A TSK-Type Recurrent Neuro-Fuzzy Systems for Fault Prognosis

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1 Jounal of Softwae Engineeing and Applications, 2012, 5, Published Online July 2012 ( 477 A SK-ype ecuent Neuo-Fuzzy Systems fo Fault Pognosis afik Mahdaoui 1,2, Leila Hayet Mouss 2 1 Laboatoie d Automatique et Poductique (LAP), Univesité de Batna, Batna, Algéie; 2 Cente Univesitaie Khenchela, Khenchela, Algéie. {mehdaoui.afik, h_mouss}@yahoo.f eceived Januay 26 th, 2012; evised Febuay 29 th, 2012; accepted Mach 11 th, 2012 ABSAC As a esult fom the demanding of pocess safety, eliability and envionmental constaints, a called of fault detection and diagnosis system become moe and moe impotant. In this aticle some basic aspects of SK (akigi Sugeno Kang) neuo-fuzzy techniques fo the pognosis and diagnosis of manufactuing systems ae pesented. In paticula, a neuo-fuzzy model that can be used fo the identification and the simulation of faults pognosis models is descibed. he pesented model is motivated by a coopeative neuo-fuzzy appoach based on a vectoized ecuent neual netwok achitectue. he neuo-fuzzy achitectue maps the esiduals into two classes: a one of fixed diection esiduals and anothe one of faults belonging to otay kiln. Keywods: SK Neuo-Fuzzy Systems; Faults Diagnosis; Fault Pognosis 1. Intoduction Failue may cause lage amount of loss. heefoe, fault diagnosis and pognosis system is vey impotant fo safe opeation and peventing escue. ecent pogess in the field of diagnostics of manufactuing systems (MS) dives is a esult of boadly conceived basic eseach caied out ove many yeas. Accoding to [1], thee is no single method that could accommodate the entie system fault. hus, the combination of ANN and fuzzy logic is consideably pactical because it combined both of the advantages and makes the entie system moe obust. ANN can opeate simultaneously on qualitative and quantitative data and vey useful when no mathematical model of the system is available wheeas fuzzy logic has an ability to mimic the sensing, genealizing, pocessing, opeating and leaning ability of human opeato [2]. In ode to achieve this goal we oganize this aticle into thee pats. he fist pat pesents pincipal achitectues of SK empoal Neuo-Fuzzy systems opeation and thei applications. he second pat is dedicated to the wokshop of clinke of cement factoy. Lastly, in the thid pat we popose a Neuo-Fuzzy system fo system of poduction diagnosis. 2. empoal Neuo-Fuzzy Systems Fuzzy neual netwok (FNN) appoach has become a poweful tool fo solving eal-wold poblems in the aea of foecasting, identification, contol, image ecognition and othes that ae associated with high level of uncetainty [2]. he Neuo-fuzzy model combines, in a single famewok, both numeical and symbolic knowledge about the pocess. Automatic linguistic ule extaction is a useful aspect of NF especially when little o no pio knowledge about the pocess is available [1,3]. Fo example, a NF model of a non-linea dynamical system can be identified fom the empiical data. his model can give us some insight about the on lineaity and dynamical popeties of the system. he most common NF systems ae based on two types of fuzzy models SK [4,5] combined with NN leaning algoithms. SK models use local linea models in the consequents, which ae easie to intepet and can be used fo contol and fault diagnosis [6]. Mamdani models use fuzzy sets as consequents and theefoe give a moe qualitative desciption. Many Neuo-fuzzy stuctues have been successfully applied to a wide ange of applications fom industial pocesses to financial systems, because of the ease of ule base design, linguistic modeling, and application to complex and uncetain systems, inheent non-linea natue, leaning abilities, paallel pocessing and fault-toleance abilities. Howeve, successful implementation depends heavily on pio knowledge of the system and the empiical data [7]. Neuo-fuzzy netwoks by intinsic natue can handle Copyight 2012 Scies.

