Automaton based on fuzzy clustering methods for monitoring industrial processes

doi:10.1016/j.engappai.2012.11.003

Engineering Applications of Artificial Intelligence

Volume 26, Issue 4, April 2013, Pages 1211-1220

https://doi.org/10.1016/j.engappai.2012.11.003 Get rights and content

Abstract

Fuzzy clustering allows finding classes through the historical data in order to associate them with functional states useful to represent the complex industrial processes behavior. By means of classes, an automaton can be established that determines the current and the next connections of functional states of a process. When fuzzy clustering is used, the connections in the historical data are considered but it does not find other important connections. To solve this limitation, a new method to seek the most important connections among functional states is proposed. Initially, the approach defines an initial transition degrees matrix, where all connections are taken into account. Through a proposed update step, the most important connections are obtained, which they describe the real behavior of a process. In addition, a new distance criterion is defined to improve the update step. The final transition degrees matrix is used to construct a fuzzy automaton that it is validated by human operator's experience. The approach was tested in a steam generator process. Applying three fuzzy clustering algorithms in case of study, the proposed method finds the same transition matrix. The new connections were validated by the human operator.

Introduction

The fault identification systems are useful to find abnormal behavior of an industrial process and it is a tool that avoids accidents for the human operators and machine damages. Moreover, these systems allow reducing the maintenance costs of industrial process. Usually, the human operator knows the normal behavior of the industrial process and can identify several failure situations in a multivariable analysis of data (Isermann, 2006). Supervision systems have five important elements:

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Situation assessment, where the process behavior is analyzed.
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Detection of abnormal situations, to identify the possible failures.
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Diagnosis, which allows finding the origin of the faults.
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Decision, where the human operator makes decisions regarding the process.
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Reconfiguration, to carry out the corrective action of the process.

If the exact mathematical model of the industrial process is known, the supervision system can identify the abnormal situations. However, in a complex industrial process, sometimes the completed model is unknown (Kempowsky, 2004). One alternative to establish a functional states model based on historical data analysis is to use fuzzy clustering methods. Fuzzy clustering methods have been used with good results in supervision and diagnosis of processes (Henriques et al., 1999, Ahvenlampi and Kortela, 2005, Zio et al., 2008, Quevedo et al., 2010, Jyoti and Singh, 2011, Hu et al., 2012). The advantage of these methods is that they allow finding classes that can be associated to functional states (these states describe the process behavior including the abnormal situations) (Lamrini et al., 2005). These classes are determined through the similar characteristics between historical data. Afterwards, when the process is online, recognition is carried out in order to identify the membership degree to each class or functional state. Recognition not only allows knowing the functional state of process but also the belonging to other states, which it is useful to avoid critical faults (Gentil, 2007).

To observe all possible changes in the process behavior, connections among states can be established. The set of functional states and their connections determine a fuzzy automaton applied to task of prediction, for example, to know the new changes of the process behavior. This advantage allows carrying out decision-making, in such a way that the human operator knows the next functional state of process. By definition, a fuzzy automaton is a set of initial, internal and final states (Klir and Yuan, 1995). There exist two types of automata, the deterministic fuzzy automaton which generates a connection from an initial state to a final state, and the non-deterministic fuzzy automaton that establishes connections from an initial state to all final states (Omlin et al., 1998). Fuzzy automata have been constructed through fuzzy rule-based inference, considering the knowledge of the system (Chang and Chen, 2011). Nevertheless, there are no methods to construct and update a fuzzy automaton through fuzzy clustering. We focus our attention is to find a fuzzy automaton considering the membership degree matrix obtained by any fuzzy clustering method.

In industrial process applications, the connections among functional states are an important aspect to obtain an automaton. Waissman et al. (2000) established connections among states known by the human operator. This method constructs the automaton considering the classification result according to the number of samples belonging to a class (Waissman et al., 2005). Another method, using finite state machine was proposed by Kempowsky et al. (2006). This approach defined transition and frequency matrices according to the changes among classes obtained by the classification of historical data. Both methods provide an automaton based on the sequences of changes between functional states through fuzzy classification. Moreover, the methods are based on the expert knowledge to identify the transitions between states. It is important to take into account that the human operator knows the process performance, the observed functional states and their connections in the historical data. However, other transitions of the functional states of the process may appear but do not occur in the historical data.

One alternative is using the membership degrees obtained with a fuzzy clustering method, to calculate the transition degrees matrix of all connections among functional states and to update them afterwards. The result is a matrix where the strongest connections (or transitions) are considered to build up the automaton. In this paper, a method to establish automatically the connections is presented, through the membership degrees of the historical data whose classes are represented by the functional states. This method can be applied for any fuzzy clustering method and it is not necessary the expert knowledge to identify the state transitions. The connections are shown by a transition matrix that allows constructing a fuzzy automaton. To determine the transition matrix, the fuzzy states machine theory (Reyneri, 1997, Mordeson and Malik, 2002) will be used to define a mathematical model of the connections among functional states. By means of this matrix, the proposed method considers all connections among functional states present, or not, in the historical data. On the other hand, to find the strongest connections, Hebbian functions (Bishop, 2006) and the self-organizing map algorithm (Kohonen, 1995) is used to propose an updated method of the transition matrix. In this step, a mathematical model is defined to update connections and to establish which they could be the most representative by the human operator's criterion of process. Moreover, two distance functions are proposed in order to guarantee and find the strongest connections in the update step of transition matrix.

