- Email: [email protected]
Diagnosis of Sugar Factory Processes Using GMDH Neural Networks
Copyright @ lFAC Fault Detection, Supervision and Safety for Technical Processes. Budapest, Hungary, 2000
DIAGNOSIS OF SUGAR FACTORY PROCESSES USING GMDH NEURAL NETWORKS J6zef Korbicz* and Janusz Kus** * Institute of Robotics and Software Engineering
Technical University of Zielona G6ra, Poland ** ComputerLand S.A ., Wroclaw, Poland
Abstract: This paper deals with GMDH (Group Method of Data Handling) neural networks and their application in Fault Detection and Isolation (FDI) systems. Such networks can be considered as feedforward networks with a 'growing' structure during the training process. To apply the GMDH networks in the FDI for real technological processes we propose some extentions of the GMDH theory to multi-output networks and dynamic modelling. The proposed networks and their extensions have been implemented in an industrial model-based diagnostic system for some units of the Lublin sugar factory in Poland. Finally, simulation results show the effectiveness of the proposed neural networks in FDI systems. Copyright (£)2000 IFAC Keywords: fault detection, neural networks, intelligent knowledge-based systems, industrial control.
1. INTRODUCTION
our previous paper (Korbicz and Kus, 1997; 1999), here an industrial application problem using data from the Lublin sugar factory is considered. The distinctive features of the presented approach are the insensitivity to the unknown inputs (noise, disturbances, parameter drifts, measurement errors, etc.) and a high efficiency under the lack of information about the structure and dynamics of the system to be diagnosed. The effectiveness of the proposed approach is demonstrated by several examples.
Growing requirements for the effectiveness and reliability of modern control systems stimulate the search for effective FDI methods (Chen and Patton , 1999). The model-based diagnosis of complex technical processes is still unsatisfactory due to inevitable model mismatches, noise disturbances and inherent nonlinearities. That is why particular attention has been paid to the application of artificial intelligence approaches and techniques (Frank and K6ppen-Seliger, 1997; Korbicz et al., 1999; Patton and Korbicz, 1999).
2. GMDH NETWORKS
The aim of this paper is to propose a neural-based FDI system. The main emphasis is placed on the design of a neural residual generator using GMDH networks. To apply GMDH networks in FDI systems for real industrial processes, some extentions of the GMDH theory to multi-output dynamic networks are proposed as well. In comparision with
A GMDH network, as any other neural network, is constructed by the connections of elementary neurons processing signals (Pham and Xing, 1995; Korbicz and Kus, 1998). The only condition for the transition function is the linearity with respect to its parameters. In the described solution the 349
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the neuron selection procedure (Korbicz and Kus, 1999). In a simplest solution the transition errors calculated for each output (Q~) , Q~) , Qg) , ... ) are used to determine an average error Q(I). In consequence, only one criterion, as in the classic (oneoutput) approach , can be used to evaluate the efficiency of each neuron action. Only after completing the synthesis process partial components of . (l) (l) (I) t h e processmg error (Q A ,Q B ,Qc, .. . ) are used to classify the outputs in the last layer.
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In an alternative solution, only the neurons which introduce a too large estimation error (I) (I) (l) (QA ,QB ,Qc , ... ) of the outputs YA,YB,YC ,' " are removed. The efficiency of a neuron in processing at least one output signal is satisfactory to hold the neuron in the network.
Fig. 1. The selection of the neurons in the layer. transition function is a second-degree polynomial (Korbicz and Kus , 1998):
It is possible to apply the described analytical ap-
where Ul and 112 denote inputs, y is the output and ao, aI, ... , U5 denote the unknown parameters. Each neuron is trained separately before connecting to the network (Pham and Xing, 1995) . It is assumed that the Least Mean Squares (LMS) method will be used to identify the unknown parameters in (1) . The synthesis process of the GMDH network consists in iterative repetition of a specific sequence of procedures leading to evolution of the resulting structure (Farlow, 1984; Ivakhnenko, 1990). The process ends up when for the resulting network structure complexity some performance index value is satisfactory.
proach to calculate an unknown value of the signal U at the moment tk on the basis of u values measured at moments t 1 , • .• , t m , and hence to estimate the dynamic system (Korbicz and Kus, 1999) . The only modification necessary in connection with other types of processing data refers to the GMDH neuron structure and particularly to the transition function . In the analysis of discrete processes by means of a GMDH network an arbitrarily defined template (time frame) of dependencies among the input signals of each neuron as the transition function is often used . Sometimes a modification of the transition function which takes into account time as an additionally processed signal is used.
