Fractional Generalized Cauchy Prediction Model with 1/f Process for RUL of Rolling Bearing

Aiming at the non-stationary and slowly varying stochastic nature of bearing degradation from normal operation to failure, this paper proposes a fratcional Generalized Cauchy (fGC) prediction model with 1/f process and dual parameters: fractal dimension and Hurst exponent. First, 1/f process sequences exhibit long-range dependence and power-law characteristics. Next the fGC degradation model is established, and the Hurst exponent and fractal dimension are calculated using the R/S method and box-counting dimension method, respectively. Then a dimensionless jump descriptor is employed as a Health Indicator to detect incipient faults and estimate degradation parameters. The maximum likelihood algorithm method is applied to parameter estimation. Finally, a experiment verifies the satisfactory prediction performance through compared with CNN and LSTM predicting model.