Stochastic-Hamiltonian And Bayesian Framework for Early Fault Detection Using Electric Motor Vibration Signals
DOI:
https://doi.org/10.55640/eijmrms-06-02-11Keywords:
Vibrodiagnostics, stochastic model, Hamiltonian systemAbstract
Reliable performance of electric motors is crucial for the continuous operation of robotic systems, pneumatic transport setups, and automated manufacturing lines. Traditional vibration diagnostics typically assume signal stationarity, yet real-world industrial vibrosignals exhibit heavy noise, time-varying parameters, and nonlinear dynamics, leading to fault detection only at late stages.
This work presents an integrated mathematical framework that merges stochastic differential equations, Hamiltonian energy formalism, the optimal Kalman-Bucy filter, and Bayesian inference to model electric motor vibrodynamics. The approach enables fault prediction prior to amplitude growth by tracking system energy drift, innovation energy discrepancies between model and process, and spectral shifts.
Theoretical evaluation reveals that the diagnostic metric features minimal variance and markedly superior sensitivity compared to conventional RMS deviation or kurtosis measures.
References
Kalman, R.E.: A new approach to linear filtering and prediction problems, Journal of Basic Engineering, Vol. 82, pp. 35–45, 1960.
Simon, D.: Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches, Wiley, 2006.
Jazwinski, A.H.: Stochastic Processes and Filtering Theory, Academic Press, 1970.
Øksendal, B.: Stochastic Differential Equations: An Introduction with Applications, Springer, 2003.
Arnold, L.: Random Dynamical Systems, Springer, 1998.
Gardiner, C.: Stochastic Methods: A Handbook for the Natural and Social Sciences, Springer, 2009.
Luenberger, D.G.: Optimization by Vector Space Methods, Wiley, 1969.
Särkkä, S.: Bayesian Filtering and Smoothing, Cambridge University Press, 2013.
Doucet, A., de Freitas, N., Gordon, N.: Sequential Monte Carlo Methods in Practice, Springer, 2001.
Van Trees, H.L.: Detection, Estimation, and Time Series Analysis, Wiley, 2001.
Isermann, R.: Model-based fault detection and diagnosis, Annual Reviews in Control, Vol. 29, pp. 71–85, 2005.
Blanke, M., Kinnaert, M., Lunze, J., Staroswiecki, M.: Diagnosis and Fault-Tolerant Control, Springer, 2016.
Randall, R.B.: Vibration-based Condition Monitoring, Wiley, 2011.
Antoni, J.: The spectral kurtosis: a useful tool for characterising non-stationary signals, Mechanical Systems and Signal Processing, Vol. 20, pp. 282–307, 2006.
Lei, Y., Yang, B., Jiang, X., Jia, F., Li, N., Nandi, A.K.: Applications of machine learning to machine fault diagnosis: A review and roadmap, Mechanical Systems and Signal Processing, Vol. 138, 106587, 2020.
Peng, Z.K., Chu, F.L.: Application of wavelet transform in machine condition monitoring, Mechanical Systems and Signal Processing, Vol. 18, pp. 199–221, 2004.
Heng, A., Zhang, S., Tan, A.C.C., Mathew, J.: Rotating machinery prognostics: state of the art, challenges and opportunities, Mechanical Systems and Signal Processing, Vol. 23, pp. 724–739, 2009.
Bishop, C.M.: Pattern Recognition and Machine Learning, Springer, 2006.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Kurbanov Mahmudjon Khusanboy oglu, Tohirjonov Mahmudjon Sobitjon oglu, Abdukarimov Azamjon Abdukadir oglu, Tokhtasinov Davron, Sharibayev Rosuljon Nasir oglu, Taratyn Igor Aleksandrovich
This work is licensed under a Creative Commons Attribution 4.0 International License.
Individual articles are published Open Access under the Creative Commons Licence: CC-BY 4.0.