An input layer of neurons described by transition functions (1) for any possible combinations of input signals is formed in the first step of the network synthesis (Fariow, 1984). The selection of the component elements is performed before connecting the created layer to the network. In fact, the selection procedure is an element of the network structural optimization. Taking into account some selection criterion (Ivakhnenko, 1990), we can define the quality of the transition error Q~l) for each neuron. Then the neurons for which the transition error is larger than an assumed threshold are removed from this layer (Fig. 1).
4. GMDH MODEL BASED DIAGNOSTIC SYSTEM GMDH neural networks were tested on technical diagnosis tasks. The problem consists in assessing, on the basis of measured values of input u and output y, whether the state is a normal state or an emergency state and indicating a faulty element. A suitable diagnostic system should consist of two main elements (Korbicz and Kus, 1997): i) an empirical knowledge base, constituting a neural network of GMDH type, ii) an inference engine, containing a residual generator and analyzer.
In the next steps of the GMDH procedure, the output signals of the previous layer are treated as the input signals. The procedure of the neuron identification and then selection are repeated once again. In this way, further layers are formed until the so called optimality criterion is met. It is based on achieving in the constructed layer a minimum value of the selected criterion (Ivakhnenko, 1990) .
5. RESULTS OF DIAGNOSTIC EXPERIMENTS The above approach to fault detection and isolation has been tested using real industrial data. The problem of modelling and detecting some faults in various units of the Lublin sugar factory has been considered. Particular attention has been paid
3. NEURAL MODELS OF MULTI-OUTPUT DYNAMIC SYSTEMS Extension of the synthesis algorithm to multioutput networks requires only a correction of 350
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Fig. 3. Results of prediction of the syrup temperature calculated for various neuron definitions.
visible difference has been observed between the results for the networks built from two- and threeinput neurons (see Fig. 3). The evolution mechanism guarantees achieving the best solution in a given class (described by a transition function form) after stating the configuration of a proper option for the particular system. For example, an algorithm for a class of polynomial functions has been implemented in the tested computer application .
to the relation of the characteristic features of the neural network of GMDH type with the accuracy of the obtained solutions. The proposed approach offers a wide range of possibilities as for the configuration connected with the preliminary data preparation (selection of the normalization method , a clusterisation algorithm) , definition of a neuron (the number of inputs, a transition function) , and also with the synthesis process of the resulting network (selection of a learning algorithm , a method of neuron selection, rules of the evolution of neuron layers) . That is why the impact of the selected variant of GMDH networks on the accuracy of modelling has been checked.
For an empirically selected variant of the GMDH network, prediction of dynamics of the changes in the searched signals determined with one step ahead prediction gives satisfactory results for both the value estimation and foreseen trend changes. The sampled results achieved while examining the density and level of the syrup in the evaporator's station are presented in Fig. 4.
The set of the sampled results for the prediction task (one step ahead) of the variability of the syrup level in an evaporator is illustrated in Fig. 2. The comparison of the runs of the signal estimated for various variants of the modelling network with the computed values allows us to draw the conclusion that the essential element of the preparation of the diagnostic system of GMDH type is the empirical selection of the configuration of the network synthesis algorithm.
Testing the diagnostic hypotheses in the presented system takes place by using the mechanism of the residue analysis. Figure 5 presents charts of the residue variability for the experiments illustrated in Fig. 4. It can be observed that in the normal state the residue values are close to zero (values normalized with respect to the signal level are shown on the charts) and do not show a tendency to sudden and large changes.
The impact of the neuron definition on the model accuracy has been examined after the completion of the alternate stage of the diagnostic system. No
The considered diagnostic system is particularly good for identifying faults in the complex automation systems for which it is impossible to ob351
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the possibilities of change prediction of the searched running in a time longer than one step are interesting. The results of such an experiment are illustrated by the chart of the changes in the error modelling of the syrup flow while extending the prediction horizon presented in Fig. 7. The estimation of the signal dynamics for ten steps ahead without clear deterioration of the accuracy has been possible in the experiment.
