic denotations andreasoning, the concurrent or parallel ability of Petri Netsdoesn't be embodied during reasoning; also there is short ofthe algorithm to produce the fuzzy Petri net from fuzzy rules.As for applying FPN into the fault diagnosis of TVtransmitter, the related work hasn't been known for ourknowledge.

In this paper, FPN is studied relating to the fault diagnosisofTV transmitters. FPN is used to describe the fault diagnosisnetwork. A new algorithm is used for parallel reasoningaccording to the fuzzy Petri net, which gives the fault

Manuscript received June 30, 2006.This work was supported by the Science Research Fund of

Communication University of China under Grant YNG0303.Chunlai Zhou is with the Department of Automation Control,

Communication University of China, Beijing, 100024, China,phone:86-10-65779291; (e-mail: clzhouAcuc.edu.cn).

Zhongcheng Jiang is a graduate student of master degree with theDepartment of Automation Control, Communication University of China,Beijing, 100024, China.

diagnosis on-line.

II. FuzzY PETRI NET

A. Petri NetsDefinition 1. 3-tuple N = (P, T; F) is called a Directed

Net, if following terms are satisfied,*PUTT 0ePnT =0*FcPxTUTxP* dom(F) U cod(F) = P U TWhere P is a set of places; T is a set of transitions; F is a setof directed arcs that consist of directed pair. The directions ofarcs are either p -* T or T -* P . dom(F) denotes the firstelement of the pair, cod(F) denotes the second element ofthe pair. i.e.dom(F) {x 3y:(x,y) E F}

cod(F) {x 3y: (y, x) E F}Definition 2. 4-tuple PN = (P, T; F, M0 ) is called a

Petri Net, if following terms are satisfied,* N (P, T; F) Directed Net;*M P -* Z Marking (or State) Function, initial state ofPetri net is called the initial marking MO that specifies theinitial assignment of the tokens to the places.

Definition 3. 8-tuple FPN = (P, T; F, MO, cx, ,, ,u, w) iscalled a Fuzzy Petri Net, if following terms are satisfied.x: P -> [0,1] Association function. Each premise place is

assigned a certainty factor.p::P [0,1] Association function. Each conclusion

place is assigned a certainty factor.,u T - [0,1] Association function. Each transition is

assigned a threshold value.w: dom(F) -> [0,1] Association function. Each directional

arc is assigned a weight value.

B. Fuzzy logic relations denoted byfuzzy Petri nets

In practical applications, fuzzy logic production rules areused for knowledge presentation. The fuzzy productionrules are a fuzzy relationship description between twopropositions. The logic operators can be used to connectpropositions to produce compound fuzzy production rules.Furthermore, if the contribution of a proposition toconclusion is considered, that is a weighted fuzzy productionrule.

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IMACS Multiconference on "Computational Engineering in Systems Applications"(CESA), October 4-6, 2006, Beijing, China.

Let R be a set of fuzzy production rules:R = R1R2,*R Rn}X ith rule is expressed by

R, IF d, Then dk(CF=,8) p,w (i=t2,...,n)

where di is a premise of the production; dk is a conclusion

ofthe production; p, is a certainty factor ofthe conclusion; ,uis a threshold value ofthe production holds; w is a weight ofthe premise.Usually, there are tree types of productions [6].

Type] Simple fuzzy production rule:R :if dj then dk (CF=/,) p,w

Type2 Compound joined fuzzy production rule:R: if diANDd 2AND ...ANDd n then d(CF = 4)

,, W1I W2 * I Wn

Type3 Compound disjoined fuzzy production rule:R: f dIORd 20R ORdn then d(CF = /)

PI ,P12 ...,/ln,W1W2 ... Wn

The denotations of fuzzy Petri nets of above rules areexpressed in Fig. 1, Fig.2 and Fig 3 respectively.

