Extraction of rotor unbalance characteristics from non-stationary vibration signals during speed fluctuations

Speed fluctuations introduce pronounced non-stationarity into rotor vibration signals, which makes the accurate extraction of rotational-frequency, amplitude, and phase characteristics considerably more difficult than under steady-speed conditions. To address this problem, a rotor-unbalance characteristic-extraction method is developed for speed-fluctuation conditions. The procedure first evaluates supervised normalized least mean square (NLMS) filtering followed by fixed forward–backward zero-phase filtering for noise suppression without additional phase distortion. The multisynchrosqueezing transform (MSST) is then applied to improve time-frequency energy concentration and track the instantaneous rotational-frequency component of the non-stationary vibration signal. The instantaneous phase is subsequently resampled using the keyphasor signal, and phase tracking regression (PTR) is applied to estimate the rotational-frequency phase under speed fluctuation and keyphasor jitter. Simulation results show that the combined NLMS and zero-phase filtering method achieves the highest output signal-to-noise ratio and the lowest root mean square error among the compared filtering methods. MSST provides better time-frequency energy concentration than the other investigated time-frequency methods, while PTR maintains relatively stable phase-estimation performance under variations in noise level, keyphasor jitter, frequency modulation ratio, and sampling duration. Experiments on the investigated three-disk rotor further show that PTR yields a phase standard deviation of 4.363° across the segmented steady-state measurements, and the vibration amplitudes at all three measurement locations are reduced by more than 70% in both balancing tests at 5000 rpm, demonstrating the effectiveness of the proposed method for the present rotor configuration and tested operating condition.