Signal Validation Using an Adaptive Neural Fuzzy Inference System (accepted for publication by Nuclear Technology by: Wesley Hines and Robert E. Uhrig Department of Nuclear Engineering The University of Tennessee Knoxville, Tennessee 37996
[email protected] [email protected] and Darryl J. Wrest Systems Health Management Group Honeywell Technology Center Minneapolis, Minnesota, 55418
[email protected]
MS #9385
Biographies J. Wesley Hines (BS, Electrical Engineering, Ohio University, 1985, MS, Nuclear Engineering, Ohio State University, 1992, MBA, Ohio State University, 1992, PhD, Ohio State University, 1994) is a research assistant professor in the Nuclear Engineering Department at The University of Tennessee where he teaches classes in expert systems, fuzzy logic and neural networks. Current research involves the application of artificial intelligence and other advanced technologies to solving engineering problems. Robert E. Uhrig (BS, Mechanical Engineering, University of Illinois, 1948, MS, Theoretical and Applied Mechanics, Iowa State University, 1950, PhD, Theoretical and Applied Mechanics, Iowa State University, 1954) holds a joint appointment in the Nuclear Engineering Department at The University of Tennessee and in the Instrumentation and Control Division at the Oak Ridge National Laboratory under the UT/ORNL Distinguished Scientist Program. His work at both institutions concerns the application of advanced technologies to enhance the performance of nuclear poser plant systems. Darryl J. Wrest (BS, electrical engineering, University of Missouri at Columbia, 1993; BS, nuclear engineering, University of Missouri at Rolla, 1994; MS, nuclear engineering, University of Tennessee at Knoxville, 1996) is a research scientist in the Systems Health Management Group at the Honeywell Technology Center in Minneapolis, Minnesota. His research interest is in the application of artificial intelligence to systems health management issues.
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ABSTRACT An Adaptive Neural Fuzzy Inference System (ANFIS) modeling technique is introduced for sensor and associated instrument channel calibration validation. This method uses an inferential modeling technique after a genetic algorithm search is used to empirically determine the appropriate combinations of input variables to optimally model each signal to be monitored. These variables are used as input to a fuzzy inference system which is trained to estimate the monitored signals. The estimates are compared to the actual signals and a statistical decision technique known as the Sequential Probability Ratio Test (SPRT) is used to detect sensor anomalies. The sensor fault detection system is demonstrated using data supplied from Florida Power Corporation's Crystal River #3 Nuclear Power generating station.
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I. INTRODUCTION In large power generating systems and process control systems, outputs from many different channels are used in control systems, safety critical systems, and for plant state identification. It is necessary to validate these outputs to increase the reliability of operator decisions and automatic plant operations. A common problem faced by designers of computer based systems intended to monitor the performance of a dynamic process with the objective of assuring operation within specifiable constraints is that of sensor reliability. Since the output of sensors provides the only objective source of information for decision making, it is essential that the condition of these sensors be known. The dual problems of sensor validation and faulted sensor replacement must be considered as an integral part of the design of a modern monitoring, diagnostic, or control system. Traditional approaches to instrument calibration at nuclear power plants are expensive both in labor and money. These approaches vary from calibration by replacement, to transfer calibration using standard instruments. Technical Specifications require specific instruments be calibrated on time tables that coincide with the original fuel cycle of the plant. These calibrations require that the instrument be taken out of service and be falsely-loaded to simulate actual in-service stimuli. This can lead to damaged equipment and incorrect calibrations due to adjustments made under non-service conditions. The end result is that many instruments are unnecessarily calibrated. While correct adjustment is vital to maintaining proper plant operation, an alternative condition based technique is desirable. As utilities desire to move to 24 month fuel cycles, there is an increased need for performance based calibration requirements. When implementing performance based calibrations, the instruments are calibrated only when they are determined to be out of calibration. Monitoring instruments for calibration performance will allow nuclear utilities to reduce the efforts necessary to assure the instruments are calibrated. Benefits include an industry wide cost savings, less outage time, decreased radiation exposure to workers, a decrease in low level radioactive waste, decrease in work scheduling, and easier compliance
