Dynamic Prediction Model for Rolling Bearing Friction Torque Using Grey Bootstrap Fusion Method and Chaos Theory

Synthesizing the grey bootstrap fusion method and the five chaos forecasting methods (viz., the adding-weight zero-rank local-region method, the one-rank local-region method, the adding-weight one-rank local-region method, the improved adding-weight one-rank local-region method, and the maximum Lyapunov exponent method), a dynamic prediction model is proposed to calculate the predicted true value and the predicted interval of a chaotic time series under the condition of unknown probability distributions and trends. At the same time, the five forecasting values are acquired with the help of the five chaos forecasting methods, respectively, and the five forecasting values are fused to deduce the predicted true value and the predicted interval by means of the grey bootstrap fusion method. As time goes on, a series of the predicted true value and the predicted interval is obtained dynamically. Experimental investigation of the rolling bearing friction torque shows that using the grey bootstrap fusion method, the predicted true value and the measured values have an identical trend only with a small error, the predicted interval is acquired along with a high reliability, and the dynamic prediction of the rolling bearing friction torque as a chaotic time series is made without any prior knowledge of probability distributions and trends.