Actuated Hydraulic System Fault Detection: A Fuzzy Logic Approach
Engineering Letters, 18:1, EL 18 1 08Actuated Hydraulic System Fault Detection: A FuzzyLogic ApproachSeraphin C. Abou, Manali Kulkarni, and Marian StachowiczAbstract — Accurate detection of fault in a hydraulic systemis a crucial and equally challenging task. A fuzzy logic topologyis developed for the diagnosis of simulated faults in hydraulicpower systems. The method proposed is a combination ofanalytical and fuzzy logic approach. Residuals generated bynonlinear observer are evaluated using fuzzy logic. The faultseverity of the system is evaluated based on the membershipfunctions and rule base developed by the fuzzy logic system.This paper demonstrates the use of fuzzy logic as an extension toanalytical system to enhance the overall performance of thesystem. The decision of whether ‘a fault has occurred or not?’ isupgraded to ‘what is the severity of that fault?’ at the output.Simulation results showed that fuzzy logic is more sensitive andinformative regarding the fault condition, and less sensitive touncertainties and disturbances.Index Terms — Fault detection, fault severity, fuzzy logic,hydraulic system.Since proportional valves have less precise manufacturingtolerances, they suffer from performance degradation. Thelarger tolerances on spool geometry result in responsenonlinearities, especially in the vicinity of neutral spoolposition. Proportional valves lack the smooth flow propertiesof “critical center” valves, a condition closely approximatedby servo valves at the expense of high machining cost. As aresult, small changes in spool geometry (in terms of lapping)may have large effects on the hydraulic system dynamics [4].Especially, a closed-center spool (overlapped) of proportionalvalve, which usually provides the motion of the actuator in aproportional hydraulic system, may result in the steady stateerror because of its dead-zones characteristics in flow gain[4]. Fig.1 illustrates the characteristics of proportional valve.Continuous online monitoring of fault in hydraulic systembecomes increasingly important day-by-day.Q (l / min)g (u )QAI. INTRODUCTIONHydraulic systems are very commonly used in industry.Like any other system these systems too are prone todifferent types of faults. Proportional valves are much lessexpensive in hydraulic control applications; they are moresuitable for industrial environments. Since proportionalvalves do not contain sensitive, precision components, theyoffer various advantages over servo valves because they areless prone to malfunction due to fluid contamination.However, these advantages are offset by their nonlinearresponse characteristics.Manuscript received July 26, 2009. The financial support of theUniversity of Minnesota, Grant In Aid FY 2008 is gratefully acknowledgedhere.Seraphin Abou is Assistant Professor in Mechanical and IndustrialEngineering Department, University of Minnesota, Duluth, 1305 Ordean Ct,Duluth, MN 55812, USA., Phone: 218-726-8250; Fax: 218-726-8596(email: sabou@d.umn.edu).Manali Kulkarni is a research assistant in Mechanical and IndustrialEngineering Department; e-mail: kulka056@d.umn.edu.Marian Stachowicz is Professor in Electrical and Computer EngineeringDepartment, University of Minnesota, Duluth, mstachow@d.umn.edua bbuQBFig.1 Characteristics of 4/3 closed-center proportional valveThe characteristics of the proportional valve with deadzones, g (u ) is described as follow, fig.1:if u b a (u b) g (u ) 0if b u b(1) a (u b)if u b where b, a 0 . a represents the slope of the responseoutside the dead-zone, while the width of the dead-zoneequals 2b.Remarkable efforts have been devoted to developcontrollers. However, PID controllers are not robust to the(Advance online publication: 1 February 2010)
