Control of phases by ESPRIT and WLSE methods for the early detection of gear cracks

The early detection of gear faults remains a major problem, especially when the gears are subjected to non stationary phenomena due to defects. In industrial applications, the crack of tooth is a default very difficult to detect whether using the time descriptors or the frequency analysis. In this work and based on a numerical model, we prove that the crack default affects directly the phase of the frequency component of the defective wheel (frequency modulation). To properly estimate the phases, we suggest two high-resolution techniques (Estimation of Signal Parameters via Rotational Invariance Techniques ESPRIT with a sliding window and Weighted Least Squares Estimator WLSE). The results of both methods are compared to the phase obtained by Hilbert transform. The three techniques are then applied on a multiplicative signal with a frequency modulation to show the influence of the amplitude modulation on the quality of phase estimation. We note that the ESPRIT method is much better in the estimation of frequencies while WLSE shows much efficiency in the estimation of phases if we keep the frequencies almost stables.

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