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A Stacked Auto-Encoder Based Fault Diagnosis Model for Chemical Process
Anton A. Kiss, Edwin Zondervan, Richard Lakerveld, Leyla Özkan (Eds.) Proceedings of the 29th European Symposium on Computer Aided Process Engineering June 16th to 19th, 2019, Eindhoven, The Netherlands. © 2019 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/B978-0-12-818634-3.50218-6
A Stacked Auto-Encoder Based Fault Diagnosis Model for Chemical Process Yi Qiu, Yiyang Dai,* College of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu 610500, China [email protected]
Abstract Fault detection and diagnosis (FDD) is one of the key technologies to ensure the safe operation of chemical processes. With the widespread application of automation technology in chemical plants and the era of big data, data-based methods have become a hot research topic in the field of fault diagnosis. How to effectively extract the fault characteristics from the data and determine the cause of the fault is the key to help the operator deal with the abnormal conditions. Stack auto-encoder is a deep learning model with strong feature extraction and generalization capabilities. This paper proposes a SAE-based chemical process fault diagnosis model and applies it to Tennessee Eastman process. The performance of the SAE-based model is illustrated by comparison with the results of other methods. Keywords: fault diagnosis, chemical engineering, stacked auto-encoder, neural network.
1. Introduction With the development of science and technology, the chemical production process has become increasingly large-scale and complicated. When an abnormal situation occurs in the system, if it cannot be discovered and dealt with in time, it will cause huge economic losses and even casualties. Therefore, fault detection and diagnosis (FDD) have important application significance for chemical process. Since Beard (1971) proposed the concept of fault diagnosis, many scholars have conducted related research in the field of fault diagnosis. Venkatasubramanian et al. (2003) classify fault diagnosis methods into three general categories according to models: quantitative model-based methods, qualitative model-based methods, and process history data based (data-driven) methods. With the widespread use of automation technology in the process industry, researchers can easily obtain a large amount of process history data. Therefore, the data-based FDD method has become a hot research topic in the field of fault diagnosis. There are two types of FDD methods based on historical data. One type is statistical methods, such as principal component analysis (PCA), independent component analysis (ICA), kernel principal component analysis (KPCA), partial least squares (PLS) and their derivatives. The other type is pattern recognition methods, such as artificial neural networks (ANN), support vector machines (SVM), and so on. However, with the largescale and complicated development of chemical units, the application of statistical methods and traditional pattern recognition methods will be limited by high-
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dimensional data and high-correlation data. Since Hinton & Salakhutdinov (2006) proposed deep learning, the development and application of artificial intelligence technology has achieved great success in the past decade. Today, artificial intelligence is widely used in computer science, finance, and natural language processing. Zhang & Zhao (2017) proposed a chemical process fault diagnosis model based on deep belief network (DBN). Wu & Zhao (2018) proposed a chemical process fault diagnosis model based on convolutional neural network (CNN). The application of artificial intelligence technology in the field of chemical process fault diagnosis has also shown excellent performance. In this paper, we propose a chemical process fault diagnosis model based on stack autoencoder (SAE) and apply it to the fault diagnosis of Tennessee Eastman Process (TEP). The remainder of this paper is organized as follows: A brief introduction to SAE is given in Section 2. Section 3 shows a SAE-based fault diagnosis model. In section 4, The SAE-based model is applied in the TE process. Finally, we conclude the paper and describe some work in the future.
2. Stacked Auto-Encoder The auto-encoder (AE) is proposed by Rumelhart et al. (1986), which is a typical single hidden layer neural network. The stack auto-encoder (SAE) is a modified model proposed by Hinton & Salakhutdinov (2006) based on the auto-encoder. SAE is an important deep learning model and it is a deep neural network essentially. 2.1. Structure of SAE A SAE with 5 hidden layers is shown in Fig. 1. Structurally, the SAE consists of a coder layer (Layer-1 to Layer-4) and a decoder layer (Layer-4 to Layer-7), which assume a symmetrical structure. Each two adjacent layers from left to right is an AE, the weighted connections of neurons exist between each two adjacent layers.
