When an incipient fault develops, rolling-element bearing produces stochastic cyclostationary vibrations. In practice, this symptomatic property is usually masked by second vibration sources that contain cyclostationary deterministic components produced by neighboring operating gears. In the case of stationary speed conditions, the synchronous average has proven its usefulness for estimating the signal mean, thus separating these two sources. Once separated, the mean instantaneous power can be estimated by the synchronous average applied to the envelope of the residual signal. This tool proves efficient for extracting bearing fault contribution. However, in speed varying conditions, the cyclostationary nature of the vibration signal turns to become cyclo-non-stationary. This leads to an inaccurate estimation of the gear deterministic vibration part and the bearing fault vibration, which results in misleading diagnosis features. This paper aims at proposing a new procedure of estimating the synchronous average under high and random speed variations in order to efficiently (i) separate deterministic and random sources, and (ii) relax the mean instantaneous power. Being based on a structured discretization of the speed profile, this method is able to track the amplitude and the phase variations imposed by the speed changes. Successful examples are then demonstrated on simulated and actual vibration data measured from a test-rig operating in run-up regime.
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