Fig. 1 The Fuzzy Petri net denotation of fuzzy rule of Type 1

Fig. 2 The Fuzzy Petri net denotation of fuzzy rule of Type 2

discussion is based on the supposition that Type 3 has beentransformed into Typel.

c, W

112

I n

Fig. 4 The decomposition of fuzzy rule of Type 3

In the fuzzy Petri net models above, propositions arepresented by places, rules are presented by transitions,holding of a rule is depended on the threshold value of therule. All rules denoted by fuzzy Petri nets of typel or type2connected together will form a fuzzy Petri net system (FPNS).The differences between a FPNS and a classical Petri Netwhen a FPNS is used in fuzzy reasoning are:* When an enabled transition fires, tokens are not

removed from its input places. On the contrary, inputtokens are only copied and remain at there originalplaces [5].

* A premise tokens can be applied to several transitions atsame time and there isn't conflict among transitions, fora premise of a rule is a fact, which can be used at sametime without conflict. It is to say that there is no conflictin the fuzzy Petri net as classical Petri net.

* There are various definitions of fuzzy reasoningmanipulation, reasoning manipulations should beselected according to applying purpose.

III. THE MODEL OF FAULT DIAGNOSIS OF TVTRANSMMTTERS BASED UPON FUZZY PETRI NET

Fig. 3 The Fuzzy Petri net denotation of fuzzy rule of Type 3

In above models of fuzzy Petri net, the propositions are

presented by places, including premise and conclusionpropositions. The reasoning rule is presented by transition.The threshold of transition is a fire value that the rule holds.A fuzzy Petri net system is constructed when all fuzzy Petrinets denoting rules are connected together according to thenotation names of place.Actually, the Petri net of Type 3 can be decomposed into

Type 1. Fig.4 is the decomposition of Fig.3. So, following

A. Analog Signal Television Transmitters SystemsA block diagram of analog signal television transmitting

system (TTS) is shown in Fig. 5. The main function of theTTS is to transmit video image signals and audio signals.

Analog VideoInput

Fig. 5 A block diagram of an analog signal television transmitting system

The TTS is complicated electronic equipment, variousfaults may happen during the TTS working. In order toexplain the approach of fault diagnosis presented in this paper,

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IMACS Multiconference on "Computational Engineering in Systems Applications"(CESA), October 4-6, 2006, Beijing, China.

we take the Electrical Control System (ECS) ofthe TTS as anexample.

The ECS is composed oftwo parts in some type of 10 kWcolor TV transmitter [7]. One is Logical control circuitry,another is Alternative current supply circuitry as shown inFig.6. The ECS is the core of the TTS that controls the workof the TTS according to given logical functions, besides thatthe ECS has the functions to monitor and protect the TTS.

,A 2JC1 6KV 6KV

380VoBB -+ -Ac 3KV

3KV

2JC2

Fig. 6 A block diagram of Electrical Control System

In the Fig.6, the four input signals ofthe logic part are A, B,C and D. A denotes outside catenation signal used forindicating if the gate switch and coaxial antenna switch areclosed; B signal denotes that the high voltage can't be appliedto the TTS, because the first over-loading happens; C signaldenotes the high voltage can't be applied to the TTS, becausesecond over-loading happens in 4 seconds after first one; Dsignal denotes the middle voltage is at good status. Inworking status of the ECS, all magnitudes of analog signalsare around 14V1 6V, ifany ofthe signals is out ofthe normalmagnitude value too far, a fault may happen. When thesignals are less than 0.3V, that denotes a fault has appeared.The block Y denotes the AND gate; the block S is a onesecond time delay circuitry; the block Ft and block F2 aredriven amplifiers; two Silicon Controlled Rectifier (SCR) areused for switching on high voltage in two steps. In first step,2/3 full of power is applied to TTS, and in second step, fullpower is applied to. The reason the high power is applied intwo steps is to reduce the impulse of large current for theTTS.