Engineering Letters, 18:1, EL 18 1 08parameter variation to the plants being controlled. Moreover,it takes time for the automatically self tuned PID controllersto online adapt themselves up to their final stable state.The fault detection problem can be solved using differentapproaches like Wald’s Sequential Test, as in [4] which is aconventional approach or using innovative approaches likegenetic algorithms as in [12], neural networks as in [7], [8],fuzzy logic as in [6] etc. each having its own advantages anddisadvantages.Human experts play central roles in troubleshooting orfault analysis. In power systems, it is required to diagnoseequipment malfunctions as well as disturbances. Theinformation available to perform equipment malfunctiondiagnosis is most of the time incomplete. In addition, theconditions that induce faults may change with time.Subjective conjectures based on experience are necessary.Accordingly, the expert systems approach has proved to beuseful. As stated previously, fuzzy theory can lend itself tothe representation of knowledge and the building of an expertsystem. In this paper we used fuzzy logic to detect theseverity of fault at the output.The concept of fuzzy logic was first introduced in 1964 byProfessor Lofti Zadeh in [13] which represented thevagueness of human concepts in terms of linguistic variables.After the introduction of fuzzy sets, their applications tosolve real world problems were concentrated [2], [11].Reference [1] concentrates on robust fault detection on anaircraft flight control system. A model based fault diagnosismethod for an industrial robot is proposed in [10]. Residualsare calculated by the observer using a dynamic robot modeland later evaluated using fuzzy logic.In this paper we demonstrate a similar model basedapproach for evaluating of severity of fault in the hydraulicactuator using fixed threshold approach, [5]. The objectiveknowledge on the system is represented by mathematicalmodeling (calculating the residuals using nonlinear observer),[4] while the subjective knowledge is represented using fuzzylogic (fuzzy rules and membership functions).II. SYSTEM UNDER CONSIDERATIONThe schematic of the hydraulic system underconsideration, the mathematical model and the design ofnonlinear observer can be found in [4]. General nonlineardynamical systems can be described as follows: f ( x, y, u , t ) A0 x Bh( x) ( x) T y C x(5)where h( x) l ( x) ( x )u (t T ) ( x) ; , and lare unknown smooth functions. x ( x1 , x2 , x3 ,., xn ) is thestate vector, x R , u and y R ; znoutput vector; yˆ is the observer ( x) represents the uncertainty in the systemdynamics that may include parameter perturbations, externaldisturbances, noise, etc. All long this study, we considerabrupt fault at time T. As a result, (t T ) is the timeprofile of failures as shown in fig. 2. (t T )1 1 for t T 0 otherwise (t T ) 0.80.60.40.2000.1T0.40.60.81time [s]Fig.2 Function (t T ) in (2) ( x) is another function which represent a failure in thesystem. Mathematical description of the nonlinear observeras follows: xˆ Ax Bhˆ( x) K ( y Cxˆ )(3) T z yˆ C xˆwhere hˆ( x f ) lˆ( x f ) ˆ ( x f )u ( x f ) ; K isthe observer gain matrix which is selected such asA A0 KC T is strictly Hurwitz matrix.In the discrete time system, consider from (2) and (3)e(k ) y (k ) z (k ) . The actual state of the system y(k) isknown through the sensors. The residual e(k) is calculated asfollows:e( k ) M p y ( k ) M p z ( k )(4)Mp is an identity matrix of size m n , M p I 4 1It is perceived that the performance of the actuated systemis selected based on four parameters having a range of valuefrom zero (0) to one (1). The elements of the state vector z [v Pi Po xsp] T are: velocity x v , input pressure Pi, outputpressure Po and xsp spool displacement. The residual of thesefour can be measured. In this paper we have concentrated onthe velocity residual and the identity matrix Mp [1 0 0 0].(Advance online publication: 1 February 2010)