Fig. 5. Changes in the residuals of the one step ahead prediction. 34
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The robustness of the diagnostic system to any kind of disturbances is of great importance in complex control systems. It has not been possible to introduce noise to the real technological process of the sugar plant owing to some technical reasons. That is why a noise of controlled amplitude has been put over the planned off-line signals. The changes in the modelling error have been observed while changing the noise amplitude in the subsequent experiments. Their influence on the accuracy of the GMDH network model is not large (see Fig. 8(a)) up to a certain level of disturbances. The noise amplitude at which the error starts to pass over the level which can be described as close to zero, is different for different signals (see Fig. 8(b)) . However, in most cases the impact of disturbances has become noticeable with noise amplitude passing over 20% of the usable signal level, which can be accepted in practical applications as a satisfactory result.
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Fig. 6. Comparison results of measurements and modelling (in one-output and multioutput networks). tain mathematical models and so applied analytical methods (Chen and Patton, 1999). That is why it is interesting to test the impact of the complexity of the modelling system on the magnitude of the estimation error. The dependence has been examined during the observation of the syrup level while modelling three other signals in the same neural network. The comparison of the results with the experiment completed for one output network (see Fig. 6) does not reveal essential differences for the results obtained for both the models. The evolutionary character of the synthesis process of the GMDH network guarantees the achievement of the optimal accuracy. The evolution process is interrupted only after constructing a solution giving a minimal estimation error, and hence the number of the approximated signals has a visible impact on the size of network, but little on its accuracy.
6. CONCLUSIONS The presented approach always leads to structural and parametric optimization of GMDH networks. It can be stated that the GMDH networks constitute a new class of solutions the FDI systems. The problems of multi-output network synthesis and their use in dynamic systems analysis as an extra effect have been solved. Experimental results have shown a good efficiency of the solution in the fault detection tasks and confirm the assumption of the expected robustness. The study demonstrates that GMDH networks provide an efficient tool for system modelling and identification and can be applied in FDI systems for industrial processes.
Some faults found in various types of the units are characterized by a slow increase in the symptoms. This makes them difficult to be detected by diagnostic systems based on the signal analysis performed only for the current moment. That is why 352
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REFERENCES
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Chen J. and R.J. Patton (1999) . Robust modelbased fault diagnosis for dynamic systems. Kulwer Academic Publishers, Berlin. Farlow S.J. (1984). Self organizing methods in modelling: GMDH-type algorithms. Mcrscl Dekker Inc., New York. Frank P.M. and B. Koppen-Seliger (1997). New developments using AI in fault diagnosis . Engng. Applic. Arti/. Intell., 10, 3- 14. Ivakhnenko A.G. (1990). Nepreryvnost i dyskretnost. Naukova Dumka, Kiev (in Russian). Korbicz J . and J . Kus (1997) . Knowledge-based fault detection system using evolutive observer approach. Systems Science, 3 , 77- 87. Korbicz J . and J . Kus (1998). A fault detection and isolation system using GMDH neural networks. Proc. UKACC Int. Con/. CONTROL '98, Swansea, UK, Sept. 1-4,2, 952-957. Korbicz J. and J. Kus (1999) . Dynamic GMDH neural networks and their application in fault detection systems. Proc. European Control Conference, Karlsruhe, Germany, August 31 - Sept . 3 , CD-ROM. Korbicz J ., K. Patan and A. Obuchowicz (1999) . Dynamic neural networks for process modelling in fault detection and isolation systems. Int. J . Appl. Math. Comp. Sci., 9, 519-546. Patton R.J. and J. Korbicz (Eds.) (1999) . Advances in computational intelligence for fault diagnosis systems. Special issue of Int. J. Appl. Math. Comp. Sci., 9, No.3. Pham DJ. and L. Xing (1995) . Neural networks for identification, prediction and control. Springer-Verlag, London.
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ACKNOWLEDGEMENT The authors wish to acknowledge the financial support from the INCO COPERNICUS project IQ2 F D and the State Committee for Scientific Research (KBN).
