Generalization of the synchronous average for Deterministic/Random Separation under speed varying conditions.

In rotating machinery vibration analysis, the synchronous average is perhaps the most widely used technique for extracting periodic components which are deterministic in their nature. These components are typically related to the gear vibrations and should be separated from other noisy source contributions. This method proved its efficiency when the machine operates under stationary conditions. Though being order tracked, the synchronous average efficiency is jeopardized in large speed-varying conditions because of the time-varying distortion in the magnitude and phase of the gear response. This distortion is provoked by the transfer function of the mechanical system transmission path from the excitation to the accelerometer. This paper introduces a novel non-parametric approach for estimating the deterministic components in a signal, which happens to be a generalization of the classical synchronous average to the cyclo-non-stationary regime. Once the speed profile is discretized to a defined set of intervals called regimes, the cycles are then averaged with respect to each regime to obtain a discrete-speed dependent synchronous average. Afterwards, the obtained representation is smoothed by means of cubic spline kernels in order to estimate the missing inter-interval speeds leading to an accurate estimation of the deterministic component. The efficiency of the proposed approach is finally proved on simulated and actual gear signals.