Estimation of geometric characteristics of three-component oscillations for system monitoring

International audienceThe estimation of the geometric properties of the elliptical trajectory followed by a three-component sinusoidal signal in three-dimensional Euclidean space with the objective of system monitoring is addressed in this paper. In system monitoring problems, multicomponent signals are frequently encountered. Most physical quantities are naturally composed of three components. In this paper, a three-component sinusoidal signal is studied. Three sinusoids of the same frequency follow a trajectory in the shape of an ellipse when plotted in three- dimensional Euclidean space. It is the geometric properties of this elliptical trajectory that are estimated in this paper. The geometric properties of interest are the norm of the position vector, the binormal vector, curvature and torsion. Straightforward expressions of these quantities are given which allow the geometric properties of the ellipse to be recovered from three-component data. Definition and interpretation of the expressions are also included, followed by a step-by-step explanation of the approach used to estimate these quantities. The performance and limitations of the method with respect to various parameters such as noise, frequency of the sinusoids and ellipticity are discussed. The usefulness of this method as an informative means of describing three-component sinusoidal signals is illustrated with two applications

Estimation de propriétés géométriques de signaux à trois composantes pour la surveillance de systèmes

Most methods for condition monitoring are based on the analysis and characterization of physical quantities that are three-dimensional in nature. Plotted in a three-dimensional Euclidean space as a function of time, these quantities follow a trajectory whose geometric characteristics are representative of the state of the monitored system. Usual techniques of condition monitoring study the measured quantities component by component, without taking into account their three-dimensional nature or the geometric properties of their trajectory. A significant part of the information is thus ignored. In this research work, we would therefore like to develop a method for the analysis and processing of three-component quantities capable of highlighting the special geometric features of such data and providing complementary information for condition monitoring. The proposed method has been applied to two different cases: voltage dips monitoring in three-phase power networks and bearing faults monitoring in rotating machines. In these two cases, the results obtained are promising and show that the estimated geometric indicators lead to complementary information that can be useful for condition monitoring.La plupart des méthodes de surveillance des systèmes sont basées sur l'analyse et la caractérisation de grandeurs physiques qui sont par nature tridimensionnelles. Tracées dans un repère euclidien à trois dimensions, ces grandeurs parcourent en fonction du temps une trajectoire dont les caractéristiques géométriques sont représentatives de l'état du système surveillé. Les techniques classiques de surveillance des systèmes étudient les grandeurs mesurées composante par composante, sans prendre en compte leur nature tridimensionnelle et les propriétés géométriques de leur trajectoire. Une part importante de l'information est ainsi ignorée. Dans le cadre de ce travail de recherche, on se propose de développer une méthode d'analyse et de traitement de grandeurs à trois composantes permettant de mettre en évidence les spécificités géométriques des données et de fournir une information complémentaire pour la surveillance des systèmes. La méthode proposée à été appliquées à deux cas différents : la surveillance des creux de tension des réseaux de puissance triphasés et la surveillance des défauts de roulements des machines tournantes. Dans les deux cas, les résultats obtenus sont prometteurs et montrent que les indicateurs géométriques estimés mènent à une information complémentaire qui peut être utile pour la surveillance des systèmes

Analysis of three-dimensional physical quantities for system diagnosis

International audienceMost methods for system diagnosis are based on analysis of three-dimensional physical quantities. For example, electrical system monitoring is based on three-phase electrical measurements and 3D vibration analysis involves studying three-dimensional mechanical measurements. In three-dimensional space, such quantities follow a trajectory whose geometric characteristics are representative of the state of the monitored system. Usual techniques for diagnosis analyze such quantities component by component, without taking into account their three-dimensional nature or the geometric characteristics of their trajectory. A significant part of the information that may be useful for diagnosis is thus ignored. The main objective of this work is to estimate the geometric characteristics and trajectories of three-dimensional quantities using basic differential geometry concepts with the aim of developing tools for processing and analyzing 3D data. Such tools provide additional information for system diagnosis with respect to conventional methods and therefore increase their performance in terms of fault detection and localization. Simulated and experimental data concerning electrical power systems will be used to demonstrate the usefulness of this approach

Estimation of geometric properties of three-component signals for system monitoring

International audienceMost methods for condition monitoring are based on the analysis and characterization of physical quantities that are three-dimensional in nature. Plotted in a three-dimensional Euclidian space as a function of time, such quantities follow a trajectory whose geometric characteristics are representative of the state of the monitored system. Usual condition monitoring techniques often study the measured quantities component by component, without taking into account their three-dimensional nature and the geometric properties of their tra-jectory. A significant part of the information is thus ignored. This article details a method dedicated to the analysis and processing of three-component quantities, capable of highlighting the special geometric features of such data and providing complementary information for condition monitoring. The proposed method is applied to two experimental cases: bearing fault monitoring in rotating machines, and voltage dips monitoring in three-phase power networks. In this two cases, the obtained results are promising and show that the estimated geometric indicators lead to complementary information that can be useful for condition monitoring