353
DIAGNOSIS OF SUGAR FACTORY PROCESSES USING GMDH NEURAL NETWORKS J6zef Korbicz* and Janusz Kus** * Institute of Robotics and Software Engineering
Technical University of Zielona G6ra, Poland ** ComputerLand S.A ., Wroclaw, Poland
Abstract: This paper deals with GMDH (Group Method of Data Handling) neural networks and their application in Fault Detection and Isolation (FDI) systems. Such networks can be considered as feedforward networks with a 'growing' structure during the training process. To apply the GMDH networks in the FDI for real technological processes we propose some extentions of the GMDH theory to multi-output networks and dynamic modelling. The proposed networks and their extensions have been implemented in an industrial model-based diagnostic system for some units of the Lublin sugar factory in Poland. Finally, simulation results show the effectiveness of the proposed neural networks in FDI systems. Copyright (£)2000 IFAC Keywords: fault detection, neural networks, intelligent knowledge-based systems, industrial control.
1. INTRODUCTION
our previous paper (Korbicz and Kus, 1997; 1999), here an industrial application problem using data from the Lublin sugar factory is considered. The distinctive features of the presented approach are the insensitivity to the unknown inputs (noise, disturbances, parameter drifts, measurement errors, etc.) and a high efficiency under the lack of information about the structure and dynamics of the system to be diagnosed. The effectiveness of the proposed approach is demonstrated by several examples.
Growing requirements for the effectiveness and reliability of modern control systems stimulate the search for effective FDI methods (Chen and Patton , 1999). The model-based diagnosis of complex technical processes is still unsatisfactory due to inevitable model mismatches, noise disturbances and inherent nonlinearities. That is why particular attention has been paid to the application of artificial intelligence approaches and techniques (Frank and K6ppen-Seliger, 1997; Korbicz et al., 1999; Patton and Korbicz, 1999).
2. GMDH NETWORKS
The aim of this paper is to propose a neural-based FDI system. The main emphasis is placed on the design of a neural residual generator using GMDH networks. To apply GMDH networks in FDI systems for real industrial processes, some extentions of the GMDH theory to multi-output dynamic networks are proposed as well. In comparision with
A GMDH network, as any other neural network, is constructed by the connections of elementary neurons processing signals (Pham and Xing, 1995; Korbicz and Kus, 1998). The only condition for the transition function is the linearity with respect to its parameters. In the described solution the 349
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the neuron selection procedure (Korbicz and Kus, 1999). In a simplest solution the transition errors calculated for each output (Q~) , Q~) , Qg) , ... ) are used to determine an average error Q(I). In consequence, only one criterion, as in the classic (oneoutput) approach , can be used to evaluate the efficiency of each neuron action. Only after completing the synthesis process partial components of . (l) (l) (I) t h e processmg error (Q A ,Q B ,Qc, .. . ) are used to classify the outputs in the last layer.
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In an alternative solution, only the neurons which introduce a too large estimation error (I) (I) (l) (QA ,QB ,Qc , ... ) of the outputs YA,YB,YC ,' " are removed. The efficiency of a neuron in processing at least one output signal is satisfactory to hold the neuron in the network.
Fig. 1. The selection of the neurons in the layer. transition function is a second-degree polynomial (Korbicz and Kus , 1998):
It is possible to apply the described analytical ap-
where Ul and 112 denote inputs, y is the output and ao, aI, ... , U5 denote the unknown parameters. Each neuron is trained separately before connecting to the network (Pham and Xing, 1995) . It is assumed that the Least Mean Squares (LMS) method will be used to identify the unknown parameters in (1) . The synthesis process of the GMDH network consists in iterative repetition of a specific sequence of procedures leading to evolution of the resulting structure (Farlow, 1984; Ivakhnenko, 1990). The process ends up when for the resulting network structure complexity some performance index value is satisfactory.
proach to calculate an unknown value of the signal U at the moment tk on the basis of u values measured at moments t 1 , • .• , t m , and hence to estimate the dynamic system (Korbicz and Kus, 1999) . The only modification necessary in connection with other types of processing data refers to the GMDH neuron structure and particularly to the transition function . In the analysis of discrete processes by means of a GMDH network an arbitrarily defined template (time frame) of dependencies among the input signals of each neuron as the transition function is often used . Sometimes a modification of the transition function which takes into account time as an additionally processed signal is used.
An input layer of neurons described by transition functions (1) for any possible combinations of input signals is formed in the first step of the network synthesis (Fariow, 1984). The selection of the component elements is performed before connecting the created layer to the network. In fact, the selection procedure is an element of the network structural optimization. Taking into account some selection criterion (Ivakhnenko, 1990), we can define the quality of the transition error Q~l) for each neuron. Then the neurons for which the transition error is larger than an assumed threshold are removed from this layer (Fig. 1).