2 478 A SK-ype ecuent Neuo-Fuzzy Systems fo Fault Pognosis limited numbe of inputs. When the system to be identified is complex and has lage numbe of inputs, the fuzzy ule base becomes lage. NF models usually identified fom empiical data ae not vey tanspaent. anspaency accounts a moe meaningful desciption of the pocess i.e. less ules with appopiate membeship functions. In ANFIS [2] a fixed stuctue with gid patition is used. Antecedent and consequent paametes ae identified by a combination of least squaes estimate and gadient based method, called hybid leaning ule. his method is fast and easy to implement fo low dimension input spaces. It is moe pone to lose the tanspaency and the local model accuacy because of the use of eo back popagation that is a global and not locally nonlinea optimization pocedue. One possible method to ovecome this poblem can be to find the antecedents & ules sepaately e.g. clusteing and constain the antecedents, and then apply optimization. Hieachical NF netwoks can be used to ovecome the dimensionality poblem by decomposing the system into a seies of MISO and/o SISO systems called hieachical systems [6]. he local ules use subsets of input spaces and ae activated by highe level ules [7]. he citeia on which to build a NF model ae based on the equiements fo faults diagnosis and the system chaacteistics. he function of the NF model in the FDI scheme is also impotant i.e. Pepocessing data, Identification (esidual geneation) o classification (Decision Making/Fault Isolation). Fo example a NF model with high appoximation capability and distubance ejection is needed fo identification so that the esiduals ae moe accuate. Wheeas in the classification stage, a NF netwok with moe tanspaency is equied. he following chaacteistics of NF models ae impotant: Appoximation/Genealisation capabilities; anspaency: easoning/use of pio knowledge/ules; aining Speed/Pocessing speed; Complexity; ansfomability: o be able to convet in othe foms of NF models in ode to povide diffeent levels of tanspaency and appoximation powe. Adaptive leaning. wo most impotant chaacteistics ae the genealising and easoning capabilities. Depending on the application equiement, usually a compomise is made between the above two. In ode to implement this type of Neuo-Fuzzy Systems fo Fault Diagnosis and Pognosis and exploited to diagnose of dedicated poduction system we have to popose data-pocessing softwae NEFDIAG (Neuo- Fuzzy Diagnosis). he akagi-sugeno type fuzzy ules ae discussed in detail in Subsection A. In Subsection B, the netwok stuctue of FENN is pesented empoal Fuzzy ules ecently, moe and moe attention has paid to the akagi-sugeno type ules [8] in studies of fuzzy neual netwoks. his significant infeence ule povides an analytic way of analyzing the stability of fuzzy contol systems. If we combine the akagi-sugeno contolles togethe with the contolled system and use state-space equations to descibe the whole system [9], we can get anothe type of ules to descibe nonlinea systems as below: ule : is is IF X1 x AND AND X n x AND N 1 u1 is is U1 AND ANDU M M U HEN X AXBU whee X x 1 x 2 xn is the inne is the inne state vecto of the nonlinea system; U u 1 u 2 u n is the input vecto to the system, and N, M ae the dimensions; x, 1 u ae linguistic tems (fuzzy sets) defining the 1 conditions fo x i and u j espectively, accoding to ule ; A a is a matix of N N and B ij * bij * N N of N M N M When consideed in discete time, such as modeling using a digital compute, we often use the discete statespace equations instead of the continuous vesion. Concetely, the fuzzy ules become: ule : IF X1 tis AND AND X tis AN D N x1 n x u 1 M U M X t1 A X tb U t U1 t is AND ANDU t is HEN whee X x1 t x2 t xn t is the discete sample of state vecto at discete time t. In following discussion we shall use the latte fom of ules. In both foms, the output of the system is always defined as: Y CX o Y t CX t (1) whee C= (c ij ) Px Xis a matix of P N, and P is the dimension of output vecto Y. he fuzzy infeence pocedue is specified as below. Fist, we use multiplication as opeation AND to get the fiing stength of ule : whee xi N M i (2) f x t t i1 xi i1 i xi. and xi xi ui ae the membeship functions of and espectively? Afte nomalization of the fi- Copyight 2012 Scies.

