Multifractional Brownian Motion and Quantum-Behaved Partial Swarm Optimization for Bearing Degradation Forecasting

Gradual degradation of the bearing vibration signal is usually studied as a nonstationary stochastic time series. Roller bearings are working at high speed in a heavy load environment so that the combination of bearing faults gradually degraded during the rotation might lead to unpredicted catastrophic accidents. The degradation process has the property of long-range dependence (LRD), so that the fractional Brownian motion (fBm) is taken into account for a prediction model. Because of the dramatic changes in the bearing degradation process, the Hurst exponent that describes the fBm will change during the degradation process. A priori Hurst value of the conventional fBm in the prediction is fixed, thus inducing a minor accuracy of the prediction. To avoid this problem, we propose an improved prediction method. Based on the following steps, at the initial data processing, a skip-over factor is selected as the characteristics parameter of the bearing degradation process. A multifractional Brownian motion (mfBm) replaces the fBm for the degradation modeling. We will show that also our mfBm has the same property of long-range dependence as the fBm. Moreover, a time-varying Hurst exponent H(t) is taken to replace the constant H in fBm. Finally, we apply the quantum-behaved partial swarm optimization (QPSO) to optimize H(t) for a finite interval. Some tests and corresponding experimental results will show that our model QPSO + mfBm have a much better performance on the prediction effect than fBm.