An enhanced method for instantaneous angular speed accuracy improvement and its application in variable-speed scenarios

Tacholess speed estimation serves as a powerful preprocessing method for condition monitoring of variable-speed machinery in scenarios where speed reference sensors are unavailable. However, for a mono amplitude modulated (AM)-frequency modulated (FM) signal contaminated by background noise, the instantaneous frequency (IF) retrieved via phase demodulation tends to fluctuate around its theoretical value. In this study, we first derive the influence of three key factors—carrier signal amplitude, amplitude modulation characteristics, and background noise variance—on the fluctuation (i.e., variance) of the estimated IF. Based on this theoretical insight, instantaneous angular speed (IAS) estimates derived from all vibration harmonics, together with their corresponding instantaneous IAS variance, can be estimated from the vibration signal. The optimal IAS estimate is then obtained by leveraging the maximum likelihood estimation (MLE) framework. Accordingly, this study proposes an enhanced IAS accuracy improvement (EIASAI) method for iterative refinement of IAS estimation accuracy. The efficacy of the proposed method is evaluated and benchmarked against existing state-of-the-art methods using both numerical simulations and vibration signals collected from operational wind turbines.