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Diagnosis of process valve actuator faults using a multilayer neural network
ARTICLE IN PRESS
Control Engineering Practice 11 (2003) 1289–1299
Diagnosis of process valve actuator faults using a multilayer neural network M. Karpenkoa, N. Sepehria,*, D. Scuseb a
Department of Mechanical and Industrial Engineering, The University of Manitoba, Winnipeg, Man., Canada R3T 5V6 b Department of Computer Science, The University of Manitoba, Winnipeg, Man., Canada R3T 5V6 Received 4 March 2002; accepted 29 October 2002
Abstract This paper investigates the ability of a multilayer neural network to diagnose actuator faults in a Fisher-Rosemount 667 process control valve. A software package that comes with the valve is used to obtain experimental figures of merit related to the position response of the valve given a step command. The particular values of the dead time, peak time, percent overshoot, steady state error, 63% and 86% rise times, and gain are shown to depend on the severity of three commonly occurring faults: incorrect supply pressure, actuator vent blockage, and diaphragm leakage. The relationships between these parameters form fault signatures for each operating condition that are subsequently learned by a multilayer feedforward neural network. The results show that the trained network has the capability to detect and identify various magnitudes of the faults of interest. In addition, it is observed that the network has the ability to estimate fault levels not seen by the network during training. The approach presented in this paper allows the existing instrumentation to be utilised without modification. Thus, the proposed methodology is practical to implement. r 2002 Elsevier Ltd. All rights reserved. Keywords: Condition monitoring; Fault diagnosis; Pneumatic actuators; Actuator faults; Neural networks
1. Introduction A common component found in modern process plants is the pneumatic control valve. It is used in industries such as petrochemical, to control the flow of a fluid, gas, or slurry. In order to avoid unnecessary downtime resulting from process disturbances such as valve failures, manufacturers have been known to use conservative operating conditions during production (Tzafestas & Dalianis, 1994). This practice, however, results in less efficient operation of the plant and increases the overall production costs. Another common practice, which may be used in conjunction with conservative operation of the valve, is known as corrective maintenance. Here, the idea is to operate the process until a complete failure of the control valve, at which time the plant is shut down and the valve is refurbished. Conversely, in preventative maintenance schemes, plant engineers conduct scheduled shutdowns *Corresponding author. Tel.: +1-204-474-6834; fax: +1-204-2757507. E-mail address: [email protected] (N. Sepehri). 0967-0661/03/$ - see front matter r 2002 Elsevier Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 6 1 ( 0 2 ) 0 0 2 4 5 - 9
during which control valves are subjected to dismantle and overhaul (McGhee, Henderson, & Baird, 1997). In the latter case, valve components that are otherwise functioning normally may be needlessly replaced, thereby adding unnecessarily to operating costs. The ability to detect the occurrence of faults and more importantly identify the causes of faults in pneumatic control valves can reduce downtime, increase product quality, and eliminate the unnecessary replacement of functioning valve components. Thus, there is a need for suitable fault detection and identification (FDI) schemes for pneumatic control valves. Modern methods for FDI of dynamic systems can be grouped into three broad categories, the first being a model-based approach. The model-based approach uses a priori mathematical information about the system to model the normal process (Isermann & Balle! , 1997). Then, the output of the system is compared to the prediction given by the model and a vector of residuals (differences between the actual and the predicted outputs) is generated. The residuals are used to ascertain the condition of the dynamic system. However, it is well known that constructing mathematical models for
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complex systems or for nonlinear systems can be difficult, if not impossible. Furthermore, a great deal of experimentation is generally required to validate the model. Consequently, the model-based approach can be difficult to implement. An alternate approach to the model-based FDI has been to train neural networks to estimate the model of the dynamic system (Bernieri, D’Apuzzo, Sansone, & Savastano, 1994). The approximate model generated by the network is then used in conjunction with measurements of actual system outputs to generate the residuals. McGhee et al. (1997) used this technique to predict the output torque of a rotary pneumatic control valve. The predicted output torque was used along with actual torque measurements to perform fault detection. Since only one variable was available for analysis, the cause of the fault was not identified in their work. Another category of techniques that can be used to perform FDI is based on expert or qualitative reasoning (Zhang, Roberts, & Ellis, 1991). FDI schemes that fall into this category can be thought of as fault analysers since they make decisions about whether or not a fault has occurred based on a set of logical rules that are either pre-programmed by an expert or learned via some form of training. When information about the operation of a dynamic system is presented to the fault analyser, it is tested against the logic and a decision about the condition of the system is made. Sharif and Grosvenor (2000) developed computer software for FDI of a class of process control valves using this approach. They studied faults due to sticking of the valve stem, damaged valve stem packing and blockage of the actuator vent. Furthermore, they suggested that the accuracy of the software could be improved for some faults through the use of pattern recognition techniques. The third class of approaches uses neural networks as pattern classifiers to solve the FDI problem. Here, the networks are trained to recognise data representing the different failure modes of the dynamic system. This approach has been used in a variety of applications. To name a few, Le, Watton, and Pham (1997, 1998) and Crowther, Edge, Burrows, Atkinson, and Woollons (1998) used this approach for FDI in hydraulic fluid power systems. Yen and Lin (2000) and Wang, Propes, Khiripet, Li, and Vachtsevanos (1999) employed neural network classifiers in conjunction with wavelet transforms to perform FDI in machine dynamics and vibration problems. Zhang, Ma, and Yan (2000) as well as Zhao, Chen, and Shen (1998) have also demonstrated the usefulness of this approach in the applications of sensor fault diagnosis and fault diagnosis of chemical processes, respectively. In this paper, a neural network is implemented to detect and identify actuator faults in a typical pneumatic control valve. The faults of interest are incorrect supply pressure, actuator vent blockage, and actuator dia-
phragm leakage. These faults are amongst the common faults causing abnormal operation of control valves (McGhee et al., 1997; Sharif & Grosvenor, 1998; Karpenko & Sepehri, 2001a). The approach taken is to train the network to identify the faults from sets of valve performance data. For each operating condition, a software package that comes with the valve is utilised to automatically calculate seven figures of merit related to the valve step response. These performance parameters are: gain, dead time, peak time, percent overshoot, steady-state error, as well as 63% and 86% rise times. Their particular values are shown to depend upon both the type and magnitude of the fault. Hence, these metrics form information-rich fault signatures that can be used by the neural network to discriminate amongst the faults. The fault signatures are subsequently learned by a multilayer feedforward neural network which estimates the operating condition of the valve in terms of the supply pressure, actuator vent blockage and diaphragm leakage. The multilayer feedforward structure was selected for use as it has been shown to perform well in similar FDI problems (Sorsa, Koivo, & Koivisto, 1991; Koivo, 1994; Crowther et al., 1998). The proposed neural network approach eliminates the need for the human evaluation of the valve performance data, which often requires specialist knowledge (Karpenko, Sepehri, & Scuse, 2001b) and is prone to misinterpretation (Sharif & Grosvenor, 2000). The organisation of the remainder of this paper is as follows: Section 2 describes the typical process control valve under investigation, a Fisher-Rosemount 667, as well as its operation. The available valve performance data are defined and the methods used to introduce the faults into the experimental system are described. In Section 3, the architecture and training of the network is described. It is shown that the measured features of the valve step responses are sufficient to characterise the faults of interest and are suitable inputs to the neural network. Finally, the performance of the network is discussed in Section 4, where it is shown that the network has the ability to correctly detect and identify the faults and generalise well to fault levels not present in the training data. The paper is brought to a close by some concluding remarks in Section 5.
2. Experimental test rig 2.1. Pneumatic control valve Fig. 1 shows the pneumatic control valve under investigation. The valve was modified so that the faults of interest could be introduced experimentally. The flow control device, or valve body, is stroked by a pneumatically driven diaphragm type actuator. The digital valve
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actuator
digital valve controller
normalised response
tp Mp 1
t86
ess
t63 0.5
td 0 0
1
2
3
4
5
time (s) valve body
Fig. 2. Performance parameters associated with a typical valve step response.
parameters associated with the valve step response are: Fig. 1. Fisher–Rosemount 667 process valve.
controller (DVC) closes the loop so that position control of the valve stem is realised. The DVC module consists of a current to pressure (I=P) converter and a pneumatic relay. The I=P converter is a field-controlled flapper-nozzle arrangement that transforms an analog control current into a corresponding control pressure. The pneumatic relay then amplifies the control pressure so that a relatively large volume of air can be delivered to, or vented from, the lower chamber of the actuator. This results in a force unbalance across the diaphragm that subsequently causes the valve to open or close. In addition to the control electronics, the DVC also contains a potentiometer type position sensor that measures the position of the valve stem and a pressure transducer that monitors the output pressure of the DVC. The ValveLinkt (Fisher Controls Inc., 1999a) software, which comes with the valve, communicates with the onboard sensors of the DVC through standard RS-232 protocol. The software is used herein to carry out the valve step response tests and automatically calculate the performance parameters associated with each curve.
