Patrice Billaudel

A fuzzy hybrid hierarchical clustering method with a new criterion able to find the optimal partition

Classical fuzzy clustering methods are not able to compute a partition in a set of points when classes have nonconvex shape. Furthermore we know that in this case, the usual criteria of class validity such as fuzzy hypervolume or compactness-separability, do not allow to find the optimal partition. The purpose of our paper is to provide a clustering method able to divide a set of points into nonconvex classes without knowing a priori their number. We will show that it is possible to reconcile a fuzzy clustering method with a hierarchical ascending one while maintaining a fuzzy partition by a method called unsupervised fuzzy graph clustering. To that effect, we shall use the Fuzzy C-Means algorithm to divide the set of points into an overspecified number of subclasses. A fuzzy relation is then established between them in order to extract the structure of the set of points. It can be represented by a graduated hierarchy. Finally, we present a new criterion to find the cut of the hierarchy giving the optimal regrouping. This one allows to find the real classes existing into the set of points. The given results are compared with those obtained by other classical cluster validity criteria and we propose to study the influence of the number of initial subclasses on the final computed partition.

A semi-supervised dynamic version of Fuzzy K-Nearest Neighbours to monitor evolving systems

Data issued of most real-world applications are evolving; they change constantly over time. In such applications, it is difficult to induce correctly a model (classifier) using traditional classification methods. Thus, it is important to use an adapted classification method to build a classifier and to update its parameters as new data is available. In this paper, we propose an adaptive classification approach based on the Fuzzy K-Nearest Neighbours (FKNN) method to monitor online evolving systems. The developed method, named semi-supervised Dynamic FKNN, comprises the following phases. In the first phase (detection phase), a class evolution can be detected and confirmed after the classification of each new pattern. Then in the second phase (adaptation phase), the parameters of the evolved class are updated incrementally. In the last phase (validation phase) the adapted classes are validated in order to keep only the representative ones. This approach is illustrated using an example of system which switches between several functioning modes.

A process monitoring module based on fuzzy logic and pattern recognition

This article presents a plastic injection moulding monitoring module based on knowledge built on-line using feedback from production data. A fuzzy classifier was especially developed for this application. It is based on unsupervised and supervised classification methods. The role of the first one is to identify the functioning modes of the process whereas the role of the second one is to associate the state of the process to one of the identified functioning modes at the moment where a workpiece is injected. Furthermore this diagnosis module integrates an on-line learning method which allows to enrich and upgrade the initial knowledge during production. The results obtained show that the monitoring system is a solution for quality and productivity control having serious economical advantages. For example maintenance tasks can be anticipated and the size of the training set can be considerably reduced. The computing times show that the monitoring system can be used for the purpose of industrial applications without any decrease of production rate.

Performance evaluation of fuzzy classification methods designed for real time application

This paper proposes a comparative appraisal of the fuzzy classification methods which are Fuzzy C-Means, K Nearest Neighbours, method based on Fuzzy Rules and Fuzzy Pattern Matching method. It presents the results we obtained in applying those methods on three types of data that we present in the second part of this article. The classification rate and the computing times are compared from a method to another. This paper describes the advantages of the fuzzy classifiers for an application to a diagnosis problem. To finish it proposes a synthesis of our study which can constitute a base to choose an algorithm in order to apply it to a process diagnosis in real time. It shows how we can associate unsupervised and supervised methods in a diagnosis algorithm.

Switched Hybrid Dynamic Systems identification based on pattern recognition approach

Hybrid Dynamic Systems (HDS) can switch between different functioning modes. Their identification requires the determination of the number of discrete modes as well as the time switching sequence between them. In this paper, an approach to estimate the number of discrete modes of a Switched HDS (SHDS) is proposed. This approach is based on two steps. The first one aims at determining the statistical features required to discriminate the SHDS modes. The second step uses a non-supervised classification method to determine online the number of modes as well as their model (i.e. membership function).

