Research on the Algorithm of Avionic Device Fault Diagnosis Based on Fuzzy Expert System

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1 Chiese Joural of Aeroautics 20(2007) Chiese Joural of Aeroautics Research o the Algorithm of Avioic Device Fault Diagosis Based o Fuzzy Expert System LI Jie*, SHEN Shi-tua School of Electroics ad Iformatio Egieerig, Beijig Uiversity of Aeroautics ad Astroautics, Beijig 00083, Chia Received 7 July 2006; accepted 3 October 2006 Abstract Based o the fuzzy expert system fault diagosis theory, the kowledge base architecture ad iferece egie algorithm are put forward for avioic device fault diagosis. The kowledge base is costructed by fault query etwork, of which the basic elemet is the test-diagosis fault uit. Every uderlyig fault cause's membership degree is calculated usig fuzzy product iferece algorithm, ad the fault aswer best selectio algorithm is developed, to which the deep kowledge is applied. Usig some examples, the proposed algorithm is aalyzed for its capability of sythesis diagosis ad its improvemet compared to greater membership degree first priciple. Keywords: fuzzy expert system; fault query etwork; fault aswer best selectio algorithm; fuzzy theory; test-diagosis fault uit As oe of the most promisig research domais of artificial itelligece (AI), fuzzy theory has bee widely studied i recet years. Fuzzy reasoig ca simulate huma thought based o both fuzzy theory ad fuzzy characteristic of kowledge. Combied with fuzzy reasoig, the idea of employig expert system to fault diagosis for complicated o-liear system has got extesive attetio. Recetly some approaches have bee proposed for fuzzy reasoig method ad kowledge base architecture, both of which are importat compoets of fuzzy expert system (FES). Nevertheless, it still eeds further study to apply FES to avioic device fault diagosis (ADFD). Every fault cause s membership degree was obtaied by the fuzzy relatioship matrix i Refs.[-2], wherei the requiremets of strictess ad locality caot be meet for diagosis rules. I Refs.[3-4], by calculatig the rule s match degree or certaity *Correspodig author. Tel.: address: lucy_lj@hotmail.com Foudatio item:the th Five-year Natioal Defese Prelimiary Research Projects (B ) grade, those rules with higher priority were selected from kowledge base. Usig this iferece method, the iformatio provided by those rules with lower priority will be lost. Additioally, due to the high self-learig ability of eural etwork (NN), it was utilized to costruct the kowledge base for fault diagosis i Refs.[5-6]. However, sometimes the NN loses the IF-THEN rules comprehesibility, iterpretability ad Huma expert s prior kowledge [7]. The aim of this paper is to desig the fuzzy iferece algorithm ad the kowledge base that cosists of comprehesible IF-THEN rules for ADFD, which usually comes with the followig difficulties: the less test-poit for every phase of fault diagosis, the complex fault hierarchy ad the large umber of fault category et al. To achieve so, this paper desigs the kowledge base costructed by fault query etwork (FQN), which combies the testig with the diagosis. I order to meet the requiremets of strictess of IF-THEN rules, the fuzzy product iferece egie [8] is applied for fault reasoig. Additioally, the fault

2 224 LI Jie et al. / Chiese Joural of Aeroautics 20(2007) aswer best selectio algorithm (FABSA) is proposed to satisfy the fault pervasio [9], by meas of which the fault diagosis result depeds o the iformatio of all IF-THEN rules ad all fault symptoms istead of the oly oe with higher priority or higher membership degree. Fuzzy Expert System Architecture Geerally, the avioic device is comprised by so may of sub-systems, so that the physical ad logic relatioships betwee each other are too complicated to represet the avioic device by mathematical model for this goal of accurate fault diagosis. Prior kowledge, however, ca be largely got together from device operatio ad maiteace. As the shallow kowledge, most of them are cases or rules that are valuable for ADFD. The kowledge base is just composed of the basic elemet IF-THEN rule usig shallow kowledge recorded i a pre-specified format or applyig machie self-learig algorithm. Associated with the iformatio provided by the kowledge base, FES ca diagose the avioic device correspodig to the symptom show out by employig the fuzzy iferece egie. That is, the kowledge base ad fuzzy iferece egie are the two importat compoets of FES [0] as show i Fig.. Fig. The architecture of fault diagosis fuzzy expert system. It should be oted that the modified CHC geetic algorithm [] is used for kowledge selflearig of the FES i this literature. Prior to geeratig the rule prototypes from the diagosis cases, those origial cases should be classified. The the practical diagosis rules are obtaied by optimizatio usig the modified CHC geetic algorithm. 