- Email: [email protected]
A new fault tolerant control approach for the three-tank system using data mining
Computers and Electrical Engineering 38 (2012) 1627–1635
Contents lists available at SciVerse ScienceDirect
Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng
A new fault tolerant control approach for the three-tank system using data mining q Umut Altinisik a,⇑, Mehmet Yildirim b a b
Department of Informatics, Kocaeli University, Umuttepe, 41380 Kocaeli, Turkey Networked Control Systems Laboratory, Kocaeli University, Umuttepe, 41380 Kocaeli, Turkey
a r t i c l e
i n f o
Article history: Received 8 September 2011 Received in revised form 20 June 2012 Accepted 21 June 2012 Available online 16 July 2012
a b s t r a c t In this study, we propose a knowledge-based approach for detection and isolation of sensor faults in fault tolerant control (FTC) of the three-tank system. Farthest first traversal algorithm (FFTA) of data mining is used first-time for the classification of faults in an FTC system. The sliding window is used to detect signal changes, which contain possible transients due to faults. The variance-changing ratio is calculated to extract the features of the sensor signal in each window. Then, FFTA is utilized for the isolation of sensor faults. In order to demonstrate the efficiency of the proposed method, seven types of artificial faults were applied to closed-loop fault tolerant control system in certain periods. All faults were detected and isolated immediately after they occurred. Moreover, fault isolation was achieved when multiple faults occurred simultaneously. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The capability of a system to carry out its operation correctly even in the occurrence of faults is called fault tolerance [1]. When the complexity of technical process increases, the probability of fault occurrence also increases and therefore, reliability and safety become important system requirements. Occurrences of faults cause to decrease in performance of closed-loop control and may reduce the profits. Thus, some methods have been developed for the design of sophisticated fault tolerant control (FTC) systems. An FTC system contains a fault detection and isolation (FDI) and a function that cause predefined corrective actions [2,3]. According to Zhang and Qin [4] fast counteraction to the fault is as important as detection and isolation of the fault. Faulttolerant control has been developed to keep the system stable, regardless of the occurrence of a fault. The reason of designing a fault detection is to determine whether a fault occurs in the process by monitoring the significant changes in the process states of the usual closed-loop action [5]. Fault tolerance is fundamentally interested with identification of improper action of process components, which are actuators and sensors, and abnormal drifts in parameters of the process [6]. In order to keep the performance of the system stable, after a process fault is detected and isolated, a controller that can compensate for the faults should be developed. FTC systems have been designed by means of model-based methods for several decades. The generalized likelihood ratio (GLR) and the model predictive control (MPC) based fault-tolerant schemes were used in control of linear processes [7,8] and for nonlinear processes [9,10]. The model-based FDI depends mainly on a process model. Model-based FDI techniques can be properly established if a process model has given [11]; however, when the model is not completely known or when the process is nonlinear, these methods may be unsuccessful.
q
Reviews processed and approved for publication by Editor-in-Chief Dr. Manu Malek.
⇑ Corresponding author. Tel.: +90 262 303 13 01; fax: +90 262 303 13 02.
E-mail addresses: [email protected] (U. Altinisik), [email protected] (M. Yildirim). 0045-7906/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compeleceng.2012.06.011
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In [10], Deshpande et al. emphasized the disadvantages of the model-based FDI as follows: The prediction model is constructed before the realization of nonlinear MPC. On the other hand, as time goes on, slow deviations in unmeasured disturbances and process parameters may give rise to serious unconformity between model and process actions. Moreover, nonlinear MPC methods are generally designed with assuming that actuators and sensors are fault-free. Some actuators and sensors may fail during operation and can give rise to a severe model-plant unconformity or instability. In order to overcome the problems of model-based FDI, new methods, which were based on knowledge, have been proposed in recent years. In order to estimate the process behavior, these methods use the archived process data. Knowledgebased techniques rely on extracting information only from the historical process data without any requirement to precisely analytical model. In the knowledge-based case, normal and abnormal operating conditions of a process, which are namely called features, are stored in the knowledge base. Features are extracted offline from previously taken process data, before the FTC is in use. While the FTC is being served, real-time process data are measured, analyzed and the instantaneous (online) features of them are extracted. Then, online features of process data are compared with the offline features in the knowledge base, in order to identify whether a fault occurs or not. One major advantage of these knowledge-based FDI methods is their excellent ability for isolating and classifying the faults [12]. Usually, the most frequently faced faults are sensor and actuator faults in process control. These faults can lead to decrease in the closed-loop performance and may have adverse effects on productivity and safety of the system if these faults are not timely detected and counteracted [7]. Therefore, it is necessary to develop FTC systems, which can compensate sensor and actuator faults. In this study, a knowledge-based method is proposed for detection and isolation of sensor faults in fault tolerant control of the three-tank system. It is a scheme that combines the farthest first traversal algorithm (FFTA) of data mining with statistical analysis techniques. The three-tank system is used as a benchmark process and artificial faults are applied to level sensors of the system. The sliding window is applied to detect signal variations, including possible fault-induced transients. In order to explore the features of a sensor signal, the variance-changing ratio is calculated in the sliding window. The FFTA runs for generating the knowledge base and