1. td (dead time)—a measure of the transport lag, the time to achieve a change in position of 1% of the desired step; 2. t63—the time to achieve a change in position of 63% of the desired step; 3. t86—the time to achieve a change in position of 86% of the desired step; 4. tp—the peak time; 5. Mp—the percent overshoot; 6. ess—the steady-state error; 7. K (gain)—the ratio of the percent change in the position of the valve stem to the percent change in magnitude of the input signal (not shown in Fig. 2). Referring to Fig. 2, it is observed that these parameters describe the main features of the valve step response and are indicative of the dynamic and static characteristics of the response. For example, the dead time, peak time and rise times, reflect the shape of the transient portion of the curve. The percent overshoot is indicative of the effective damping and the steady-state error is representative of the continuous response. Parameter K provides a measure of the relative degree of control effort required to position the valve stem. As will be seen later, these metrics are sufficient to characterise the changes in the performance of the valve due to the occurrence of the faults under investigation.
2.2. Valve performance parameters 2.3. Failure modes The valve step response indicates the condition of the valve by the nature of the position–time curve resulting from a step-input command. To facilitate comparison for condition monitoring, several figures of merit are associated with the response in order to quantify the curve. With reference to Fig. 2, seven performance
Although pneumatic control valves can fail in a variety of modes (see McGhee et al., 1997), only faults manifesting themselves in the actuator are considered here. The faults of interest are: (i) incorrect supply pressure, (ii) actuator vent blockage, and (iii) diaphragm
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leakage. These faults can be easily quantified and simulated experimentally, with minimal modification of the valve. The motivation for considering the incorrect supply pressure fault is the fact that the supply pressure directly influences the volume of air that can be delivered to the actuator (Fisher Controls Inc., 1999b). This adversely affects the position response of the valve. The incorrect supply pressure fault can occur from a blockage or leak in the supply line, or by increased demand placed on the plant air supply. As shown in Fig. 3, an adjustable pressure regulator was placed between the DVC and the main air supply to produce the supply pressure fault. Detecting the actuator vent blockage is also important since it changes the system dynamics by increasing the effective damping of the system. When air is supplied to the lower chamber of the actuator, the pressure increases allowing the diaphragm to move upwards against the spring force. As the diaphragm moves upward, air that is trapped in the upper chamber escapes through the vent. When the vent becomes partially blocked due to debris, the pressure in the upper chamber increases creating a pressure surge that opposes the motion of the diaphragm. Similarly, when air is purged from the lower chamber, and the vent is partially blocked, a partial vacuum is created in the
upper chamber. Again, the motion of the diaphragm is hindered and the performance of the system is impaired. In cases when the vent is entirely blocked, the valve cannot be stroked through its full range. Placing an adjustable needle valve in the vent port, as illustrated in Fig. 3, simulated the vent blockage. The full-open position of the needle valve was designated as 0% blockage and the full-closed position was designated as 100% blockage. Finally, the condition of the diaphragm should be monitored due to the cyclic nature of the stresses induced upon the diaphragm as it flexes. As a result, fatigue failure of the diaphragm will inevitably occur. Thus, it is important to detect and identify diaphragm leakage since it is an indicator of the condition of the diaphragm. With reference to Fig. 3, diaphragm leakage was simulated by diverting air around the diaphragm by means of a flexible hose connecting the output of the DVC to the upper chamber of the actuator. The leakage flow was controlled by a needle valve with 100% leakage (total diaphragm failure) denoting the adjustment where the valve ceased to respond to any input signal.
3. Neural network implementation 3.1. Network structure
needle valve (vent blockage) needle valve (diaphragm leakage)
DVC
plant air supply pressure regulator (incorrect supply pressure)
Fig. 3. Schematic of the experimental setup illustrating the methods by which various faults are introduced into the system. The pressure regulator allows incorrect supply pressures to be set while the two needle valves allow diaphragm leakage and upper casing vent blockage to be simulated.
A feedforward network can be operated in one of two ways to solve the FDI problem presented here: (i) the network assigns each operating condition to a specific class, or (ii) the network estimates the magnitude of the faulty condition. In the first case, each vector of input data is assigned a class vector that represents a specific mode of operation (either normal or faulty). Then, the number of output neurons is set equal to the number of class vectors. The network is trained such that the neuron with the largest output indicates the condition of the valve. Clearly, the size of the output layer grows as the number of possible fault classes increases. This leads to a larger network, greater number of adjustable weights, and possibly longer training times. Furthermore, the ability of the network to generalise to fault levels not present in the training data is poor. The size of the network can be significantly reduced if it is operated such that the outputs estimate the magnitude of each fault. In this case, only one output neuron is required for each failure mode. This methodology was employed here. With reference to Fig. 4, the seven inputs to the network included all of the step response features listed in Section 2.2. The network was restricted to have a single hidden layer with a variable number of hidden neurons. Single layer networks were not considered due to their poor generalisation ability as compared with multilayer networks (Sorsa et al., 1991).
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bias x0 td t63
bias z0
x1 x2
supply pressure
t86
y1
x3 tp Mp
K
percent vent blockage x4 x5
y2 percent diaphragm leakage
…
ess
1293
y3
x6 x7 INPUT LAYER
HIDDEN LAYER
OUTPUT LAYER
Fig. 4. Network architecture.
Neurons in the hidden layer used hyperbolic tangent activation functions. The three linear output neurons estimate the magnitude of the supply pressure, percent vent blockage and percent diaphragm leakage according to the following relation: ! m 7 X X yk ¼ wjk tanh wij xi þ w0k z0 ; k ¼ 1; 2; 3; ð1Þ j¼1
i¼0
hysteresis and deadband in the actuator, data arising from the negative (reset) steps were discarded. This procedure was carried out for each of the 17 operating conditions resulting in 238 input/output vectors of data available for training and testing the FDI network. Table 2 lists the ranges of each of the seven performance parameters that were obtained from the experiments. In practice, a similar set of tests would be carried out to obtain training data from which a unique FDI network
where xi is the input and yk is the network output. wij is the adjustable weight between input i and hidden neuron j and wjk is the adjustable weight between hidden neuron j and output neuron k. Index m denotes the number of neurons in the hidden layer. Note that the bias terms are absorbed into Eq. (1) by setting x0=1 and z0=1.
Table 1 Listing of the faults and their magnitudes
3.2. Training data
Normal operating condition 1 124
0
0
Sixteen faulty conditions were examined in this study. They are listed in Table 1 along with the normal operating condition. The faulty operating conditions were chosen to reflect a wide range of variation in the severity of each failure mode. While possible in practice, situations where two or more faults occur simultaneously were not considered here due to the exceedingly large number of possible fault combinations. This represents a potential limitation of the approach. Step response tests were carried out to ascertain the seven performance parameters associated with each operating condition. The test signal consisted of a series of steps beginning with the valve positioned at its lower stop. First, the valve was brought to 10% of its full travel and allowed to reach equilibrium. Then, the valve was moved from 10% to 25% of its stroke and back to the 10% position. This sequence was repeated 14 times so that the slight variations in the responses would be captured. Fig. 5 shows the first few periods of the responses for a healthy valve. Due to the effects of
Incorrect supply pressure fault 2* 117 3 110 4* 103 5 97 6* 90 7 83 8* 76 9 69
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
Diaphragm 10 11 12* 13
0 0 0 0
10 20 30 40
50 75 87.5 100
0 0 0 0
Data set
Supply pressure (kPa)
leakage fault 124 124 124 124
Vent blockage fault 14 124 15 124 16* 124 17 124
Vent blockage (%)
Diaphragm leakage (%)
Data for those faults with an asterisk were unseen during training and were used to test the generalisation capabilities of the network.