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with NRC Generic Letter 91-04 for extending calibration intervals. The EPRI/Utility On-Line Monitoring Working Group estimates an industry wide cost savings of $40M to $290M over the next 20 years depending on the values applied to indirect benefits. Several methods for on-line sensor validation have been investigated. The methodology most similar to the Adaptive Neural Fuzzy Inference System (ANFIS) (Jang1) uses inferential neural networks (Black2). Also closely related is the use of autoassociative neural networks (AANNs) [Upadhyaya3, Kramer4, Dong and McAvoy5, Hines6, Wrest7]. Other methods investigated by Upadhyaya8 include generalized consistency checking process empirical modeling, univariate autoregression modeling, and multi-dimensional process hypercube comparison. A comparison of the ANFIS methodology with that of artificial neural networks will be given in Section V. The sensor fault detection system proposed in this paper consists of two main components. The first component is an Adaptive Neural Fuzzy Inference System which is implemented in MATLAB9 and their Fuzzy Logic Toolbox10. This system requires somewhat correlated signals as inputs so that the ANFIS model will infer the best output estimate of the signal of interest. The amount of required correlation is further discussed in Section V.C. The ANFIS model is a fuzzy inference system (FIS) that is tuned with a backpropagation algorithm based on a collection of input/output data. Thus, like a neural network model, ANFIS has the ability to learn a desired input/output mapping. By comparing the actual signal (sensor output) to the ANFIS model's best estimate of the signal, we can detect a drifting sensor condition. The second component of the sensor validation system is the Sequential Probability Ratio Test (SPRT) module. The residual, which is the difference between the actual sensor output and the model's estimate of the signal is used as input to the SPRT module which then determines whether the sensor has failed. II. ADAPTIVE NEURO-FUZZY INFERENCE SYSTEM (ANFIS) An ANFIS is a fuzzy inference system (FIS) that can be trained with a backpropagation algorithm to model some collection of input/output data. Allowing the system to adapt
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provides the fuzzy system with the ability to learn the input/output relationships embedded in the collected data. The ANFIS network structure facilitates the computation of a gradient vector that relates the reduction of an error function to a change in the parameters of the fuzzy inference system. Once this gradient vector is obtained, a number of optimization routines can be applied to reduce the error between the actual and desired outputs. In the neural network literature, this process is called learning by example. II.A. General ANFIS Description The ANFIS system described here uses the Sugeno-style fuzzy model (also known as the TSK fuzzy model) proposed by Takagi, Sugeno11, and Kang12. In a Sugeno style model, a singleton (single spike) output membership function is used instead of a fuzzy set as used in the more common Mamdani style inference system (Mamdani13). This singleton can be thought of as a defuzzified fuzzy set. Using singleton output membership functions enhances the efficiency of the defuzzification process because it greatly simplifies the computation required to find the centroid of the output fuzzy set. Rather than integrating across a continuously varying two-dimensional shape to find the centroid, one can simply find the weighted average of a few data points. A more detailed discussion of the ANFIS model can be found in Jang's original paper14 or in his recent book15. The following description of the ANFIS architecture is given as a brief introduction only. A typical fuzzy rule in the Sugeno fuzzy model has the form: if x1 is A and x2 is B then z = f(x)
[eqn. 2.1]
where A and B are fuzzy sets in the antecedent and z = f(x) is a crisp function in the consequent. When f(x) is a first order polynomial, as in equation 2.2, the resulting fuzzy inference system is called a first-order Sugeno fuzzy model. This is the model that is used in this study. When f is a constant, we then have a zero-order Sugeno model. Jang points out that a zero-order Sugeno fuzzy model is functionally equivalent to a radial basis function neural network under certain minor constraints16. z = f(x) = px1 + qx2 + r
[eqn 2.2] 6
A fuzzy inference system is composed of several rules that relate the input to the output. These rules are initially chosen so that their premise membership functions cover the entire input space. The membership functions are then adapted during training to optimally cover the portion of the space where there is input data. A very simple first-order Sugeno fuzzy model with only two rules would be represented by the following equations. Rule 1: If x1 is A1 and x2 is B1, then
f1 = p1x1+q1x2+r1
Rule 2: If x1 is A2 and x2 is B2, then
f2 = p2x1+q2x2+r2
[eqn 2.3]
In these two rules, x1 and x2 are the inputs and A1 and A2 are the premise membership functions that cover x1's input space and B1 and B2 are the premise membership functions that cover x2's input space. Each rule has a singleton output fi and those outputs are combined with a weighted average to form the output of the FIS:
f =
w1 f 1 + w 2 f 2 = w1 f 1 + w 2 f 2 w1 + w 2
[eqn. 2.4]
where the weights are the firing strengths of the premises. Figure 1 shows the corresponding equivalent ANFIS architecture for a model with two rules. The fuzzy sets (A, B) are generalized bell membership functions (eqn 2.5) with three trainable parameters: {ai , bi , ci }. These parameters are known as the premise parameters and are adapted through the training process with a backpropagation training paradigm. µ ( x ) ==
1
[eqn. 2.5]
b
x − ci 2 i 1 + ai
The Π nodes perform the AND function of the fuzzy rules (eqn. 2.3). And the output is the activation level of the rule.
w i = µ Ai ( x1 ) ∗ µBi ( x2 ), i = 1,2.
