Estimation of geometric characteristics of three-component oscillations for system monitoring
Résumé
The 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.
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