Fig. 1 Structure of a SAE with 5 hidden layers
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Because the network structure of SAE has multiple hidden layers, it can well represent complex high-dimensional functions and has powerful feature extraction capabilities. 2.2. Training of SAE The SAE training process consists of the following two stages: Pre-training stage and fine-tuning stage. The first stage is to initialize the weight of the deep neural network by means of layer-by-layer unsupervised learning (unsupervised greedy algorithm). The layer-by-layer greedy algorithm can effectively avoid the network falling into local optimum. The second stage is to fine-tune the model produced in the previous step by supervised learning (such as backpropagation algorithm). For a training set x containing m samples, each of the data passes through the encoder to obtain a characteristic expression of the hidden layer, as shown in Eq. (1). y ( i ) = fT ( x ( i ) ) = s (Wx ( i ) + b )
(1)
Where T = (Wx, b) is the network parameter, W is the weight, b is the bias term, and s is the activation function. The reconstructed vector is obtained by the y(i ) input decoder, as shown in Eq. (2). z (i ) = gT ' ( y (i ) ) = s (W ' y (i ) + b' )
(2)
Where T ' = (W ', b ') , W ' = W T . In order to prevent the model from over-fitting, a penalty term (regularization) needs to be added. The cost function is shown in Eq. (3). J=
1 m 1 (i ) O (i ) 2 ¦ ( & z x &)+ & W & m i =1 2 2
(3)
Where O is the regularization parameter. Iterative calculation is performed by the gradient descent method, and the optimal weight is obtained when the cost function is the minimum. In each iteration, the update process of the weight W and the bias term b as shown in Eq. (4) and Eq. (5). W mW D
b m b K
wJ wW
wJ wb
(4)
(5)
Where K is the learning rate. After the pre-training stage, the weight of the pre-training model is iterated and updated again using the backpropagation algorithm until the error between the predicted label and the input label is lower than the expected value. Finally, the best weights and bias terms for each layer of AE are obtained.
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3. Fault diagnosis model According to the training process of SAE, we constructed a SAE-based chemical process fault diagnosis model. The fault diagnosis model is shown in Fig. 2, which includes the offline stage and the online stage. 80% of the historical data is used as training data, and its corresponding label is generated. The model is trained using the training set and its corresponding labels, and the remaining data is entered into the model for testing. Compare the test results to the label, and apply the model to onlinestage if it performs well. If the model has a low correct rate on the test set, the parameters should be changed for retraining.
Fig 2. The framework of the SAE based fault diagnosis model
4. Application to Tennessee Eastman process In order to verify the performance of the model which is proposed in this paper. The dataset of Tennessee Eastman (TE) process is applied to the SAE-based fault diagnosis model. The results are compared to some other FDD methods. 4.1. TE process TE process is a simulation based on the actual chemical industry process, which was proposed by Downs & Vogel (1993). TE process includes 12 manipulated variables and 41 measured variables. Since the 12th manipulated variable is a constant, the diagnosis model involves a total of 52 variables. There are 20 faults in TE process. All simulation data come from http://web.mit.edu/braatzgroup/links.html. There are 2 sets in this data set. Each set contains 21 sets of data, which are normal state data and 21 types of fault state data. The first dataset was first simulated in the normal state for 1
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hour, and simulation was continued for 24 hours after adding the disturbance. The second dataset was first simulated in the normal state for 8 hours, and simulation was continued for 40 hours after the disturbance was added. The sampling period for both sets of data is 3 minutes, so the dataset includes 30,260 samples. 4.2. Diagnosis results and comparison We conducted comparative experiments by setting different hyperparameters. A multivariate hyperparameter set was obtained through experiments. The SAE model includes 6 layers of neurons, and the number of neurons in each layer is 52, 100, 50, 50, 100, 21. The number of pre-trainings is 200, the size of each batch in pre-training stage and fine-tuning stage is 89, the learning rate is 1, and the regularization parameter is 0.0000005. The performance of the model is usually evaluated by the fault diagnosis rate (FDR). pi is the count of type i samples that are classified to type i . FDRi =