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1294 30
position (%)
25 20 15 10 5 0 0
5
10
15
20
time (s)
Fig. 5. Typical experimental step responses of a healthy valve.
could be formed prior to installation of the valve. Then, the performance parameters would be evaluated periodically while the valve is in service and the network queried in order to assess the condition of the valve. Presently, it is assumed that the valve would be taken off-line to ensure that the position information is
unaffected by process flow forces and that the process itself is not disturbed by the step response test. Furthermore, since accurate position information is required, it is assumed that the performance of the position transducer would be validated prior to administering the step response tests. Fig. 6 illustrates the effects of the faults upon the step response curve for the most severe case of each fault: 69 kPa supply pressure, 40% diaphragm leakage, and 100% vent blockage. A typical step response curve for a healthy valve is included in Fig. 6 for reference. Clearly, the most severe case of each fault has a significant effect on the performance of the valve, which is captured as changes in the particular values of the performance parameters. However, from Fig. 6, it is seen that the valve performance for the 100% vent blockage fault is similar to that of the healthy valve. This indicates that the vent blockage fault is potentially the most difficult to diagnose. In contrast, Fig. 7 shows the changes in the valve step response corresponding to the onset of each fault:
Table 2 Ranges of the performance parameters Data set 1 2* 3 4* 5 6* 7 8* 9 10 11 12* 13 14 15 16* 17
min max min max min max min max min max min max min max min max min max min max min max min max min max min max min max min max min max
td (s)
t63 (s)
t86 (s)
tp (s)
Mp (%)
ess (%)
K
0.132 0.143 0.133 0.275 0.106 0.287 0.268 0.291 0.264 0.292 0.224 0.295 0.237 0.244 0.231 0.354 0.267 0.331 0.125 0.136 0.128 0.278 0.121 0.285 0.130 0.288 0.246 0.341 0.255 0.261 0.244 0.246 0.281 0.292
0.177 0.237 0.158 0.293 0.159 0.297 0.298 0.302 0.302 0.309 0.305 0.353 0.369 0.376 0.398 0.479 0.734 0.788 0.248 0.266 0.158 0.293 0.165 0.295 0.255 0.298 0.466 0.526 0.378 0.384 0.353 0.358 0.301 0.303
0.210 0.335 0.168 0.364 0.168 0.410 0.310 0.334 0.311 0.346 0.314 0.463 0.497 0.504 0.535 0.687 1.173 1.231 0.361 0.391 0.168 0.358 0.182 0.361 0.308 0.384 0.676 0.762 0.498 0.508 0.458 0.468 0.311 0.325
0.245 0.438 0.178 0.485 0.179 0.569 0.320 0.368 0.322 0.386 0.325 0.586 0.634 0.640 0.681 0.926 1.619 1.701 0.479 0.525 0.178 0.477 0.200 0.479 0.318 0.516 0.886 1.024 0.624 0.640 0.569 0.584 0.321 0.348
16.47 18.11 16.37 17.48 16.30 17.30 16.64 17.41 16.20 16.94 15.16 15.84 14.39 15.29 12.73 13.14 5.21 6.28 10.95 12.37 12.83 13.36 15.14 16.07 10.03 10.46 6.92 7.83 10.63 11.77 12.72 13.46 14.32 15.57
0.30 0.39 0.43 0.55 0.54 0.60 0.72 0.80 0.87 0.93 1.02 1.07 1.11 1.21 1.28 1.33 1.41 1.52 0.13 0.28 0.18 0.26 0.27 0.38 0.52 0.60 2.81 2.93 2.03 2.16 1.49 1.60 0.90 1.00
1.007 1.015 1.006 1.019 1.008 1.016 1.004 1.012 1.005 1.015 1.015 1.022 1.010 1.022 1.013 1.024 1.017 1.034 1.007 1.015 1.016 1.021 1.005 1.023 0.996 1.005 0.971 0.987 0.982 0.991 0.988 1.005 0.988 1.006
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healthy valve
12
vent blockage
position (%)
10 8
incorrect supply pressure
6
diaphragm leakage
4 2 0 0
1
2
3
4
5
time (s)
Fig. 6. Representative experimental step response plots corresponding to the most severe failure modes: 69 kPa supply pressure, 40% diaphragm leakage, and 100% vent blockage. The step response of a healthy valve is included for comparison.
14
healthy valve
12
vent blockage position (%)
were unseen during training and were used to assess the ability of the trained network to generalise to fault levels not present in the training data. All input/output vectors were normalised to lie on the interval [1, 1], a common pre-processing technique used to improve the performance of the network. The training process establishes the mapping between the values of the performance parameters and the corresponding operating condition of the valve through adjustment of the network weights in (1). To begin training, the adjustable weights of the hidden layer neurons were initialised using the Nguyen–Widrow algorithm which has the effect of accelerating training by distributing the active regions of the neurons more evenly over the range of inputs (Nguyen & Widrow, 1990). The algorithm was implemented by first assigning the weights random numbers on the interval [0.5, 0.5]. The weights were then scaled as follows: pffiffiffiffi 0:7 n m wij;new ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi wij;old Pn 2 l¼1 wlj i ¼ 1; 2; y; n; j ¼ 1; 2; y; m;
10 8
diaphragm leakage
6
incorrect supply pressure
4 2 0 0
1
2
3
4
5
time (s)
Fig. 7. Representative experimental step response plots corresponding to the onset of each failure mode: 117 kPa supply pressure, 10% diaphragm leakage, and 50% vent blockage. The step response of a healthy valve is included for comparison.
117 kPa supply pressure, 10% diaphragm leakage and 50% vent blockage. It is seen that the step response, and hence the values of the performance parameters, change slightly in the presence of the faults. It is noted that it is difficult to visually determine the condition of the valve when the fault level is small. However, as will be shown later, the proposed neural network scheme has the ability to perform this task. 3.3. Network training To facilitate the assessment of the generalisation ability of the trained network, the available experimental data were subdivided into training and test sets. The test set consisted of those input/output vectors corresponding to the faults followed by an asterisk in Tables 1 and 2. Consequently, only 154 of the 238 available input/output vectors were used directly in the training process. The remaining 84 input/output vectors
1295
ð2Þ
where n is the number of network inputs. The bias weights, w0j ; were pffiffiffiffi given pffiffiffiffirandom initial values on the interval [0:7 n m; 0:7 n m]. The remaining adjustable parameters were given random initial values on the interval [1, 1]. The goal of training is to minimise the mean squared error between the desired network outputs and the actual network outputs which is written for batch mode training, where the error is evaluated over the entire training data set, as EðtÞ ¼
P X 3 2 1 X dk;p yk;p ðtÞ ; P p¼1 k¼1
ð3Þ
where dk,p is the desired output corresponding to input vector xp ; yk,p(t) is the network output corresponding to input vector xp after training epoch t, and P is the total number of input/output vectors in the training data set. To minimise (3), the gradient descent method with momentum (Haykin, 1999) was employed. The weights were updated according to DWðtÞ ¼ ZrEjwðtÞ þm DWðt 1Þ:
ð4Þ
In Eq. (4), W is the matrix of adjustable weights, Z is the learning rate, m is the momentum term, r is the gradient operator and DWðtÞ ¼ WðtÞ Wðt 1Þ: To accelerate convergence, the learning rate was continuously adjusted during training as follows: ( rZold ; DEo0; Znew ¼ ð5Þ sZold ; DE > 0; where DE is the change in the network error, Enew Eold ; resulting from the last weight update. Parameters r
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where ropt is the fraction of the available data that should remain in the training data subset, P is the total number of available input/output vectors, and a is the number of adjustable weights in the network. The training subset was used to adapt the weights via Eqs. (3)–(5). After each epoch, the network was queried with the input vectors in the validation subset and the mean squared validation error was calculated. If the validation error increased with continued training, training was terminated due to the potential for overfitting. If the validation error remained the same for more than 10 successive epochs, it was assumed that the network had converged. Typical network learning curves are shown in Fig. 8. As is seen, both the training error and the validation error decrease rapidly at the beginning of training. Small oscillations in the training error are a result of adjusting the learning rate during training. As training continues, performance enhancement begins to diminish and the training error curve levels out. A similar result is noted for the curve representing the validation error. The training process was terminated after 450 weight updates since the validation error failed to decrease for more than 10 successive epochs. Fig. 8 also verifies that additional training, beyond the early stopping point, yields only minimal improvement in the network accuracy at the expense of longer training time. The ideal number of hidden neurons was determined by increasing the number of neurons in the hidden layer until improvements in the accuracy of the network diminished. For each hidden layer size, 500 networks were trained. The results were averaged in order to minimise the effects of the random assignment of the initial weights. Referring to Fig. 9, it was found that the overall network accuracy, measured as the unscaled mean absolute error, increased as the number of hidden
10.000
mean squared error
and s were set to standard values of 1.1 and 0.5, respectively (Bishop, 1995). Setting the momentum term, m, in (4) to 0.9 was also found to increase the speed of learning. Early stopping (Haykin, 1999) was used to ensure the network would generalise well to unseen data. This required the available training data pool to be further divided into training and validation subsets. The optimal number of input/output vector pairs in each subset depends upon the number of input/output vectors available as well as the number of adjustable weights in the network. The number of input/output vectors in each subset was determined by the following equation that has been proposed by Amari, Murata, Muller, . Finke, and Yang (1996): 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi > 2a 1 1 < for Pp30a; 1 ropt ¼ ð6Þ 2ð a 1Þ > : 1 for P > 30a;
training error validation error stop
training terminated
1.000
0.100
0.010
0.001 0
200
400
600
800
1000
epoch
Fig. 8. Typical learning curves.
10 unscaled mean absolute error
1296
excess hidden neurons 8
6
4
2
0 2
3
4
5
6
7
8
9
10 11 12 13 14
hidden neurons
Fig. 9. Unscaled mean absolute error over the entire training data set versus the number of hidden neurons.
neurons was increased from 2 to 6. The networks having 5 or 6 neurons in the hidden layer resulted in the lowest error, with the former performing only marginally better. As the number of hidden neurons was increased past 6, there was no marked improvement in accuracy. Consequently, a network with 5 hidden neurons was chosen as the solution to the FDI problem.
