Monitoring of Non Stationary Systems Using Dynamic Pattern Recognition

Introduction

Monitoring industrial systems, like robots, vehicles, …, at each instant increases their productivity and decreases the production costs. When a fault is detected, the monitoring system executes a correction procedure to bring back the process in normal operating conditions. These systems are constantly evolving between different functioning modes in the course of time. In statistical Pattern Recognition (PR) (Dubuisson, 1990),(Dubuisson, 2001),(Duda et al., 2001),(Jain et al., 2000), historical patterns or observations about system functioning modes are divided into groups of similar patterns, called classes, using an unsupervised learning method (Bezdek, 1981),(Frigui & Khrisnapuram, 1997) or human experience. Each class is associated to a functioning mode (normal or faulty). These patterns, with their class assignments, constitute the learning set. They are represented by a set of d features, or attributes, so they can be viewed as d-dimensional features vectors, or points, in the feature space. A supervised learning method [Therrien, 89] uses the learning set to build a classifier that best separates the different classes in order to minimize the misclassification error. The model of each class can be represented by a membership function which determines the membership value of a pattern to a class. Then, new incoming patterns are assigned to the class for which they have the maximum membership value. In supervised learning methods, the membership function can be generated using Probability Density Function (PDF) estimation based methods or heuristic based ones. In the first category, the membership function is equal to either the PDF or to the a posterior probability function. The estimation of PDF can be parametric, as the Bayesian classifier (Dubuisson, 1990), or non parametric, as the Parzen window (Parzen, 1962), voting k nearest neighbor rules (Cover & Hart, 1967)(Denoeux & Zouhal, 2001) or by histograms (Medasani et. al, 1998). In heuristic based methods (Medasani et al., 1998), the shape of the membership function and its parameters are predefined either by experts to fit the given data set, or by learning to construct directly the decision boundaries as the potential functions (Dubuisson, 1990), neural networks (Ripley, 1996) or support vector machines (Vapnik, 1998).

One of the applications of PR methods is the diagnosis of dynamic systems. The patterns, describing the system functioning, can be static or dynamic. A static pattern is represented by a point in the feature space while a dynamic pattern is represented by a multidimensional trajectory. In this case, the feature space has an added dimension which is the time (Angstenberger, 2000). Classes can also be static or dynamic. Static classes are represented by restricted areas formed by similar static patterns in the feature space. Hence, the way in which patterns occur is irrelevant to their membership values. Therefore, the classifier's parameters remain unchanged with the time. However, data issued from evolving processes are non stationary. In this case, classes become dynamic and their characteristics change in the course of time. Thus, the classes’ membership functions must be adapted to take into account these temporal changes. This requires an adaptive classifier with a mechanism for adjusting its parameters over the time. Hence, some of the new incoming points reinforce and confirm the information contained in the previous data, but the other ones could bring new information (creation, drift, fusion, splitting of classes, etc.). This new information could concern a change in operating conditions, development of a fault or simply more significant changes in the dynamic of the process.