pi total count of type i samples
(6)
The comparison of diagnosis performance with several statistical methods and traditional pattern recognition methods is shown in Table 1. Table 1 Diagnosis performance comparison of different methods. (a) based partitioning PCA (Wang et al., 2016); (b) based dynamic ICA (Hsu et al., 2010); (c) based designing a hierarchical neural network (Eslamloueyan, 2011); (d) based support vector machines(Yélamos et al., 2009); (e) based SAE (proposed in this paper). FDR (%) Fault01 Fault02 Fault03 Fault04 Fault05 Fault06 Fault07 Fault08 Fault09 Fault10 Fault11 Fault12 Fault13 Fault14 Fault15 Fault16 Fault17 Fault18 Fault19 Fault20 Average
(a) 99.8 98.8 13.6 86.5 100.0 99.5 100.0 98.3 13.4 64.4 77.1 99.3 94.6 100.0 16.9 49.0 96.3 91.3 39.4 54.0 74.6
(b) 100.0 99.0 2.0 97.0 100.0 100.0 100.0 98.0 1.0 82.0 54.0 100.0 95.0 100.0 2.0 82.0 90.0 90.0 81.0 88.0 78.1
(c) 97.0 98.0 53.0 95.0 96.0 100.0 100.0 60.0 29.0 47.0 48.0 46.0 32.0 67.0 66.0 37.0 72.0 94.0 52.0 67.0 67.8
(d) 95.0 100.0 0.0 57.0 64.0 93.0 100.0 100.0 0.0 53.0 21.0 0.0 91.0 0.0 0.0 88.0 68.0 82.0 16.0 100.0 56.4
(e) 98.2 99.6 34.6 96.3 99.2 100.0 100.0 95.3 37.8 89.2 74.3 94.7 94.0 95.2 84.9 82.6 92.4 90.0 86.3 86.4 86.5
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5. Conclusions and prospects With the widespread use of automation technology in chemical processes, it has become increasingly convenient for researchers to access historical data. Many new data-based methods have been applied to the study of chemical process fault diagnosis. In the increasingly complex chemical process, SAE has strong feature extraction and generalization capabilities. This paper proposes a SAE-based chemical process fault diagnosis model, and uses the data generated by the TE process for model construction and training, the average fault diagnosis rate reaches 86.5%. Compared to traditional shallow neural networks, deep learning requires a larger training sample to present its advantages. Therefore, our next work is to simulate the TE process to get more data. Then, the key variables are divided according to the relevance of the variables.
Acknowledgement The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (NSFC) (No. 21706220).
References Beard, Vernon, R., 1971. Failure accommodation in linear systems through selfreorganization. Eslamloueyan, R., 2011. Designing a hierarchical neural network based on fuzzy clustering for fault diagnosis of the Tennessee ̢ Eastman process. APPL SOFT COMPUT, 1407-1415. GuozhuWang, JianchangLiu, YuanLi, ChengZhang, 2016. Fault diagnosis of chemical processes based on partitioning PCA and variable reasoning strategyƿ. CHINESE J CHEM ENG, 869-880. Hinton, G.E.H.C., Salakhutdinov, R.R., 2006. Reducing the Dimensionality of Data with Neural Networks. SCIENCE, 504-507. Hsu, C.C.C.E., Chen, M., Chen, L., 2010. A novel process monitoring approach with dynamic independent component analysis. CONTROL ENG PRACT, 242-253. Rumelhart, D.E., Hinton, G.E., Williams, R.J., 1986. Learning representations by backpropagating errors. NATURE, 533-536. Venkatasubramanian, V.V.C.P., Rengaswamy, R.R.C.E., Yin, K., Kavuri, S.N., 2003. A review of process fault detection and diagnosis Part I: Quantitative model-based methods. Computers and Chemical Engineering, 293-311. Vogel, J.J.D.A., 1993. A plant-wide industrial process control problem. Computers and Chemical Engineering, 245-255. Wu, H., Zhao, J., 2018. Deep convolutional neural network model based chemical process fault diagnosis. COMPUT CHEM ENG, 185-197. Yélamos, I., Escudero, G., Graells, M., Puigjaner, L., 2009. Performance assessment of a novel fault diagnosis system based on support vector machines. Computers and Chemical Engineering, 244-255. Zhang, Z.Z.Z., Zhao, J.Z.J., 2017. A deep belief network based fault diagnosis model for complex chemical processes. COMPUT CHEM ENG, 395-407.
