Arnaud Devillez

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.

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.

Four fuzzy supervised classification methods for discriminating classes of non-convex shape

Our work deals with modelling and optimising industrial processes such as metal cutting with high-speed machining. In this field we have chosen to use fuzzy supervised classification methods in order to design a diagnosis system or a process-monitoring module. The problem, we currently meet, concerns the shape of the classes, we generally obtain. These shapes are often non-convex and non-separable by a hyperplane. For these reasons, we focus on fuzzy supervised classification methods in order to discriminate these classes. The choice of a method is not obvious and we perform a comparative study. The two classical methods tested were the fuzzy K-nearest-neighbours method and a method based on distributed fuzzy rules. Furthermore, we propose two adaptations of the fuzzy pattern matching algorithm called fuzzy pattern matching with exponential function and fuzzy pattern matching multidensity. After some refresher on supervised classification, the four tested methods are detailed and compared according to the following criteria: quality of the discrimination, computation time and ability to decide. The response of each classifier is illustrated by membership level curves and the quality of diagnosis is studied by the introduction of membership and ambiguity rejects.

Analytical and Finite Element Approaches for the Drilling Modelling

Perform drill point design is one of the major problems for the drill manufacturers. To enhance drill performance they have to elaborate prototypes and carry out many tests to progress step by step to an optimised geometry. Model and simulate drilling operations is a very interesting way to obtain useful information for the drill manufacturing process. In this work, a geometrical and thermomechanical analytical model and a finite element approach of drilling were used. While the first gives very quickly some global information, the second gives more details but after a long calculation time. It is shown that the two approaches are complementary and that they may be used with advantage for the drill design.

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.

Système de supervision d'un processus industriel avec apprentissage en ligne

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 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 used for the purpose of industrial applications without any decrease of production rate.

A New Criterion for Obtaining a Fuzzy Partition from a Hybrid Fuzzy/Hierarchical Clustering Method

Classical fuzzy clustering methods are not able to compute a partition into a set of points, when classes have non-convex shape. Furthermore, we know that in this case, the usual criteria of class validity, such as fuzzy hyper volume or compactness - separability, do not allow one to find the optimal partition.