Engineering Letters, 18:1, EL 18 1 08III. ROLE OF FUZZY LOGICFrom the point of view of human–machine cooperation, itis desirable that faults classification process would beinterpretable by humans in such a way that experts could beable to evaluate easily the classifier solution. Another interestof an intelligent interface lies in the implementation of such asystem in a control room. Operators have to be informed veryquickly if a fault is occurring. They have to understand whatexactly the process situation is, in order to make the rightcounteraction if possible or to stop the system if necessary.For instance, as shown in fig.3, the fuzzification vectorcan be assigned to an index of a color map, representing acolor code, by defuzzification.Figure 3depicts the overall architecture of the hydraulicsystem fault detection where u(t) is the control input. Themapping of the inputs to the outputs for the fuzzy system isin part characterized by a set of condition action rules (IfThen) form:If premise then consequent(7)The inputs of the fuzzy system are associated with thepremise, and the outputs are associated with the consequent.y (k )u (k )e(k ) e( k )z (k )Rule-baseTheoretically, these residuals should be zero under no faultcondition. However, in practical context, due to noise,inexact mathematical modeling and system nonlinearity, thisresidual is never zero even under no fault condition.Reference [4] uses a conventional method called Wald’sSequential Test to detect fault. In this method, the cumulativeresidual error is calculated over a period of time and fault isdetected using the fixed threshold concept.This conventional method has some disadvantages. Avalue just below the threshold is not considered as a faultwhile some value just above the threshold will be consideredas a fault. This can also lead to missing alarms and falsetriggers. This information could be potentially misguiding tothe operators working on the hydraulic system. This is thedrawback of binary logic. The conventional method is rigidand does not consider a smooth transition between the faultyand the no fault condition. The probability assignmentprocedure is heuristic and depends on the number ofZeros/Ones in the failure signature. This does not give anyinformation about the fault in between the thresholds. Inorder to take care of this condition we try to replace thisbinary logic by multi-valued one using fuzzy logic.Evaluating these residuals using fuzzy logic replaces theyes/no decision of fault by the severity of fault at the output.Fig. 3 The structure of Fuzzy fault diagnosisAs already seen, the difference between the expected statez(k) and the actual state of the system y(k) gives the residuale(k). The value of residual is added over a period of timewhich gives the cumulative residual e(k). This value issubtracted from the predicted threshold and is calledcumulative residual difference. The lower the value of thiscumulative residual difference, higher is the fault severity,indicating that the cumulative residual is approaching thethreshold and vice versa. The threshold is determined throughobservations. It will vary depending upon the fault toleranceof the application in which the hydraulic system is used.Even if there is no fault, the modeling errors or noise driveseveral residuals beyond their threshold. This is usuallyindicated by all suspect residuals being weak. The residual isbounded between the upper and the lower threshold. As soonas it approaches these thresholds, the fault severity increases.Thus, the residual and the cumulative residual difference aregiven as two inputs to the fuzzy logic controller. Based onthese two inputs, the controller decides the fault severity atthe output.One of the equations of fuzzy equality can be written as:nS A, B min i 1A(i ), B (i ) n n max A (i ), B (i ) i 1 i 1 (6)where n is the dimension number of the discretespace, A is the membership function of fuzzy set A, B is themembership function of fuzzy set B.Suppose that a fuzzy rule set to be detected F representsthe current working class of the actuated hydraulic system,and the other fuzzy reference rule set Fi stands for oneworking class of the system. Since both the fuzzy reference(Advance online publication: 1 February 2010)