4. Results Fig. 10 shows the performance of the FDI network when queried with data representing the incorrect supply pressure fault. Dashed vertical lines separate the data sets. Each discrete point represents a different input vector taken from the available data and the entire set is shown in a sequential fashion for comparative purposes. The desired network outputs, representing the actual operating condition of the system, are shown as solid lines. Data points represented by circles, K, are the actual network outputs for input vectors used in the training process. Data points represented by diamonds, B, are the actual network outputs for input vectors that
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supply pressure (kPa)
150 125 100 75 50 25
125 100 75 50 25
120
120
100
100
vent blockage (%)
0
80 60 40 20 0
80 60 40 20 0
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–20
120
120
100 80 60 40 20 0 –20
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2*
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8*
9
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150
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diaphragm leakage (%)
diaphragm leakage (%)
vent blockage (%)
supply pressure (kPa)
M. Karpenko et al. / Control Engineering Practice 11 (2003) 1289–1299
100 80 60 40 20 0
–20
10
11
12*
13
data set
data set
Fig. 10. Output of the network for the supply pressure fault: —actual operating condition; network output when queried with training data; network output when queried with unseen data.
Fig. 11. Output of the network for the diaphragm leakage fault: — actual operating condition; network output when queried with training data; network output when queried with unseen data.
were unseen by the network during training. The later data serve to assess the ability of the network to generalise to fault levels not present in the training data. With reference to Fig. 10, the outputs of the trained neural network are observed to follow the changes in the supply pressure quite well. Thus, the network is able to detect the incorrect supply pressure fault since the output of the supply pressure neuron varies in accordance with the changes in the supply pressure. Furthermore, it is observed that the network is able to estimate fault magnitudes not present in the training data. Fig. 10 also shows that the outputs of the neurons representing the vent blockage and diaphragm leakage faults remain relatively close to the actual values as the supply pressure is varied. This indicates that the network has successfully learned to isolate the incorrect supply pressure fault from the other two. Figs. 11 and 12 show the performance of the network when queried with data representing the diaphragm leakage and vent blockage faults, respectively. Again, the network outputs are seen to track the changes in the fault levels and generalise well to fault levels not present in the training data. As before, the network exhibits the ability to both detect and isolate each fault from the others.
Upon inspection of Figs. 10–12, one notes that the largest scatter is observed in the output of the vent blockage neuron. This can be explained with reference to Fig. 6. As is seen, both the incorrect supply pressure fault and the diaphragm leakage fault result in relatively large changes in the step response. Conversely, the vent blockage fault results in only small changes in the step response, from normal, even in the limiting case where the vent was completely blocked off. This implies that the vent blockage is inherently difficult to diagnose and explains why the scatter is relatively large when the blockages are small. The network performance is, however, quite acceptable and improves as the magnitude of the vent blockage fault increases.
5. Conclusions This paper has investigated a neural-network-based scheme for detection and identification of actuator faults in a typical process control valve. The faults of interest were various incorrect supply pressures, actuator vent blockages and diaphragm leakages. These faults are amongst the common problems associated with the abnormal operation of the valve. Valve position
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150 125 100 75
Acknowledgements
50 25
The authors would like to acknowledge the assistance of Controltech Inc., Winnipeg, Canada, who granted partial funding for this work in addition to providing the control valve used in the research. The authors would also like to extend their deepest thanks to Mr. Larry Mercado (of Controltech Inc.) for generously offering both his time and technical expertise during the course of the project.
0
vent blockage (%)
120 100 80 60 40 20 0
diaphragm leakage (%)
–20
References
120 100 80 60 40 20 0
–20
14
15
16*
17
data set
Fig. 12. Output of the network for the actuator vent blockage fault: — actual operating condition; network output when queried with training data; network output when queried with unseen data.
response parameters, dead time, peak time, percent overshoot, steady-state error, 63% and 86% rise times, and gain were obtained experimentally for a number of operating conditions. The specific values of these performance parameters were observed to depend upon both the magnitude and type of fault. For each operating condition, the performance parameters formed a discriminatory fault signature that was subsequently learned by a multilayer feedforward neural network with the goal of successfully detecting and identifying the faults. The experimental results proved that the trained network has the capability to detect and identify the various magnitudes of the faults of interest, as they occur singly. Furthermore, the results indicate that the network can accurately estimate fault levels unseen during the training process. This information is vital to a process valve condition monitoring strategy since it can be used to detect problems and assist in the timely scheduling of repairs to the valve, before a severe failure occurs. Future work in this area includes training the network to discriminate against other control valve failure modes, such as increased valve stem friction, or wear of mechanical components. However, the scheme
. Amari, S., Murata, N., Muller, K.-R., Finke, M., & Yang, H. (1996). Statistical theory of overtraining—Is cross-validation asymptotically effective? Advances in Neural Information Processing Systems, 8, 176–182. Bernieri, A., D’Apuzzo, M., Sansone, L., & Savastano, M. (1994). A neural network approach for identification and fault diagnosis on dynamic systems. IEEE Transactions on Instrumentation and Measurement, 43(6), 867–873. Bishop, C. M. (1995). Neural networks for pattern recognition. New York: Oxford University Press Inc. Crowther, W. J., Edge, K. A., Burrows, C. R., Atkinson, R. M., & Woollons, D. J. (1998). Fault diagnosis of a hydraulic actuator circuit using neural networks—an output vector space classification approach. Journal of Systems and Control Engineering, 212(1), 57–68. Fisher Controls Inc. (1999a). FIELDVIEWs ValveLinkt VL2000 series software user guide. Iowa: Fisher Controls International Inc. Fisher Controls Inc. (1999b). Control valve handbook. Iowa: Fisher Controls International Inc. Haykin, S. (1999). Neural networks: A comprehensive introduction (2nd ed.). New Jersey: Prentice-Hall. Isermann, R., & Ball!e, P. (1997). Trends in the application of modelbased fault detection and diagnosis of technical processes. Control Engineering Practice, 5(5), 709–719. Karpenko, M., & Sepehri, N. (2001a). A neural network based fault detection and identification scheme for pneumatic process control valves. Proceedings of the IEEE Conference on Systems, Man and Cybernetics, Tucson, AZ, 1, 93–98. Karpenko, M., Sepehri, N., & Scuse, D. (2001b). Neural network detection and identification of actuator faults in a pneumatic process control valve. Proceedings of the IEEE international symposium on computational intelligence in robotics and automation, Banff, Canada, 166–171. Koivo, H. N. (1994). Artificial neural networks in fault diagnosis and control. Control Engineering Practice, 2(1), 89–101. Le, T. T., Watton, J., & Pham, D. T. (1997). An artificial neural network based approach to fault diagnosis and classification of fluid power systems. Journal of Systems and Control Engineering, 211(4), 307–317. Le, T. T., Watton, J., & Pham, D. T. (1998). Fault classification of fluid power systems using a dynamics feature extraction technique and neural networks. Journal of Systems and Control Engineering, 212(2), 87–97. McGhee, J., Henderson, I. A., & Baird, A. (1997). Neural networks applied for the identification and fault diagnosis of process valves and actuators. Measurement: Journal of the International Measurement Confederation, 20(4), 267–275.
ARTICLE IN PRESS M. Karpenko et al. / Control Engineering Practice 11 (2003) 1289–1299 Nguyen, D., & Widrow, B. (1990). Improving the learning speed of 2layer neural networks by choosing initial values of the adaptive weights. Proceedings of the International Joint Conference on Neural Networks, San Diego, CA, 3, 21–26. Sharif, M. A., & Grosvenor, R. I. (1998). Fault diagnosis in industrial control valves and actuators. Proceedings of the IEEE Instrumentation and Measurement Technology Conference, St. Paul, MN, 2, 770–778. Sharif, M. A., & Grosvenor, R. I. (2000). The development of novel control valve diagnostic software based on the visual basic programming language. Journal of Systems and Control Engineering, 214(2), 99–127. Sorsa, T., Koivo, H. N., & Koivisto, H. (1991). Neural networks in process fault diagnostics. IEEE Transactions on Systems, Man, and Cybernetics, 21(4), 815–825. Tzafestas, S. G., & Dalianis, P. J. (1994). Fault diagnosis in complex systems using artificial neural networks. Proceedings of the IEEE Conference on Control Applications, Glasgow, UK, 2, 877–882.
