Stochastic-Hamiltonian And Bayesian Framework for Early Fault Detection Using Electric Motor Vibration Signals

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.

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