B. The Fuzzy Rules ofFaults DiagnosisThe knowledge of fault diagnosis can be represented by

rules. Knowledge representation with rules is convenient toknowledge utilization in fault diagnosis expert systems. Thefault diagnosis knowledge ofthe TTS can also be representedby rules. For example, in the ECS, there is one kind offault HVF (High Voltage Fail), i.e., the high voltage can'tbe applied to the transmitter when some faults appear, in thisway to protect the transmitter from being destroyed. The HVFfault is one of faults in the ECS, many factors can lead to theHVF. Therefore the possibilities of different factors leadingto the HVF need to be considered. The rules considered suchfactors are fuzzy rules. In order to represent the faultdiagnosing knowledge with fuzzy rules, there are twoproblems to be solved. One problem is that the circuitries of

the TTS are mixed ones with both digital circuitries andanalog circuitries. The magnitudes of analog signals vary inthe wide range. Therefore, the difference of the dimensionsshould be eliminated before constructing the fuzzy faultdiagnosing rules.

Another problem is that the TTS is a complicated system,there are complicated relationship among fault phenomenaand fault results. When the magnitude values of some signalsare off normal ones at same time, which is the importantfactor to lead the fault? The important factor is main factorthat leads to the fault.To solve first problem, the standardization of all fault

factors are used in this paper.Let xi be a physical parameter, when it is out of normal

value to some extension, it becomes a factor to lead fault ofthe TTS. The following formula (1) is used to weigh thethreshold of a fault happening.

min{x -x.X IX. -x. Il<i<n Iximax inor 1, IXimin xinorIIpUi =

max{xi}- min{xi }l<i<n l<i<n

(1)

Here, ,ui E [0,1], X., denotes the normal value of xi;

ximax denotes the maximum value above normal one, and

ximin denotes the minimum value below the normal one, at

both values no fault happens. min{x1 } denotes the minimum

value among total n fault samples; max{x1 } denotes the

maximum value. The larger pui is, the more tolerant to the

departure of xi is.

The parameter xi of a signal then is transferred into a

fraction by formula (2) if it isn't a logic variable before beingapplied to fuzzy rules.

Ixmax{xi }-

l<i<n

*Xnor- min{xi }

l<i<n

(2)

To solve second problem, in the diagnosing rules, a powerweight w is used for each fault factor when a fault is causedby several factors. The larger w is, the more possibility thefault is caused by the factor.

According to above analysis and the principle of the TTS,the HVF fault diagnosing of the ECS can be represented byfollowing fuzzy rule set.

Fuzzy Rules ofthe HVFR.1) if di ORd2thenddo2) if d3OR d4 then d1,3) if d5OR d6 OR d7 then d2;4) if d8 ORdg thend5,5) if d1o OR di, then d6;6) if d12 OR d13 OR d4 OR d15 then d4;7) if d16 ORd17 then d3-8) if d18 OR di9 OR d20 then(0.80) d16,

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IMACS Multiconference on "Computational Engineering in Systems Applications"(CESA), October 4-6, 2006, Beijing, China.

9) if d21(0. 6) AND d22(0.4) then(0.9) d]2,10) , if d23 OR d24 OR d25 then(0. 75) d]7,11) if d26OR d27 then (0.9)d]3;12) if d28 then (0.9) dl4,13) if d29 ORd30then (0.7) d15.