tries to match the features of the real-time sensor signal to a known fault pattern in the knowledge base. 2. Design of fault detection and isolation scheme Controlling the liquid level in a tank system is a fundamental problem in process control. There are experimental benchmarks of single, couple, triple and quadruple tank systems. In this section, the three-tank system is demonstrated for a stable closed-loop control process even in the presence of sensor faults. It contains three interconnected water tanks, two pumps and associated valves as shown in Fig. 1. The inputs of the system are the currents supplied to the control valves to manipulate the flow rate (Qin,1 and Qin,3) of the pumps. The outputs of the system are the water level measurements of the tanks. The aim is to keep the level of tank-2 (H2) stable by controlling the levels of tank-1 (H1) and tank-3 (H3), which interact with the tank-2. The three-tank system uses the balance equations below [13]:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q in;1 dH1 k1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi k12 sgnðH1 ðtÞ H2 ðtÞÞ gjH1 ðtÞ H2 ðtÞj þ ¼ gH1 ðtÞ dt S1 S1 S1
ð1Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k23 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dH2 k2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi k12 sgnðH1 ðtÞ H2 ðtÞÞ gjH1 ðtÞ H2 ðtÞj sgnðH2 ðtÞ H3 ðtÞÞ gjH2 ðtÞ H3 ðtÞj gH2 ðtÞ þ ¼ dt S2 S2 S2
ð2Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q in;3 dH3 k3 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi k23 sgnðH2 ðtÞ H3 ðtÞÞ gjH2 ðtÞ H3 ðtÞj þ gH3 ðtÞ þ ¼ dt S3 S3 S3
ð3Þ
k1 ¼
q R1
;
k2 ¼
q R2
;
k3 ¼
q R3
;
k12 ¼
q R12
;
k23 ¼
q R23
ð4Þ
The variables used in the tank system are given below: S1: Tank-1 base area (8:107 103 m2 ) S2: Tank-2 base area (4:560 103 m2 ) S3: Tank-3 base area (8:107 103 m2 ) q: Liquid density (for water, 1 103 kg/m3) Hi: Tank i liquid level (m) Qin,i: The fluid flow of inlet rate from the Pump i (m3/sn) Qi,0: The fluid flow of outlet rate from the Tank i (m3/sn) Qi,j: Liquid flow rate between Tank i and j (m3/sn) Ri: Drainage resistance of valve i (kg/m5) Ri,j: Flow resistance between the tanks i and j (kg/m5). In the three-tank system, flow rates of the inlets Qin,1 and Qin,3 are same, flow rates of the outlets Q10 and Q30 are same, and the tank-2 liquid level (H2) is kept at the desired level by using a controller. The simulations were carried out by using
U. Altinisik, M. Yildirim / Computers and Electrical Engineering 38 (2012) 1627–1635
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Fig. 1. Structure of experimental three-tank system.
Fig. 2. The FDI system structure.
a PID controller which controls the variables Qin,1 and Qin,3. The transfer function of the PID controller is given in below equation:
CðsÞ ¼ 4:8 þ
0:02 þ 0:5 s: s
ð5Þ
The structure of the FTC system used in this study is shown in Fig. 2. In the figure, the FDI section consists of feature extraction, clustering and knowledge base modules. In the feature extraction module, statistical techniques, which are sliding window and variance-changing ratio, are used for analysis of sensor signals to detect deviations from regular conditions. The FFTA classifies the variance changing-ratios of normal and particular faulty conditions, and then records them into the knowledge base. The knowledge base is initially produced by FFTA according to predefined sensor faults. The proposed FDI system is explained in the following sections, in detail.
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2.1. Feature extraction Faults in processes generally lead to changes in the process responses. On the other hand, a usual operation of the process (e.g. giving a new set-point) can result in same changes. By observing and analyzing the changes in sensory signals, the normal and abnormal responses of the process due to a fault can be identified. First of all, the sliding window is used to detect signal changes, which contain possible transients due to faults. Measured sensor signals (samples) are divided into windows and observed if there is any change in signal in that window. As shown in Fig. 3, the sliding window includes two concurrent windows in the same length, called as previous and current windows. The previous window consists of previously collected data, while the current window consists of recently gathered data. The early section in the current window is called as new data zone, that contains the latest samples [14]. The following variance-changing ratio equation is used for the sliding window to bring out the features of the signal
r¼
varðcurrent windowÞ varðprev ious windowÞ : varðprev ious windowÞ þ e
ð6Þ
Here var() is the signal variance. This equation is used to detect the variations in the sensor signal due to a fault. Moreover, the variance-changing ratio is useful in eliminating the system noise [12]. If there is not any fault, no change will be seen in the signal, variances of the previous and the current windows will be the same and therefore, the variance-changing ratio will be zero. If any fault occurs on one of the sensors, the variance of the current window for that sensor signal is changed immediately, so does the variance-changing ratio. The windowing and the variance changing ratios are calculated in parallel for all the three of level sensors in the three-tank system. For a particular fault type, simultaneous variance-changing ratios of three sensor signals are caught and recorded in the knowledge base as the feature vector of that fault type. By considering all possible fault types for that system, a knowledge base that consists of feature vectors is constructed. 2.2. Clustering with the farthest first traversal algorithm An ordinary process contains many variables, and these are measured frequently. These measurements may explore beneficial properties related to the status of the process. Knowledge-based methods are often preferred over model-based methods, because it makes an effort to extract lots of information from the historical data, and it does not need any information about the process itself. Mining the historical data, these types of FDI methods examine the patterns in process variables that show whether a fault occurs [15]. Data mining is the exploration and analysis of large amounts of data to explore significant patterns. The patterns obtained by the data mining process vary according to data mining techniques used. These techniques include association rules, clustering and classification methods, etc. In recent years; some of the data mining methods have been used to detect and isolate
Fig. 3. Sliding window technique.