Abrupt and Drift-Like Fault Diagnosis of Concurent Discrete Event Systems

Discrete Event Systems (DES) are dynamical systems that evolve according to the asynchronous occurrence of certain changes called events. This paper proposes a modular approach for abrupt and drift-like fault diagnosis of concurrent DES. In this class of DES, the system consists of several components or subsystems that operate concurrently. Each component is modeled as a sequence of predetermined actions as well as the responses to these actions. Each component model represents the desired (nominal) system behavior. An abrupt fault is viewed as a violation of the component desired behavior. While a drift-like fault is viewed as a drift in the normal characteristics of component response to actions. An indicator measuring the change in the response characteristics of the component is used to detect a drift. This detection can be then used to warn a human operator when the component behavior starts to deviate from its normal behavior. The proposed approach is illustrated using a manufacturing system.

Dynamic K-Nearest Neighbors for the monitoring of evolving systems

In this article, a new Pattern Recognition (PR) approach is proposed to monitor the functioning modes evolutions in dynamic systems. When a functioning mode evolves, the system characteristics change and the observations, i.e. the patterns, obtained on the system change too. In this case, classes representing the system functioning modes have to be updated by keeping representative patterns only. The developed PR approach is based on the K-Nearest Neighbors (KNN) method. It is named Dynamic KNN (DKNN) and comprises two phases: a detection phase to detect and confirm classes evolutions and an adaptation phase realized incrementally to update the evolved classes parameters and reduce the dataset. To illustrate this approach, the monitoring of weldings quality (good or bad) is realized on an industrial system, based on acoustic noises issued of weldings operations.

Dynamic Fuzzy Pattern Matching for the monitoring of non stationary processes

Abstract In the domain of diagnosis by Pattern Recognition, a pattern is a simplified observation about the system state and each class, containing similar patterns, represents a functioning mode. Classes issued of non stationary processes are dynamic and their characteristics vary over the time. In this paper, the classification method Incremental Fuzzy Pattern Matching (IFPM) is developed for the monitoring of non stationary processes. This development is based on the monitoring of the accumulative changes in the data distribution. When these changes reach a threshold prefixed by an expert, the data distribution will be recursively updated online using the recent and useful patterns.

Adaptive and Predictive Diagnosis Based on Pattern Recognition

Systems work in either normal or abnormal functioning modes. Pattern Recognition (PR) is a set of methods used to classify a pattern into one of a set of predefined classes. Each class is associated to a functioning mode. If the pattern is considered as the observation of the actual functioning mode, then the diagnosis by PR is realized by deciding the class of the actual pattern. PR is particularly adapted to realize the diagnosis when the prior information about system functioning modes is not sufficient to construct an analytical or structural model of the system functioning. However this knowledge is often incomplete because it cannot contain information about all system functioning modes. Thus the diagnosis method must be adaptive to include into its database all the new functioning modes. In addition, the diagnosis must be predictive in order to follow the evolution of the system from one mode to another one. We use the supervised classification method Fuzzy Pattern Matching (FPM) to realize the diagnosis of non-evolutionary systems with a complete database. Indeed, FPM cannot realize the adaptive and predictive diagnosis. Therefore, a solution to this problem is proposed in this paper. The performance of the proposed approach is illustrated using different examples.

Recursive learning in real time using fuzzy pattern matching

Our team of research “diagnosis of industrial processes” works on diagnosis in using classification method for data coming from industrial and medical sectors. The goal is to develop a decision-making system. We use the fuzzy pattern matching (FPM) as a method of classification and the transformation probability–possibility of Dubois and Prade to construct the densities of possibilities. These densities are used to assign the new observations to their suitable class. Sometimes we cannot have enough observations in the learning set for several reasons, especially the cost and the time. The insufficient number of observations in the learning set involves several negative effects: bad classification, inability to detect the real number of operating states, inability to know the real shapes of the classes and inability to follow their evolution. The solution is to increase our knowledge about the system in accumulating the information obtained from each classified observation. This solution called incremental learning needs to remake the learning process after the classification of each new observation. This incremental learning must be made in real time to take the advantage of the information added by each new classified point. When the number of points in the learning set increases, the time needed to do the learning process also increases, which makes the incremental learning in real time difficult. In this paper, we recall the principle of the FPM algorithm. Then we show how we can include the incremental learning in this method, and we compare the obtained computing times with the ones of classical method. To conclude we expose the advantages of such learning in real time.