Neural Network for Fault Detection and Isolation of te Tree-Tank System Panagiotis Tzionas Tecnological Educational Institute of Tessaloniki, Greece Tessaloniki 574, Greece tzionas@teite.gr Dimitrios Krontsos Tecnological Educational Institute of Tessaloniki, Greece Tessaloniki 574, Greece krontsosd@yaoo.gr Simira Paadooulou Tecnological Educational Institute of Tessaloniki, Greece Tessaloniki 574, Greece smira@teite.gr Abstract-Tis aer resents te design, training, verification and validation of a neural network arcitecture caable of early fault detection and fault isolation in a tyical tree tank system. Certain fault tyes are induced to te system and its beavior is monitored. Parameters suc as water-level and temerature in te tanks, togeter wit delayed samles are used to design, train and validate te neural network arcitecture. Te neural network is furter tested on a set of signal values derived from subseuent oeration of te system, wit considerable success. Index Terms -Neural networks, fault detection, fault interretation. I. INTRODUCTION Faults can be defined as non-ermitted deviations of some caracteristic roerties of a rocess tat will cause a certain level of deterioration in te erformance of te rocess []. Faults are generated since te mecanical arts and materials used in devices and rocesses undergo aging, wear, etc., and, briefly, teir roerties are time deendent and tend mostly in te direction of lowering te oerational caabilities, safety and reliability []. Fault detection rocedures are called to decide weter a system is in normal oerating conditions or in faulty ones, on te basis of real-time observations. On-line (real time) rocedures are necessary for fault tolerant control, wile off-line rocedures can be used for maintenance uroses []. A variety of aroaces ave been roosed in recent years, for te design of efficient real-time fault detection and isolation rocedures by bot te control and artificial intelligence communities [4-8]. Real-time fault detection and isolation rocedures can only make use of te system observables, i.e. te system inuts and oututs, along wit teir derivatives for a continuous-time model or along wit teir delayed (memorized) values on a given time orizon, for discretetime models. Using tese observables, fault detection and isolation is essentially a two-level rocedure: i) te first level is tat of detection and alarm generation (decision weter te system is in normal conditions or not) and ii) alarm interretation, i.e., deciding wic faults are resent among a re-defined fault set and wic are teir caracteristics (occurrence time, fault size, class, conesuences etc.). In tis aer we restrict our attention to te class of ysical rocesses, making use of te following two yoteses: a)te system may be described by a set of state variables: let x R n be te state vector at time t, b)ten, te true beavior obeys a set of differential euations: dx = * φ( x, u, v, θ ) () were u R m and v R l are, resectively, te control and te erturbation inuts, and θ * R is a vector of te true arameters. Tree basic models ave been roosed for te descrition of te normal oeration of te system: ) Te beavioral model describes te way te system state evolves in time, as a conseuence of te system inuts (controls and erturbations). Te model closest to euation () would be a set of differential euations of te form: dx = f ( x, u, v, θ ) () were f is an aroximation of φ and θ is te vector of te reviously defined model arameters. ) Te measurements model describes te measurements tat are available, in te form : y=g(x,u,v,θ,ε) () were y R is te outut vector and ε R is te measurements noise. Tis model exresses te way under wic te sensors transform some states of te rocess into outut signals tat can be used for fault detection and isolation. ) Te oerating range model defines te values te system variables are allowed to take under normal conditions. A direct reresentation is given by: (x,u) η (4) were η R k, and euation (4) defines a domain in te state and control sace in wic te system oerates safely. According to wic form of a model is used, system teory, signal rocessing and artificial intelligence aroaces were used extensively in te literature [-7].
