Sensor Fault Detection in a Real Hydraulic System Using a Classification Approach

SENSOR FAULT DETECTION IN A REAL HYDRAULIC SYSTEM USING A CLASSIFICATION APPROACH

Oriane Le Pocher, Eric Duviella Univ. Lille Nord de France, F-59000 Lille, France EMDouai, IA, F-59500 Douai, France

Karine Chuquet VNF - Service de la navigation du Nord Pas-de-Calais, 37 rue du Plat, 59034 Lille Cedex, France

Keywords: Supervision, Fault detection, Classiﬁcation algorithm, Large scale system, Hydraulic system.

Abstract: This paper focuses on the sensor fault detection of a hydraulic channel used for navigation. This system has the particularities to have large scale dimension, without slope, with several inputs and ouputs, and thus difficult to be modelled according to classical modelling methods. For recent years, it was equipped with level sensors in order to have better knowwledge of its behavior, to detect its state online and thus improve its management. However, level sensors are subjected to measurement or transmission errors, setting errors, and quick or slow drifts. In order to detect these sensor errors, a classification approach is proposed. It appears adapted to the fault detection of large scale hydraulic systems without model. The classification approach is used on data measured from 2006 to 2009. The first results and analysis show that the classification method is effective for addressing the problem of sensor fault detection.

1 INTRODUCTION by following a systematic approach. The first step consists in characterizing the operating modes of the Hydrographical networks are large scale systems system to be supervised. Several model-based ap- characterized by nonlinear dynamics and varying time proaches were proposed (Frank et al., 2000), based delays. They are used for several human activities, on parameters identification technique (Weihua et al., especially navigation and transport. In the northern 2003), parity equations method (Gertler, 1998), diag- Europe, navigation channels assure the transport of nosis observers (Akhenak et al., 2004), or Kalman fil- goods with the objective, within a few years, of ac- ters (Xie et al., 1994). Even if these FDI techniques comodating large broad gauge boats. The control of have proven to be as powerful and effective, they re- the water level in navigation channels becomes cru- quire an accurate model of the system by minimizing cial. In order to achieve this objective, sensor net- the uncertainties and the process noise. Very recently, works have been implemented. These sensors allow fault detection methods based on residual generation, the measurement of water levels or water discharges, extended Kalman filter and finite memory observer and the implementation of level control algorithms for are proposed in (Bedjaoui and Weyer, 2010), in order a local water management. At a larger scale, the level to detect and localize leak in an irrigation network. and discharge measurements are essential to provide This detection method is based on physical hydraulic an efficient water managementof the navigation chan- system model, in particular on the Saint-Venant par- nel networks, by mainly characterizing their state on- tial differential equations (Chow et al., 1998). How- line. However, sensor networks are impacted by mea- ever, due to their physical characteristics, i.e. large sure errors, transmission faults, or drifts of operation. dimensions, no slope, etc., navigation channels can So, in order to improve the management of navigation not always be modelled using physical laws without channels, sensor fault detection techniques have to be requiring numeric models. In this way, traditionnal employed. FDI techniques cannot reach the fault detection aims. Fault Detection and Isolation (FDI) techniques When the physical modelling of the system is are largely proposed in the litterature and employed not realizable, pattern recognition techniques consti-

382 Le Pocher O., Duviella E. and Chuquet K.. SENSOR FAULT DETECTION IN A REAL HYDRAULIC SYSTEM USING A CLASSIFICATION APPROACH. DOI: 10.5220/0003571603820387 In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2011), pages 382-387 ISBN: 978-989-8425-74-4 Copyright c 2011 SCITEPRESS (Science and Technology Publications, Lda.) SENSOR FAULT DETECTION IN A REAL HYDRAULIC SYSTEM USING A CLASSIFICATION APPROACH

