Fractional Order Derivative and Time-Delay Feedback Enabled Stochastic Resonance for Bearing Fault Diagnosis

The benefits of noise can be found in nonlinear systems where a type of resonances can inject the noise into systems to enhance weak signals of interest, including stochastic resonance, vibrational resonance, and chaotic resonance. Such benefits of noise can be improved further by adding some items into the nonlinear systems. Considering the time-dependent memory of fractional-order derivative and time-delay feedback which makes the nonlinear systems take advantage of their historical information and makes the output of nonlinear systems affect the input by feedback control, therefore, we attempt to design the model of stochastic resonance (SR) enhanced by both fractional-order derivative and time-delay feedback. Among them, fractional-order derivative and time delay would reinforce the memory of nonlinear systems for historical information and feedback would use the output of systems to control the systems precisely. Therefore, we hope that their advantages would be fused to improve the weak signal detection performance of SR further. Then, it would be applied to bearing fault diagnosis and compared with that without fractional-order derivative and time-delay feedback and even other diagnostic methods. The experimental results indicate that the SR enhanced by fractional-order derivative and time-delay feedback where a local signal-to-noise ratio is designed as the objective function to optimize these tuning parameters of the proposed method could enhance early fault signature of bearings and outperform that without fractional-order derivative and time-delay feedback and even infogram method.