[eqn. 2.6]
The activation levels are normalized with equation 2.7
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wi =
wi , w1 + w2
i = 1,2.
[eqn. 2.7]
and these activation levels are used in equation 2.4 to produce the output. The polynomial parameters: {pi , qi , ri }, called the consequent parameters, are optimized using a least squares methodology as will be explained in Section II.A.2. II.A.1 Partitioning of the Input Space The membership functions (A1, A2, B1, and B2), called the antecedents, partition the input space into a number of local fuzzy regions. In the case of a FIS with two fuzzy rules and two membership functions as defined in Section II.A, there are two partitions resulting in four fuzzy regions. This type of partitioning is the simplest and is called grid partitioning. As the number of inputs increases, the number of fuzzy rules and partitions increase. This explosion in the number of rules is commonly referred to as the curse of dimensionality. A fuzzy system with n inputs and two membership functions for each rule results in 2n rules. It is apparent that as the number of inputs increases, the size of the fuzzy system soon becomes unmanageable. This unmanageability can be reduced by using more complex partitioning strategies (Jang14 Kosko17). Grid partitioning was used in this study because it is the method used in the ANFIS function supplied in the MATLAB Fuzzy Logic Toolbox9. II.A.2 Hybrid Learning Algorithm A FIS of this form is trained using input/output patterns using a hybrid training algorithm. It is termed a hybrid algorithm because the premise and consequent parameters are trained using entirely different procedures. The premise parameters, that define the placement and shape of the membership functions, are trained with a backpropagation algorithm while the consequent parameters, that define how to combine the rule outputs, are solved for with a least squares algorithm. Training begins with a forward pass to find the activation levels of the rules, and a least squares solution is used to solve for the consequent parameters. This can be accomplished
8
because the equations of Section II.A can be rearranged so that the output is expressed as a linear combination of the consequent parameters:{pi , qi , ri }.
f = ( w1 x ) p1 + ( w1 x)q1 + ( w1 )r1 + ( w2 x ) p2 + ( w2 x )q2 + ( w2 )r2
[eqn 2.8]
Next, a gradient descent based training algorithm is used to backpropagate the error signals and modify the premise parameters to reduce the error. This hybrid procedure is iteratively applied until the error is reduced to a desired goal or until a maximum number of training cycles is reached. This same training algorithm can be used to train neural networks (Masters18). II.B. MATLAB's ANFIS Implementation MATLAB's software package9 and its associated Fuzzy Logic Toolbox10 were used to create the ANFIS based signal validation system. MATLAB's ANFIS supports first order Sugeno systems that have a single output and unity weights for each rule. The ANFIS system is developed by using a training data set that contains the desired input/output data pairs of the system to be modeled and a validation data set that checks the generalization capability of the resulting fuzzy inference system (FIS). The root mean square error (RMSE) for both the training set and the validation set are computed at each epoch. The fuzzy inference system parameters with the minimum validation set error is chosen as optimal. Conversely, choosing the parameter set with the smallest training set error may result in a network that is overfitted or simply does not generalize well. Overfitting is characterized by a network that fits the peculiarities of the training set well but does not generalize to the test set. III. SEQUENTIAL PROBABILITY RATIO TEST (SPRT) The SPRT technique, which was originally developed by Wald19 and later used by Upadhyaya3 for signal validation, uses a statistical method to determine if a sensor has failed. Rather than computing a new mean and variance at every new sample, the SPRT continuously monitors the sensors performance by processing the residuals. This SPRT based method is
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optimal in the sense that a minimum number of samples is required to detect a fault existing in the signal. The residual signals, which are the difference between the sensor measurements and the estimates from the trained ANFIS system, are used to generate a likelihood ratio. When a sensor is operating correctly, the residual should have a mean of zero, and a variance comparable to that of the sensor. If there is sensor drift, the residual mean shifts. Due to the shift in residual mean, the likelihood ratio increases. If the likelihood ratio increases above a certain predefined boundary (user specified by false and missed alarm probabilities), the residuals are more likely to be from the faulted distribution than from the unfaulted distribution, and an alarm is initiated. IV. SYSTEM DEVELOPMENT IV.A. Input Parameter Selection Plant safety points to be monitored were estimated using an inferential methodology. This methodology uses the information inherent in related signals to estimate the signal of interest. These correlated input signals were selected with a Genetic