tute an interesting alternative approach for fault de- m to allow the navigation (NNL = Normal Naviga- tection problem. They consist in extracting information Level). The main issue for the management of tion on the system state by using the signals collected this reach is to counterbalance the navigation flow from sensors (Hartert et al., 2010). The operating of 3 m3/s at Fontinettes. A part of the water comes modes of the system are represented by classes which from the navigation flow at Cuinchy which represents are built according to dynamic classification algo- 0.6 m3/s. The difference between the two navigation rithms, as the CDL algorithm (Cluster Detection and flows comes from the size of the lock at Fontinettes Labeling), algorithms based on adaptive resonance which is 13 m high whereas the lock at Cuinchy is theory (ART) networks (Su and Liu, 2005), (Eltoft only 2 m high. The counterpart of water comes from and de Figueiredo, 1998), FMC algorithm (Fuzzy different hydrants and discharges. A high number of Min-max Clustering) (Mouchaweh et al., 2002) or rivers are inverted siphon and pass under the reach AUDyC (Auto-Adaptive Dynamical Clustering) al- but three of them feed directly the reach. Another gorithm (Lecoeuche et al., 2004). In (Traore et al., solution to feed the reach is the Cuinchy gate. This 2009), the AUDyC algorithm is employed to super- gate allows a controlled feeding of the reach with the vise a thermo-regulator system subjected to slow and water of the Deûle river. In the same way, the gate quick drifts in its dynamics. called ”Porte de Garde” at Aire sur la Lys allows con- This paper focuses on sensor fault detection of the trolled exchanges between the Lys river and the reach. Cuinchy-Fontinettes navigation channel. This sys- Finally a high number of anthropogenic discharges tem, located in the north of France, is characterized (more than 320) feed the reach in an unknown way. by large dimensions and no slope. Thus, it is not pos- Fontinettes Lock sible to be modelled according to physical approach. Thus, a classification approach is proposed to address Fontinettes level sensor the fault detection problem. In section II, the real hydraulic system and the problem of sensor fault detec- Gate ‘Porte de Garde’ tion are presented. The classification approach based on AUDyC algorithm is detailed in section III. This Aire basin Fort Gassion lock fault detection technique allows the determination of Aire level sensor indicators characterizing the real-time drift of sensors. Fort Gassion gate Finally, in section V, the proposed approach is applied Cuinchy level sensor on real data measured from 2006 to 2009, and its per- formance for the detection of sensor faults are high- Cuinchy lock lighted. Figure 1: Scheme of the navigation canal Cuinchy- Fontinettes.

For recent years the reach has been equipped with 2 PROBLEM STATEMENT level sensors in order to better know its behaviour. The level sensors used for this study are located The channel studied is the reach Cuinchy-Fontinettes downstream from the lock of Cuinchy, upstream from which is located in the North of France between the the lock of Fontinettes and in the Aire basin. The lock of Cuinchy at the East of the town Bethune and, Cuinchy and Aire sensors are composed of an ultra- at the Southwest of the town Saint-Omer, the lock of sonic transducer linked with a level transformer. The Fontinettes (see Figure 1). With 42.3 km long and Fontinettes sensor is a Probe with a transducer inte- 51.8 m large, this reach is part of the broad gauge grated. The technology used is based on ultrasonic river network of North of France. It is characterized sound and allows the processing of echoes. The data by no significant slope. It can handle boats until 185 processing and transmission are realized by telepro- m long and 11.4 m large. This channel is entirely arti- cessing equipments. The three sensors deliver the ficial. The first part of the channel, i.e. 28.7 km from mean of the levels measured every quarter hour. The Cuinchy to Aire sur la Lys, is called ”canal d’Aire” waves due to navigation or Fontinettes lock opera- and has been built in 1820. The second part of the tions are averaged. channel, i.e. 13.6 km from Aire sur la Lys to Saint Sensors are subjected to the weather and the en- Omer, is called ”canal de Neuffossé” and has been vironment and as every electronic device can break built in the eleventh century. down or be impacted over time. Several types of er- The Cuinchy-Fontinettes is managed by VNF rors can occur. A badsetting of the sensors can lead to (Voies Navigables de France). The role of VNF is systematic errors. Aberrant data are caused by local to maintain the level of the channel at NNL = 19.52 and temporal errors. Blockade of data can be due to

