Instantaneous Angular Speed Tracking of Rotating Machines Using a Bayesian Framework

Abstract Accurate estimation of instantaneous angular speed is crucial for the condition monitoring and diagnosis of rotating machinery. Traditional methods often struggle in noisy, non-stationary, and multi-interfering source environments. This paper proposes a Bayesian framework for tracking instantaneous angular speed from vibration measurements, offering enhanced precision, robustness, and reliability. Our approach models the instantaneous angular speed as a hidden Markov process. The likelihood is derived from the observed spectrogram and the kinematics of the rotating machine, taking into account harmonics. A prior distribution is introduced to leverage the frequency’s continuity and incorporate domain-specific knowledge. By combining the prior and likelihood using Bayes’ theorem, we obtain the posterior distribution, which represents the probability of the instantaneous angular speed trajectory given the observed data. The Bayesian estimator is determined through Viterbi dynamic programming algorithm, yielding the most probable sequence of speed states even in the presence of significant noise. This approach effectively handles non-stationary signals and can adapt to varying operating conditions. Simulation results demonstrate the superior accuracy and robustness of our approach compared to state-of-the-art methods, especially under harsh conditions. This innovative methodology has significant potential for applications in predictive maintenance, fault detection, and improving the overall operational efficiency of rotating machinery in various industrial settings.