A Novel Algorithm for Instantaneous Angular Speed Estimation Based on Vibration Signatures

Gabriel Davidyan, Renata Klein, Jacob Bortman

Research output: Contribution to journalArticlepeer-review


Introduction: In the Israel Railways rolling stock, some train cars suffer from damaged bearings of the condenser fans of the A/C system. For these systems, vibration analysis is an effective method for detecting various faults and malfunctions. The diverse methods for processing vibration signals require knowledge of the rotational speed of the machine in question, since in rotating parts, fault events occur at specific angular positions rather than at specific times. For this reason, an accurate estimate of the instantaneous angular speed (IAS) is important for reliable diagnosis. In practice, direct measurement of the rotational speed of the A/C system Israel Railways fleet of train cars is impossible due to regulations and operational constraints. Objective: In this context, this work focuses on estimating the IAS directly from the measured vibration signal. Method: A new method is proposed to automatically extract the IAS from the vibration data. This new method is suitable for non-stationary rotating speeds, and is applicable to any range of rotational speed and its rate of change. The algorithm requires the input of the basic parameters of the system, while all the other parameters controlling the process are determined automatically. Results: The algorithm was validated with simulated and experimental data. The simulations and experimental data allowed the verification of the proposed algorithm by calculating the relative error between the estimated IAS and the simulated and measured rotational speed in all scenarios. A maximum error of 0.08% was found, reflecting the high quality of the algorithm. Conclusions: The method is robust since it correlates between several characteristic frequencies of the rotating parts of the system. The algorithm was verified and validated using simulated and experimental data.

Original languageEnglish
JournalJournal of Vibration Engineering and Technologies
StateAccepted/In press - 1 Jan 2023


  • Bearing fault diagnosis
  • Instantaneous angular speed
  • Order tracking
  • Rotational speed estimation
  • Time–frequency representation

All Science Journal Classification (ASJC) codes

  • Acoustics and Ultrasonics
  • Mechanical Engineering


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