A Stacked Auto-Encoder Based Fault Diagnosis Model for Chemical Process Yi Qiu, Yiyang Dai,* College of Chemistry and Chemical Engineering, Southwest Petroleum University, Chengdu 610500, China [email protected]
Abstract Fault detection and diagnosis (FDD) is one of the key technologies to ensure the safe operation of chemical processes. With the widespread application of automation technology in chemical plants and the era of big data, data-based methods have become a hot research topic in the field of fault diagnosis. How to effectively extract the fault characteristics from the data and determine the cause of the fault is the key to help the operator deal with the abnormal conditions. Stack auto-encoder is a deep learning model with strong feature extraction and generalization capabilities. This paper proposes a SAE-based chemical process fault diagnosis model and applies it to Tennessee Eastman process. The performance of the SAE-based model is illustrated by comparison with the results of other methods. Keywords: fault diagnosis, chemical engineering, stacked auto-encoder, neural network.
1. Introduction With the development of science and technology, the chemical production process has become increasingly large-scale and complicated. When an abnormal situation occurs in the system, if it cannot be discovered and dealt with in time, it will cause huge economic losses and even casualties. Therefore, fault detection and diagnosis (FDD) have important application significance for chemical process. Since Beard (1971) proposed the concept of fault diagnosis, many scholars have conducted related research in the field of fault diagnosis. Venkatasubramanian et al. (2003) classify fault diagnosis methods into three general categories according to models: quantitative model-based methods, qualitative model-based methods, and process history data based (data-driven) methods. With the widespread use of automation technology in the process industry, researchers can easily obtain a large amount of process history data. Therefore, the data-based FDD method has become a hot research topic in the field of fault diagnosis. There are two types of FDD methods based on historical data. One type is statistical methods, such as principal component analysis (PCA), independent component analysis (ICA), kernel principal component analysis (KPCA), partial least squares (PLS) and their derivatives. The other type is pattern recognition methods, such as artificial neural networks (ANN), support vector machines (SVM), and so on. However, with the largescale and complicated development of chemical units, the application of statistical methods and traditional pattern recognition methods will be limited by high-
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dimensional data and high-correlation data. Since Hinton & Salakhutdinov (2006) proposed deep learning, the development and application of artificial intelligence technology has achieved great success in the past decade. Today, artificial intelligence is widely used in computer science, finance, and natural language processing. Zhang & Zhao (2017) proposed a chemical process fault diagnosis model based on deep belief network (DBN). Wu & Zhao (2018) proposed a chemical process fault diagnosis model based on convolutional neural network (CNN). The application of artificial intelligence technology in the field of chemical process fault diagnosis has also shown excellent performance. In this paper, we propose a chemical process fault diagnosis model based on stack autoencoder (SAE) and apply it to the fault diagnosis of Tennessee Eastman Process (TEP). The remainder of this paper is organized as follows: A brief introduction to SAE is given in Section 2. Section 3 shows a SAE-based fault diagnosis model. In section 4, The SAE-based model is applied in the TE process. Finally, we conclude the paper and describe some work in the future.
2. Stacked Auto-Encoder The auto-encoder (AE) is proposed by Rumelhart et al. (1986), which is a typical single hidden layer neural network. The stack auto-encoder (SAE) is a modified model proposed by Hinton & Salakhutdinov (2006) based on the auto-encoder. SAE is an important deep learning model and it is a deep neural network essentially. 2.1. Structure of SAE A SAE with 5 hidden layers is shown in Fig. 1. Structurally, the SAE consists of a coder layer (Layer-1 to Layer-4) and a decoder layer (Layer-4 to Layer-7), which assume a symmetrical structure. Each two adjacent layers from left to right is an AE, the weighted connections of neurons exist between each two adjacent layers.