Fig. 4. The FFTA solution for 10-point data set with three cluster centers.
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faults in control systems of a process. The clustering techniques, such as k-means and its variants are the most widely used clustering algorithms. Attempts have also been made to use different clustering algorithms for the task of FDI. In [16], González uses what might be called a farthest-first traversal algorithm for the k-center problem, that of finding an optimal k-clustering under a cost function of maximum cluster radius. On the other hand, FFTA has not ever been used in the FDI. Fig. 4 shows an example of FFTA with a data set of ten points, three of which are thought to be the cluster centers. The idea is to select three cluster center points sequentially, which are the farthest from the previously picked cluster centers (the points 1–3 in the figure). These points are taken as cluster centers and each remaining point is assigned to the closest cluster centers as a member. In this study, FFTA is utilized to design the knowledge base of the FDI system. Feature vectors of normal and all possible faulty conditions are recorded in the knowledge base. A feature vector constituted from simultaneous variance-changing ratios, which are calculated in parallel for level sensors in the three-tank system. A feature vector in the knowledge base may be assumed as a point and FFTA can classify these vectors into clusters as is done in Fig. 4. Since each feature vector has three elements, the point must be represented in a three-dimensional space. In this case, it can be thought that a feature vector contains the coordinates of a point in three-dimension. Therefore, distances between the feature vectors are calculated in three-dimension. The FFTA can determine a predefined number of cluster centers among the knowledge base, initially. These selected cluster centers are the farthest ones to each other, and each one is for the normal condition or for one of the fault types. The knowledge base may contain more fault types than desired; however, FFTA selects the predefined number of major ones. While the FTC is being served, variance-changing ratios are calculated and extracted feature vector is assigned to the closest cluster center, which is one of the previously determined cluster centers by FFTA. Hence, the operating status is classified, and a probable fault is detected and isolated. After the isolation, the predefined action for that fault type must be taken, even though the action does not totally compensate the error. 3. Case study: the three-tank system In the three-tank experiment, the system worked without the FTC for normal and predefined seven faulty conditions to create a knowledge base. Different types of artificial faults [13] were applied on the system; these were additive, multiplicative and stuck type sensor faults as given in the Table 1. Each one of the normal and faulty conditions consisted of 6000 sample data, which were taken from the level sensor signals. After that, these signals were windowed in length of 60 samples size, and the windows were shifted in length of 20 samples size. Feature vectors were extracted by calculating the variance-changing ratios for each windowed level sensor signal. These vectors were classified into different clusters that represent normal or faulty operation by the FFTA. The feature vectors, which mean the coordinate of cluster centers, are given in the Table 2. While the FTC is in use, the system operation is classified according to the similarity between the feature vectors of knowledge base and the feature vectors of instantaneous sensor data. The Euclidean distances between the coordinate of instantaneous data and the normal or faulty conditions are calculated to decide whether a fault has been occurring or
Table 1 Predefined sensor fault types for the three-tank system. ID
Fault type
N Fl F2 F3 F4 F5 F6 F7
Normal Additive 0.1 fault for level sensor 2 Multiplicative 1.1 fault for level sensor 3 Multiplicative 0.8 fault for level sensor 2 Multiplicative 0.7 fault for level sensor 1 Additive 0.1 fault for level sensor 3 Stuck type fault for level sensor 1 Additive +0.05 fault for level sensor 2
Table 2 Coordinates of cluster centers for the predefined fault types. ID
Cluster centers
N Fl F2 F3 F4 F5 F6 F7
0 1573.54 0 639.03 10018.08 0 12141 387.75
0 304.39 0 126.79 0 0 0 76.40
0 1573.54 1116.30 639.03 0 12308.11 0 387.75
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Fig. 5. Occurrence of fault F1 without and with fault tolerance.
Fig. 6. Occurrence of fault F5 without and with fault tolerance.
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not. The isolation is made by checking which cluster center is the closest one to the feature vector of instantaneous sensor data. In control of the three-tank experiment system, the aim is to keep stable the level of tank-2. The set-point is taken as 0.3 m and an artificial fault is applied at the time of 30 s. In case of a deviation in the level of tank-2; the controller acts immediately and brings it again to the set-point by raising or reducing the levels of tank-1 and tank-3. When the FTC is not in use, if a fault occurs on the sensor of tank-2 even though there is not any deviation from the true (actual) level, the controller imagines that a change occurs in the true level, and therefore, it attempts to change the levels of tank-1 and tank-3, so do tank-2 (see Fig. 5a). While the FTC is in use, after the detection and isolation of the fault at tank-2 level sensor, FTC accommodates the levels in a short time of a period (see Fig. 5b). On the other hand, if a fault occurs in level sensor of tank-1 or tank-3, no changes occur in true levels of any tank since the controller does not consider of tank-1 and tank-3 level sensors. Fig. 6a shows the occurrence of F5 of tank-3 without fault tolerance, and Fig. 6b does with fault tolerance. This is an example that the proposed FTC does not declare a false alarm. In order to show the efficiency of the proposed FDI method, all the faults specified in the Table 1 were applied to closedloop fault tolerant control system in certain periods. As shown in the Table 3, each fault was detected and isolated in 0.2 s immediately after it was applied. For example, fault F1 was applied on 30th sec., it was detected, isolated and accommodated on 30.2nd sec. After the 130th sec., the fault was removed and the system was operated under normal conditions without a fault, until the 200th sec. The other faults were applied subsequently as was the condition of fault F1. Figs. 7 and 8 show the results of operating conditions in Table 3 without and with fault tolerance, respectively. As shown in the Fig. 7, true level of the tank-2 rises to 0.4 m to compensate the fault of additive 0.1 m, since there is no fault tolerance. This condition is seen in the figure in every sensor fault related to tank-2; however, the true level of the tank-2 is stable on the set-point when the fault tolerance is in use, as shown in Fig. 8. It is also shown from the figures that, higher clustering and matching-up precisions are achieved by FFTA to isolate the sensor faults. Furthermore, the offset between the true value of the measured variable and the set-point are precisely compensated.
