A Multi-Order Synchrosqueezing Transform Approach for Instantaneous Angular Speed Estimation

Abstract

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), designed to overcome these limitations. 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. What sets MOST apart is an automatic setting that distinguishes between informative and noisy harmonics at each time instant. 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 assessment includes performance evaluations based on simulated data as well as on two benchmark experimental datasets.

Keywords: Time-Frequency representation, Synchrosqueezing transform, Multiple harmonics, Vibration analysis, Condition monitoring, Instantaneous angular speed