Fig. 1 Structure of a SAE with 5 hidden layers
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Because the network structure of SAE has multiple hidden layers, it can well represent complex high-dimensional functions and has powerful feature extraction capabilities. 2.2. Training of SAE The SAE training process consists of the following two stages: Pre-training stage and fine-tuning stage. The first stage is to initialize the weight of the deep neural network by means of layer-by-layer unsupervised learning (unsupervised greedy algorithm). The layer-by-layer greedy algorithm can effectively avoid the network falling into local optimum. The second stage is to fine-tune the model produced in the previous step by supervised learning (such as backpropagation algorithm). For a training set x containing m samples, each of the data passes through the encoder to obtain a characteristic expression of the hidden layer, as shown in Eq. (1). y ( i ) = fT ( x ( i ) ) = s (Wx ( i ) + b )
(1)
Where T = (Wx, b) is the network parameter, W is the weight, b is the bias term, and s is the activation function. The reconstructed vector is obtained by the y(i ) input decoder, as shown in Eq. (2). z (i ) = gT ' ( y (i ) ) = s (W ' y (i ) + b' )
(2)
Where T ' = (W ', b ') , W ' = W T . In order to prevent the model from over-fitting, a penalty term (regularization) needs to be added. The cost function is shown in Eq. (3). J=
1 m 1 (i ) O (i ) 2 ¦ ( & z x &)+ & W & m i =1 2 2
(3)
Where O is the regularization parameter. Iterative calculation is performed by the gradient descent method, and the optimal weight is obtained when the cost function is the minimum. In each iteration, the update process of the weight W and the bias term b as shown in Eq. (4) and Eq. (5). W mW D
b m b K
wJ wW
wJ wb
(4)
(5)
Where K is the learning rate. After the pre-training stage, the weight of the pre-training model is iterated and updated again using the backpropagation algorithm until the error between the predicted label and the input label is lower than the expected value. Finally, the best weights and bias terms for each layer of AE are obtained.
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3. Fault diagnosis model According to the training process of SAE, we constructed a SAE-based chemical process fault diagnosis model. The fault diagnosis model is shown in Fig. 2, which includes the offline stage and the online stage. 80% of the historical data is used as training data, and its corresponding label is generated. The model is trained using the training set and its corresponding labels, and the remaining data is entered into the model for testing. Compare the test results to the label, and apply the model to onlinestage if it performs well. If the model has a low correct rate on the test set, the parameters should be changed for retraining.
Fig 2. The framework of the SAE based fault diagnosis model
4. Application to Tennessee Eastman process In order to verify the performance of the model which is proposed in this paper. The dataset of Tennessee Eastman (TE) process is applied to the SAE-based fault diagnosis model. The results are compared to some other FDD methods. 4.1. TE process TE process is a simulation based on the actual chemical industry process, which was proposed by Downs & Vogel (1993). TE process includes 12 manipulated variables and 41 measured variables. Since the 12th manipulated variable is a constant, the diagnosis model involves a total of 52 variables. There are 20 faults in TE process. All simulation data come from http://web.mit.edu/braatzgroup/links.html. There are 2 sets in this data set. Each set contains 21 sets of data, which are normal state data and 21 types of fault state data. The first dataset was first simulated in the normal state for 1
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hour, and simulation was continued for 24 hours after adding the disturbance. The second dataset was first simulated in the normal state for 8 hours, and simulation was continued for 40 hours after the disturbance was added. The sampling period for both sets of data is 3 minutes, so the dataset includes 30,260 samples. 4.2. Diagnosis results and comparison We conducted comparative experiments by setting different hyperparameters. A multivariate hyperparameter set was obtained through experiments. The SAE model includes 6 layers of neurons, and the number of neurons in each layer is 52, 100, 50, 50, 100, 21. The number of pre-trainings is 200, the size of each batch in pre-training stage and fine-tuning stage is 89, the learning rate is 1, and the regularization parameter is 0.0000005. The performance of the model is usually evaluated by the fault diagnosis rate (FDR). pi is the count of type i samples that are classified to type i . FDRi =