Table 3 Duration and FDI times of each fault. ID
Fault duration (s) FDI (s)
Fl
F2
F3
F4
F5
F6
F7
30–130 30.2
200–300 200.2
400–500 400.2
600–700 600.2
800–900 800.2
1000–1100 1000.2
1200–1300 1200.2
Fig. 7. Results of all faults without fault tolerance.
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Fig. 8. Results of all faults with fault tolerance.
Fig. 9. Occurrence of multiple faults.
In condition of simultaneously occurrence of multiple faults, FFTA detects and isolates the faults correctly as shown in Fig. 9. The fault F1 introduced at time of 30th sec., and while it keeps going on, the fault F7 introduced at the time of 45th sec. FTC can detect and isolate the second fault even though it has been already running under a faulty condition.
4. Conclusion In this study, we have improved an alternative knowledge-based technique to detect and isolate sensor faults of the three-tank system. The system worked without the FTC for normal and predefined seven faulty conditions to create a knowledge base by utilizing the FFTA. While the FTC was in use, the system operation was classified according to the similarity between the feature vectors of knowledge base and the feature vectors of instantaneous sensor data. In order to demonstrate the efficiency of the improved method, additive, multiplicative and stuck type sensor faults were applied to closed-loop fault tolerant control system in certain periods. Each fault was detected and isolated in approximately 0.2 s. High clustering and matching-up precisions were achieved to isolate the sensor faults. Furthermore, the bias between the true value of the
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measured variable and the set-point were precisely compensated. In condition of simultaneous occurrences of multiple faults, FFTA detected and isolated the faults correctly. References [1] Khan FG, Quresh K, Nazir B. Performance evaluation of fault tolerance techniques in grid computing system. Comput Electr Eng 2010;36(6):1110–22. [2] El-Gamal MA, Abdulghafour M. Fault isolation in analog circuits using a fuzzy inference system. Comput Electr Eng 2003;29(1):213–29. [3] Sourander M, Vermasvuori M, Sauter D, Liikala T, Jämsä-Jounela SL. Fault tolerant control for a dearomatisation process. J Process Control 2009;19:1091–102. [4] Zhang Y, Qin SJ. Adaptive actuator fault compensation for linear systems with matching and unmatching uncertainties. J Process Control 2009;19:985–90. [5] Gani A, Mhaskar P, Christofides PD. Fault-tolerant control of a polyethylene reactor. J Process Control 2007;17:439–51. [6] Manuja S, Narasimhan S, Patwardhan SC. Unknown input modeling and robust fault diagnosis using black box observers. J Process Control 2009;19:25–37. [7] Patwardhan SC, Manuja S, Narasimhan S, Shah SL. From data to diagnosis and control using generalized orthonormal basis filters, Part II: model predictive and fault tolerant control. J Process Control 2006;16:157–75. [8] Prakash J, Patwardhan SC, Narasimhan S. A supervisory approach to fault tolerant control of linear multivariable systems. Ind Eng Chem Res 2002;41:2270–81. [9] Zhang X, Parisini TM, Polycarpou M. Adaptive fault-tolerant control of nonlinear uncertain systems: an information-based diagnostic approach. IEEE Trans Autom Control 2004;49:1259–74. [10] Deshpande AP, Patwardhan SC, Narasimhan S. Intelligent state estimation for fault tolerant nonlinear predictive control. J Process Control 2009;19:187–204. [11] Ding SX, Zhang P, Naik A, Ding EL, Huang B. Subspace method aided data driven design of fault detection and isolation systems. J Process Control 2009;19:1496–510. [12] Zhao Q, Xu Z. Design of a novel knowledge-based fault detection and isolation scheme. IEEE Trans Syst Man Cybern—Part B: Cybern 2009;34:1089–95. [13] Postalcioglu S, Erkan K. Soft computing and signal processing based active fault tolerant control for benchmark process. J Neural Comput Appl 2009;18(1):77–85. [14] Xu Z, Zhao Q. A novel approach to fault detection and isolation based on wavelet analysis and neural network. In: Proceedings of the 2002 IEEE Canadian conference on electrical & computer engineering; 2002. p. 572–77. [15] Detroja KP, Gudi RD, Patwardhan SC. A possibilistic clustering approach to novel fault detection and isolation. J Process Control 2006;16(10):1055–73. [16] Gonzalez TF. Clustering to minimize the maximum intercluster distance. Theor Comput Sci 1985;38:293–306. U. Altinisik received the bachelor’s degree in Computer Engineering from Marmara University in 1998, Istanbul, and the PhD degree from Kocaeli University in 2012. He is currently an instructor in the department of Informatics, Kocaeli University, Turkey. His primary research interests are in the area of software, fault tolerant control, data mining. M. Yildirim received the bachelor’s degree in Electronics and Computer Education from Marmara University, Istanbul, in 1995 and the PhD degree from Kocaeli University in 2003. He is currently an associate professor in the department of Electronics and Computer Education, Kocaeli University, Turkey. His research interest includes dynamic system modelling, computer networks, genetic algorithms and simulated annealing.