Here.do. High Voltage can't be applied;d1. Logical control circuitry fault;d2. Alternative currentpower supplyfault;d3. Control Alternative currentpower supplyfault;d4. Control signalfault;d5: 110 Vsupply fault;d6: 2/3 full ofpower can 't be applied;d7: Full ofpower signal;d8: Middle voltage switch signal;dg: Signal ofswitch linked with 2JC1,d10.2JCJ signal;d11. Wire linkage signal;d12: Middle voltage D is absent;d]3. High voltage signal B is absent;dl4. High voltage signal C is absent;d51. Catenation signal A is absent;d16. 2/3 full ofpower control isfault;d]7. Full ofpower control is fault;d18. AND gate Y signal;d19. Driven amplifier F1 signal;d2o. SCR1 signal,d21. Output signal ofmiddle voltage control circuitry signal;d22. Control signal ofmiddle voltage control signal;d23. Delay circuitry S signal;d24. Driven amplifier F2 signal;d25. SCR2 signal;d26. 6 kV over load sampling circuitry signal;d27:Over load recovering circuitry signal;d28. Latch circuitry ofover load recovering circuitry signal;d29. Switch K1 ofAudio gate signal;d30. Switch K2 ofvideo gate signal;

The generic forms of the fuzzy rules above are:Ifd, OR dj ... OR dkthen (/p) dm (,),If di (w) AND (wj) d ...AND dk (wk) then (/) dm (/3)For all fuzzy rules above without w,p, ,8 , they take

default values 1.0.It isn't straightforward for fault diagnosis to use above

fuzzy rules, especially when the fuzzy rules are complicated.Notice that above fuzzy rules deal only one kind offault HVF, moreover there only list parts ofthe rules not allof them. Therefore, it is necessary to use other model torepresent the fault diagnosis knowledge to betterunderstanding.

C. The Fuzzy Petri Nets Model offaults diagnosis ofthe TTSThe Fuzzy Petri Nets Model of faults diagnosing can be got

from translating the fuzzy rules into fuzzy Petri netsaccording to the methodology discussed in section II part B.The fuzzy rule that has the form of type 3 should bedecomposed into type 1 before translating the rule into fuzzy

Petri net. . The fuzzy Petri net denotation of the HVFR fuzzyrules is in Fig. 7.

Fig.7 The Fuzzy Petri Net representation of the HVFR

IV. FuzzY RULES TRANSLATING AND FuzzY PETRI NETREASONING ALGORITHMS

Definition 4. A fuzzy rule is a fuzzy proposition thatcontains a main implication that divides it into a left hand sideand a right hand side, where the left hand side contains one ormore conjuncted fuzzy propositions and the right hand sidecontains an atomic fuzzy proposition.Common terminology from traditional Artificial

Intelligence uses the words antecedent or premise for the lefthand side of a rule and consequence or conclusion for theright hand side. Therefore, the premise and conclusion areused in following paragraphs.Definition 5. An atomic fuzzy proposition is a proposition

that can't be decomposed into simpler propositions. That isthere is only one fuzzy proposition.Definition 6. An initial atomic fuzzy proposition is an

atomic fuzzy proposition and its premise doesn't belong tothe conclusion of any an atomic fuzzy proposition of the ruleset.Definition 7. An initial fuzzy proposition is a fuzzy

proposition and its premise doesn't belong to the conclusionof any a fuzzy proposition of the fuzzy rule set.

Algorithm-CFPN. Constructing a Fuzzy Petri Net basedupon fuzzy rules.INPUT:A set of fuzzy rules of typel or type 2: RfProgram flag: Flag e- F;Work buffers: Ras 0 , Rm <-0;The level number of Petri net: LoopN <- 0;Premise notation matrix: PM(i), i - 0;Conclusion notation matrix Rm(i);The number of rules: PN X- 0.OUTPUT:The Fuzzy Petri Net of RfLoopN; RM(i), PM(i), i = 0,1,***, LoopN - 1; PN.

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IMACS Multiconference on "Computational Engineering in Systems Applications"(CESA), October 4-6, 2006, Beijing, China.

Stepi. Scan the fuzzy rules in the set Rf, transfer all initial

atomic fuzzy rules in the set Rf into Ras; PM(i) <- the

premises of rules; RM(i) <- the conclusions of rules;PN e the number of initial atomicfuzzy rules;Step2. Scan each fuzzy rule in Rf , when find a initialfuzzy

proposition in the fuzzy rule, then transfer the fuzzy rule fromRf into Ras; PN - PN +1; if the premise of the fuzzy

rule isn't in PM(i), copy it into PM(i); if the conclusion ofthe rule isn't in RAIM(i), copy it into RM(i);Step3. For each fuzzy rule of Ras produce a fuzzy Petri net.