2 Fault Query Network It is kow that the testig task caot be performed completely for ADFD i oe sigle step of testig so that the fault cause caot be specified accordig to the result of the sigle step of testig eve though the operator of ADFD is domai expert. Thus, the fault diagosis accuracy depeds o a series of testig, aalysis ad reasoig, where the iteractio betwee kowledge base ad operator is far more frequet. That is, kowledge base should release the ext testig task efficietly i order to attai the more effective symptom as the iput of fuzzy iferece egie. To do so, this paper desigs the architecture of kowledge base: fault query etwork, which cosists of test-diagosis fault uit (TDFU) [2-3]. Defiitio TDFU cosists of seve-elemet model ( N T A B R Q E), where () N is the symbol of a TDFU. As the uit address, N is used to oriet the TDFU i FQN. Obviously, N ad TDFU are oe-to-oe correspodig. (2) T represets the set of test-task to be released, T = { } t t2 t (3) A represets the set of all of the fault symptoms. Every elemet of A represets a stadard fuzzy subset with correspodig T, A = { } a a2 a k (4) B represets the set of all of the diagosis aswers for a TDFU. Every elemet of B will be assumed as the address of the ext TDFU if diagosis eeds aother phase testig-diagosis based o the curret TDFU, B = { } B B2 B j (5) R represets the set of IF-THEN rules. The cofidece of every rule is deoted by R = { } r r2 r m

3 LI Jie et al. / Chiese Joural of Aeroautics 20(2007) R A A A B (6) Q represets the set of the distaces betwee every uderlyig fault cause ad ideal fault aswer. The greater the distace is obtaied, the less possibility correspodig fault occurs, Q = { Γ Γ 2 Γ j } (7) E represets the iferece fuctio of curret TDFU. It is carried out by product iferece egie together with FABSA for every TDFU, E : A A A B Q Uder Defiitio, the FQN cosists of a umber of TDFUs. As a example, a FQN with three of the max umbers of testig-diagosis phase is show i Fig.2, where Γ ij represets the distace betwee the jth uderlyig fault cause ad the ideal fault aswer for the ith TDFU. The defiitio of Γ ij is give i Sectio 3.2. This paper will ot completely describe a FQN for ADFD due to the complexity of avioic device. I order to describe how the FQN is costructed, a example of oe TDFU of a airbore-radio is show i Fig.3. After diagosis reasoig i previous TDFU, the correspodig curret TDFU is addressed for the curret phase of testig-diagosis. First, accordig to the testig task assiged by T, the operator will perform the followig three measuremet idexes: whole-machie_sigal parameter, cotroller_voltage for frequecy switch tured o, ad cotroller_voltage for frequecy switch tured off. The, accordig to IF-THEN rules of R FES will combie E( ) with FABSA to obtai the distaces { Γ Trasceiver Γ Cotroller } betwee every elemet of set B{Trasceiver Cotroller} ad ideal fault aswer. Fig.3 A test-diagosis fault uit for a airbore-radio. (a) Fault query etwork (b) Test-diagosis fault uit Fig.2 The kowledge base of expert system. 3 Fuzzy Reasoig Algorithm Traditioally, the fuzzy relatioship matrix was applied to represet the relatioship betwee the vector of symptom ad the vector of cause i fuzzy diagosis [4]. The vector of cause is deoted by Y = { } () y y2 y The vector of Symptom is deoted by X = { } (2) x x2 x m The matrix of fuzzy relatioship matrix is deoted by [4] r r2 r r2 r22 r2 R = (3) rm rm2 rm