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Wang, P., Propes, N., Khiripet, N., Li, Y., & Vachtsevanos, G. (1999). An integrated approach to machine fault diagnosis. Proceedings of the IEEE annual textile, fiber and film industry technical conference, Atlanta, GA, 59–65. Yen, G. G., & Lin, K. (2000). Wavelet packet feature extraction for vibration monitoring. IEEE Transactions on Industrial Electronics, 47(3), 650–667. Zhang, J., Ma, J., & Yan, Y. (2000). Assessing blockage of the sensing line in a differential-pressure flow sensor by using the wavelet transform of its output. Measurement Science and Technology, 11(3), 178–184. Zhang, J., Roberts, P. D., & Ellis, J. E. (1991). A self-learning faultdiagnosis system. Transactions of the Institute of Measurement and Control, 13(1), 29–35. Zhao, J., Chen, B., & Shen, J. (1998). Multidimensional nonorthogonal wavelet-sigmoid basis function neural network for dynamic process fault diagnosis. Computers and Chemical Engineering, 23, 83–92.
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Diagnosis of process valve actuator faults using a multilayer neural network M. Karpenkoa, N. Sepehria,*, D. Scuseb a
Department of Mechanical and Industrial Engineering, The University of Manitoba, Winnipeg, Man., Canada R3T 5V6 b Department of Computer Science, The University of Manitoba, Winnipeg, Man., Canada R3T 5V6 Received 4 March 2002; accepted 29 October 2002
Abstract This paper investigates the ability of a multilayer neural network to diagnose actuator faults in a Fisher-Rosemount 667 process control valve. A software package that comes with the valve is used to obtain experimental figures of merit related to the position response of the valve given a step command. The particular values of the dead time, peak time, percent overshoot, steady state error, 63% and 86% rise times, and gain are shown to depend on the severity of three commonly occurring faults: incorrect supply pressure, actuator vent blockage, and diaphragm leakage. The relationships between these parameters form fault signatures for each operating condition that are subsequently learned by a multilayer feedforward neural network. The results show that the trained network has the capability to detect and identify various magnitudes of the faults of interest. In addition, it is observed that the network has the ability to estimate fault levels not seen by the network during training. The approach presented in this paper allows the existing instrumentation to be utilised without modification. Thus, the proposed methodology is practical to implement. r 2002 Elsevier Ltd. All rights reserved. Keywords: Condition monitoring; Fault diagnosis; Pneumatic actuators; Actuator faults; Neural networks
1. Introduction A common component found in modern process plants is the pneumatic control valve. It is used in industries such as petrochemical, to control the flow of a fluid, gas, or slurry. In order to avoid unnecessary downtime resulting from process disturbances such as valve failures, manufacturers have been known to use conservative operating conditions during production (Tzafestas & Dalianis, 1994). This practice, however, results in less efficient operation of the plant and increases the overall production costs. Another common practice, which may be used in conjunction with conservative operation of the valve, is known as corrective maintenance. Here, the idea is to operate the process until a complete failure of the control valve, at which time the plant is shut down and the valve is refurbished. Conversely, in preventative maintenance schemes, plant engineers conduct scheduled shutdowns *Corresponding author. Tel.: +1-204-474-6834; fax: +1-204-2757507. E-mail address: [email protected] (N. Sepehri). 0967-0661/03/$ - see front matter r 2002 Elsevier Ltd. All rights reserved. PII: S 0 9 6 7 - 0 6 6 1 ( 0 2 ) 0 0 2 4 5 - 9
during which control valves are subjected to dismantle and overhaul (McGhee, Henderson, & Baird, 1997). In the latter case, valve components that are otherwise functioning normally may be needlessly replaced, thereby adding unnecessarily to operating costs. The ability to detect the occurrence of faults and more importantly identify the causes of faults in pneumatic control valves can reduce downtime, increase product quality, and eliminate the unnecessary replacement of functioning valve components. Thus, there is a need for suitable fault detection and identification (FDI) schemes for pneumatic control valves. Modern methods for FDI of dynamic systems can be grouped into three broad categories, the first being a model-based approach. The model-based approach uses a priori mathematical information about the system to model the normal process (Isermann & Balle! , 1997). Then, the output of the system is compared to the prediction given by the model and a vector of residuals (differences between the actual and the predicted outputs) is generated. The residuals are used to ascertain the condition of the dynamic system. However, it is well known that constructing mathematical models for
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complex systems or for nonlinear systems can be difficult, if not impossible. Furthermore, a great deal of experimentation is generally required to validate the model. Consequently, the model-based approach can be difficult to implement. An alternate approach to the model-based FDI has been to train neural networks to estimate the model of the dynamic system (Bernieri, D’Apuzzo, Sansone, & Savastano, 1994). The approximate model generated by the network is then used in conjunction with measurements of actual system outputs to generate the residuals. McGhee et al. (1997) used this technique to predict the output torque of a rotary pneumatic control valve. The predicted output torque was used along with actual torque measurements to perform fault detection. Since only one variable was available for analysis, the cause of the fault was not identified in their work. Another category of techniques that can be used to perform FDI is based on expert or qualitative reasoning (Zhang, Roberts, & Ellis, 1991). FDI schemes that fall into this category can be thought of as fault analysers since they make decisions about whether or not a fault has occurred based on a set of logical rules that are either pre-programmed by an expert or learned via some form of training. When information about the operation of a dynamic system is presented to the fault analyser, it is tested against the logic and a decision about the condition of the system is made. Sharif and Grosvenor (2000) developed computer software for FDI of a class of process control valves using this approach. They studied faults due to sticking of the valve stem, damaged valve stem packing and blockage of the actuator vent. Furthermore, they suggested that the accuracy of the software could be improved for some faults through the use of pattern recognition techniques. The third class of approaches uses neural networks as pattern classifiers to solve the FDI problem. Here, the networks are trained to recognise data representing the different failure modes of the dynamic system. This approach has been used in a variety of applications. To name a few, Le, Watton, and Pham (1997, 1998) and Crowther, Edge, Burrows, Atkinson, and Woollons (1998) used this approach for FDI in hydraulic fluid power systems. Yen and Lin (2000) and Wang, Propes, Khiripet, Li, and Vachtsevanos (1999) employed neural network classifiers in conjunction with wavelet transforms to perform FDI in machine dynamics and vibration problems. Zhang, Ma, and Yan (2000) as well as Zhao, Chen, and Shen (1998) have also demonstrated the usefulness of this approach in the applications of sensor fault diagnosis and fault diagnosis of chemical processes, respectively. In this paper, a neural network is implemented to detect and identify actuator faults in a typical pneumatic control valve. The faults of interest are incorrect supply pressure, actuator vent blockage, and actuator dia-
phragm leakage. These faults are amongst the common faults causing abnormal operation of control valves (McGhee et al., 1997; Sharif & Grosvenor, 1998; Karpenko & Sepehri, 2001a). The approach taken is to train the network to identify the faults from sets of valve performance data. For each operating condition, a software package that comes with the valve is utilised to automatically calculate seven figures of merit related to the valve step response. These performance parameters are: gain, dead time, peak time, percent overshoot, steady-state error, as well as 63% and 86% rise times. Their particular values are shown to depend upon both the type and magnitude of the fault. Hence, these metrics form information-rich fault signatures that can be used by the neural network to discriminate amongst the faults. The fault signatures are subsequently learned by a multilayer feedforward neural network which estimates the operating condition of the valve in terms of the supply pressure, actuator vent blockage and diaphragm leakage. The multilayer feedforward structure was selected for use as it has been shown to perform well in similar FDI problems (Sorsa, Koivo, & Koivisto, 1991; Koivo, 1994; Crowther et al., 1998). The proposed neural network approach eliminates the need for the human evaluation of the valve performance data, which often requires specialist knowledge (Karpenko, Sepehri, & Scuse, 2001b) and is prone to misinterpretation (Sharif & Grosvenor, 2000). The organisation of the remainder of this paper is as follows: Section 2 describes the typical process control valve under investigation, a Fisher-Rosemount 667, as well as its operation. The available valve performance data are defined and the methods used to introduce the faults into the experimental system are described. In Section 3, the architecture and training of the network is described. It is shown that the measured features of the valve step responses are sufficient to characterise the faults of interest and are suitable inputs to the neural network. Finally, the performance of the network is discussed in Section 4, where it is shown that the network has the ability to correctly detect and identify the faults and generalise well to fault levels not present in the training data. The paper is brought to a close by some concluding remarks in Section 5.
2. Experimental test rig 2.1. Pneumatic control valve Fig. 1 shows the pneumatic control valve under investigation. The valve was modified so that the faults of interest could be introduced experimentally. The flow control device, or valve body, is stroked by a pneumatically driven diaphragm type actuator. The digital valve
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tp Mp 1
t86
ess
t63 0.5
td 0 0
1
2
3
4
5
time (s) valve body
Fig. 2. Performance parameters associated with a typical valve step response.
parameters associated with the valve step response are: Fig. 1. Fisher–Rosemount 667 process valve.
controller (DVC) closes the loop so that position control of the valve stem is realised. The DVC module consists of a current to pressure (I=P) converter and a pneumatic relay. The I=P converter is a field-controlled flapper-nozzle arrangement that transforms an analog control current into a corresponding control pressure. The pneumatic relay then amplifies the control pressure so that a relatively large volume of air can be delivered to, or vented from, the lower chamber of the actuator. This results in a force unbalance across the diaphragm that subsequently causes the valve to open or close. In addition to the control electronics, the DVC also contains a potentiometer type position sensor that measures the position of the valve stem and a pressure transducer that monitors the output pressure of the DVC. The ValveLinkt (Fisher Controls Inc., 1999a) software, which comes with the valve, communicates with the onboard sensors of the DVC through standard RS-232 protocol. The software is used herein to carry out the valve step response tests and automatically calculate the performance parameters associated with each curve.