3 A SK-ype ecuent Neuo-Fuzzy Systems fo Fault Pognosis 479 ing stengths, we get (assuming is the total numbe of ules) S f h f S (3), 1, n whee S is the summation of fiing stengths of all the ules, and h is the nomalized fiing stength of ule. When the defuzzification is employed, we have X t1 A X t B U t, AX t BU t X t h X t whee, h A X t B U t hax t hb 1 1 U t 1 1 A ha B hb Using Equation (4), the system state tansient equation, we can calculate the next state of system by cuent state and input he Stuctue of empoal Neuo-Fuzzy System he main idea of this model is to combine simple feed fowad fussy systems to abitay hieachical models. he stuctue of ecuent Neuo-fuzzy systems is pesented in Figue 1. In this netwok, input nodes which accept the envionment inputs and context nodes which copy the value (4) of the state-space vecto fom laye 3 ae all at laye 1 (the Input Laye). hey epesent the linguistic vaiables known as u j and x i in the fuzzy ules. Nodes at laye 2 act as the membeship functions, tanslating the linguistic vaiables fom laye 1 into thei membeship degees. Since thee may exist seveal tems fo one linguistic vaiable, one node in laye 1 may have links to seveal nodes in laye 2, which is accodingly named as the tem nodes. he numbe of nodes in the ule Laye (laye 3) and the one of the fuzzy ules ae the same each node epesents one fuzzy ule and calculates the fiing stength of the ule using membeship degees fom laye 2. he connections between laye 2 and laye 3 coespond with the antecedent of each fuzzy ule. Laye 4, as the Nomalization Laye, simply does the nomalization of the fiing stengths. hen with the nomalized fiing stengths h, ules ae combined at laye 5, the Paamete Laye, whee A and B become available. In the Linea System Laye, the 6th laye, cuent state vecto X(t) and input vecto U(t) ae used to get the next state X(t + 1), which is also fed back to the context nodes fo fuzzy infeence at time (t + 1). he last laye is the Output Laye, multiplying X(t + 1) with C to get Y(t + 1) and outputting it. Next we shall descibe the feed fowad pocedue of NFS by giving the detailed node functions of each laye, taking one node pe laye as example. We shall use notations like u to denote the i th i k input to the node in laye k, and o[k] the output of the node in laye k. Anothe issue to mention hee is the initial values of the context Figue 1. he stuctue of a simple NFS. Copyight 2012 Scies.

4 480 A SK-ype ecuent Neuo-Fuzzy Systems fo Fault Pognosis nodes. Since NFS is a ecuent netwok, the initial values ae essential to the tempoal output of the netwok. Usually they ae peset to 0, as zeo-state, but non-zeo initial state is also needed fo some paticula case. Laye 1. hee is only one input to each node at laye 2. he Gaussian function is adopted hee as the membeship function: 1 u c s 2 o e (5) whee c and s give the cente (mean) and width (vaiation) of the coesponding u[1] linguistic tem of input u[2] in ule. Laye 2. his laye has seveal nodes, one fo figuing matix A and the othe fo B. hough we can use many nodes to epesent the components of A and B sepaately, it is moe convenient to use matices. So with a little specialty, its weights of links fom laye 4 ae matices A (to node fo A) and B (to node fo B). It is also fully connected with the pevious laye. he functions of nodes fo A and B ae espectively. 2 [2] 2 [2] fo A o u A, fo B o u B (6) 1 1 Laye 3. he Linea System Laye has only one node, which has all the outputs of laye 1 and laye 2 connected to it as inputs. Using matix fom of inputs and output, we have 3. Pognostics Pocess he fist step in building a pognostics system, as published in the ISO standad, is the identification of the set of failue modes (FM), thei influence factos on each othe and the detection measues (desciptos) that allow to tack the evolution of the degadation. he intenational standad IEC [10] has pesented a pocedue named Pocedue fo failue mode and effects analysis (FMECA), which helps the identification of all the failue modes fo a specific system, by the analysis of its subsystem s and components. Also, the FMECA method classifies the FMs using isk pioity numbes (PN) that ae calculated with thee failue mode paametes: occuence (Occ), detection (Det) and seveity (Sev). So, the FMECA [11] allows the definition of the appopiate detection method and measues to be used in the diagnostics as well as in the pognostics of the failue modes. he netwok stuctue is build in thee steps: Step 1. he detemination of fuzzy subsets fo evey input vaiable. he initial values of the centes and vaiances chaacteising the membeship functions of the fist laye down, can be abitaily established (equidistant on the domain of definition of the linguistic vaiable) o applying a clusteing algoithm of the type Fuzzy C-Means. Step 2. Obtain the minimal dimension of the ule base. he extaction of most significant ule that detemines the numbe of the nodes in the second laye. Step 3. Optimization of the paametes of ules detemined at Step 2. he objective is to altenate the paamete values (c,w) of the netwok in ode to impove the ule base minimizing the quadatic citeia of pefomance, 4. Expeimental esults o test the quality of the model, seveal actions wee geneated, and fixed goals wee defined. he goals wee defined in a way that the esults wee undestood without ambiguity by human knowledge, the Figue 2 illustate the fuzzy base ules with 3 paametes to classify the defaults modes In ode to illustate the leaning effect of the poposed immune based FNN (IM-FNN), we use One of the most impotant types of systems pesent in the pocess industy is wokshop of SCIMA clinke. A fault in a wokshop of SCIMA clinke may lead to a halt in poduction fo long peiods of time. Apat fom these economic consideations faults may also have secuity implications. A fault in an actuato may endange human lives, as in the case of a fault in an elevato s emegency bakes o in the stems position contol system of a nuclea powe plant [9,12]. he design and pefomance testing of fault diagnosis systems fo industial pocess often equies a simulation model since the actual system is not available to geneate nomal and faulty opeational. In Figue 3 the detection of fault mode in the otay kiln is obseved with the classification afte taining the neuo-fuzzy system. Data needed fo design and testing, due to the economic and secuity easons that they would imply. Accod- Figue 2. he geneated ules base. Copyight 2012 Scies.

