A novel shift-invariant dictionary learning approach integrated with a hidden Markov model for diagnosing bearing faults in time-varying conditions

Bearing fault diagnosis is crucial for mechanical system reliability. Numerous techniques have been developed to identify faults in bearings. However, the signals under time-varying speed condition are nonstationary, and most diagnosis methods suffer from the nonstationary property caused by time-varying speed problem. The change of speed changes the fault pulse frequency, but the structure of pulse remains the same. Shift-invariant dictionary learning (SIDL) can learn the repetitive structure in the signal without the limitation of the structure's size. Thus, the fault pulses in the fault signal under time-varying speed condition. Union of circulants dictionary learning (UCDL) is a kind of SIDL, where the algorithm takes the advantage of explicit circulant structures and has the powerful ability to learn the fault pulses into the atoms. In this work, we use UCDL to extract features under time-varying speed condition, and hidden Markov model (HMM) is used to diagnose faults. We further found that UCDL with the global sparse coding named basis pursuit, which can maintain the stability of the coefficient solution, has a better performance in the time-varying diagnosis. To validate the performance of the proposed method named improved SIDL, both simulation and experimental signals are processed, and the diagnosis results prove the high efficiency of the proposed method in the time-varying diagnosis. The improved SIDL method achieved an average diagnostic accuracy of 100% in simulations and 98.32% in experiments, both of which are superior to traditional methods.