4. GMDH MODEL BASED DIAGNOSTIC SYSTEM GMDH neural networks were tested on technical diagnosis tasks. The problem consists in assessing, on the basis of measured values of input u and output y, whether the state is a normal state or an emergency state and indicating a faulty element. A suitable diagnostic system should consist of two main elements (Korbicz and Kus, 1997): i) an empirical knowledge base, constituting a neural network of GMDH type, ii) an inference engine, containing a residual generator and analyzer.
In the next steps of the GMDH procedure, the output signals of the previous layer are treated as the input signals. The procedure of the neuron identification and then selection are repeated once again. In this way, further layers are formed until the so called optimality criterion is met. It is based on achieving in the constructed layer a minimum value of the selected criterion (Ivakhnenko, 1990) .
5. RESULTS OF DIAGNOSTIC EXPERIMENTS The above approach to fault detection and isolation has been tested using real industrial data. The problem of modelling and detecting some faults in various units of the Lublin sugar factory has been considered. Particular attention has been paid
3. NEURAL MODELS OF MULTI-OUTPUT DYNAMIC SYSTEMS Extension of the synthesis algorithm to multioutput networks requires only a correction of 350
a. 50.5 , - - - - - - - - - - - - - - - - - - - ,
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Fig. 4. Changes in the dynamics of the measured and estimated signals in one step ahead prediction.
estim (3-input neurons)
Fig. 3. Results of prediction of the syrup temperature calculated for various neuron definitions.
visible difference has been observed between the results for the networks built from two- and threeinput neurons (see Fig. 3). The evolution mechanism guarantees achieving the best solution in a given class (described by a transition function form) after stating the configuration of a proper option for the particular system. For example, an algorithm for a class of polynomial functions has been implemented in the tested computer application .
to the relation of the characteristic features of the neural network of GMDH type with the accuracy of the obtained solutions. The proposed approach offers a wide range of possibilities as for the configuration connected with the preliminary data preparation (selection of the normalization method , a clusterisation algorithm) , definition of a neuron (the number of inputs, a transition function) , and also with the synthesis process of the resulting network (selection of a learning algorithm , a method of neuron selection, rules of the evolution of neuron layers) . That is why the impact of the selected variant of GMDH networks on the accuracy of modelling has been checked.
For an empirically selected variant of the GMDH network, prediction of dynamics of the changes in the searched signals determined with one step ahead prediction gives satisfactory results for both the value estimation and foreseen trend changes. The sampled results achieved while examining the density and level of the syrup in the evaporator's station are presented in Fig. 4.
The set of the sampled results for the prediction task (one step ahead) of the variability of the syrup level in an evaporator is illustrated in Fig. 2. The comparison of the runs of the signal estimated for various variants of the modelling network with the computed values allows us to draw the conclusion that the essential element of the preparation of the diagnostic system of GMDH type is the empirical selection of the configuration of the network synthesis algorithm.
Testing the diagnostic hypotheses in the presented system takes place by using the mechanism of the residue analysis. Figure 5 presents charts of the residue variability for the experiments illustrated in Fig. 4. It can be observed that in the normal state the residue values are close to zero (values normalized with respect to the signal level are shown on the charts) and do not show a tendency to sudden and large changes.
The impact of the neuron definition on the model accuracy has been examined after the completion of the alternate stage of the diagnostic system. No
The considered diagnostic system is particularly good for identifying faults in the complex automation systems for which it is impossible to ob351
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the possibilities of change prediction of the searched running in a time longer than one step are interesting. The results of such an experiment are illustrated by the chart of the changes in the error modelling of the syrup flow while extending the prediction horizon presented in Fig. 7. The estimation of the signal dynamics for ten steps ahead without clear deterioration of the accuracy has been possible in the experiment.
