Fractional frequency band entropy for bearing fault diagnosis under varying speed conditions

Fault diagnosis under varying speed conditions has become a research hotspot in rotating machinery monitoring. Due to the energy concentration property of linear frequency-modulated signals, fractional Fourier transform (FrFT) is helpful to bearing fault detection with varying speed. However, its performance depends on FrFT filter parameters, which are difficult to determine. So fractional frequency band entropy (FrFBE) is proposed to solve this problem, constructing optimized FrFT filter to extract time-varying fault characteristics. First, short-time fractional Fourier transform (STFrFT) is performed on the demodulated signal. Then, FrFBE is developed based on the obtained fractional time-frequency matrix to locate aggregation positions of fault harmonics. Next, a global/local minimum FrFBE criterion is proposed to determine FrFT filtering centers. Finally, the fault characteristics are extracted by computed order tracking (COT) from the filtered results. Simulation and experiment cases show good diagnosis result with different operating conditions, with recognition error kept within 1%.