Contents lists available at SciVerse ScienceDirect
Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng
A new fault tolerant control approach for the three-tank system using data mining q Umut Altinisik a,⇑, Mehmet Yildirim b a b
Department of Informatics, Kocaeli University, Umuttepe, 41380 Kocaeli, Turkey Networked Control Systems Laboratory, Kocaeli University, Umuttepe, 41380 Kocaeli, Turkey
a r t i c l e
i n f o
Article history: Received 8 September 2011 Received in revised form 20 June 2012 Accepted 21 June 2012 Available online 16 July 2012
a b s t r a c t In this study, we propose a knowledge-based approach for detection and isolation of sensor faults in fault tolerant control (FTC) of the three-tank system. Farthest first traversal algorithm (FFTA) of data mining is used first-time for the classification of faults in an FTC system. The sliding window is used to detect signal changes, which contain possible transients due to faults. The variance-changing ratio is calculated to extract the features of the sensor signal in each window. Then, FFTA is utilized for the isolation of sensor faults. In order to demonstrate the efficiency of the proposed method, seven types of artificial faults were applied to closed-loop fault tolerant control system in certain periods. All faults were detected and isolated immediately after they occurred. Moreover, fault isolation was achieved when multiple faults occurred simultaneously. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The capability of a system to carry out its operation correctly even in the occurrence of faults is called fault tolerance [1]. When the complexity of technical process increases, the probability of fault occurrence also increases and therefore, reliability and safety become important system requirements. Occurrences of faults cause to decrease in performance of closed-loop control and may reduce the profits. Thus, some methods have been developed for the design of sophisticated fault tolerant control (FTC) systems. An FTC system contains a fault detection and isolation (FDI) and a function that cause predefined corrective actions [2,3]. According to Zhang and Qin [4] fast counteraction to the fault is as important as detection and isolation of the fault. Faulttolerant control has been developed to keep the system stable, regardless of the occurrence of a fault. The reason of designing a fault detection is to determine whether a fault occurs in the process by monitoring the significant changes in the process states of the usual closed-loop action [5]. Fault tolerance is fundamentally interested with identification of improper action of process components, which are actuators and sensors, and abnormal drifts in parameters of the process [6]. In order to keep the performance of the system stable, after a process fault is detected and isolated, a controller that can compensate for the faults should be developed. FTC systems have been designed by means of model-based methods for several decades. The generalized likelihood ratio (GLR) and the model predictive control (MPC) based fault-tolerant schemes were used in control of linear processes [7,8] and for nonlinear processes [9,10]. The model-based FDI depends mainly on a process model. Model-based FDI techniques can be properly established if a process model has given [11]; however, when the model is not completely known or when the process is nonlinear, these methods may be unsuccessful.
q
Reviews processed and approved for publication by Editor-in-Chief Dr. Manu Malek.
⇑ Corresponding author. Tel.: +90 262 303 13 01; fax: +90 262 303 13 02.
E-mail addresses: [email protected] (U. Altinisik), [email protected] (M. Yildirim). 0045-7906/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compeleceng.2012.06.011
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In [10], Deshpande et al. emphasized the disadvantages of the model-based FDI as follows: The prediction model is constructed before the realization of nonlinear MPC. On the other hand, as time goes on, slow deviations in unmeasured disturbances and process parameters may give rise to serious unconformity between model and process actions. Moreover, nonlinear MPC methods are generally designed with assuming that actuators and sensors are fault-free. Some actuators and sensors may fail during operation and can give rise to a severe model-plant unconformity or instability. In order to overcome the problems of model-based FDI, new methods, which were based on knowledge, have been proposed in recent years. In order to estimate the process behavior, these methods use the archived process data. Knowledgebased techniques rely on extracting information only from the historical process data without any requirement to precisely analytical model. In the knowledge-based case, normal and abnormal operating conditions of a process, which are namely called features, are stored in the knowledge base. Features are extracted offline from previously taken process data, before the FTC is in use. While the FTC is being served, real-time process data are measured, analyzed and the instantaneous (online) features of them are extracted. Then, online features of process data are compared with the offline features in the knowledge base, in order to identify whether a fault occurs or not. One major advantage of these knowledge-based FDI methods is their excellent ability for isolating and classifying the faults [12]. Usually, the most frequently faced faults are sensor and actuator faults in process control. These faults can lead to decrease in the closed-loop performance and may have adverse effects on productivity and safety of the system if these faults are not timely detected and counteracted [7]. Therefore, it is necessary to develop FTC systems, which can compensate sensor and actuator faults. In this study, a knowledge-based method is proposed for detection and isolation of sensor faults in fault tolerant control of the three-tank system. It is a scheme that combines the farthest first traversal algorithm (FFTA) of data mining with statistical analysis techniques. The three-tank system is used as a benchmark process and artificial faults are applied to level sensors of the system. The sliding window is applied to detect signal variations, including possible fault-induced transients. In order to explore the features of a sensor signal, the variance-changing ratio is calculated in the sliding window. The FFTA runs for generating the knowledge base and tries to match the features of the real-time sensor signal to a known fault