383 ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

a transmission fault for example. Level sensor can be monitor slow drifts and jumps, is based on the AU- subjected to slow temporal drifts. In order to use re- DyC algorithm. AUDyC is an evolutionary data clas- liable measured data, it is essential to propose a fault sification algorithm whose role is to model, in a con- detection technique. tinuous way, the operating modes of dynamical sys- The main problem for the fault detection tech- tems. The technique is inspired from the mixed Gaus- nique proposal is the major difficulty of modeling sian model (Lecoeuche et al., 2004). The Gaussian the Cuinchy-Fontinettes channel without numeric ap- classes are represented by prototypes P j characterized proach. A fault detection technique by a pattern by a center and a matrix of covariance. The proto- recognition approach is proposed in the next section types characteristics are adapted to each new obser- in order to be freed from a model of the channel. vation X = (x1, x2, ... xn), with n the number of pertinent data, by using rules of recursive update on a sliding window of size Nf en, and by considering the 3 FAULT DETECTION BY A totality of the prototype P j, noted Card (P j) on previ- ous instant k−1, according to the algorithm described PATTERN RECOGNITION below. A new observation X is rejected if is too far APPROACH from the current class. In other case, this observation is assigned to one of the N existing classes according The fault detection method proposed in this paper is to an adaptation procedure of the prototypes. based on a classification technique. This classifica- • If Card(P j)=nb < N : add information tion technique consists in characterizing an operating f en mode of the dynamic system by a Gaussian model 1 M j (k)= M j (k − 1)+ (X − M j (k − 1)), which constitutes a class. A class is determined ac-  P P nb + 1 k P  cording to pertinent selected data which present same  nb − 1  W j (k)= W j (k − 1)+ similarities. According to these selected data, a Rep-  P nb P resentation Space can be built, and the class can be  1 ⊤  (Xk − MP j (k − 1)) (Xk − MP j (k − 1)). represented in this space. Thus, the class of the nor-  nb + 1  (1) mal operating mode, denoted Cn, can be determined (see Figure 2). A new class is create when a sufficient numberof points is presentin an area of the Represen- • If nb ≥ Nf en: add or retreive information tation Space. The new class, which is updated or cre- 1 d + d − ated, is denoted evolutionary class Ce. It corresponds MP j (k) = MP j (k − 1) + ( X − X ), Nf en to a new operating mode.   W W When a measurement or transmission error oc-  P j (k) = P j (k − 1)+  curs, a new point appears in the Representation Space  1 1  Nf en Nf en(Nf en−1)  far from the normal class Cn (see Figure 2.a). This D D ⊤  X X , point has to be detected and rejected if it is isolated.  (Nf en+1)   1 −  When the level sensor is subjected to slow drifts, the   Nf en(Nf en−1) Nf en(Nf en−1)   class updates online (see Figure 2.b). The character- (2) where istics of the normal class evolve during time. Finally, d + new catalectic failures lead to a jump in the representation X = X − MP j (k − 1),  − old d − j − space (see Figure 2.c).  X = X MP (k 1), (3) D X =[d X+ d X−],  x1 x1 x1 Ce Ce W with MP j (k) and P j (k) respectively the center and the covariance matrix of the prototype P j at instant k, Cn Cn Cn new old Nf en the width of the slipping window, X and X new and old observation vectors, respectively. This fault detection method based on AUDyC algorithm allows rejecting measurement or transmis- x2 x2 x2 (a) (b) (c) sion errors, following slow drifts and catalectic fail- Figure 2: (a) Measurement or transmission errors, (b) slow ures. In order to detect drifts, fault indicators have drifts, (c) jump characterising catalectic failure, in a two to be calculated. A first indicator corresponds to the dimensions representation space. mean of the measured levels on the sliding window Nf en. It allows the visualisation of quick and slows The classification technique which is proposed to drifts. A second indicator consists in computing the