4 226 LI Jie et al. / Chiese Joural of Aeroautics 20(2007) The relatioship betwee X ad Y is represeted as [4] Y = X R (4) [8, 4] the m y = ( x r ), j =,2,, (5) j i ij i= The kowledge base is composed of IF-THEN rules, which costruct the aforemetioed FQN. Furthermore, the relatioship amog those rules with locality is fuzzy uio. Hece, it is ifeasible to apply fuzzy relatioship matrix for ADFD. Assume that there is oly oe rule for the kowledge base, IF A ad A 2 ad A 3, THEN B. The membership degrees of A, A 2 ad A 3 are 0, 0.5, ad 0.6 respectively, which are attaied via their membership fuctios. By usig fuzzy relatioship matrix ad Eq.(5), the followig iequatio is derived: μb = μ a r + μa r μa r (6) Clearly, Eq.(6), by which μ b is ot always equal to zero whe μ a = 0, is icosistet with the locality of IF-THEN rules. To guaratee to meet the requiremet for this characteristic feature of rules, this paper demostrates that the modified product iferece egie ca be applied to the FES of ADFD i Sectio Product iferece egie algorithm Product iferece egie has bee successfully applied to various cotrol system owadays. The egie fuctio [8] is give by μb' ( y) = max[sup( μa' ( x ) μa ( x ) ( ))] i,l i μb y (7) l= x U i= where deotes the umber of iput dimesio ad deotes the umber of IF-THEN rules i kowledge base. The IF-THEN rules have the followig forms [8] : Rule R l : IF x is A,l ad ad x is A l,, THEN y is B l. The relatioship of fuzzy uio amog the IF-THEN rules of ADFD is satisfied by usig the above-metioed product iferece egie. Besides, the mamdai product strategy applied to IF part esures the IF-THEN rule s locality isofar as the THEN part of a rule follows oly if all coditios of the IF part are satisfied. As the iput of iferece egie, the testig-task assiged by TDFU is fuzzified by sigleto-shape membership fuctio [8], x = x* μa' ( x) = (8) 0 otherwise The membership degree of every rule s THEN part correspodig to a elemet of the set B is equal to if it is just the fault aswer. Otherwise, the degree is equal to zero. The membership fuctio [8] is writte as = * μ ( y ) = y y B (9) 0 otherwise The cofidece of every rule deoted by CF is viewed as the rule degree, which represets the possibility that the THEN part happes give the occurrece of the coditio of IF part. That is, the cofidece ca be cosidered as a product factor of the fault membership degree for Eq.(7). I that case, usig Eqs.(8)-(9), Eq.(7) ca be modified as [8] μ B' ( y) i= where μ μ ( ) = ( =,2,, ) A = il, l xl * μl y yl l (0) 0 otherwise. deotes the cofidece of the lth rule. I practice, every uderlyig fault aswer, the elemet of set B, is discrete i the solutio space. As show i Eq.(0), the membership degree of ay poit ot equal to oe elemet of B must be zero. That is, the fial fault aswer must be selected from the set B. Therefore, what Eq.(0) assesses is the membership value at which the elemet of set B occurs actually. 3.2 Fault aswer best selectio algorithm Several fuzzy diagosis approaches have bee discussed for selectig fial fault aswer from the set B. ost of them [4] are based o the greater membership degree first priciple, e.g., threshold value priciple algorithm, max subordiatio priciple algorithm, et al.

5 LI Jie et al. / Chiese Joural of Aeroautics 20(2007) However, this paper aims at the fault diagosis for avioic device composed of so may subsystems, which have fault relevace as well as fault pervasio, that it is impossible to aalyze them idepedetly by each other. While two give sub-systems fault ca be represeted as two elemets of set B cotaied i TDFU, either oe symptom may be caused by both of them or oe sub-system fault that possibly causes aother sub-system fault does ot show remarkable symptom. That is, the diagosis by the greater membership degree first priciple is ot comprehesible ad complete because of the complicated relatioship amog the sub-systems of avioic device. I fact, the membership values computed by Eq.