Te aroac roosed in tis aer uses, essentially, te measurements model alied to a tree-tank system. A multi-layered artificial neural network is emloyed for te detection and isolation of faults tat are induced to te system. Measurable uantities tat are sensitive and informative about te system oeration are used as symtoms tat discriminate articular faults. II. THE THREE-TANK SYSTEM II.A. System Descrition Te tree-tank system is a commonly used rocess [9], consisting of tree cylindrical water tanks connected by ies of circular cross-section. Usually, te first tank as an incoming flow tat can be controlled by means of a um and te outflow is located in te last tank. Te relative ositions of te tanks and te existence of additional features suc as water eating or cooling results in a variety of configurations for tree-tank rocesses. Te tree-tank rocess used in tis aer is sown in Figure. Two electronic valves control te water flow between te tanks, wereas, te um recirculates water from te bottom tank to te to tank. A eating element (resistor) located at te bottom tank eats u te water, wereas a cooling fan laced in a erendicular direction to te water flow cools down te water. A PID controller controlling te resistor and cooling fan is resonsible for attaining an almost steady water temerature. Two water level sensors are laced in te two to tanks measuring water level and tree termocoules monitor te water temerature of eac tank. Te overall rocess is monitored and controlled troug a Suervisory Control and Data Acuisition interface imlemented using LabView []. Let u be te incoming water volumetric flow to te to tank, s i te cross-section of tank i, i te water level of tank i, ii a volumetric flow due to ossible leakage in te i-tank and l is te water volumetric flow after te um. Let, also, T i be te temerature in tank i, Tu te temerature after te fan, Q ii te eat losses in tank i, Q F te eat removal by te fan and Q te eat suly rovided by te resistor. Assuming tat te density ρ and te secific eat c are constants and te incoming and outgoing water volumetric flows are indeendent since tey are controlled by te valves and not by ydrostatic ressure te matematical model of te system is: d d s = u s = d s = l u = l dt u Q s = [ Tu T ] (5) dt s dt s T u = T = = [ T T ] [ T T ] Q F l + Q Q Togeter wit ossible leakages, a number of additional uncertainty factors influence te oeration of te system. Te incomleteness of te knowledge about a comonent s beavior and ageing rocess needs to be examined. Te ies, in te roosed system are only artially known, for examle it is not exactly clear wat cemical reactions are actually aening between te ie walls and te inside flow. On te oter and, te conditions of use of a ie can ave large variations in te temerature of te flow [5]. Moreover, in a ot-water vessel, te temerature of te main water volume increases raidly, and te temerature of te water in front of te cooling fan decreases raidly (uneven temeratures of te flows). Te eated water results in te dissolved mineral articles solidifying into a scale deosit in te eated tank. Q Tank u Water level sensor ( ) Water temerature sensor (T ) T u valve Tank Water level sensor ( ) Water temerature sensor (T ) valve Water temerature sensor (T ) Tank Q eating element um Q F Cooling fan l Figure : Te tree-tank system wit sensors
Finally, erosions at te valve lugs, variations in water ardness, ie and valve clogging, measuring sensor inaccuracies and system non-linearities wen combined wit te above mentioned inaccuracy factors make te system very difficult, or even imossible, to be exressed analytically in te form of euation (5) [,9,]. II.B. System oeration and fault tyes Te normal oeration of te roosed system is deicted in Figure (a). A simle water-level control algoritm uses te level sensor inuts to control te oeration of te valves. If te water level in tank exceeds l ig cm ten valve is oened (ket closed u to tis level) and water flows to tank. Valve is closed wen te water level falls below l low cm. Similarly, if te water level in tank exceeds l ig ten valve is oened and water flows to tank. Valve is closed wen te water level falls below l low. A PID controller is emloyed to set water temerature at 5 o C, wit te aid of te eating resistance and cooling fan. In order to investigate te beavior of te roosed system under faulty conditions, a series of deliberate faults were induced. Te abnormal beavior of te system under faulty conditions was monitored troug te level and temerature sensors and it is sown on Figures (b-), for te different fault tyes. After fault manifestation, te system is restored to normal oerating conditions by removing te corresonding fault cause. Tis is in accordance to te most common faults scenarios used for suc systems [7,5,] and tese scenarios are briefly described as follows: i) Fault tye : Valve stuck closed. Tis fault is sown in Figure (b) and it