5 A SK-ype ecuent Neuo-Fuzzy Systems fo Fault Pognosis 481 Figue 3. Detection of fault mode. Figue 4. he failue mode of otay kiln. Copyight 2012 Scies.

6 482 A SK-ype ecuent Neuo-Fuzzy Systems fo Fault Pognosis ing to this Figue 4 we can say the pediction of a faults is a complex poblem and need the coection of invese poblem. 5. Conclusion he successful of implementing neuon-fuzzy is heavily depends on pio knowledge of the system and the taining data. In the intinsic natue, the neuo-fuzzy only can handle a limited numbe of inputs and can usually be identified in a not vey tanspaent way fom the empiical data [2]. he tanspaency is the detemination of the pocess with a less amount of fuzzy ules with appopiate membeship function. Fo the complex system, a lage achitectue is needed to epesent a model. EFEENCES [1]. J. Patton, P. M. Fank and. N. Clak, Issues of Fault Diagnosis fo Dynamic Systems, Spinge, London, [2] L. Mainai, Gas Path Diagnostics and Pognostics fo Aeo-Engines Using Fuzzy Logic and ime Seies Analysis, Ph.D. hesis, School of Engineeing, Canfield Univesity, Canfield, [3] J. M. Koscielny and M. Syfet, Fuzzy Logic Applications to Diagnostics of Industial Pocesses, Pepints of the 5th IFAC Symposium on Fault Detection, Supevision and Safety fo echnical Pocesses, Washington, 9-11 June 2003, pp [4] C.-F. Juang, A SK-ype ecuent Fuzzy Netwok fo Dynamic Systems Pocessing by Neual Netwok and Genetic Algoithms, IEEE ansactions on Fuzzy Systems, Vol. 10, No. 2, 2002, pp doi: / [5] C. D. Bocaniala and J. Sa da Costa, uning the Paametes of a Fuzzy Classifie fo Fault Diagnosis. Hill- Climbing vs Genetic Algoithms, Poceedings of the 6th Potuguese Confeence on Automatic Contol, Fao, 7-9 June 2004, pp [6] J. He, Neuo-Fuzzy Based Fault Diagnosisf o Nonlinea Pocesses, Ph.D. hesis, he Univesity of New Bunswick, New Bunswick, [7] F. J. Uppal and. J Patton, Fault Diagnosis of an Electo-pneumatic Valve Actuato Using Neual Netwoks with Fuzzy Capabilities, [8] C. D. Bocaniala, J. Sa da Costa and V. Palade, A Novel Fuzzy Classification Solution fo Fault Diagnosis, Intenational Jounal of Fuzzy and Intelligent Systems, Vol. 15, No. 3-4, 2004, pp [9] K. B. Aiffin, On Neuo-Fuzzy Applications fo Automatic Contol, Supevision, and Fault Diagnosis fo Wate eatment Plant, Ph.D. hesis, Faculty of Electical Engineeing Univesiti, eknologi, [10] D. Heny, X. Olive and E. Bonschlegl, A Model-Based Solution fo Fault Diagnosis of huste Faults: Application to the endezvous Phase of the Mas Sample etun Mission, Euopean Confeence fo Aeo-Space Sciences, St. Petesbug, 4-8 July [11] F. Xi, Q. Sun and G. Kishnappa, Beaing Diagnostics Based on Patten ecognition of Statistical Paametes. Jounal of Vibation and Contol, Vol. 6, No. 3, 2000, pp doi: / [12] J. Biteus, Distibuted Diagnosisand Simulation Based esidualgeneatos, Ph.D. hesis, Vehicula Systems- Depatment of Electical Engineeing, Linkopings Univesitet, Linkoping, Copyight 2012 Scies.