1. td (dead time)—a measure of the transport lag, the time to achieve a change in position of 1% of the desired step; 2. t63—the time to achieve a change in position of 63% of the desired step; 3. t86—the time to achieve a change in position of 86% of the desired step; 4. tp—the peak time; 5. Mp—the percent overshoot; 6. ess—the steady-state error; 7. K (gain)—the ratio of the percent change in the position of the valve stem to the percent change in magnitude of the input signal (not shown in Fig. 2). Referring to Fig. 2, it is observed that these parameters describe the main features of the valve step response and are indicative of the dynamic and static characteristics of the response. For example, the dead time, peak time and rise times, reflect the shape of the transient portion of the curve. The percent overshoot is indicative of the effective damping and the steady-state error is representative of the continuous response. Parameter K provides a measure of the relative degree of control effort required to position the valve stem. As will be seen later, these metrics are sufficient to characterise the changes in the performance of the valve due to the occurrence of the faults under investigation.
2.2. Valve performance parameters 2.3. Failure modes The valve step response indicates the condition of the valve by the nature of the position–time curve resulting from a step-input command. To facilitate comparison for condition monitoring, several figures of merit are associated with the response in order to quantify the curve. With reference to Fig. 2, seven performance
Although pneumatic control valves can fail in a variety of modes (see McGhee et al., 1997), only faults manifesting themselves in the actuator are considered here. The faults of interest are: (i) incorrect supply pressure, (ii) actuator vent blockage, and (iii) diaphragm
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leakage. These faults can be easily quantified and simulated experimentally, with minimal modification of the valve. The motivation for considering the incorrect supply pressure fault is the fact that the supply pressure directly influences the volume of air that can be delivered to the actuator (Fisher Controls Inc., 1999b). This adversely affects the position response of the valve. The incorrect supply pressure fault can occur from a blockage or leak in the supply line, or by increased demand placed on the plant air supply. As shown in Fig. 3, an adjustable pressure regulator was placed between the DVC and the main air supply to produce the supply pressure fault. Detecting the actuator vent blockage is also important since it changes the system dynamics by increasing the effective damping of the system. When air is supplied to the lower chamber of the actuator, the pressure increases allowing the diaphragm to move upwards against the spring force. As the diaphragm moves upward, air that is trapped in the upper chamber escapes through the vent. When the vent becomes partially blocked due to debris, the pressure in the upper chamber increases creating a pressure surge that opposes the motion of the diaphragm. Similarly, when air is purged from the lower chamber, and the vent is partially blocked, a partial vacuum is created in the
upper chamber. Again, the motion of the diaphragm is hindered and the performance of the system is impaired. In cases when the vent is entirely blocked, the valve cannot be stroked through its full range. Placing an adjustable needle valve in the vent port, as illustrated in Fig. 3, simulated the vent blockage. The full-open position of the needle valve was designated as 0% blockage and the full-closed position was designated as 100% blockage. Finally, the condition of the diaphragm should be monitored due to the cyclic nature of the stresses induced upon the diaphragm as it flexes. As a result, fatigue failure of the diaphragm will inevitably occur. Thus, it is important to detect and identify diaphragm leakage since it is an indicator of the condition of the diaphragm. With reference to Fig. 3, diaphragm leakage was simulated by diverting air around the diaphragm by means of a flexible hose connecting the output of the DVC to the upper chamber of the actuator. The leakage flow was controlled by a needle valve with 100% leakage (total diaphragm failure) denoting the adjustment where the valve ceased to respond to any input signal.
3. Neural network implementation 3.1. Network structure
needle valve (vent blockage) needle valve (diaphragm leakage)
DVC
plant air supply pressure regulator (incorrect supply pressure)
Fig. 3. Schematic of the experimental setup illustrating the methods by which various faults are introduced into the system. The pressure regulator allows incorrect supply pressures to be set while the two needle valves allow diaphragm leakage and upper casing vent blockage to be simulated.
A feedforward network can be operated in one of two ways to solve the FDI problem presented here: (i) the network assigns each operating condition to a specific class, or (ii) the network estimates the magnitude of the faulty condition. In the first case, each vector of input data is assigned a class vector that represents a specific mode of operation (either normal or faulty). Then, the number of output neurons is set equal to the number of class vectors. The network is trained such that the neuron with the largest output indicates the condition of the valve. Clearly, the size of the output layer grows as the number of possible fault classes increases. This leads to a larger network, greater number of adjustable weights, and possibly longer training times. Furthermore, the ability of the network to generalise to fault levels not present in the training data is poor. The size of the network can be significantly reduced if it is operated such that the outputs estimate the magnitude of each fault. In this case, only one output neuron is required for each failure mode. This methodology was employed here. With reference to Fig. 4, the seven inputs to the network included all of the step response features listed in Section 2.2. The network was restricted to have a single hidden layer with a variable number of hidden neurons. Single layer networks were not considered due to their poor generalisation ability as compared with multilayer networks (Sorsa et al., 1991).
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K
percent vent blockage x4 x5
y2 percent diaphragm leakage
…
ess
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Fig. 4. Network architecture.
Neurons in the hidden layer used hyperbolic tangent activation functions. The three linear output neurons estimate the magnitude of the supply pressure, percent vent blockage and percent diaphragm leakage according to the following relation: ! m 7 X X yk ¼ wjk tanh wij xi þ w0k z0 ; k ¼ 1; 2; 3; ð1Þ j¼1
i¼0
hysteresis and deadband in the actuator, data arising from the negative (reset) steps were discarded. This procedure was carried out for each of the 17 operating conditions resulting in 238 input/output vectors of data available for training and testing the FDI network. Table 2 lists the ranges of each of the seven performance parameters that were obtained from the experiments. In practice, a similar set of tests would be carried out to obtain training data from which a unique FDI network
where xi is the input and yk is the network output. wij is the adjustable weight between input i and hidden neuron j and wjk is the adjustable weight between hidden neuron j and output neuron k. Index m denotes the number of neurons in the hidden layer. Note that the bias terms are absorbed into Eq. (1) by setting x0=1 and z0=1.
Table 1 Listing of the faults and their magnitudes
3.2. Training data
Normal operating condition 1 124
0
0
Sixteen faulty conditions were examined in this study. They are listed in Table 1 along with the normal operating condition. The faulty operating conditions were chosen to reflect a wide range of variation in the severity of each failure mode. While possible in practice, situations where two or more faults occur simultaneously were not considered here due to the exceedingly large number of possible fault combinations. This represents a potential limitation of the approach. Step response tests were carried out to ascertain the seven performance parameters associated with each operating condition. The test signal consisted of a series of steps beginning with the valve positioned at its lower stop. First, the valve was brought to 10% of its full travel and allowed to reach equilibrium. Then, the valve was moved from 10% to 25% of its stroke and back to the 10% position. This sequence was repeated 14 times so that the slight variations in the responses would be captured. Fig. 5 shows the first few periods of the responses for a healthy valve. Due to the effects of
Incorrect supply pressure fault 2* 117 3 110 4* 103 5 97 6* 90 7 83 8* 76 9 69
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
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leakage fault 124 124 124 124
Vent blockage fault 14 124 15 124 16* 124 17 124
Vent blockage (%)
Diaphragm leakage (%)
Data for those faults with an asterisk were unseen during training and were used to test the generalisation capabilities of the network.