384 SENSOR FAULT DETECTION IN A REAL HYDRAULIC SYSTEM USING A CLASSIFICATION APPROACH drifts. A second indicator consists in computing the The second step consisted in building the Repre- drifts.distance A between second indicator the evolutive consists class inC computinge and the nor- the sentationThe second Space step with consisted the three in measured building data the Repre-xa, xc distance between the evolutive class Ce and the nor- The second step consisted in building the Repre- distancemal class betweenCn. The the normal evolutive classclass is takenCe asand reference. the nor- andsentationx f , and Space to represent with the the three normal measured class C datan (see xaFig-, xc mal class Cn. The normal class is taken as reference. sentation Space with the three measured data xa, xc malA fault class occurenceCn. The normal can lead class to the is taken drift of as the reference. evolu- ureand 3).x f , andThe to normal represent class the is normal built with class accurateCn (see mea-Fig- A fault occurence can lead to the drift of the evolu- and x f , and to represent the normal class Cn (see Fig- Ative fault class occurenceCe from thecan normal lead to class the driftCn. Increasingof the evolu- of suredure 3). data The from normal April class to June isbuilt 2006 with according accurate to amea- slid- tive class Ce from the normal class Cn. Increasing of ure 3). The normal class is built with accurate mea- tivethis class distanceC from reveals, the in normal some class cases,C the. Increasing presence of ingsured window data fromNf en Aprilequal to to June 2500 2006 values. according The center to a slid- of this distancee reveals, in some cases,n the presence of sured data fromApril to June 2006accordingto a slid- thisfaults. distance Amongst reveals, the several in some existing cases, metrics, the presence the Eu- of theing class windowCn Nisf around en equal zero to 2500 (relative values. levels The according center of faults. Amongst the several existing metrics, the Eu- ing window Nf en equal to 2500 values. The center of faults.clidian Amongst distance, denotedthe severald M existinge Mn , ismetrics, considered: the Eu- tothe the class NNL),Cn isi.e. around0 034 zero (relative 0 058 levels 0 059 according , and its clidian distance, denoted d(Me,Mn), is considered: the class Cn is around zero (relative levels according clidian distance, denoted d Me Mn , is considered: covarianceto the NNL), matrixi.e. is0 equal 034 to: 0 058 0 059 , and its d M M M M M M (4) to the NNL), i.e. [−0.034 − 0.058 − 0.059], and its e n e n e n covariance matrix0 is 0060 equal 0 to: 0052 0 0055 d(M ,M )= (M − M )(M − M )⊤, (4) covariance matrix is equal to: d MeeMnn Mee Mnn Mee Mnn (4) with Me is the center of the class Ce and Mn the center n 0 00520060 0 00550052 0 0052 0055 . (5) of the normal class C . The center of the normal class 00. 005500520060 0 0. 005200550052 0. 00650055 0052 . (5) withwithMMeeisis the the center centern of of the the class classCCeeandandMMnnthethe center center n   M is fixed. S n = 0.0052 0.0055 0.0052 . (5) ofofn the the normal normal class classCCnn.. The The center center of of the the normal normal class class 0 0055 0 0052 0 0065 Moreover, by considering, for causal systems, that 0.0055 0.0052 0.0065 MMnnisis fixed. fixed.   theMoreover, outputsMoreover, depend by by considering, considering, on the variation for for causal causal of the systems, systems, inputs, cor- that that therelationthe outputs outputs indicators depend depend between on on the the variation variation the center of of of the the the inputs, inputs, evolutive cor- cor- relationclassrelation according indicators indicators to betweeneach between direction the the center center of the of of the theRepresenta- evolutive evolutive classtionclass Space, according according denoted to to each eachKi j directionfor direction data xi of ofand the thex j Representa-, Representa- can reveal a fault occurence. That leads to compute correlation tiontion Space, Space, denoted denotedKKii j, jforfor data dataxxiiandandxxjj,, can can reveal reveal acoefficientsa fault fault occurence. occurence. between That That the leadsmean leads toof to computeeach compute measured correlation correlation level coefficientsoncoefficients a sliding betweenwindow betweenof the the size mean meanNf enof of. each In each a second measured measured step, level level error indicators are computed between the center of the onon a a sliding sliding window window of of size sizeNNff en en.. In In a a second second step, step, er- er- rorevolutiveror indicators indicators class are are amongst computed computed each between between direction the the of center center the Repre- of of the the evolutivesentationevolutive Spaceclass class amongst also. amongst The each each error direction direction indicators of of are the the denoted Repre- Repre- sentationfor data Spacex and also.x . The Finally, error the indicators quadratic are error denoted in- sentationi j Spacei also.j The error indicators are denoted Figure 3: Normal class C in the Representation Space. dicatorse for data2 arex and computedx . Finally, according the quadratic to . error in- n ii j, jfor datai j xi iand x j.j Finally, the quadratici j error in- Figure 3: Normal class C in the Representation Space. 