A multi-order synchrosqueezing transform leveraging informative harmonics selection for instantaneous angular speed estimation

Under nonstationary conditions, estimating the instantaneous angular speed (IAS) of rotating machines from vibration measurements is a practical way for encoder-free condition monitoring. Existing IAS estimation methods typically proceed from two main approaches: phase demodulation and time–frequency representation (TFR). However, several methods from these two categories often face challenges such as a single-harmonic focus and difficulty in distinguishing between clean and noisy harmonics. Noisy harmonics are characterized by low signal-to-noise ratio, energy attenuation, and interference from other components. In contrast, clean harmonics, revolve around the actual IAS, thus improving the accuracy of its estimation. This paper introduces a novel approach, the Multi Order Synchrosqueezing Transform (MOST), which stands out due to its ability to automatically identify and utilize informative harmonics, setting it apart from traditional methodologies. MOST aims at providing a more accurate IAS estimation under nonstationary conditions. It proceeds from an initial IAS estimate from a synchrosqueezing transform and then introduces a normalized threshold aimed at preserving the energy of harmonics in the TFR at each time bin. Next, it constructs a probability density function using multiple harmonics. By doing so, it retains essential information from selected harmonics while effectively filtering out irrelevant noise. To emphasize the effectiveness of this approach, the paper conducts an exhaustive investigation. The evaluation includes rigorous performance testing across multiple noise levels to demonstrate its robustness, alongside assessments based on simulated data and two benchmark experimental datasets. This shows the impaction of MOST in its generalizability to various rotating machinery types and vibration signals, highlighting its potential for broader industrial applications. • Innovative Synchrosqueezing leveraging normalized thresholds. • Informative Harmonic Map identification based on energy accumulation. • Validation on simulated and experimental data sets. • High performance on highly nonstationary machine vibrations.