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25 20 15 10 5 0 0
5
10
15
20
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Fig. 5. Typical experimental step responses of a healthy valve.
could be formed prior to installation of the valve. Then, the performance parameters would be evaluated periodically while the valve is in service and the network queried in order to assess the condition of the valve. Presently, it is assumed that the valve would be taken off-line to ensure that the position information is
unaffected by process flow forces and that the process itself is not disturbed by the step response test. Furthermore, since accurate position information is required, it is assumed that the performance of the position transducer would be validated prior to administering the step response tests. Fig. 6 illustrates the effects of the faults upon the step response curve for the most severe case of each fault: 69 kPa supply pressure, 40% diaphragm leakage, and 100% vent blockage. A typical step response curve for a healthy valve is included in Fig. 6 for reference. Clearly, the most severe case of each fault has a significant effect on the performance of the valve, which is captured as changes in the particular values of the performance parameters. However, from Fig. 6, it is seen that the valve performance for the 100% vent blockage fault is similar to that of the healthy valve. This indicates that the vent blockage fault is potentially the most difficult to diagnose. In contrast, Fig. 7 shows the changes in the valve step response corresponding to the onset of each fault:
Table 2 Ranges of the performance parameters Data set 1 2* 3 4* 5 6* 7 8* 9 10 11 12* 13 14 15 16* 17
min max min max min max min max min max min max min max min max min max min max min max min max min max min max min max min max min max
td (s)
t63 (s)
t86 (s)
tp (s)
Mp (%)
ess (%)
K
0.132 0.143 0.133 0.275 0.106 0.287 0.268 0.291 0.264 0.292 0.224 0.295 0.237 0.244 0.231 0.354 0.267 0.331 0.125 0.136 0.128 0.278 0.121 0.285 0.130 0.288 0.246 0.341 0.255 0.261 0.244 0.246 0.281 0.292
0.177 0.237 0.158 0.293 0.159 0.297 0.298 0.302 0.302 0.309 0.305 0.353 0.369 0.376 0.398 0.479 0.734 0.788 0.248 0.266 0.158 0.293 0.165 0.295 0.255 0.298 0.466 0.526 0.378 0.384 0.353 0.358 0.301 0.303
0.210 0.335 0.168 0.364 0.168 0.410 0.310 0.334 0.311 0.346 0.314 0.463 0.497 0.504 0.535 0.687 1.173 1.231 0.361 0.391 0.168 0.358 0.182 0.361 0.308 0.384 0.676 0.762 0.498 0.508 0.458 0.468 0.311 0.325
0.245 0.438 0.178 0.485 0.179 0.569 0.320 0.368 0.322 0.386 0.325 0.586 0.634 0.640 0.681 0.926 1.619 1.701 0.479 0.525 0.178 0.477 0.200 0.479 0.318 0.516 0.886 1.024 0.624 0.640 0.569 0.584 0.321 0.348
16.47 18.11 16.37 17.48 16.30 17.30 16.64 17.41 16.20 16.94 15.16 15.84 14.39 15.29 12.73 13.14 5.21 6.28 10.95 12.37 12.83 13.36 15.14 16.07 10.03 10.46 6.92 7.83 10.63 11.77 12.72 13.46 14.32 15.57
0.30 0.39 0.43 0.55 0.54 0.60 0.72 0.80 0.87 0.93 1.02 1.07 1.11 1.21 1.28 1.33 1.41 1.52 0.13 0.28 0.18 0.26 0.27 0.38 0.52 0.60 2.81 2.93 2.03 2.16 1.49 1.60 0.90 1.00
1.007 1.015 1.006 1.019 1.008 1.016 1.004 1.012 1.005 1.015 1.015 1.022 1.010 1.022 1.013 1.024 1.017 1.034 1.007 1.015 1.016 1.021 1.005 1.023 0.996 1.005 0.971 0.987 0.982 0.991 0.988 1.005 0.988 1.006
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6
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4 2 0 0
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3
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5
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Fig. 6. Representative experimental step response plots corresponding to the most severe failure modes: 69 kPa supply pressure, 40% diaphragm leakage, and 100% vent blockage. The step response of a healthy valve is included for comparison.
14
healthy valve
12
vent blockage position (%)
were unseen during training and were used to assess the ability of the trained network to generalise to fault levels not present in the training data. All input/output vectors were normalised to lie on the interval [1, 1], a common pre-processing technique used to improve the performance of the network. The training process establishes the mapping between the values of the performance parameters and the corresponding operating condition of the valve through adjustment of the network weights in (1). To begin training, the adjustable weights of the hidden layer neurons were initialised using the Nguyen–Widrow algorithm which has the effect of accelerating training by distributing the active regions of the neurons more evenly over the range of inputs (Nguyen & Widrow, 1990). The algorithm was implemented by first assigning the weights random numbers on the interval [0.5, 0.5]. The weights were then scaled as follows: pffiffiffiffi 0:7 n m wij;new ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi wij;old Pn 2 l¼1 wlj i ¼ 1; 2; y; n; j ¼ 1; 2; y; m;
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incorrect supply pressure
4 2 0 0
1
2
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5
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Fig. 7. Representative experimental step response plots corresponding to the onset of each failure mode: 117 kPa supply pressure, 10% diaphragm leakage, and 50% vent blockage. The step response of a healthy valve is included for comparison.
117 kPa supply pressure, 10% diaphragm leakage and 50% vent blockage. It is seen that the step response, and hence the values of the performance parameters, change slightly in the presence of the faults. It is noted that it is difficult to visually determine the condition of the valve when the fault level is small. However, as will be shown later, the proposed neural network scheme has the ability to perform this task. 3.3. Network training To facilitate the assessment of the generalisation ability of the trained network, the available experimental data were subdivided into training and test sets. The test set consisted of those input/output vectors corresponding to the faults followed by an asterisk in Tables 1 and 2. Consequently, only 154 of the 238 available input/output vectors were used directly in the training process. The remaining 84 input/output vectors
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ð2Þ
where n is the number of network inputs. The bias weights, w0j ; were pffiffiffiffi given pffiffiffiffirandom initial values on the interval [0:7 n m; 0:7 n m]. The remaining adjustable parameters were given random initial values on the interval [1, 1]. The goal of training is to minimise the mean squared error between the desired network outputs and the actual network outputs which is written for batch mode training, where the error is evaluated over the entire training data set, as EðtÞ ¼
P X 3 2 1 X dk;p yk;p ðtÞ ; P p¼1 k¼1
ð3Þ
where dk,p is the desired output corresponding to input vector xp ; yk,p(t) is the network output corresponding to input vector xp after training epoch t, and P is the total number of input/output vectors in the training data set. To minimise (3), the gradient descent method with momentum (Haykin, 1999) was employed. The weights were updated according to DWðtÞ ¼ ZrEjwðtÞ þm DWðt 1Þ:
ð4Þ
In Eq. (4), W is the matrix of adjustable weights, Z is the learning rate, m is the momentum term, r is the gradient operator and DWðtÞ ¼ WðtÞ Wðt 1Þ: To accelerate convergence, the learning rate was continuously adjusted during training as follows: ( rZold ; DEo0; Znew ¼ ð5Þ sZold ; DE > 0; where DE is the change in the network error, Enew Eold ; resulting from the last weight update. Parameters r
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where ropt is the fraction of the available data that should remain in the training data subset, P is the total number of available input/output vectors, and a is the number of adjustable weights in the network. The training subset was used to adapt the weights via Eqs. (3)–(5). After each epoch, the network was queried with the input vectors in the validation subset and the mean squared validation error was calculated. If the validation error increased with continued training, training was terminated due to the potential for overfitting. If the validation error remained the same for more than 10 successive epochs, it was assumed that the network had converged. Typical network learning curves are shown in Fig. 8. As is seen, both the training error and the validation error decrease rapidly at the beginning of training. Small oscillations in the training error are a result of adjusting the learning rate during training. As training continues, performance enhancement begins to diminish and the training error curve levels out. A similar result is noted for the curve representing the validation error. The training process was terminated after 450 weight updates since the validation error failed to decrease for more than 10 successive epochs. Fig. 8 also verifies that additional training, beyond the early stopping point, yields only minimal improvement in the network accuracy at the expense of longer training time. The ideal number of hidden neurons was determined by increasing the number of neurons in the hidden layer until improvements in the accuracy of the network diminished. For each hidden layer size, 500 networks were trained. The results were averaged in order to minimise the effects of the random assignment of the initial weights. Referring to Fig. 9, it was found that the overall network accuracy, measured as the unscaled mean absolute error, increased as the number of hidden
10.000
mean squared error
and s were set to standard values of 1.1 and 0.5, respectively (Bishop, 1995). Setting the momentum term, m, in (4) to 0.9 was also found to increase the speed of learning. Early stopping (Haykin, 1999) was used to ensure the network would generalise well to unseen data. This required the available training data pool to be further divided into training and validation subsets. The optimal number of input/output vector pairs in each subset depends upon the number of input/output vectors available as well as the number of adjustable weights in the network. The number of input/output vectors in each subset was determined by the following equation that has been proposed by Amari, Murata, Muller, . Finke, and Yang (1996): 8 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi > 2a 1 1 < for Pp30a; 1 ropt ¼ ð6Þ 2ð a 1Þ > : 1 for P > 30a;
training error validation error stop
training terminated
1.000
0.100
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400
600
800
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Fig. 8. Typical learning curves.
10 unscaled mean absolute error
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excess hidden neurons 8
6
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0 2
3
4
5
6
7
8
9
10 11 12 13 14
hidden neurons
Fig. 9. Unscaled mean absolute error over the entire training data set versus the number of hidden neurons.
neurons was increased from 2 to 6. The networks having 5 or 6 neurons in the hidden layer resulted in the lowest error, with the former performing only marginally better. As the number of hidden neurons was increased past 6, there was no marked improvement in accuracy. Consequently, a network with 5 hidden neurons was chosen as the solution to the FDI problem.