is clear te water level in te first tank exceeds by far te normal value. ii) Fault tye : Valve stuck oen. Tis fault is dislayed in Figure (c) and te water level in tank reaces its minimum value. iii) Fault tye : Valve stuck oen: Figure (d) dislays te minimum water level reaced for tank and te temerature dro (due to lack of water). iv) Fault tye 4: Valve stuck closed. Obviously, in tis case te water level in tank is raised far above te maximum value, as sown in Figure (e). v) Fault tye 5: Valves & bot stuck oen. In tis case te water levels reac teir minimum values in bot tanks (first in tank and ten in tank, Figure (f)). vi) Fault tye 6: Pum switced off. In tis case, water levels will also reac teir minimum values, as long as te valves are oerating (Figure (g)). vii) Fault tye 7: Wile te um is switced off, valve is closed. Tis results to a minimum level attained in tank and an intermediate level attained in tank (Figure ()). A fault detection and isolation rocedure is reuired in order to detect faults as early as ossible and to roceed to te necessary correcting rocedures tat will restore te rocess to its normal oeration. Due to te inerent uncertainties and measuring errors described in te revious section, te measurements model aroac is adoted in tis aer. Inut /outut measurements of te system under normal and faulty oerating conditions are used to train a multi-layered feedforward neural network tat is caable to generalize and discriminate among normal and faulty system beavior. Tis neural network can ten be used for fault rediction and identification. III. NEURAL NETWORK ARCHITECTURE III.A. System Identification Te determination of te inut signals tat influence te system outut in suc a way tat different outut beaviors can be differentiated (i.e. differentiate among te different beaviors deicted in Figure ) is, essentially, a arameter identification roblem [,]. Te coice of inut signals influencing te outut can be made by observing te outut beavior. Additionally, inut delays can be determined by observation of te time delay occurring between a cange in te inut signal and te related reaction of te outut. Tis leads to te system model sown in Figure. However, te exact measurement of te delay time may be difficult, esecially in te resence of noise []. Moreover, since in our case te system structure is assumed unknown, te coice of te model s structure is not evident. In tis aer, te determination of te delayed samle oints tat are needed for fault tye discrimination was acieved by comaring te estimation error acieved by a large number of ossible neural network arcitectures. Te maximum number of samles er variable k was increased, starting from k=. For eac k, a large number of ossible combinations were evaluated by te resective neural network arcitectures and k was increased until te minimal estimation error ε min (k) is acieved. It as been sown [] tat tese metods may lead to local minima, wic means, tat te obtained model structure is satisfactory for te identification data, but does not describe te system s beavior correctly in oter nominal oerational modes. In te neural network arcitecture roosed in tis aer, te risk of coosing suc a local model was minimized by model validation [] for sets of measurements not used in te training set. Moreover, model cecking for new data sets, after inducing te same faults, served as measure of te neural network erformance [,4].
4 4 4 45 (a)normal oeration (b) fault tye 4 4 4 9 (c) fault tye (d) fault tye 4 4 5 5 4 (e) fault tye 4 (f) fault tye 5 4 4 5 (g) fault tye 6 () fault tye 7 Water level Tank ( ): Horizontal axes: samling time (s) Water level Tank ( ): Vertical axes: levels (cm) Water temerature Tank (T ): Temeratures ( o C) Water temerature Tank (T ): Water temerature Tank (T ): (diagrams not to scale) Figure : a) normal oeration b-) fault tyes
inut inut z - z - z - z - inut z - Neural network z - Arcitecture z - z - inut k z - z - z - z - System outut Figure : Identifying te network structure III.B. Neural network design In real-time systems, one cannot wait for a large number of delayed samles in order to rovide an accurate fault rediction, since fault detection must be acieved as soon as ossible (and trigger te roer alarms). In tis aer, te number of revious samles for eac of te 5 inut arameters (water level in tank, tank, and water temeratures in tanks,,, resectively) was ket witin te range n- to n- (moreover, tis limits someow te enormous number of ossible inut combinations, wic is still, very ig). By reetitive design, training, verification and validation of a large number of neural network arcitectures it was revealed tat te delays in te temerature signals did not lay significant role in fault discrimination, wereas, te temerature signals temselves, are uite imortant. Tis was as exected, since te temerature signals do not exibit significant gradient canges in normal oeration, excet