algorithm technique which is a non-linear optimization technique. Three safety points were selected to be monitored; a steam generator level, reactor flow, and reactor outlet temperature. Genetic Algorithms (GAs) were used to empirically determine the proper process signals that contain information that could be used to best estimate the monitored signal. The GA method to determine the proper inferential parameter groupings was successfully implemented in a previous study using neural networks for signal calibration monitoring (Uhrig20). A detailed discussion of genetic algorithms can also be found in Goldberg's book21. Not all inferential process signals determined by GAs in the study were used. In each case, the number of input parameters for each ANFIS system was limited to three to ease the computational burden imposed by the curse of dimensionality. Table 1 lists the process signals selected for this study. The table is separated into three sections, one for each ANFIS system. The signal in bold type indicates the monitored signal 10
and the three signals above are the signals used to estimate the monitored signal. Note that 2 signals are used in two separate ANFIS systems (A323 and S288), thus there are a total of 7 signals used to estimate the 3 monitored process sensors (total of 10 signals). Plots of the 10 process signals are shown as Figures 9 through 13.. VI.B. Training, Validation, and Testing Data The digitized data used for this study was collected with the Safety Parameter Display computer system from Florida Power Corporations Crystal River #3 Nuclear Power Plant. Data from the 10 parameters listed above was sampled at 15 minute intervals for approximately 1 month of plant operation (July 17, 1992 to August 14, 1992) which gave a total of 2612 patterns. The plant operational cycle included reactor startup to about 18 days of steady state plant operation. Several transients were included to test the networks ability to accurately follow them. To train the ANFIS system, the first 1300 patterns of the entire data set (approximately half) were used. This set was further broken down into two sets: a training set, and a validation set. The validation set monitors the fuzzy system's ability to generalize during training (the same principle as cross validation training in neural networks terminology). For the training data set, every 7th pattern was selected from the first 1300 patterns resulting in 185 patterns while the checking data set used every 4th pattern yielding a total of 325 validation patterns. Patterns found in the training set were excluded from the validation set. In addition, each data set contained the maximum and minimum data value for each signal in the entire data set. It is important to cover the entire span of a process signal's operating range so that all values will be covered in the membership functions domain. Testing of the system was performed with the entire data set consisting of 2612 patterns from startup to steady state and also included several transients. Note that the system has never seen the later half of this set. The testing procedure will be discussed further in Section V.
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IV.C. ANFIS Structure and Training For each of the three sensor validation systems (steam generator level, temperature, and flow), two generalized bell membership functions (MFs) were used to model each input signal in the antecedent. Through training and testing trials, the use of two MFs was found to be optimal; one MF could not correctly model all the information in the data, and three or more MFs offered no performance benefit. Figure 2 shows the initial membership function domains (Degree of Membership) for each of the three temperature system input signals. After the MFs were initialized, the sensor validation system was trained. Each of the three systems were allowed to train to a maximum of 100 epochs, which took approximately 5 minutes. After training was complete, the system parameters (weights and biases in neural networks terminology) with the least validation error was used for final system testing. Figure 3 shows a plot of the RMS training and validation error for a typical training session. As expected, the training data set error monatomically decreases, while error for the validation data set initially decreases, reaches a minimum, then begins to increase. At the point where the validation error begins to increase, the system is learning the noise in the training data and system generalization begins to deteriorate. Figure 4 shows a plot of the MFs after training. The training algorithm shifted the membership functions to reduce the error. This is most readily apparent in the last plot which shows a large shift in both shape and location of the MFs. IV.D. SIMULINK System Integration To monitor the performance of the fuzzy inference system, the sequential probability ratio test (SPRT) was implemented using SIMULINK22. The integrated system block diagram is shown in Fig. 5. The 10 plant process signals are input into the SIMULINK system where the input signals used for parameter estimation are routed to their respective ANFIS models and the three monitored parameters are routed to their respective summing blocks. The summing blocks compare each signal estimate to the actual monitored signal and forms residuals. The residuals are then sent to an SPRT block which outputs the status of each sensor (0 = good, 1 = bad) based on the variance of the residuals, a given faulted mean, a preset false alarm 12