4. Results Fig. 10 shows the performance of the FDI network when queried with data representing the incorrect supply pressure fault. Dashed vertical lines separate the data sets. Each discrete point represents a different input vector taken from the available data and the entire set is shown in a sequential fashion for comparative purposes. The desired network outputs, representing the actual operating condition of the system, are shown as solid lines. Data points represented by circles, K, are the actual network outputs for input vectors used in the training process. Data points represented by diamonds, B, are the actual network outputs for input vectors that
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11
12*
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data set
Fig. 10. Output of the network for the supply pressure fault: —actual operating condition; network output when queried with training data; network output when queried with unseen data.
Fig. 11. Output of the network for the diaphragm leakage fault: — actual operating condition; network output when queried with training data; network output when queried with unseen data.
were unseen by the network during training. The later data serve to assess the ability of the network to generalise to fault levels not present in the training data. With reference to Fig. 10, the outputs of the trained neural network are observed to follow the changes in the supply pressure quite well. Thus, the network is able to detect the incorrect supply pressure fault since the output of the supply pressure neuron varies in accordance with the changes in the supply pressure. Furthermore, it is observed that the network is able to estimate fault magnitudes not present in the training data. Fig. 10 also shows that the outputs of the neurons representing the vent blockage and diaphragm leakage faults remain relatively close to the actual values as the supply pressure is varied. This indicates that the network has successfully learned to isolate the incorrect supply pressure fault from the other two. Figs. 11 and 12 show the performance of the network when queried with data representing the diaphragm leakage and vent blockage faults, respectively. Again, the network outputs are seen to track the changes in the fault levels and generalise well to fault levels not present in the training data. As before, the network exhibits the ability to both detect and isolate each fault from the others.
Upon inspection of Figs. 10–12, one notes that the largest scatter is observed in the output of the vent blockage neuron. This can be explained with reference to Fig. 6. As is seen, both the incorrect supply pressure fault and the diaphragm leakage fault result in relatively large changes in the step response. Conversely, the vent blockage fault results in only small changes in the step response, from normal, even in the limiting case where the vent was completely blocked off. This implies that the vent blockage is inherently difficult to diagnose and explains why the scatter is relatively large when the blockages are small. The network performance is, however, quite acceptable and improves as the magnitude of the vent blockage fault increases.
5. Conclusions This paper has investigated a neural-network-based scheme for detection and identification of actuator faults in a typical process control valve. The faults of interest were various incorrect supply pressures, actuator vent blockages and diaphragm leakages. These faults are amongst the common problems associated with the abnormal operation of the valve. Valve position
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presented here can be used directly to perform the detection and isolation of incorrect supply pressure, diaphragm leakage and vent blockage faults.
150 125 100 75
Acknowledgements
50 25
The authors would like to acknowledge the assistance of Controltech Inc., Winnipeg, Canada, who granted partial funding for this work in addition to providing the control valve used in the research. The authors would also like to extend their deepest thanks to Mr. Larry Mercado (of Controltech Inc.) for generously offering both his time and technical expertise during the course of the project.
0
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References
120 100 80 60 40 20 0
–20
14
15
16*
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Fig. 12. Output of the network for the actuator vent blockage fault: — actual operating condition; network output when queried with training data; network output when queried with unseen data.
response parameters, dead time, peak time, percent overshoot, steady-state error, 63% and 86% rise times, and gain were obtained experimentally for a number of operating conditions. The specific values of these performance parameters were observed to depend upon both the magnitude and type of fault. For each operating condition, the performance parameters formed a discriminatory fault signature that was subsequently learned by a multilayer feedforward neural network with the goal of successfully detecting and identifying the faults. The experimental results proved that the trained network has the capability to detect and identify the various magnitudes of the faults of interest, as they occur singly. Furthermore, the results indicate that the network can accurately estimate fault levels unseen during the training process. This information is vital to a process valve condition monitoring strategy since it can be used to detect problems and assist in the timely scheduling of repairs to the valve, before a severe failure occurs. Future work in this area includes training the network to discriminate against other control valve failure modes, such as increased valve stem friction, or wear of mechanical components. However, the scheme
. Amari, S., Murata, N., Muller, K.-R., Finke, M., & Yang, H. (1996). Statistical theory of overtraining—Is cross-validation asymptotically effective? Advances in Neural Information Processing Systems, 8, 176–182. Bernieri, A., D’Apuzzo, M., Sansone, L., & Savastano, M. (1994). A neural network approach for identification and fault diagnosis on dynamic systems. IEEE Transactions on Instrumentation and Measurement, 43(6), 867–873. Bishop, C. M. (1995). Neural networks for pattern recognition. New York: Oxford University Press Inc. Crowther, W. J., Edge, K. A., Burrows, C. R., Atkinson, R. M., & Woollons, D. J. (1998). Fault diagnosis of a hydraulic actuator circuit using neural networks—an output vector space classification approach. Journal of Systems and Control Engineering, 212(1), 57–68. Fisher Controls Inc. (1999a). FIELDVIEWs ValveLinkt VL2000 series software user guide. Iowa: Fisher Controls International Inc. Fisher Controls Inc. (1999b). Control valve handbook. Iowa: Fisher Controls International Inc. Haykin, S. (1999). Neural networks: A comprehensive introduction (2nd ed.). New Jersey: Prentice-Hall. Isermann, R., & Ball!e, P. (1997). Trends in the application of modelbased fault detection and diagnosis of technical processes. Control Engineering Practice, 5(5), 709–719. Karpenko, M., & Sepehri, N. (2001a). A neural network based fault detection and identification scheme for pneumatic process control valves. Proceedings of the IEEE Conference on Systems, Man and Cybernetics, Tucson, AZ, 1, 93–98. Karpenko, M., Sepehri, N., & Scuse, D. (2001b). Neural network detection and identification of actuator faults in a pneumatic process control valve. Proceedings of the IEEE international symposium on computational intelligence in robotics and automation, Banff, Canada, 166–171. Koivo, H. N. (1994). Artificial neural networks in fault diagnosis and control. Control Engineering Practice, 2(1), 89–101. Le, T. T., Watton, J., & Pham, D. T. (1997). An artificial neural network based approach to fault diagnosis and classification of fluid power systems. Journal of Systems and Control Engineering, 211(4), 307–317. Le, T. T., Watton, J., & Pham, D. T. (1998). Fault classification of fluid power systems using a dynamics feature extraction technique and neural networks. Journal of Systems and Control Engineering, 212(2), 87–97. McGhee, J., Henderson, I. A., & Baird, A. (1997). Neural networks applied for the identification and fault diagnosis of process valves and actuators. Measurement: Journal of the International Measurement Confederation, 20(4), 267–275.
ARTICLE IN PRESS M. Karpenko et al. / Control Engineering Practice 11 (2003) 1289–1299 Nguyen, D., & Widrow, B. (1990). Improving the learning speed of 2layer neural networks by choosing initial values of the adaptive weights. Proceedings of the International Joint Conference on Neural Networks, San Diego, CA, 3, 21–26. Sharif, M. A., & Grosvenor, R. I. (1998). Fault diagnosis in industrial control valves and actuators. Proceedings of the IEEE Instrumentation and Measurement Technology Conference, St. Paul, MN, 2, 770–778. Sharif, M. A., & Grosvenor, R. I. (2000). The development of novel control valve diagnostic software based on the visual basic programming language. Journal of Systems and Control Engineering, 214(2), 99–127. Sorsa, T., Koivo, H. N., & Koivisto, H. (1991). Neural networks in process fault diagnostics. IEEE Transactions on Systems, Man, and Cybernetics, 21(4), 815–825. Tzafestas, S. G., & Dalianis, P. J. (1994). Fault diagnosis in complex systems using artificial neural networks. Proceedings of the IEEE Conference on Control Applications, Glasgow, UK, 2, 877–882.
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Wang, P., Propes, N., Khiripet, N., Li, Y., & Vachtsevanos, G. (1999). An integrated approach to machine fault diagnosis. Proceedings of the IEEE annual textile, fiber and film industry technical conference, Atlanta, GA, 59–65. Yen, G. G., & Lin, K. (2000). Wavelet packet feature extraction for vibration monitoring. IEEE Transactions on Industrial Electronics, 47(3), 650–667. Zhang, J., Ma, J., & Yan, Y. (2000). Assessing blockage of the sensing line in a differential-pressure flow sensor by using the wavelet transform of its output. Measurement Science and Technology, 11(3), 178–184. Zhang, J., Roberts, P. D., & Ellis, J. E. (1991). A self-learning faultdiagnosis system. Transactions of the Institute of Measurement and Control, 13(1), 29–35. Zhao, J., Chen, B., & Shen, J. (1998). Multidimensional nonorthogonal wavelet-sigmoid basis function neural network for dynamic process fault diagnosis. Computers and Chemical Engineering, 23, 83–92.