To apply the proposed method, the historical data of the process must be obtained offline. When the fuzzy clustering method is used, the obtained classes are associated with the functional states (normal and abnormal) of the process. Once the functional states are known, our proposal only uses the membership degree matrix (N samples×K classes or functional states) to find the connections among functional states. Initially, the method finds all connections among states. Nevertheless, an update step is defined to find the strongest connections due to not all them represent the behavior of a given industrial process. This step allows constructing a fuzzy automaton with the current connections in the historical data and some new connections. Finally, fuzzy automaton is verified by the human operator who valid the new connections useful to predict new possible situations of the complex industrial process behavior.

In order to verify the independency of our proposal to the clustering method used to obtain the membership degrees of historical data. Three fuzzy clustering methods, LAMDA (Piera et al., 1989), FCM (Bezdek, 1981) and GK-means (Gustafson and Kessel, 1979) were applied to obtain the classes associated with functional states. The objective is to observe that the same connections among functional states are established by using different fuzzy clustering methods. The proposed method was used to find a fuzzy automaton in a boiler steam generator subsystem (the characteristics of this process are described in Section 5).

The structure of paper is organized as follows: In Section 2, the fuzzy state machines theory and the Hebbian learning are presented. In Section 3, we explain the general theory of the fuzzy clustering and discuss the proposed method with the distance criterion of similarity among classes for obtaining and updating the transition degrees matrix. In Section 4, a new distance criterion for the updating step is explained. In Section 5, the test results are presented. The method was tested on a steam generator system. The results obtained with the two distance criteria used are shown. Finally, in Section 6 some conclusions and future works are mentioned.

Section snippets

Fuzzy state machine and Hebbian learning

A Fuzzy State Machine (FμMS) is a representation of a set of initial and final states with their respective transitions associated with membership degrees. The first mathematical model was proposed by Wee and Fu (1969). The connections among states are represented in a transition matrix. Considering a Fuzzy Automaton with finite states, it is represented by the six-tuple M={Σ, Q, R, Z, δ, ω}, where:

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Σ is the alphabet set.
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Q is the set of states.
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R is the initial state fuzzy automaton (R∈Q).
•
Z is

Fuzzy automaton based on membership degrees matrix

The result of any fuzzy clustering method is a membership degree matrix (see Eq. (3)) which assigns the membership degrees of each sample to each class (the classes are associated to functional states of the process). Our proposal only uses this matrix to calculate the transition degrees matrix. Then, it is possible to use any fuzzy clustering method. In Section 5, the independence of our proposal to the fuzzy clustering method is tested.

By means of the membership degrees matrix, the initial

A new distance criterion for the updating step

After finding the strongest connections and constructing the fuzzy automaton, it was stated from both application examples that some current transitions in the historical data were removed and some new connections unlikely to happen, according to the human operator. This situation may be present by low transition degrees and the choice of the distance criterion (see Eq. (14)). The choice of the distance function is critical to find a reliable fuzzy automaton for the human operator. Therefore, a

Case of study

The method is applied in a Steam Generator process. To establish if a new connection found with the proposed method is likely presented or not, the description of classes or functional states (include the physical variable behavior) and the human operator's knowledge are available. By means of this information, the new connections among functional states are validated by the human operator and/or by test data. On the other hand, to analyze the independence of the proposed method with respect to

Conclusion

A new method for obtaining an automaton for complex industrial processes was proposed, based on the membership degrees matrix. This method is useful for supervision systems, it can be considered as a tool to identify abnormal states in complex processes. By means of the application of any fuzzy clustering technique, the proposed method allows constructing a fuzzy automaton in order to find new connections (none included in the historical or learning data) among functional states. To obtain the

Acknowledgments

This work was supported by CODI at the University of Antioquia and the ECOSNORD program–COLCIENCIAS, Colombia.

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Automaton based on fuzzy clustering methods for monitoring industrial processes

Abstract

Introduction

Section snippets

Fuzzy state machine and Hebbian learning

Fuzzy automaton based on membership degrees matrix

A new distance criterion for the updating step

Case of study

Conclusion

Acknowledgments

Comput. Chem. Eng.

Int. J. Approximate Reasoning

ISA Trans.

Eng. Appl. Artif. Intell.

Comptes Rendus Phys.

Control Eng. Pract.

Inteligencia Artificial para la Supervisión de Procesos Industriales

Process Monitoring Using Residuals and Fuzzy Classification with Learning Capabilities, Advances in Soft Computing—Theoretical Advances and Applications of Fuzzy Logic and Soft Computing

Clustering algorithms in process monitoring and control application to continuous digesters

Informatica