probability of 0.01% and a missed alarm probability of 10%. The faulted mean values were optimized (minimal faulted mean values with a minimum number of false alarms) using the entire data set. The output of the SPRTs are then processed by a logic filter with a 2 out of 4 delayed status voting scheme to eliminate false alarms due to spurious spikes in the plant data. V. SYSTEM TESTING AND RESULTS V.A. System Simulation As discussed previously, data for the test consisted of approximately 1 month of reactor startup and full power plant operation sampled every 15 minutes, resulting in 2612 test patterns. Initially, a test was performed using plant data that contained several transients to verify that no false alarms occurred with error free plant data. Simulations were performed to show the ability of the fuzzy signal validation system to detect drifting sensors. V.B. Drift Error Detection A drift error is defined as a slow rate of change in a signal's expected nominal value. To test the performance of the fuzzy inference systems, both high and low drift faults of 0.2% per day of the instruments maximum scale value were inserted starting at time 1300. These drifts were artificially added to each of the 3 monitored sensors. Only one drift was inserted at a time. For each simulation, the fault detection time, the percent error of the drift (with respect to the full scale deflection of the signal) at the time of detection, and the number of false alarms in all the channels were recorded for both high and low drift scenarios. Figures 6, 7, and 8 are plots of typical drift test cases for each of the three sensors. The top plot for each case shows the actual drifting signal and the neural network estimate, the middle plot shows the residual between the two, and the bottom plot shows the SPRT fault hypothesis index. Although initial study of these plots suggests that an operator could probably identify these faults at a time similar to that of the system, that is not the case. One must remember that the faults are only apparent because the ANFIS estimate is plotted on the same plot. Without knowing the correct sensor value (the ANFIS estimate), it would be very difficult to make a decision pertaining to the validity of the sensor output. Table 2 13
summarizes the results for the three sensors. It lists the computer point tag ID, the SPRT faulted mean value, the calculated residual variance, the percent (of maximum scale deflection) detected drift error, and the number of false alarms. The results show that the system performed very well. The detection time generally depended on the level of noise in the signal; the more noise, the longer the detection times. The average detection level for a low noise sensor (temperature for example) was approximately 0.22% in less than a day. The only false alarms recorded were in the steam generator level. The data contained a few spikes (around time interval 475) that the system could not model. V.C. Comparison With Neural Network Results Several recent studies investigated the use of Autoassociative Neural Networks (AANNs) to detect both artificially induced and actual sensor faults in the Crystal River Data (Uhrig 1996, Wrest 1996). The results of the AANN based studies were similar to that of the ANFIS based system. Neither system showed overwhelming performance advantages for the test cases. The major differences between the two methods involves their design and training. The AANN technique uses neural networks with 6 to 12 inputs signals. Therefore, each estimate is based on more information and should be more accurate. This is apparent by looking at the amount of noise in the estimates. The AANN sensor estimates contain less noise because the noise in the 6 to 12 inputs tend to cancel each other out. This filtering improvement is an advantage in that is allows for tighter SPRT faulted mean setpoint tolerances. The major advantage of the ANFIS system is its ease of implementation and fast training time. There is no pre or post scaling of the data that is required for fast AANN training and the training time is on the order of minutes rather than hours which is usually required by the AANN technique. As discusses in Section II.A.1, the major disadvantage of the ANFIS technique is commonly referred to as the "curse of dimensionality". This explosion of rules limits the number of inputs to a fairly small number and thus limits the amount of information used to 14
