A new method for the estimation of the instantaneous speed relative fluctuation in a vibration signal based on the short time scale transform

In this paper we propose an original method for the estimation of the instantaneous speed relative fluctuation (ISRF) in a vibration signal measured on a system submitted to relatively heavy load and speed fluctuations and without speed measurement available. Our approach is based on the estimation of an instantaneous time-scaling factor along the vibration signal, related to the instantaneous relative speed gap from time t=0t=0. It extends a previous work related to the estimation of the relative speed gap between two stationary signals via the Scale transform. In a non-stationary situation the method is performed between segments of the signal, which we coin the short time scale transform. In order to adjust the optimal length of the segments we propose an optimisation scheme based on the Kurtosis maximisation of the amplitude spectrum of the angular resampled signal using the estimated ISRF. Contrary to conventional methods based on the instantaneous frequency estimation of one spectral component, the proposed method for ISRF estimation does not depend on the choice of one particular component. The algorithm is relatively simple to implement and has a reasonable computation cost. However, it is not advised to use it in the case of very large speed variations such as during a speed-up. The method is then applied to the vibration measurements of two different planetary gearboxes used in the mining industry, first one with available speed measurement for validation, and second one with advanced wear of the planetary stage and without speed information. In this latter case the estimated ISRF is used in order to establish a diagnosis of the system.