Fig. 5. Changes in the residuals of the one step ahead prediction. 34
!~bt-'~"sJ .~
ID 28 >
The robustness of the diagnostic system to any kind of disturbances is of great importance in complex control systems. It has not been possible to introduce noise to the real technological process of the sugar plant owing to some technical reasons. That is why a noise of controlled amplitude has been put over the planned off-line signals. The changes in the modelling error have been observed while changing the noise amplitude in the subsequent experiments. Their influence on the accuracy of the GMDH network model is not large (see Fig. 8(a)) up to a certain level of disturbances. The noise amplitude at which the error starts to pass over the level which can be described as close to zero, is different for different signals (see Fig. 8(b)) . However, in most cases the impact of disturbances has become noticeable with noise amplitude passing over 20% of the usable signal level, which can be accepted in practical applications as a satisfactory result.
~ 27 t-------------------------------~ 26t-------------------------------~ 25~,,~~~~~~~~,,~~~~.rl
51
101
151
201
251
301
351
time -measured -
estimated (in one-output network) esimated (in multi-output network)
Fig. 6. Comparison results of measurements and modelling (in one-output and multioutput networks). tain mathematical models and so applied analytical methods (Chen and Patton, 1999). That is why it is interesting to test the impact of the complexity of the modelling system on the magnitude of the estimation error. The dependence has been examined during the observation of the syrup level while modelling three other signals in the same neural network. The comparison of the results with the experiment completed for one output network (see Fig. 6) does not reveal essential differences for the results obtained for both the models. The evolutionary character of the synthesis process of the GMDH network guarantees the achievement of the optimal accuracy. The evolution process is interrupted only after constructing a solution giving a minimal estimation error, and hence the number of the approximated signals has a visible impact on the size of network, but little on its accuracy.
6. CONCLUSIONS The presented approach always leads to structural and parametric optimization of GMDH networks. It can be stated that the GMDH networks constitute a new class of solutions the FDI systems. The problems of multi-output network synthesis and their use in dynamic systems analysis as an extra effect have been solved. Experimental results have shown a good efficiency of the solution in the fault detection tasks and confirm the assumption of the expected robustness. The study demonstrates that GMDH networks provide an efficient tool for system modelling and identification and can be applied in FDI systems for industrial processes.
Some faults found in various types of the units are characterized by a slow increase in the symptoms. This makes them difficult to be detected by diagnostic systems based on the signal analysis performed only for the current moment. That is why 352
Ca)
REFERENCES
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Chen J. and R.J. Patton (1999) . Robust modelbased fault diagnosis for dynamic systems. Kulwer Academic Publishers, Berlin. Farlow S.J. (1984). Self organizing methods in modelling: GMDH-type algorithms. Mcrscl Dekker Inc., New York. Frank P.M. and B. Koppen-Seliger (1997). New developments using AI in fault diagnosis . Engng. Applic. Arti/. Intell., 10, 3- 14. Ivakhnenko A.G. (1990). Nepreryvnost i dyskretnost. Naukova Dumka, Kiev (in Russian). Korbicz J . and J . Kus (1997) . Knowledge-based fault detection system using evolutive observer approach. Systems Science, 3 , 77- 87. Korbicz J . and J . Kus (1998). A fault detection and isolation system using GMDH neural networks. Proc. UKACC Int. Con/. CONTROL '98, Swansea, UK, Sept. 1-4,2, 952-957. Korbicz J. and J. Kus (1999) . Dynamic GMDH neural networks and their application in fault detection systems. Proc. European Control Conference, Karlsruhe, Germany, August 31 - Sept . 3 , CD-ROM. Korbicz J ., K. Patan and A. Obuchowicz (1999) . Dynamic neural networks for process modelling in fault detection and isolation systems. Int. J . Appl. Math. Comp. Sci., 9, 519-546. Patton R.J. and J. Korbicz (Eds.) (1999) . Advances in computational intelligence for fault diagnosis systems. Special issue of Int. J. Appl. Math. Comp. Sci., 9, No.3. Pham DJ. and L. Xing (1995) . Neural networks for identification, prediction and control. Springer-Verlag, London.
20 15 10 ~---------------------------1
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10
20
30
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noise amplitude (% of signal level) -
sirup temp ...- - vapour flow sirup level
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Fig. 8. Influence of disturbances on the estimation results: (a) approximation of the dynamics of the vapour flow calculated on the basis of disturbed signals, (b) dependence of the mean estimation error on the amplitude of the disturbances.
ACKNOWLEDGEMENT The authors wish to acknowledge the financial support from the INCO COPERNICUS project IQ2 F D and the State Committee for Scientific Research (KBN).
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