make the estimates. Several methods are available to reduce this influence including partitioning methods (Jang15) and optimal rule choice (Kosko23). If a signal not strongly correlated with a few signals but is slightly correlated with many signals, many inputs to the system would be needed and this methodology may not be practical. The amount of correlation needed in a group of variables is not easy to calculate or quantify. A calculated correlation coefficient between two signals may only show slight linear correlations but the two signals may have strong non-linearly correlations. Since neural networks and fuzzy systems perform non-linear mappings, a strong non-linear correlation, although difficult to quantify, may provide the redundant information necessary for the calibration monitoring system. A complete and rigorous testing program is needed to verify that the correlations between the signals are sufficient. Both the neural network techniques and the ANFIS technique can be adversely affected by drifts in the sensors being used to estimate a specific sensor value. There are several techniques that have been used to reduce these effects. The first is to use a robust training set (Kramer4) that trains the system to give correct outputs when one input is drifting (Hines6, Uhrig18). This method introduces artificial drifts into the inputs and trains the network to still give the correct output. This techniques requires stronger sensor correlation that normal training techniques which may require additional inputs. The second method uses a post processing logic module to determine which input sensor is causing the drift alarms (Uhrig18). Through the use of both of these methods, sensor drift detection can be made insensitive to individual input sensor drifts. VI. CONCLUSIONS The results of this study have shown that a signal validation system using an Adaptive Neural Fuzzy Inference System is not only feasible but very practical. The system is composed of an inferential ANFIS module, that estimates the correct sensor output, coupled with a sequential probability ratio test module for fault detection. The most significant requirement for the correct operation of this system is for redundancy in the signals. This
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redundancy criteria can be met through physically redundant sensors or through linear and non-linear correlations between measured variables. The signal validation system has been integrated using MATLAB's SIMULINK software. The system has been tested using plant data from Florida Power Corporations Crystal River #3 Nuclear Power Plant. The results show that sensor degradation can be detected at levels as low as 0.2% of the sensor's full scale range. Overall, the ANFIS signal validation system can clearly detect a fault or drift in a single channel without affecting the other channels being monitored. Thus the network not only detects the fault, but also isolates the channel in which the fault has occurred. REFERENCES 1. J. S. JANG, "ANFIS: Adaptive-Network-Based Fuzzy Inference Systems", IEEE Transactions on Systems, Man, and Cybernetics, 23(3), pp. 665-685, (1993). 2. C. J. BLACK, J. W. HINES and R. E. UHRIG "Inferential Neural Networks for Nuclear Power Plant Sensor Channel Drift Monitoring", published in the proceedings of The 1996 American Nuclear Society International Topical Meeting on Nuclear Plant Instrumentation, Control and Human Machine Interface Technologies, University Park, PA, May 6-9, 1996. 3. B. R. UPADHYAYA, F. P. WOLVARRDT and O. GLOCKLER, "An Integrated Approach for Sensor Failure Detection in Dynamic Systems", Research Report prepared for the Measurement & Control Engineering Center, Report No. NE-MCEC-BRU-87-01, (1987). 4. M. Q. KRAMER "Autoassociative Neural Networks", Computers in Chemical Engineering, 16(4), pp. 313-328, (1992). 5. D. DONG, and T. J. McAVOY, "Sensor Data Analysis Using Autoassociative Neural Nets," Proceedings Of World Congress On Neural Networks, 1, pp. 161-166, San Diego, June 5-9, 1994.
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6. J. W. HINES, D. J. WREST, and R. E. UHRIG, "Plant Wide Sensor Calibration Monitoring", published in the proceedings of The 1996 IEEE International Symposium on Intelligent Control, Sept. 15-18, pp. 378-383, 1996. 7. W. WREST, J. W. HINES and R. E. UHRIG, "Instrument Surveillance and Calibration Verification to Improve Nuclear Power Plant Reliability and Safety Using Autoassociative Neural Networks", published in the proceedings of The International Atomic Energy Agency Specialist Meeting on Monitoring and Diagnosis Systems to Improve Nuclear Power Plant Reliability and Safety, Barnwood, Gloucester, United Kingdom, May 14-17, 1996. 8. B. R. UPADHYAYA and E. ERYUREK, "Application of Neural Networks for Sensor Validation and Plant Monitoring," NUCLEAR TECHNOLOGY, 97, pp. 170-176, February, (1992). 9. MATLAB, High Performance Numeric Computation and Visualization Software, The Math Works, Natick, MA, (1993). 10. J.-S. R. JANG, and N. GULLEY, Fuzzy Logic Toolbox, The MathWorks Inc., Natick, Mass, (1995). 11. T. TAKAGI and M. SUGENO, "Fuzzy Identification of Systems and its Applications to Modeling and Control," IEEE Trans. on Systems, Man and Cybernetics, 15, pp.116-132, (1985). 12. M. SUGENO and G. T. KANG, "Structure Identification of Fuzzy Models," Fuzzy Sets and Systems, 28, pp.15-33, (1988). 13. E. H. MAMDANI and S. ASSILIAN, "An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller", International Journal of Man Machine Studies, 7(1), pp. 1-13, (1975). 14. J.-S. R. JANG, and C.-T. SUN, "Neuro-Fuzzy Modeling and Control," The Proceedings of the IEEE, 5, pp. 378-406, (1995). 15. J.-S. R. JANG, and C.-T. SUN, and E. Mizutani, Neuro-Fuzzy and Soft Computing, Prentice Hall, Upper Saddle River, NJ, (1997).