pattern in the knowledge base. 2. Design of fault detection and isolation scheme Controlling the liquid level in a tank system is a fundamental problem in process control. There are experimental benchmarks of single, couple, triple and quadruple tank systems. In this section, the three-tank system is demonstrated for a stable closed-loop control process even in the presence of sensor faults. It contains three interconnected water tanks, two pumps and associated valves as shown in Fig. 1. The inputs of the system are the currents supplied to the control valves to manipulate the flow rate (Qin,1 and Qin,3) of the pumps. The outputs of the system are the water level measurements of the tanks. The aim is to keep the level of tank-2 (H2) stable by controlling the levels of tank-1 (H1) and tank-3 (H3), which interact with the tank-2. The three-tank system uses the balance equations below [13]:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q in;1 dH1 k1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi k12 sgnðH1 ðtÞ H2 ðtÞÞ gjH1 ðtÞ H2 ðtÞj þ ¼ gH1 ðtÞ dt S1 S1 S1
ð1Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k23 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dH2 k2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi k12 sgnðH1 ðtÞ H2 ðtÞÞ gjH1 ðtÞ H2 ðtÞj sgnðH2 ðtÞ H3 ðtÞÞ gjH2 ðtÞ H3 ðtÞj gH2 ðtÞ þ ¼ dt S2 S2 S2
ð2Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Q in;3 dH3 k3 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi k23 sgnðH2 ðtÞ H3 ðtÞÞ gjH2 ðtÞ H3 ðtÞj þ gH3 ðtÞ þ ¼ dt S3 S3 S3
ð3Þ
k1 ¼
q R1
;
k2 ¼
q R2
;
k3 ¼
q R3
;
k12 ¼
q R12
;
k23 ¼
q R23
ð4Þ
The variables used in the tank system are given below: S1: Tank-1 base area (8:107 103 m2 ) S2: Tank-2 base area (4:560 103 m2 ) S3: Tank-3 base area (8:107 103 m2 ) q: Liquid density (for water, 1 103 kg/m3) Hi: Tank i liquid level (m) Qin,i: The fluid flow of inlet rate from the Pump i (m3/sn) Qi,0: The fluid flow of outlet rate from the Tank i (m3/sn) Qi,j: Liquid flow rate between Tank i and j (m3/sn) Ri: Drainage resistance of valve i (kg/m5) Ri,j: Flow resistance between the tanks i and j (kg/m5). In the three-tank system, flow rates of the inlets Qin,1 and Qin,3 are same, flow rates of the outlets Q10 and Q30 are same, and the tank-2 liquid level (H2) is kept at the desired level by using a controller. The simulations were carried out by using
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Fig. 1. Structure of experimental three-tank system.
Fig. 2. The FDI system structure.
a PID controller which controls the variables Qin,1 and Qin,3. The transfer function of the PID controller is given in below equation:
CðsÞ ¼ 4:8 þ
0:02 þ 0:5 s: s
ð5Þ
The structure of the FTC system used in this study is shown in Fig. 2. In the figure, the FDI section consists of feature extraction, clustering and knowledge base modules. In the feature extraction module, statistical techniques, which are sliding window and variance-changing ratio, are used for analysis of sensor signals to detect deviations from regular conditions. The FFTA classifies the variance changing-ratios of normal and particular faulty conditions, and then records them into the knowledge base. The knowledge base is initially produced by FFTA according to predefined sensor faults. The proposed FDI system is explained in the following sections, in detail.
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2.1. Feature extraction Faults in processes generally lead to changes in the process responses. On the other hand, a usual operation of the process (e.g. giving a new set-point) can result in same changes. By observing and analyzing the changes in sensory signals, the normal and abnormal responses of the process due to a fault can be identified. First of all, the sliding window is used to detect signal changes, which contain possible transients due to faults. Measured sensor signals (samples) are divided into windows and observed if there is any change in signal in that window. As shown in Fig. 3, the sliding window includes two concurrent windows in the same length, called as previous and current windows. The previous window consists of previously collected data, while the current window consists of recently gathered data. The early section in the current window is called as new data zone, that contains the latest samples [14]. The following variance-changing ratio equation is used for the sliding window to bring out the features of the signal
r¼
varðcurrent windowÞ varðprev ious windowÞ : varðprev ious windowÞ þ e
ð6Þ
Here var() is the signal variance. This equation is used to detect the variations in the sensor signal due to a fault. Moreover, the variance-changing ratio is useful in eliminating the system noise [12]. If there is not any fault, no change will be seen in the signal, variances of the previous and the current windows will be the same and therefore, the variance-changing ratio will be zero. If any fault occurs on one of the sensors, the variance of the current window for that sensor signal is changed immediately, so does the variance-changing ratio. The windowing and the variance changing ratios are calculated in parallel for all the three of level sensors in the three-tank system. For a particular fault type, simultaneous variance-changing ratios of three sensor signals are caught and recorded in the knowledge base as the feature vector of that fault type. By considering all possible fault types for that system, a knowledge base that consists of feature vectors is constructed. 2.2. Clustering with the farthest first traversal algorithm An ordinary process contains many variables, and these are measured frequently. These measurements may explore beneficial properties related to the status of the process. Knowledge-based methods are often preferred over model-based methods, because it makes an effort to extract lots of information from the historical data, and it does not need any information about the process itself. Mining the historical data, these types of FDI methods examine the patterns in process variables that show whether a fault occurs [15]. Data mining is the exploration and analysis of large amounts of data to explore significant patterns. The patterns obtained by the data mining process vary according to data mining techniques used. These techniques include association rules, clustering and classification methods, etc. In recent years; some of the data mining methods have been used to detect and isolate
Fig. 3. Sliding window technique.
Fig. 4. The FFTA solution for 10-point data set with three cluster centers.