2 Figure 3: Normal class Cn in the Representation Space. dicatorsdicatorsQuadratice2 areare error computed computed indicators according according2 are to tousede i, j. in. order to ii j, j i j i j Although the total measured data was used, only 2 detectQuadraticQuadratic setting errorerrors. error indicators indicators Error indicatorse 2 areare used usedi j are in in order orderused into to ii, jj yearsAlthoughAlthough 2006 and the 2009 total were measured shown datato highlight was used, the only per- detectorderdetect to setting setting detect errors. slow errors. drifts Error Error and indicators indicators to determinee i, j are whichare used used sen- in in i j formanceyearsyears 2006 2006 of and and the 2009 proposed were shownapproach. to highlight Figure 4 the shows per- ordersororder is to tofaulty. detect detect slow Finally, slow drifts drifts correlation and and to to determine determine indicators which whichKi jsen- sen-al- theformanceformance measured of of the the levels, proposed proposedi.e. x approach.c, xa and x Figuref , and 4 the shows shows de- sorlowsor is the is faulty. faulty. detection Finally, Finally, of quick correlation correlation drifts and indicators indicators catalecticKKi, fail-j al-al- i j tectionthethe measured measured and isolation levels, levels, ofi.e. wrong x c, x measureda and x f , anddata the the during de- de- lowures.low the the The detection detection redondancy of of quick quick of the drifts drifts indicators and and catalectic catalectic and a cross- fail- fail- c a f thetectiontection year and and 2009. isolation isolation The wrong of wrong data measuredare depicted data by during during black ures.comparisonures. The The redondancy redondancy lead to determine of of the the indicatorswhich indicators of the and and sensors a a cross- cross- is crossthethe year year in Figure 2009. 2009. The The4. The wrong wrong classification data are depicted approach by by allows black black comparisonfaulty.comparison The faultlead lead to detection to determine determine approach which which isof of applied the the sensors sensors in the is is tocrosscross reject in in Figurethese Figure points 4. The automatically. classification approach allows faulty.casefaulty. of Thethe The Cuinchy-Fontinettes fault fault detection detection approach approach Channel is is applied applied on data in in from the the toto reject reject these these points points automatically. automatically. case2006case of ofto the the 2009. Cuinchy-Fontinettes Cuinchy-FontinettesChannel Results and analysis Channel are onpresented on data data from from in 2006the2006 next to to 2009.section. 2009. Results Results and and analysis analysis are are presented presented in in thethe next next section. section. 4 FAULT DETECTION IN THE 44 FAULTCUINCHY-FONTINETTES FAULT DETECTION DETECTION IN IN THE THE CUINCHY-FONTINETTESCHANNELCUINCHY-FONTINETTES CHANNELCHANNEL Measured data on the Cuinchy-Fontinettes Chan- nelMeasuredMeasured correspond data data to onx ona the, x thec Cuinchy-Fontinettesand Cuinchy-Fontinettesx f , for Aire in the Channel Chan- mid- neldlecorrespond correspondof the channel, to tox ,xx for, xand Cuinchyandx x, for, at for Aire the Aire upstream, in in the the middle mid- and for Fontinettes ata theac downstream,c f f respectively. These dleof ofthe the channel, channel, for for Cuinchy Cuinchy at the at the upstream, upstream, and and for Figure 4: Data xc (continuous line), xa (dotted line) and x f fordataFontinettes Fontinettes are measured at at the the downstream,with downstream, a sample respectively. respectively. time equal These toThese 15 Figure(dashed-dotted 4: Data x line)c (continuous measured line), on 2009,xa (dotted and isolate line) and wrongx f minutes from 2006 to 2009. It represents more than (dashed-dotteddata (black cross). line) measured on 2009, and isolate wrong datadata are are measured measured with with a a sample sample time time equal equal to to 15 15 dataFigure (black 4: Data cross).xc (continuous line), xa (dotted line) and x f minutes135000minutes from from 3 values. 2006 2006 to These to 2009. 2009. data It It representswere represents not recorded more more than than at (dashed-dotted line) measured on 2009, and isolate wrong 135000the135000 same× time. 33 values. values. Indeed, These These there data data are were discrepancieswere not not recorded recorded of few at at dataFigure (black cross). 5.a shows the measured levels in Cuinchy theminutesthe same same between time. time. Indeed, Indeed, measurements. there there are are discrepancies discrepancies Then, the first of of step few few (blueFigure continuous 5 a shows line), the measured in Aire (red levels dashed in Cuinchy line) minutesisminutes to resynchronize between between measurements. measurements. all the data. Then, Then, the the first first step step (blueandFigure in continuous Fontinettes 5 a shows line), (green the measuredin dashed-dotted Aire (red levels dashed line) in Cuinchy during line) isis to to resynchronize resynchronize all all the the data. data. (blue2009. continuous The distance line),d(Me in,M Airen) is depicted (red dashed in Figure line)