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16. J.-S. R. JANG, and C.-T. SUN, "Functional Equivalence Between Radial Basis Function Networks And Fuzzy Inference Systems," IEEE Trans. on Neural Networks, 4(1), pp.156159, (1993). 17. KOSKO, Fuzzy Engineering, Prentice Hall, Upper Saddle River, NJ, (1997). 18. T. MASTERS, Practical Neural Network Recipes in C++, Academic Press, San Diego CA, (1993). 19. A. WALD, "Sequential Tests of Statistical Hypothesis", Ann. Math. Statist., 16, 117-186, (1945). 20. R. E. UHRIG, J. W. HINES, C. J. BLACK, D. J. WREST, and X. XU, "Instrument Surveillance and Calibration Verification System," Report Prepared by the University of Tennessee for Sandia National Laboratories, Contract No. AQ-6982, (1996). 21. D. GOLDBERG, "Genetic Algorithms in Search, Optimization and Machine Learning", Addison Wesley Publishing Company, NY, (1989). 22. SIMULINK Dynamic System Simulation Software, The Math Works, Natick, MA, (1988). 23. B. KOSKO, "Optimal Fuzzy Rules Cover Extrema", International Journal of Intelligent Systems, 10(2), pp. 249-255, (1994).
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Table I. Selected Process Signals ANFIS
Point
Signal Description
Units
Tech Spec
SG Level SG Level SG Level SG Level
A321 A323 S284 A322
Steam Generator Low Level - A Main Steam Pressure - A Steam Generator Level - A (OP) Steam Generator High Level - A
INCHES PSIG PERCENT PERCENT
YES YES
Temp Temp Temp Temp
R200 R328 S288 R327
Pressurizer Level (L1) (Uncomp) Reactor T-hot Loop - B SG Lower Downconer Temp - A Reactor T-hot Loop - A
INCHES DEG F DEG F DEG F
Flow Flow Flow
A323 Main Steam Pressure - A R236 Reactor Loop Flow - A (CH B) S288 SG Lower Downconer Temp - A
PSIG MLB/HR DEG F
YES YES YES YES YES YES
Variance Median
Range
0.552 1.087 0.019 0.071
179.45 905 83.19 81.19
0-150 0-1200 40-640 0-100
0.107 0.043 0.012 0.047
143 600.3 537.9 601.30
0-320 120-920 0-600 120-920
1.087 0.007 0.012
905 73.7 537.9
0-1200 0-80 0-600
Table II. ANFIS signal validation system drift simulation results Detected Number SPRT Computer Pt. Drift SPRT of drift residual (Tag ID) Fault faulted false variance error in mean alarms % setpoint A322 low 0.50 0.15 0.92 1 R327 low 0.35 0.10 0.22 0 R234 low 0.30 0.05 0.58 0 A322 R327 R234
high high high
0.50 0.35 0.30
0.15 0.10 0.05
20
0.77 0.24 0.61
1 0 0
x1 x2
A1 x1
A2 B1 x2
B2 Layer 1
Π
w1
N
w1
w1f1
Σ Π
w2
N
f
w2f2 w2 x1 x2
Layer 2
Layer 3
Layer 4
Layer 5
Equivalent ANFIS architecture for a two-input first-order Sugeno fuzzy model with two rules [Jang 1995a]. Figure 1. 21
1 D of 0.5 M 0 105
110
115
120
125
130
135
140
145
1 D o f 0.5 M 0 560
565
570
575
580
585
590
595
600
1
D o f 0.5 M 0 531
532
533 534 Variable Range
535
536
Initial membership functions for the three inputs for the temperature ANFIS. J. Wesley Hines, Darryl J. Wrest, Robert E. Uhrig Figure 2. 22
0.35 0.345 0.34 0.335 Training error Checking error
0.33 0.325 RMS 0.32 E rror 0.315 0.31 0.305
0
20
40 60 Number of training iterations
Typical ANFIS training error record. J. Wesley Hines, Darryl J. Wrest, Robert E. Uhrig 23
80
Figure 2.
100
1 D of M
D of M
0.5 0 105
110
115
120
125
130
135
140
145
1 0.5 0 560
565
570
575
580
585
590
595
600
1 D of M
0.5 0 531
532
533
534
535
536
Final membership functions (after training) for the three inputs for the temperature ANFIS. J. Wesley Hines, Darryl J. Wrest, Robert E. Uhrig Figure 4. 24
A321_ A321 A323_ A323
Mux
+ Fault Hyp SG
Filter S284 A322
Fuzzy Estimate SG
-
Mux
Sum
Mux
+
Logic SPRT Filter SG Lvl
R200
Mux
SG Estima/Actual/Fault Hyp Steam Gen Level A322 Mux1
fdata.mat R328 Sensor Data
R327
Mux3
Fuzzy Estimate Temp
SPRT Sum 2 Temp
Logic Filter
R236 R234
Fault Hyp Temp
Filter
S288
Mux
Mux4 Mux
Temp Estima/Actual/Fault Hyp Temperature R327
+ Fault Hyp Flow
Filter Demux Mux6
Fuzzy Estimate Flow
Logic Sum1 SPRT Filter Flow
Mux
Mux7
Integrated ANFIS system for monitoring of three process sensors. J. Wesley Hines, Darryl J. Wrest, Robert E. Uhrig 25
Flow Estima/Actual/Fault Hyp Flow R234
Figure 5.