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faults in control systems of a process. The clustering techniques, such as k-means and its variants are the most widely used clustering algorithms. Attempts have also been made to use different clustering algorithms for the task of FDI. In [16], González uses what might be called a farthest-first traversal algorithm for the k-center problem, that of finding an optimal k-clustering under a cost function of maximum cluster radius. On the other hand, FFTA has not ever been used in the FDI. Fig. 4 shows an example of FFTA with a data set of ten points, three of which are thought to be the cluster centers. The idea is to select three cluster center points sequentially, which are the farthest from the previously picked cluster centers (the points 1–3 in the figure). These points are taken as cluster centers and each remaining point is assigned to the closest cluster centers as a member. In this study, FFTA is utilized to design the knowledge base of the FDI system. Feature vectors of normal and all possible faulty conditions are recorded in the knowledge base. A feature vector constituted from simultaneous variance-changing ratios, which are calculated in parallel for level sensors in the three-tank system. A feature vector in the knowledge base may be assumed as a point and FFTA can classify these vectors into clusters as is done in Fig. 4. Since each feature vector has three elements, the point must be represented in a three-dimensional space. In this case, it can be thought that a feature vector contains the coordinates of a point in three-dimension. Therefore, distances between the feature vectors are calculated in three-dimension. The FFTA can determine a predefined number of cluster centers among the knowledge base, initially. These selected cluster centers are the farthest ones to each other, and each one is for the normal condition or for one of the fault types. The knowledge base may contain more fault types than desired; however, FFTA selects the predefined number of major ones. While the FTC is being served, variance-changing ratios are calculated and extracted feature vector is assigned to the closest cluster center, which is one of the previously determined cluster centers by FFTA. Hence, the operating status is classified, and a probable fault is detected and isolated. After the isolation, the predefined action for that fault type must be taken, even though the action does not totally compensate the error. 3. Case study: the three-tank system In the three-tank experiment, the system worked without the FTC for normal and predefined seven faulty conditions to create a knowledge base. Different types of artificial faults [13] were applied on the system; these were additive, multiplicative and stuck type sensor faults as given in the Table 1. Each one of the normal and faulty conditions consisted of 6000 sample data, which were taken from the level sensor signals. After that, these signals were windowed in length of 60 samples size, and the windows were shifted in length of 20 samples size. Feature vectors were extracted by calculating the variance-changing ratios for each windowed level sensor signal. These vectors were classified into different clusters that represent normal or faulty operation by the FFTA. The feature vectors, which mean the coordinate of cluster centers, are given in the Table 2. While the FTC is in use, the system operation is classified according to the similarity between the feature vectors of knowledge base and the feature vectors of instantaneous sensor data. The Euclidean distances between the coordinate of instantaneous data and the normal or faulty conditions are calculated to decide whether a fault has been occurring or
Table 1 Predefined sensor fault types for the three-tank system. ID
Fault type
N Fl F2 F3 F4 F5 F6 F7
Normal Additive 0.1 fault for level sensor 2 Multiplicative 1.1 fault for level sensor 3 Multiplicative 0.8 fault for level sensor 2 Multiplicative 0.7 fault for level sensor 1 Additive 0.1 fault for level sensor 3 Stuck type fault for level sensor 1 Additive +0.05 fault for level sensor 2
Table 2 Coordinates of cluster centers for the predefined fault types. ID
Cluster centers
N Fl F2 F3 F4 F5 F6 F7
0 1573.54 0 639.03 10018.08 0 12141 387.75
0 304.39 0 126.79 0 0 0 76.40
0 1573.54 1116.30 639.03 0 12308.11 0 387.75
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Fig. 5. Occurrence of fault F1 without and with fault tolerance.
Fig. 6. Occurrence of fault F5 without and with fault tolerance.
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not. The isolation is made by checking which cluster center is the closest one to the feature vector of instantaneous sensor data. In control of the three-tank experiment system, the aim is to keep stable the level of tank-2. The set-point is taken as 0.3 m and an artificial fault is applied at the time of 30 s. In case of a deviation in the level of tank-2; the controller acts immediately and brings it again to the set-point by raising or reducing the levels of tank-1 and tank-3. When the FTC is not in use, if a fault occurs on the sensor of tank-2 even though there is not any deviation from the true (actual) level, the controller imagines that a change occurs in the true level, and therefore, it attempts to change the levels of tank-1 and tank-3, so do tank-2 (see Fig. 5a). While the FTC is in use, after the detection and isolation of the fault at tank-2 level sensor, FTC accommodates the levels in a short time of a period (see Fig. 5b). On the other hand, if a fault occurs in level sensor of tank-1 or tank-3, no changes occur in true levels of any tank since the controller does not consider of tank-1 and tank-3 level sensors. Fig. 6a shows the occurrence of F5 of tank-3 without fault tolerance, and Fig. 6b does with fault tolerance. This is an example that the proposed FTC does not declare a false alarm. In order to show the efficiency of the proposed FDI method, all the faults specified in the Table 1 were applied to closedloop fault tolerant control system in certain periods. As shown in the Table 3, each fault was detected and isolated in 0.2 s immediately after it was applied. For example, fault F1 was applied on 30th sec., it was detected, isolated and accommodated on 30.2nd sec. After the 130th sec., the fault was removed and the system was operated under normal conditions without a fault, until the 200th sec. The other faults were applied subsequently as was the condition of fault F1. Figs. 7 and 8 show the results of operating conditions in Table 3 without and with fault tolerance, respectively. As shown in the Fig. 7, true level of the tank-2 rises to 0.4 m to compensate the fault of additive 0.1 m, since there is no fault tolerance. This condition is seen in the figure in every sensor fault related to tank-2; however, the true level of the tank-2 is stable on the set-point when the fault tolerance is in use, as shown in Fig. 8. It is also shown from the figures that, higher clustering and matching-up precisions are achieved by FFTA to isolate the sensor faults. Furthermore, the offset between the true value of the measured variable and the set-point are precisely compensated.