385 ICINCO 2011 - 8th International Conference on Informatics in Control, Automation and Robotics

5.b. The correlation indicators Kc,a, Kc, f and Ka, f , their objectives. This is relevant of slow drift on the e 2 e 2 e 2 level sensor in Fontinettes. the quadratic error indicators c,a, c, f and a, f , and the error indicators e c,a, e c, f and e a, f , are computed Figure 6 shows the measured levels, i.e. xc, xa between the mean of measured levels in Cuinchy and x f , during the year 2006. The detected wrong and Aire, in Cuinchy and Fontinettes, in Aire and measured data appear during the period around the Fontinettes, respectively. Indicators between Cuinchy 55000th sample (see black cross). and Aire are depicted in blue continuous line, those 0.4 between Cuinchy and Fontinettes in red dashed line, and those between Aire and Fontinettes in green 0.2 dashed-dotted line, in Figure 5.c,5.d and 5.e, respec- 0 tively. A threshold deﬁned equal to 0.7 is considered in order to detect fault when one of the correlation −0.2 Level [m] indicators is under this threshold (see Figure 5.c). −0.4

0.2 −0.6 0.1 0 −0.1 −0.8 Level mean [m] (a)

0 −1 0 1 2 3 4 5 6 7 8 9 10 Time [steps] 4 −0.1 x 10 Eu d −0.2 Figure 6: Data x (continuous line), x (dotted line) and x −0.3 c a f (b) (dashed-dotted line) measured on 2006, and isolate wrong 1

0,5 data (black cross). i,j

K 0 The same indicators are determined for year 2006 (c)

0.02 and depicted in Figure 7, and the same conclusions 2 i,j ε 0.01 can be obtained if the distance d(Me,Mn) and corre-

0 lation indicators are taken into account. The most in- (d) teresting point to show is the detection of slow drift 0.15 0.1

i,j of the Cuinchy level sensor during all the year. From ε 0.05 th 0 the beginning of year 2006 to the 26000 sample, −0.05 0 1 2 3 4 5 6 7 8 9 10 4 2 2 (e) x 10 e e Time [step] quadratic errors c,a and c, f are constant and around e 2 Figure 5: (a) Measured levels xc (continuous line), xa (dot- 0.0025 and a, f is close to zero (see Figure 7.d). It ted line) and x f (dashed-dotted line), (b) Euclidienne dis- means that there is a setting error on the level sensor tance dEu(Me,Mn), (c) correlation indicators Kc,a (continu- in Cuinchy. The setting error is evaluated from 0.05 m ous line), Kc, f (dashed line) and Ka, f (dashed-dotted line), according to the errors e c,a and e c, f (see Figure 7.e). d quadratic error indicators e 2 (continuous line), e 2 ( ) c,a c, f Then from the 26000th sample to the 65000th sam- e 2 (dashed line) and a, f (dashed-dotted line), (e) error in- ple, all the errors are close to zero. It is possible to e e e dicators c,a (continuous line), c, f (dashed line) and a, f assume that the Cuinchy level sensor is correctly set. (dashed-dotted line), measured on 2009. th e 2 Finally, from the 65000 sample, quadratic errors c,a e 2 During 2009, by considering the distance and c, f are increasing. It is relevant of slow drift of the Cuinchy level sensor. Errors e and e are de- d(Me,Mn) (see Figure 5.b), only one period around c,a c, f the 90000th step, is relevant to significant drift of the creasing to reach −0.1 m. th The fault detection method proposed in this article class Ce. However, around the 90000 sample, oth- ers indicators are close to their objective values. This allows the detection of error setting, slow and quick means that there is no fault. In this period, the dis- drifts. It can be implemented online in order to detect these types of faults in real-time. tance d(Me,Mn) is increasing because there is a mod- ification of the operating mode, which can be the con- sequence of flood (see measured levels in Figure 5.a). Figure 5.c shows three periods where correlation in- 5 CONCLUSIONS dicators are under the fixed threashold, i.e. around th th th 20000 , 66000 and 88000 samples. For the two The sensor fault detection of real large scale systems 2 first periods, there are no significant errors e and e without model is an interesting research problem. The (see Figure 5.d,5.e). During the third period around well-known classical FDI techniques cannot be ap- th e 2 the 88000 sample, there are significant errors c, f , plied due to the difficulty of modelling. Thus, a fault e 2 e e e 2 e a, f , c, f and a, f . Errors c,a,and c,a are close to detection approach without model is proposed in or-