An atomic fuzzy rule is a fuzzy Petri net of type 1; acompound rule is a fuzzy Petri net of type 2.Step4. LoopN <-LoopN + 1,i - i +Step5. If Rf = 0, then go to step9;

Step6. Rm e Ras, Ras <-0Step7. Scan each fuzzy rule in set Rf ,if a premise of a fuzzy

rule is equal to a conclusion of a rule in Rm ,transfer this rule

in Rf into Ras; PN <- PN + 1; if the premise of the fuzzy

rule isn't in PM(i), copy it into PM(i); if the conclusion ofthe fuzzy rule isn't in RM(i), copy it into RM(i) .

Step8. For each fuzzy rule in Ras, produce a fuzzy Petri net

according to the type of the fuzzy rule. If the input place ofthe fuzzy Petri net to be produced exists in the produced fuzzyPetri net, then draw a directed arc from the existed place tothe transition, don't draw existed place.

After all fuzzy Petri net are produced according to thefuzzy rules in Ras, go to Step 4.

Step9. Output fuzzy Petri net.SteplO. Stop.

The basic idea of algorithm-CFPN is that at the beginning,both atomic fuzzy proposition and initial atomic fuzzyproposition are selected to produce the first level of fuzzyPetri net. Start from the conclusion of the first level of fuzzyPetri net to select the fuzzy rules in Rf, which have the

premises equal to the conclusions of the first level of fuzzyPetri net. Draw the fuzzy Petri net according to fuzzy rulesselected and connect the conclusion of the first level to thepremise of second level fuzzy Petri net just drawn. In thisapproach, all fuzzy rules are transferred into fuzzy Petri net.By the algorithm-CFPN, the fuzzy rule set is translated into

a fuzzy Petri net system. Fig. 7 is translated example that thefuzzy rules ofthe HVFR are translated into the fuzzy Petri netby algorithm-CFPN.Fault diagnosis can be achieved by using ofFuzzy Petri net.

The following definitions are given before discussing thereasoning algorithm of fault diagnosis.Definition 8. Incidence matrix forward Pre is P x T

matrix, where P denotes the number of places, Tdenotes the number of transitions.

Pre {w,j} , w [O,l],i = 1,2, -,I P 1;j = 1,2, -,I Twij denotes the weight between place and transition. Ifthere

isn't the relationship between Pi and T , then wij= 0.

Definition 9. Incidence matrix backward Post isP x T matrix.

Post I/1},8i3j [O,1],i =1,2,¢,I P ;j= 1,2,.-,I T,8j j denotes the certification factor of the conclusion

between transition and place. If there isn't the relationshipbetween Pi and T, then , j = 0.Definition 10. State matrix M is P x1 matrix.

M = {mi },

mi E [O,1], i = 1,2,, P I, m, is certainty factor of premise.Definition 11. Initial state matrix S0 is IPI x1 matrix

that denotes the initial state of reasoning.Definition 12. Transition threshold matrix U isT x I matrix that denotes the thresholds of transition fire.

U {p,}, p,Ei [0,1],i=1,2,.,I TIDefinition 13. Conclusion certainty factor matrix B isR x 1 matrix that denotes the certainty factor of reasoning

conclusion. B = {,} , 3,E [O,1],i = 1,2,.,I T R isthe number of reasoning rules.Definition 14. Matrix signfunction is

sign(X) =0x >O

x is element of matrix X.x <O

Definition 15. C = A ® B, C = {cj,j 3, c, = aijbj, whereA,B and C are matrices with same dimension. OperatorO denotes multiplication of corresponding position elements.