pi total count of type i samples
(6)
The comparison of diagnosis performance with several statistical methods and traditional pattern recognition methods is shown in Table 1. Table 1 Diagnosis performance comparison of different methods. (a) based partitioning PCA (Wang et al., 2016); (b) based dynamic ICA (Hsu et al., 2010); (c) based designing a hierarchical neural network (Eslamloueyan, 2011); (d) based support vector machines(Yélamos et al., 2009); (e) based SAE (proposed in this paper). FDR (%) Fault01 Fault02 Fault03 Fault04 Fault05 Fault06 Fault07 Fault08 Fault09 Fault10 Fault11 Fault12 Fault13 Fault14 Fault15 Fault16 Fault17 Fault18 Fault19 Fault20 Average
(a) 99.8 98.8 13.6 86.5 100.0 99.5 100.0 98.3 13.4 64.4 77.1 99.3 94.6 100.0 16.9 49.0 96.3 91.3 39.4 54.0 74.6
(b) 100.0 99.0 2.0 97.0 100.0 100.0 100.0 98.0 1.0 82.0 54.0 100.0 95.0 100.0 2.0 82.0 90.0 90.0 81.0 88.0 78.1
(c) 97.0 98.0 53.0 95.0 96.0 100.0 100.0 60.0 29.0 47.0 48.0 46.0 32.0 67.0 66.0 37.0 72.0 94.0 52.0 67.0 67.8
(d) 95.0 100.0 0.0 57.0 64.0 93.0 100.0 100.0 0.0 53.0 21.0 0.0 91.0 0.0 0.0 88.0 68.0 82.0 16.0 100.0 56.4
(e) 98.2 99.6 34.6 96.3 99.2 100.0 100.0 95.3 37.8 89.2 74.3 94.7 94.0 95.2 84.9 82.6 92.4 90.0 86.3 86.4 86.5
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5. Conclusions and prospects With the widespread use of automation technology in chemical processes, it has become increasingly convenient for researchers to access historical data. Many new data-based methods have been applied to the study of chemical process fault diagnosis. In the increasingly complex chemical process, SAE has strong feature extraction and generalization capabilities. This paper proposes a SAE-based chemical process fault diagnosis model, and uses the data generated by the TE process for model construction and training, the average fault diagnosis rate reaches 86.5%. Compared to traditional shallow neural networks, deep learning requires a larger training sample to present its advantages. Therefore, our next work is to simulate the TE process to get more data. Then, the key variables are divided according to the relevance of the variables.
Acknowledgement The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (NSFC) (No. 21706220).
References Beard, Vernon, R., 1971. Failure accommodation in linear systems through selfreorganization. Eslamloueyan, R., 2011. Designing a hierarchical neural network based on fuzzy clustering for fault diagnosis of the Tennessee ̢ Eastman process. APPL SOFT COMPUT, 1407-1415. GuozhuWang, JianchangLiu, YuanLi, ChengZhang, 2016. Fault diagnosis of chemical processes based on partitioning PCA and variable reasoning strategyƿ. CHINESE J CHEM ENG, 869-880. Hinton, G.E.H.C., Salakhutdinov, R.R., 2006. Reducing the Dimensionality of Data with Neural Networks. SCIENCE, 504-507. Hsu, C.C.C.E., Chen, M., Chen, L., 2010. A novel process monitoring approach with dynamic independent component analysis. CONTROL ENG PRACT, 242-253. Rumelhart, D.E., Hinton, G.E., Williams, R.J., 1986. Learning representations by backpropagating errors. NATURE, 533-536. Venkatasubramanian, V.V.C.P., Rengaswamy, R.R.C.E., Yin, K., Kavuri, S.N., 2003. A review of process fault detection and diagnosis Part I: Quantitative model-based methods. Computers and Chemical Engineering, 293-311. Vogel, J.J.D.A., 1993. A plant-wide industrial process control problem. Computers and Chemical Engineering, 245-255. Wu, H., Zhao, J., 2018. Deep convolutional neural network model based chemical process fault diagnosis. COMPUT CHEM ENG, 185-197. Yélamos, I., Escudero, G., Graells, M., Puigjaner, L., 2009. Performance assessment of a novel fault diagnosis system based on support vector machines. Computers and Chemical Engineering, 244-255. Zhang, Z.Z.Z., Zhao, J.Z.J., 2017. A deep belief network based fault diagnosis model for complex chemical processes. COMPUT CHEM ENG, 395-407.