Engineering Letters, 18:1, EL 18 1 08rule sets and fuzzy rule set to be detected have the samehypersphere subspaces, the equation (6) can be used for theircontrasts. As a result, in this study, the approximatemeasurement of the fuzzy reference rule set Fi can beexpressed by:si ( k ) ei ( k )ei(8)where ei(k) is the ith residual; si(k) is the residual-tothreshold ratio.Obviously si(k) is greater than or equal to 1 if the test isfired on the residual and si(k) is less than 1 if it did not.Fault isolation thresholds are very important parameters;their values are also decided by the statistical analysis of thefault credit degrees (9). As for unknown fault type,consulting fault isolation thresholds are selected upon ourknowledge on the system. The detection results of the normaldata of the space propulsion system are shown in fig. 5.Because normal credit degree does not exceed the threshold,the detection results are that no fault exists, and workingconditions are normal.0.2Residual (m/s)Upper ThresholdLower Threshold0.150.1IV. DESIGN OF FUZZY LOGIC CONTROLLER0.050On the one hand, note that fuzzy reference rule setsimpossibly cover the whole plant faults; on the other hand,the fuzzy rule set to be detected may bring forward theundefined symptoms which can’t be distinguished from fuzzyreference rule sets, as shown in fig. 3. How can we solve thisproblem?-0.05-0.1-0.15-0.202004006008001000Fig 5. Graph showing ‘Residual’ along with the upper and lower thresholdsvs ‘number of observations’To solve this problem, we include in the evaluationprocedure an additional credit degree of unknown classeswhich is expressed as follows:302520n e 1 max(S A, B )15ii 110Obviously, 0 S A, B 1(9)50A.Inputs-50Fig. 4 illustrates the actual and the estimate velocities. Thedifference is due to the error introduced in the actual systemby adding random noise to the velocity during simulation.Observed Shaft VelocityActual Shaft Velocity0.34006008001000Fig 6. Graph showing the cumulative residual and the cumulative residualdifference along with the upper and lower thresholds vs the number ofobservationsB.0.35200Membership FunctionsThe first input which is residual is divided into 7membership functions namely, Big Negative (BN),Negative(N), Small Negative(SN), Zero(Z), SmallPositive(SP), Positive(P) and Big Positive(BP) shown below.0.250.20.150.10.05000.20.40.60.81Fig. 4 Graph showing Actual velocity and observed velocity vs timeThe plot of residual, cumulative residual, cumulativeresidual difference along with the thresholds can be seen inthe fig. 5 and fig. 6. As seen earlier, the residual and thecumulative residual difference are the two inputs to the fuzzylogic controller.Fig 7. Membership functions for the first input 'Residual'(Advance online publication: 1 February 2010)
Engineering Letters, 18:1, EL 18 1 08severity is the highest (F6). Similarly, if the residual is Zero(Z) and the cumulative residual difference is Positive (Pos)then the output fault severity is the lowest (F0).TABLE І: RULE BASED INFERENCEResidual ‐ Cumulative ResidualDifference ‐ Similarly, we developed 5 membership functions for thesecond input which is cumulative residual difference. Theyare Large Negative(LNeg), Medium Negative(MNeg), SmallNegative(SNeg), Zero(Zero) and Positive(POS) as seen in thefollowing fig.D.Fig 8. Membership functions for the second input 'Cumulative ResidualDifference’As already seen there are 4 parameters which can be usedto calculate the residuals. Among them the velocity is themost concerned parameter in this case of study. Hence, thevelocity residual is selected to determine the fault severity atthe output.The membership functions for the output i.e. fault severityare F0, F1, F2, F3, F4, F5 and F6 where F0 represents thelowest fault severity and F6 represents the highest faultseverity. The shapes of the membership functions which aretriangular and trapezoidal were selected based on the simpleguidelines suggested in [3]. This can be seen in the followingfig.Fig 9. Membership functions for the output 'Fault Severity'C.Rule Based InferenceInference rules were developed which relate the two inputsto the output. They are summarized in the Table I. As seenfrom the table, there are in all 35 rules. For example, if theresidual is Big Positive (BP) and the cumulative residualdifference is Large Negative (LNeg) then the output 5F4F5F6F6DefuzzificationAfter converting the crisp information into fuzzy the laststep is to reverse that. Converting the fuzzy information tocrisp is known as defuzzification. The center of area/centroidmethod was used to defuzzify these sets which can berepresented mathematically as follows:Defuzzified value fi ( fi ) ( fi )(10)Where fi is the fault severity at the output and µ(fi) is theoutput membership function.E.Rule ViewerThe rules can also be seen from the rule viewer using thefuzzy logic toolbox in MATLAB software. When the residualis 0.01, it is far away from both the upper and lowerthresholds (almost at the center) and hence, has lower faultseverity. Also, the cumulative residual difference is 9 whichmeans the difference between the actual value of cumulativeresidual and threshold is high i.e. cumulative residual is faraway from the threshold. Hence, the fault severity should below. A combination of these values of residual andcumulative residual gives fault severity percentage of 9.96%which is low. Similarly, when the residual is 0.089 itindicates that it is very close to the threshold. A cumulativeresidual difference of -9 indicates that the threshold has beenalready crossed by the cumulative residual (hence it isnegative). Both of these conditions lead to a very high faultseverity of 98.4%. This can be seen with the help of the ruleviewer facility in the fuzzy logic toolbox. These examples areshown in fig. 10 and fig. 11 respectively with the help of ruleviewer.(Advance online publication: 1 February 2010)
Engineering Letters, 18:1, EL 18 1 08Fig. 11 Test results for high fault severityFig. 10 Test Results for low fault severityFig 12. MATLAB/SIMULINK mode(Advance online publication: 1 February 2010)
Engineering Letters, 18:1, EL 18 1 08V. SIMULATIONThis simulation was carried out in MATLABSIMULINK using fuzzy logic controller from the fuzzylogic toolbox as shown in fig. 12. The upper subsystemrepresents the actual system (actual state of the hydraulicsystem) and the lower subsystem is the nonlinear observer(which predicts the state of the system). The SIMULINKdiagram is the implementation of the block diagram shownin fig. 1. The simulation is carried out for a unit step input.Fault is introduced in the actual system by adding noise tothe velocity in the actual system and different faultseverities are tested at the output.VI. CONCLUSIONThe main goal here was to provide maintenance engineerscontinuous online information about the systems healthwhich would guide them to make decisions. This informationneeds to be given at an incipient stage in order to avoid anyfurther serious damage to the system. This also helps inavoiding false triggers and missing alarms. This work showsthat fuzzy logic when used in combination with analyticalmethods like non linear observer can enhance the output. Itacts as a good extension to upgrade the systemREFERENCES[1][2][3][4][5][6][7][8][9]With the fuzzy match results between the fuzzy rule set tobe detected and fuzzy reference rule sets, diagnosis logicmodule automatically judged whether the plant workingcondition is normal or not. Moreover while fuzzy rule setsare set up, the fuzzy reference rule set generated is used forrepresenting the normal working condition, which issupposed to be the first fuzzy reference rule set.[10]Simulation results showed what we all know: whateverfault type the plant generates, its symptoms always departfrom the characteristics of the fuzzy reference rule setstanding for the normal working condition. And thus, withthe credit degree representing the normal working, we judgedwhether the plant working condition is normal, further obtainthe fault degree. This study helped to assure that the plantfault existed and to report the system conditions. Future workwill be developed to identify the fault type and predict theequipment remaining life.[13][11][12]Curry T., Collins E.G.Jr., Selekwa, M., “Robust fault detection usingrobust l1 estimation and fuzzy logic,” IEEE, vol. 2, June 2001, pp.1753 - 1758.Jerry M. Mendel, “Fuzzy Logic Systems for Engineering: ATutorial,” IEEE, vol. 83, issue 3, Mar 1995, pp 345- 377.John Yen, and Reza Langari, “Fuzzy Logic: Intelligence, control andinformation,” Prentice Hall, 1999, pp. 22-27.Khan H., Seraphin C. Abou, and Sepehri N., “Nonlinear ObserverBased Fault detection Technique for Electro hydraulic Servopositioning Systems,” Elsevier Science Direct, Mechatronics, vol.15,issue 9, Nov 2005, pp. 1037-1059.Manali K., S. Chally