Algorithm-FRA: Fuzzy reasoning algorithm of fuzzy Petrinet

INPUT:* PN: Number of fuzzy rule set Rf* U, B: Matrices defined by definition 12 and 13;* LoopN: The level number of fuzzy Petri net;* PM(i), RM(i), i = 0,1,***, LoopN 1

* The Fuzzy Petri Net of Rf, produced by

Algorithm-CFPN;* SO: Initial state matrix.

OUTPUT: Reasoning result matrix R.

Stepl. Produce an incidence matrix forward Pre and anincidence matrix backward post.Step2. N *- LoopN , Determine the number of reason

operating.

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IMACS Multiconference on "Computational Engineering in Systems Applications"(CESA), October 4-6, 2006, Beijing, China.

Step3. For i = N -1 down to 0, scan PM(i), if an initialpremise of S0 is in PM(i), then the number of reason

operating is equal to D = i + 1 .Step4. Calculate R(O) = PreT x so;Step5. For i = I to D, calculate:R(i) = post x [sign (R(i - 1) - U) 0 B];where R(1), R(2),.**, R(D) are certainty factor matrices ofreasoning result.Step6. Output the final reasoning result matrix R(D).Step7. Stop.

V. FAULT DIAGNOSIS OF TV TRANSMITTERS BASED ONFuzzY PETRI NETS

Fault diagnosis is a process to find out the fault reasons byanalysing fault phenomena. Fault diagnosis based up onfuzzy Petri net is to use of the parallel ability of Petri net tofind out all possibility fault reasons. In this approach, thealgorithm CFPN is used to produce fuzzy Petri net by fuzzyrules and then algorithm FRA is used for reasoning. Here, wetake TV transmitter as an example to explain the approach.Some type TV transmitter is in HVFR fault status, the

value of signals are:* d7=d8=dg= d1o= d110=* d18 =-0.8V; dl9= 13.5V; d20=13.8V, d2l=14.OV,* d22=d23= d24 =d25=d26=d27=d28=d29= d30=0.To convert the analog values above into interval between 0

and 1 according to the formula (2) in section III, the result is:* d7=d8=dg= d1o= d110=* d18=0.9,d19=d20=d2l=d22=d23= d24 =d25=d26=d27=d28=d29=d30=0.A. Constructing a Fuzzy Petri Net

According to Algorithm-CFPN, the fuzzy Petri netproduced is in Fig.7. The outputs ofthe Algorithm-CFPN are:LoopN=4,PM(O)=d7, d8, d9, d10, d1,Ad18, d19, d20, d2l, d22, d23, d24, d25,d26, d27, d28, d29, d3d,}RM(O) =d2,d5, d6,,d12, d13, d14, d15, d16, d17},PM('1) (d2,d5, d6,,d12, d13, d14, d15, d16, d17},RM(1)=4d3, d4, d2 },PM(2)= t d3, d4, do];RM(2) = di, do},PM(3) = di]RM(3) = do];PM(4) = do,RM(4)= 'P;PN=29.

B. Fault diagnosis by Fuzzy reasoning algorithm FRABy Algorithm-FRA, according to the HVFR fault status,

initial state So is:So=[0,0,0,00,0,0,0,0,0,0,0,0,0,0,0,0,0,.9,0,0,0,0,0,0,0,0,0,0,0,0,0]

By Stepi, Constructing Incidence matrix forward Pre andpost, both have the dimension of 31 x 29 as following.

Pre=[0,0,0,0,0,00,0,0,0,0,0,0,0,,0,0,0,0,0,00,o,00,0,00,0,0o0;1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,o,o,0o,,0,0,0,0,0,0;0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,o,o,0o,0,,0,0,0,0,0,0;0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]

post=[1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,o,o,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,o,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,o,o,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,o,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,o,o,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,o,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,o,o,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,o,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,o,o,0,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,0,0,0,0,0,0;0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,o,o,0,0,0,0,0,0];

By Step2, the number D of reason operating is 4.