(0) of the elemets of set B, some of which may be greater tha zero, ca also iterpret the sub-system fault s depedecy o each other. Traditioal approaches, however, determie the fault cause that has greater membership degree. Either, re-reasoig ad backward-reasoig are applied to further diagosis after some of fault causes with less membership degree have bee eglected. Hece, those methods usig the greater membership degree first priciple lost the iformatio of symptom with less membership degree. This paper will itroduce a approach that ca make full use of all of the iformatio of symptom. The followig defiitios [5] are give first: Defiitio 2 d UV deotes the relatio alieatio degree betwee sub-system U ad sub-system V i system B. duv (0,), 0 represets that U is the same to V ad represets that U ad V are iter-idepedet. Note that both U ad V are viewed as the fault causes for ADFD. Defiitio 3 The ideal fault aswer deoted by I is the cetroid fault aswer [5] of all uderlyig fault causes i set B which cotais U ad V. It may be excluded by set B. The best fault aswer deoted by F is the earest fault cause to the ideal fault aswer. Defiitio 4 The distace betwee U ad I is deoted by Γ U which ca be determied from: Γ U = μ ( x* ) d Bl l= l= μ ( x* ) B l lu () where is the umber of IF-THEN rules i set R. If there is o rule with duplicate cosequet, will be equal to the umber of uderlyig fault causes. Fig.4 shows the relatioship amog B, I, U ad V. Fig.4 The relatioship of every fult i fault space. Sice the ideal fault aswer I may be excluded by set B accordig to Defiitio 3, it is uecessary to obtai I from set B. O the other had, by usig Eq.() the distace betwee ay uderlyig fault cause ad ideal fault aswer ca be computed. It will be used as the selectio criterio of the best fault aswer i this cotributio. The membership degree vector of set B derived from Eq.(0) is ormalized as follows where B { } (2) = μb μ μ B2 B m μ = Bi μ Bi l= μ Bl (3) The vector Q aforemetioed ca be determied from Eq.(), { Γ Γ Γ } Q= = B id (4) 2 d d2 d d2 d22 d2 D = (5) d d2 d where D deotes the matrix of relatio alieatio

6 228 LI Jie et al. / Chiese Joural of Aeroautics 20(2007) degree with d ij = d ji ad d ii = 0. As the deep kowledge, D ca be provided by domai experts. The possibility of fault cause icreases ad uderlyig testig cost decreases as the elemet of set B gets closer to the ideal fault aswer. Defiitio 4 ad Eq.(4) show how every uderlyig fault cause s membership degree ca alter the value of Γ U. I other words, this approach takes ito accout all of the membership degrees of every elemet of set B to esure the completeess of fault symptom iformatio. 4 Example Aalysis I this sectio, a example of kowledge base for ADFD of a helicopter will be itroduced to joitly diagosis reasoig by product iferece egie ad the fault aswer best selectio algorithm. The diagosis ivolves startig from oe TDFU s set R that cosists of prior kowledge either provided by domai experts or derived by ay self-learig method. R : If x (receiver audio output) is A, ad x 4 (trasmitter trasmissio power) is A 4,, the y is B (receiver low frequecy amplifier fault) with μ (0.7); R 2 : If x 2 (sesitivity) is A 22, ad x 4 (trasmitter trasmissio power) is A 42,, the y is B 2 (receiver high frequecy amplifier fault) with μ 2 (0.7); R 3 : If x 3 (receiver output value rage) is A 33, ad x 4 (trasmitter trasmissio power) is A 43,,the y is B 3 (receiver automatic gai cotrol circuit fault) with μ 3 (0.5); R 4 : If x (receiver audio output) is A 4, ad x 2 (sesitivity) is A 24, ad x 4 (trasmitter trasmissio power) is A 44,,the y is B 4 (trasmittig chael fault) with μ 4 (0.8), where x i deotes the measuremet of t i with t i T, ad T cotais the followig elemets: receiver audio output, sesitivity, receiver output value rage, trasmitter trasmissio power; Ai,j deotes the fuzzy subset correspodig to the ith measuremet idex for the jth rule with Ai, j A ; y deotes the fial fault aswer of curret TDFU; B l deotes the uderlyig fault cause with Bl B, ad B cotais the followig elemets: receiver low frequecy amplifier fault, receiver high frequecy amplifier fault, receiver automatic gai cotrol circuit fault, trasmittig chael fault; ad μ l deotes the cofidece of the lth rule of R with 0.7, 0.7, 0.5, ad 0.8 respectively. Depedig o the measuremet values of every idex ad the membership fuctios of every elemet of set A, the ormalized membership degree vector B of fault aswer ca be computed by Eq.(0), B = { μ μ μ μ } = { } (6) B B2 B3 B4 By puttig Eq.(6) ito Eq.(4), the vector Q ca be obtaied, Q = B id = { } (7) where D = (8) It follows from Eqs.(6) ad (7) that while B (receiver low frequecy amplifier fault) with the maximal membership degree has the most remarkable fault symptom, the Γ of B 2 (receiver high frequecy amplifier fault) is the smallest i the set B. This meas that other fault with remarkable symptom may be caused by B 2 though B 2 has ot remarkable symptom. This case ca be iterpreted by matrix D with d 2 = d 23 = 0. ad d 24 = 0.3, from which B 2 is more active i set B ad has tight relativity with other elemets. Cosequetly, the operator should pay more attetio to B 2 i order to improve the diagosis efficiecy ad decrease the testig cost. I additio, the vector Q ca be computed by Eq.(9) i the case that the elemets of B are homogeeous absolutely, Q = B id ={ } (9)