Abou, and Marian S. “Fault Detection inHydraulic System Using Fuzzy Logic”. Proceedings of the WorldCongress on Engineering and Computer Science 2009 Vol. II;WCECS 2009, October 20-22, 2009, San Francisco, USAPedro Vicente, Jover Rodriguez, and Antero Arkkio, “Detection ofstator winding fault in induction motor using fuzzy logic,” ElsevierScience Direct, Applied Soft Computing, vol. 8, issue 2, Mar 2007,pp. 1112-1120.Qian-jin Guo, Hai-bin Yu, and Ai-dong Xu, “Modified Morlet waveletneural networks for fault detection,” International Conference onControl and Automation (ICCA 2005), vol 2, June 2005, pp. 12091214.Sheng Qiang, Gao X. Z., and Xianyi Zhuang,, “State-of-the-art in SoftComputing-based-Motor Fault Diagnosis,” IEEE, vol. 2, June 2003,pp 1381-1386.Shing Chiang Tan, and Chee Peng Lim, “Application of an adaptiveneural network with symbolic rule extraction to fault detection anddiagnosis in a power generation plant,” IEEE Transaction on EnergyConversion, vol 19, issue 2, June 2004, pp.369-377.Shneider H., P.M. Frank, “Observer-Based Supervision and FaultDetection in Robots,” IEEE, vol. 4, issue. 3, May 1996, pp 274-282.Stephen Chiu, J. John Cheng, Charles Sitter and Elik Fooks,“Perspectives on the Industrial Application of Intelligent Control,”IEEE Proceedings of the 34th Conference on Decision & Control, vol.1, Dec 1995.Xuewu Dai, Guangyuan Liu, and Zhengji Long, “Discrete-timeRobust Fault Detection Observer design: A Genetic algorithmapproach,” IEEE Proceedings of the 7th World Congress on IntelligentControl and Automation, June 2008.Zadeh L.A., “Fuzzy Sets,” Information and control, vol.8, 1965, pp.338-353.ACKNOWLEDGMENTThe present work has been performed in the scope of theactivities of Grant In Aid project. The financial support of theUniversity of Minnesota, Grant In Aid FY 2008 is gratefullyacknowledged.(Advance online publication: 1 February 2010)
Accordingly, the expert systems approach has proved to be useful. As stated previously, fuzzy theory can lend itself to the representation of knowledge and the building of an expert system. In this paper we used fuzzy logic to detect the severity of fault at the output. The concept of fuzzy logic was first introduced in 1964 by
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illustrated in Figure 3. This is a fault occurring with phase A to ground fault at 8 km measured from the sending bus as depicted in Figure 1. The fault signals generated using ATP/EMTP are interfaced to the MATLAB for the fault detection algorithm. (a) Sending end (b) Receiving end Figure 3. Example of ATP/EMTP simulated fault signals for AG fault
CDS G3 Fault List (Numerical Order) Fault codes may be classified as sticky or not sticky: Type of fault Method to clear Not sticky Clears immediately after the fault is resolved Sticky Requires a key cycle (off and on) after the fault is resolved to clear. CDS G3 Fault Tables 90-8M0086113 SEPTEMBER 2013 Page 2G-3
Capacitors 5 – 6 Fault Finding & Testing Diodes,Varistors, EMC capacitors & Recifiers 7 – 10 Fault Finding & Testing Rotors 11 – 12 Fault Finding & Testing Stators 13 – 14 Fault Finding & Testing DC Welders 15 – 20 Fault Finding & Testing 3 Phase Alternators 21 – 26 Fault Finding & Testing
In this paper, the calculation of double line to ground fault on 66/33 kV transmission line is emphasized. Figure 3. Double-Line-to-Ground Fault 2.4 Three-Phase Fault In this case, falling tower, failure of equipment or . ground fault, fault current on phase a is I a 0. Fault voltages at phase b and c are: V b .
S0932.9 Hydraulic Reservoirs . S0932.10 Hydraulic Oil Filters . S0932.11 Hydraulic Cylinders . S0932.12 Hydraulic Pumps . S0932.13 Hydraulic Valves and Controls . S0932.14 Hydraulic Piping Supports . S0932.14 Hydraulic System Drawings . S0932.16 Hydraulic System Commissioning
Hydraulic Systems - Components and more Page 7 Contents Chapter 1: The hydraulic system 11 Hydraulic elements 12 Hydraulic fluid 13 Materials 14 Physical design 14 Chapter 2: The hydraulic cylinder 15 Classification of hydraulic cylinders 15 Type of effect 15 Working area 16 Series and working pressure 18 What's important? 21 Cylinder construction 25 Design 26