By Step3, calculate R(O) = PreT x S0, R(1), R(2), R(3):R(O)= [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.9,0,0,0,0,0,0,0,0,0,0,0,0]T;R(])= [0,0,0,100 000,0,0,0,0,0,0,0,,0.9,O,00 0,0,0,0,00 1]T;R(2)=[0,0,1,0,0,00,0,0,0,0,0,0,0,0,0,0.9,0,0,0,0,0,0,0,0,0,0,0,0] T;R(3)=[0,1,0,0,0,00,0,0,0,0,0,0,0,0,0,0.9,0,0,0,0,0,0,0,0,0,0,0,0] T;R(4)=[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.9,0,0,0,0,0,0,0,0,0,0,0,0] T;By Step4, output the reasoning result matrix R(4).

2008

IMACS Multiconference on "Computational Engineering in Systems Applications"(CESA), October 4-6, 2006, Beijing, China.

R(4)=[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.9,0,0,0,0,0,0,0,0,0,0,0,O] T

By Step5, Stop.According to the definition of Pre, the certainty of do is 1,

that means the fault -High Voltage can't be applied hashappened.

VI. CONCLUSION

Based on object-oriented fuzzy Petri net, we have studiedthe fault diagnosis ofTV Transmitters. In this paper, we focuson the algorithm of constructing the fuzzy Petri net accordingto fuzzy rules and the algorithm of fuzzy reasoning by thefuzzy Petri net and contribute a novel approach to TVtransmitter fault diagnosis. The fault diagnosis knowledgecan be represented directly based upon fuzzy Petri net and itisn't the necessary to represent the knowledge by fuzzy rulesthen translate them into fuzzy Petri net. The reason doing soin this paper is that the fuzzy rules are available in our faultdiagnosis practices.

The novel points of the paper are:* Present the algorithm to construct the fuzzy Petri Net

according to fuzzy rules and the algorithm to parallelreasoning by fuzzy Petri net. The reasoning algorithm innature is parallel approach.

* The approach to TV transmitters fault diagnosis is anovel method. It is not only suitable for TV transmittersbut also valid to other complicated equipment. That isthe method is generic approach to fault diagnosis.

REFERENCES

[1] Toshiyuki Miyamoto, "A Survey of Object-Oriented Petri Nets andAnalysis Methods," IEICE Trans. Fundamentals, Vol.E88-A, NO. 11,pp. 2964-2971,November 2005

[2] X. Li, X. Xu and F.Lara, "Modeling manufacturing systems usingobject oriented colored Petri nets," International Journal of IntelligentControl and Systems, Vol.3, pp. 359-375, 1999

[3] S. Chen, J. Ke, and J. Chang, "Knowledge representation using fuzzyPetri nets," IEEE Trans. Knowledge and Data Engineering, pp.3 11-319,2(3), 1990

[4] D.S. Yeung and E.C.C. Tsang, "A multilevel weighted fuzzy reasoningalgorithm for expert systems, "IEEE Trans. SMC-Part A: Systems andHumans, pp.149-158, 28(2), 1998

[5] X. Li, W. Yu and F. Lara, "Dynamic Knowledge Inference andLearning Under Adaptive Fuzzy Petri Net Framework," IEEE Trans.On System, Man, and Cybernetics, Part C, vol.30, no.4, pp.442-450,2000.

[6] Jens H. Jahnke, Wilhelm Schafer, Albert Ztundorf, "Generic FuzzyReasoning Nets as a Basis for Reverse Engineering Relational DatabaseApplications," http://www.uni-paderborn.de/fachbereich/AG/schaefer/index engl.html

[7] Jin Zhongxiong, Chen Fengwu, Dou Xinxiang, The Fault Analysis andMaintain of TV Transmitters & Re-transmitters, China Broadcastingand TV Press, pp.248-266, 1992. (Chinese)

2009