Table 3 Duration and FDI times of each fault. ID
Fault duration (s) FDI (s)
Fl
F2
F3
F4
F5
F6
F7
30–130 30.2
200–300 200.2
400–500 400.2
600–700 600.2
800–900 800.2
1000–1100 1000.2
1200–1300 1200.2
Fig. 7. Results of all faults without fault tolerance.
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Fig. 8. Results of all faults with fault tolerance.
Fig. 9. Occurrence of multiple faults.
In condition of simultaneously occurrence of multiple faults, FFTA detects and isolates the faults correctly as shown in Fig. 9. The fault F1 introduced at time of 30th sec., and while it keeps going on, the fault F7 introduced at the time of 45th sec. FTC can detect and isolate the second fault even though it has been already running under a faulty condition.
4. Conclusion In this study, we have improved an alternative knowledge-based technique to detect and isolate sensor faults of the three-tank system. The system worked without the FTC for normal and predefined seven faulty conditions to create a knowledge base by utilizing the FFTA. While the FTC was in use, the system operation was classified according to the similarity between the feature vectors of knowledge base and the feature vectors of instantaneous sensor data. In order to demonstrate the efficiency of the improved method, additive, multiplicative and stuck type sensor faults were applied to closed-loop fault tolerant control system in certain periods. Each fault was detected and isolated in approximately 0.2 s. High clustering and matching-up precisions were achieved to isolate the sensor faults. Furthermore, the bias between the true value of the
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measured variable and the set-point were precisely compensated. In condition of simultaneous occurrences of multiple faults, FFTA detected and isolated the faults correctly. References [1] Khan FG, Quresh K, Nazir B. Performance evaluation of fault tolerance techniques in grid computing system. Comput Electr Eng 2010;36(6):1110–22. [2] El-Gamal MA, Abdulghafour M. Fault isolation in analog circuits using a fuzzy inference system. Comput Electr Eng 2003;29(1):213–29. [3] Sourander M, Vermasvuori M, Sauter D, Liikala T, Jämsä-Jounela SL. Fault tolerant control for a dearomatisation process. J Process Control 2009;19:1091–102. [4] Zhang Y, Qin SJ. Adaptive actuator fault compensation for linear systems with matching and unmatching uncertainties. J Process Control 2009;19:985–90. [5] Gani A, Mhaskar P, Christofides PD. Fault-tolerant control of a polyethylene reactor. J Process Control 2007;17:439–51. [6] Manuja S, Narasimhan S, Patwardhan SC. Unknown input modeling and robust fault diagnosis using black box observers. J Process Control 2009;19:25–37. [7] Patwardhan SC, Manuja S, Narasimhan S, Shah SL. From data to diagnosis and control using generalized orthonormal basis filters, Part II: model predictive and fault tolerant control. J Process Control 2006;16:157–75. [8] Prakash J, Patwardhan SC, Narasimhan S. A supervisory approach to fault tolerant control of linear multivariable systems. Ind Eng Chem Res 2002;41:2270–81. [9] Zhang X, Parisini TM, Polycarpou M. Adaptive fault-tolerant control of nonlinear uncertain systems: an information-based diagnostic approach. IEEE Trans Autom Control 2004;49:1259–74. [10] Deshpande AP, Patwardhan SC, Narasimhan S. Intelligent state estimation for fault tolerant nonlinear predictive control. J Process Control 2009;19:187–204. [11] Ding SX, Zhang P, Naik A, Ding EL, Huang B. Subspace method aided data driven design of fault detection and isolation systems. J Process Control 2009;19:1496–510. [12] Zhao Q, Xu Z. Design of a novel knowledge-based fault detection and isolation scheme. IEEE Trans Syst Man Cybern—Part B: Cybern 2009;34:1089–95. [13] Postalcioglu S, Erkan K. Soft computing and signal processing based active fault tolerant control for benchmark process. J Neural Comput Appl 2009;18(1):77–85. [14] Xu Z, Zhao Q. A novel approach to fault detection and isolation based on wavelet analysis and neural network. In: Proceedings of the 2002 IEEE Canadian conference on electrical & computer engineering; 2002. p. 572–77. [15] Detroja KP, Gudi RD, Patwardhan SC. A possibilistic clustering approach to novel fault detection and isolation. J Process Control 2006;16(10):1055–73. [16] Gonzalez TF. Clustering to minimize the maximum intercluster distance. Theor Comput Sci 1985;38:293–306. U. Altinisik received the bachelor’s degree in Computer Engineering from Marmara University in 1998, Istanbul, and the PhD degree from Kocaeli University in 2012. He is currently an instructor in the department of Informatics, Kocaeli University, Turkey. His primary research interests are in the area of software, fault tolerant control, data mining. M. Yildirim received the bachelor’s degree in Electronics and Computer Education from Marmara University, Istanbul, in 1995 and the PhD degree from Kocaeli University in 2003. He is currently an associate professor in the department of Electronics and Computer Education, Kocaeli University, Turkey. His research interest includes dynamic system modelling, computer networks, genetic algorithms and simulated annealing.