for te initial warming u ase, as it is sown in Figure (a). In faulty conditions, teir beavior is also distinctive. For te water level signals, it was exected tat similar samles sould be eually imortant for bot signals, owing to teir ualitatively symmetrical (out of ase) beavior deicted in Figure. It was found tat altoug te combinations of delayed samles for eac water level signal (n-, n-5, for bot signals) resulted in small classification errors in te validation set, tey were not very successful in te rocessing of te cecking set (a data set derived from subseuent oeration of te system). Furter design and training of neural networks revealed te fact tat by using te n-, n-5 and n-8 samles for bot l and l, te training set, validation set and cecking set fault classification errors can be minimized. A standard accelerated backroagation training algoritm wit momentum was used. Tus, te minimization of te sum suared error [,4] for te elementary multilayered arcitecture sown in Figure 4 is acieved according to: e=d-y were e is te error and d te desired outut. f,g are te neuron activation function and its derivative. σ,σ,σ are te weigted sums of te inuts for eac neuron. e e = e w ( ) ( ) e w ij w ij y = w = w = x x σ w w w n v σ w w w σ n w v = = g n v ( σ ) g( σ ) vx Figure 4: Elementary two-layered feed forward neural network y (6)
Te caracteristics of te best two-layered, feedforward neural network arcitecture obtained after te large number of inut combinations are sown on Table. A re-rocessing ste of inut /outut normalization receded te training ase, normalizing inut/outut vectors for zero mean and standard deviation of one [4]. Te samles were almost evenly distributed among te different fault tyes (including te normal oeration) and outut neurons were used as a binary classification label for eac of te fault tyes and normal oeration. Te number of neurons in te idden layer was cosen by a reetitive - direct searc algoritm imlemented to coose te network structure wit te best erformance. Te biolar sigmoid activation function (denoted as tansig in MatLab) was used bot for te idden and outut layers. It can be exressed as: f = (7) ( + ex( σ )) Table : Neural Network caracteristics Inuts:,, T,T,T, delayed samles :n-, n-5, n-8 delayed samles :n-, n-5, n-8 Number of idden layer neurons: 5 Outut neurons: Number of Training set samles: 44 Number of Validation set samles: 44 Number of Cecking set samles: 5 Validation set success rate: 99% Cecking set success rate: 99% Te validation vectors were used to sto training early since furter training on te rimary vectors will urt generalization to te validation vectors. Tus, te roosed neural network arcitecture is caable of discriminating between te different tyes of faults sown in Figure. After comleting te training and validation ases, te comutational seed of te roosed neural network is uite fast since only feed forward calculations are emloyed. Terefore, faults can be detected in real-time and tis is a significant advantage since te fault restoration rocedures can begin immediately. Te comutational cost related to fault detection by using ig order correlation functions, multisectra density functions and te Fourier Transform [,5], is muc iger. Te roosed metod avoids comlex matrix inversion roblems met in te design of fuzzy relational models for fault detection []. Moreover, altoug tere exists some overla of fault features (e.g. fault tye 5 and fault tye 6, for te interval during wic bot water levels are almost at minimum values, as sown in Figure ), te use of delayed samles manages to rovide enoug information for fault discrimination, in contrast to [7] were feature overla is not comletely resolved. Tus, te roosed neural network can be used for early detection and alarm generation in case te system deviates from normal oeration. Furtermore, it is caable of alarm interretation i.e., deciding wic fault is resent among a re-defined fault set. IV. CONCLUSIONS A ysical system is secifically at risk if it is not monitored, if some of its comonents need regular maintenance, if some of its comonents are insufficiently known, regarding teir dynamical beavior and ageing rocess, or its conditions of use are not controlled and can widely fluctuate. Tis aer resented te design, training, verification and validation of a neural network arcitecture caable of early fault detection and fault isolation in a tyical tree tank system i.e., deciding wic fault is resent among a re-defined fault set. Faulty conditions were deliberately induced to te system and its beavior was monitored by aroriate sensors. In terms of system arameter identification, a number of delayed samles were reuired in order to built a neural network model tat minimizes bot training and validation errors. Te roosed arcitecture comares favorably to oter metods in terms of comlexity and seed. 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