H∞ estimator for gearbox diagnosis in variable speed conditions

It is well known that a faulty gearbox vibration signal exhibits an amplitude modulation (AM) as well as a phase modulation (PM). These modulation carry out a lot of useful information about health condition. This paper presents two approaches for modeling amplitude and phase modulation in gearbox vibration signal. These last are used to describe the vibration signal by a state space model. Then, the H
_∞
estimator is designed to estimate the modulation appearing in the vibration signal. This estimator is obtained by minimizing the worst possible amplification effects of disturbances (measurement and modeling noises) on the estimation error. Such an estimator does not require any assumption on the statistic properties of the noises. Since additive noises in gearbox vibration signal are non Gaussian and non white, this estimator is more suitable in practical gearbox diagnosis. To evaluate the performance of the two approaches, we use a synthetic and an experimental gearbox vibration signal.