7 LI Jie et al. / Chiese Joural of Aeroautics 20(2007) where D = (20) Observe that the ascedig order of the elemets of Q is cosistet with the descedig order of the membership degree of elemets of set B. Therefore, this method i this cotributio ca iduce the same diagosis result with those of approaches based o greater membership degree first priciple whe the elemets of B are homogeeous absolutely. 5 Coclusios This paper proposes the architecture of kowledge base ad fuzzy iferece algorithm to satisfy the characteristic features of ADFD. The kowledge base is costructed by FQN, which cosists of TDFU defied as a seve-elemet model. Associated with the modified product iferece egie, the fault aswer best selectio Algorithm desiged i this paper ca extract the optimal fault aswer by the matrix of relatio alieatio degree. The completeess of this approach for ADFD maily lies i the cosideratio of the shallow kowledge ad deep kowledge as well as the membership degree of every fault cause. The example shows that besides the completeess ad accuracy for ADFD, this method has compatibility with traditioal approaches applied by greater membership degree first priciple. Refereces [] Wag X G, Wei L. A fuzzy fault diagosis scheme with applicatio. IFSA World Cogress ad 20th NAFIPS Iteratioal Coferece 200; [2] Xiag Y, Wag H Y. Research ad applicatio of expert system based o fuzzy iferece model. Computer Egieer 2005; 3(0): 80-8, 87. [i Chiese] [3] Yua H F, Shi T Y, Wag X Y. The sythetic fuzzy iferece algorithm i fault diagosis expert system. Joural of Beijig Istitute of Techology 999; 9(6): [i Chiese] [4] Iserma R. O fuzzy logic applicatios for automatic cotrol, supervisio, ad fault diagosis. IEEE Trasactios o Systems, a, ad Cyberetics 998; 28(2): [5] Feg J N, Zhao. A study of the ANN learig machie of fault detectig expert systems. Joural of South Chia Uiversity of Techology 997; 25(6):46-5.[i Chiese] [6] Zhag S, Askura T, Xu X L, et al. Fault diagosis system for rotary machies based o fuzzy eural etworks. Proceedigs of the 2003 IEEE/ASE Iteratioal Coferece o Advaced Itelliget echatroics (AI 2003), 2003; [7] Xu B, Yu J S, Li X S. Itelliget fault diagosis for complex system. Iformatio ad Cotrol 2004; 33(): [i Chiese] [8] Wag L X. A course i fuzzy systems ad cotrol. Beijig: TsigHua Uiversity Press, [i Chiese] [9] Yag P, Wu J. The summary about fault diagosis of complex system. easuremet ad Cotrol Techology 998; 7(2): 8-0. [i Chiese] [0] Liu Y C, Liu Z L. Theory ad desig of fuzzy expert system. Beijig: Beijig Uiversity of Aeroautics ad Astroautics Press, 995.[i Chiese] [] Qi Y, Qi H L, She S T, et al. A study of the optimizatio for fuzzy diagostic rules based o the reformative CHC algorithm. Acta Aeroautica et Astroautica Siica 2004; 25(4): [i Chiese] [2] Jia L X, Xue J Y, Ru F. Fuzzy petri et based formalized reasoig algorithm with applicatios. Joural of Xi'a Jiaotog Uiversity 2003; 37(2): [i Chiese] [3] Su H S, Li Q Z. Study o modelig methods for fuzzy expert systems based o colored petri et model. Computer Egieerig ad Applicatios 2005; (36): [i Chiese] [4] Wu J P. Theory ad applicatio of fuzzy diagosis. Beijig: Sciece Press, 995. [i Chiese] [5] Wag L X, edel J. Geeratig fuzzy rules by learig from examples. IEEE Trasactios o System, a, ad Cyberetics 992; 22(6): Biography: LI Jie Bor i 979, she received B.S. from Beijig Uiversity of Aeroautics ad Astroautics i 200. She is curretly a Ph.D. cadidate i School of Electroics ad Iformatio Egieerig at Beijig Uiversity of Aeroautics ad Astroautics. Her curret research is maily focused o fault diagosis, auto-testig ad artificial itelligece et al. lucy_lj@hotmail.com