Multi-harmonic phase demodulation method for instantaneous angular speed estimation using harmonic weighting

Phase demodulation is arguably the most used technique for the estimation of the instantaneous angular speed from vibration signals measured on rotating machinery. Although phase demodulation offers a straightforward approach to determine accurately the rotation speed of a particular shaft in a rotating machine, it does have strict limitations that can hinder the estimation accuracy and its overall reliability. In general, phase demodulation relies on the presence of a single harmonic with a high signal-to-noise ratio for the full duration of the measured vibration signal. Such a precondition hinders its applicability for a generic speed estimation approach for rotating machinery. There are copious real-world scenarios where this requirement is not met, especially given the increasing complexity and dynamic operating range of rotating machines nowadays. In such complex rotating systems, the deterministic signals are not necessarily all harmonically related to a fundamental harmonic. The presence of crossing harmonic orders from non-synchronous rotating components or of lightly damped structural resonances can significantly skew the instantaneous phase demodulation. This paper proposes a novel approach towards phase demodulation by both incorporating multiple harmonics in the demodulation process and also giving the individual harmonic phases time-dependent weighting. This combination of incorporating multiple harmonics and weighting them allows for fully exploiting the information contained within the vibration signal while also promising to be more robust to changing operating regimes. The proposed multi-harmonic demodulation method is investigated thoroughly by assessing its performance on simulated data, on two benchmark experimental data sets, and on a large wind turbine vibration data set consisting of thousands of vibration measurements.