100
percent
50 ANFIS Sensor 0 0
500 1000 Difference Between Sensor Signal And AANN Estimate
1500
2000
2500
1500
2000
2500
1500
2000
2500
5
percent
0
-5 0
500
1000 SPRT Fault Hypothesis
Index
1
0.5
0 0
500
1000
time in 15 minute intervals (7/17/93 to 8/14/93)
ANFIS system detecting a fault drift low in the steam generator level when a drift of 0.2% per day of the instruments maximum scale deflection (100 percent) is introduced into the sensor signal at time stamp 1300. J. Wesley Hines, Darryl J. Wrest, Robert E. Uhrig Figure 6. 26
620
degrees F
600 ANFIS Sensor
580 560 0
500 1000 Difference Between Sensor Signal And AANN Estimate
1500
2000
2500
1500
2000
2500
1500
2000
2500
30
degrees F
20 10 0 0
500
1000 SPRT Fault Hypothesis
Index
1
0.5
0 0
500
1000
time in 15 minute intervals (7/17/93 to 8/14/93)
ANFIS system detecting a fault drift high in the reactor outlet temperature when a drift of 0.2% per day of the instruments maximum scale deflection (920 degrees F) is introduced into the sensor signal at time stamp 1300. J. Wesley Hines, Darryl J. Wrest, Robert E. Uhrig Figure 7. 27
80
MLB/HR
ANFIS Sensor 75
70 0
500 1000 Difference Between Sensor Signal And AANN Estimate
1500
2000
2500
1500
2000
2500
1500
2000
2500
MLB/HR
5
0
-5 0
500
1000 SPRT Fault Hypothesis
Index
1
0.5
0 0
500
1000
time in 15 minute intervals (7/17/93 to 8/14/93)
ANFIS system detecting a fault drift high in the reactor loop flow when a drift of 0.2% per day of the instruments maximum scale deflection (80 Mlb/hr) is introduced into the sensor signal at time stamp 1300. J. Wesley Hines, Darryl J. Wrest, Robert E. Uhrig Figure 8. 28
inches
150
100
50
0
500
1000
1500
2000
2500
1500
2000
2500
data sampled every 15 minutes
910 905
psig
900 895 890 885 0
500
1000 data sampled every 15 minutes
Top plot: A321- Steam generator low level - A. Bottom plot: A323 - Main steam pressure - A. J. Wesley Hines, Darryl J. Wrest, Robert E. Uhrig
29
Figure 9
80
percent
60
40
20
0
500
1000
1500
2000
2500
1500
2000
2500
data sampled every 15 minutes
80
percent
60
40
20
0
500
1000 data sampled every 15 minutes
Top plot: S284 - Steam generator level - A (operational). Bottom plot: A322 - Steam generator high level - A. J. Wesley Hines, Darryl J. Wrest, Robert E. Uhrig 30
Figure 10.
140
inches
130
120
110 0
500
1000
1500
2000
2500
1500
2000
2500
data sampled every 15 minutes
610 600
degrees F
590 580 570 560 550 0
500
1000 data sampled every 15 minutes
Top plot: R200 - Pressurizer level L1. Bottom plot: R328 - Reactor T-hot Loop - B. J. Wesley Hines, Darryl J. Wrest, Robert E. Uhrig 31
Figure 11.
540
degrees F
535
530
525 0
500
1000
1500
2000
2500
1500
2000
2500
data sampled every 15 minutes
610 600
degrees F
590 580 570 560 550 0
500
1000 data sampled every 15 minutes
Top plot: Steam generator lower downcomer temp - A. Bottom plot: R327 - Reactor T-hot Loop - A. J. Wesley Hines, Darryl J. Wrest, Robert E. Uhrig 32
Figure 12.
75
74
Mlb/hr
73
72
71
70 0
500
1000
1500
2000
2500
1500
2000
2500
data sampled every 15 minutes
75
74
Mlb/hr
73
72
71
70 0
500
1000 data sampled every 15 minutes
Top plot: R236 - Reactor loop flow - A (ch B). Bottom plot: R234 - Reactor loop flow - A (ch A). J. Wesley Hines, Darryl J. Wrest, Robert E. Uhrig 33
Figure 13.
