Gray Chaos Evaluation Model for Prediction of Rolling Bearing Friction Torque

The gray chaos evaluation model composed of the gray relation method, the adding-weight one-rank local-region method, and the gray bootstrap fusion method is proposed to predict the time series of the rolling bearing friction torque under the condition of an unknown probability distribution. First, the optimum embedding dimension and the optimum delay time for the phase space reconstruction are synchronously calculated with the gray relation method. Second, the forecasting values at different embedding dimensions and time delays, respectively, near the optimum embedding dimension and the optimum delay time are obtained via the adding-weight one-rank local-region method, the chaos forecasting method for short. Lastly, the true value and the variation domain are deduced by the gray bootstrap fusion method. It is found that the rolling bearing friction torque possesses chaotic characteristics. The experimental investigation on the friction torque of the rolling bearing for space applications shows that the gray chaos evaluation model can effectively assess the predicted true value, with more reliable predicted results than can be achieved by the chaos forecasting method, and can perfectly estimate the predicted variation domain at the 99.7 % confidence level without any prior information on the probability distribution.