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%.

变速条件下的故障诊断已成为旋转机械监测的研究热点。由于线性调频信号的能量集中特性，分数阶傅里叶变换（FrFT）有助于以可变速度进行轴承故障检测。但是，其性能取决于难以确定的FrFT滤波器参数。因此提出了分数频带熵（FrFBE）来解决这个问题，构造了优化的FrFT滤波器以提取时变故障特征。首先，对解调后的信号执行短时分数阶傅立叶变换（STFrFT）。然后，基于所获得的分数时频矩阵，开发FrFBE，以定位故障谐波的聚集位置。下一个，提出了一个全局/局部最小FrFBE准则来确定FrFT过滤中心。最后，通过计算顺序跟踪（COT）从滤波后的结果中提取故障特征。仿真和实验案例表明，在不同的工作条件下，诊断结果都很好，识别误差保持在1％以内。