Regular Article

Order tracking using H_∞ estimator and polynomial approximation

¹ PRISME Laboratory, University of Orleans, 21 rue Loigny-la-bataille, 28000 Chartres, France
² PRISME Laboratory, University of Orleans, 12 rue de Blois, 45067 Orleans, France

^* e-mail: amadou.assoumane@etu.univ-orleans.fr

Received: 12 December 2016
Accepted: 5 December 2017

Abstract

This paper presents the H_∞ estimator for discrete-time varying linear system combined with the polynomial approximation for order tracking of non-stationary signals. The proposed approach is applied to the gearbox diagnosis under variable speed condition. In this instance, it is well known that the occurrence of a fault on a gear tooth leads to an amplitude and a phase modulation in the vibration signal. The purpose is to estimate this unknown amplitude and phase modulation by tracking orders. To estimate these modulations, the vibration signal is described in state space model. Then, the H_∞ criterion is used to minimize the worst possible amplification of the estimation error related to both the process and the measurement noises. Such an approach doesn't require any assumption on the statistic properties of the noises unlike the Kalman estimator. A numerical example is given in order to evaluate the performance of the H_∞ estimator regarding the conventional Kalman estimator.