386 SENSOR FAULT DETECTION IN A REAL HYDRAULIC SYSTEM USING A CLASSIFICATION APPROACH

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0.05 work for cluster-detection-and-labeling. IEEE Trans. 0 i,j

ε Neural Networks, 9:1021–1035. −0.05 −0.1 0 1 2 3 4 5 6 7 8 9 10 Frank, P. M., Ding, S. X., and KCipper-Seligcr, B. (2000). 4 (e) x 10 Time [step] Current developments in the theory of fdi. In SAFE- Figure 7: (a) Measured levels xc (continuous line), xa (dot- PROCESS00, Budapest, Hungary, pages 16–27. ted line) and x f (dashed-dotted line), (b) Euclidienne dis- Gertler, J. (1998). Fault Detection and Diagnosis in Engi- tance dEu(Me,Mn), (c) correlation indicators Kc,a (continu- neering Systems. Dekker. ous line), Kc, f (dashed line) and Ka, f (dashed-dotted line), e 2 e 2 Hartert, L., Mouchaweh, M. S., and Billaudel, P. (2010). (d) quadratic error indicators c,a (continuous line), c, f Intelligent Industrial Systems: Modeling, Automation e 2 (dashed line) and a, f (dashed-dotted line), (e) error in- and Adaptive Behavior. IGI. e e e dicators c,a (continuous line), c, f (dashed line) and a, f Lecoeuche, S., Lurette, C., and Lalot, S. (2004). New su- (dashed-dotted line), measured on 2006. pervision architecture based on on-line modeling of non-stationary data. Neural Computing and Applica- der to reach these objectives. The technique of super- tions Journal, 13:323–338. vision which is presented in this article is based on Mouchaweh, M. S., Devillez, A., Lecolier, G., and Bil- the Pattern recognition AUDyC algorithm. It has the laudel, P. (2002). Recursive learning in real time using advantage to limit physical knowledge of the system, fuzzy pattern matching. Mathematics and Computers and aims to modelling the operating modes of dynam- in Simulation, 60:209–216. ical systems using only measured data. The charac- Su, M.-C. and Liu, Y.-C. (2005). A new approach to clus- teristics of the operating mode are updated in real- tering data with arbitrary shapes. Pattern Recognition, time in order to follow the drifts due to sensor faults, 38:1887–1901. and detect setting errors and measurement or trans- Traore, M., Duviella, E., and Lecoeuche, S. (2009). Dy- mission errors. The proposed technique is applied on namical clustering technique to estimate the proba- bility of the failure occurrence of process subjected a real hydrographical system with presents the partic- to slow degradation. In ICINCO, Milan, Italy, pages ularities to not being modelled according to classical 636–643. modelling methods. Fault indicators are determined Weihua, L., Harigopal, R., and Sirish, S. (2003). Subspace according to levels which are measured since 2006. identification of continuous time models for process The first obtained results highlight the efficiency of fault detection and isolation. Journal of Process Con- the proposed fault detection method. However, these trol, 13:407–421. results have to be improved. The futur purposes con- Xie, L., Soh, Y. C., and de Souzi, C. E. (1994). Ro- sist in proposing more pertinent fault indicators by bust kalman filtering for uncertain discrete-time sys- considering the measured upstream and downstream tems. IEEE Transaction on Automatic Control, 93:131 in the Cuinchy-Fontinettes channel. It should be also 01314. interesting to take into account the unknown inputs which correspond to overflows in the channel. In future works, a prognosis approach will be proposed to predict the future state of the level sensors in order to detect as soon as possible sensor faults. Finally, an implementation of the proposed technique on the real system may be considered at term.

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