The variation trend, failure trajectory, probability distribution, and other information vary with time and working conditions for rolling bearing vibration performance, which makes the evaluation and prediction of the evolution process difficult for the performance reliability. In view of this, the chaos theory, grey bootstrap method, and maximum entropy method were effectively fused to propose a mathematical model for the dynamic uncertainty evaluation of rolling bearing vibration performance. After reconstructing the phase space of the vibration performance time series, four local prediction methods were applied to predict the vibration values of bearings to verify the effectiveness and validity of chaos theory. The estimated true value and estimated interval were calculated using the grey bootstrap method (GBM) and maximum entropy method. Finally, the validity of the proposed model was verified by comparing the probability that the original data fall into the estimated interval with the given confidence level. The experimental results show that the proposed method can effectively predict the variation trend and failure trajectory of the vibration performance time series so as to realize the dynamic monitoring of the evolution process for rolling bearing vibration performance online.

The failure data of bearing products is random and discrete and shows evident uncertainty. Is it accurate and reliable to use Weibull distribution to represent the failure model of product? The Weibull distribution, log-normal distribution, and an improved maximum entropy probability distribution were compared and analyzed to find an optimum and precise reliability analysis model. By utilizing computer simulation technology and k-s hypothesis testing, the feasibility of three models was verified, and the reliability of different models obtained via practical bearing failure data was compared and analyzed. The research indicates that the reliability model of two-parameter Weibull distribution does not apply to all situations, and sometimes, two-parameter log-normal distribution model is more precise and feasible; compared to three-parameter log-normal distribution model, the three-parameter Weibull distribution manifests better accuracy but still does not apply to all cases, while the novel proposed model of improved maximum entropy probability distribution fits not only all kinds of known distributions but also poor information issues with unknown probability distribution, prior information, or trends, so it is an ideal reliability analysis model with least error at present.

A dynamic prediction method for accuracy maintaining reliability (AMR) of superprecision rolling bearings (SPRBs) in service is proposed by effectively fusing chaos theory and grey system theory and applying stochastic processes. In this paper, the time series of a vibration signal is used to characterize the state information for SPRB, and four runtime data points can be predicted in the future, which depends on four chaotic forecasting models to preprocess the time series. Using the grey bootstrap method and sampling from the four runtime data, a large amount of generated data (GD) are gained to analyze the changes in information on bearing service accuracy. Then, using a predefined accuracy threshold to match the Poisson count for the GD, the estimated value of variation intensity is obtained. Subsequently, with the help of the Poisson process, the dynamic evolution process is forecast in real time for AMR of the SPRB for each step in the future. Finally, according to a novel concept for maintaining relative reliability in an SPRB, the failure degree of a bearing maintaining an optimum accuracy status (BMOAS) is effectively described. Experimental investigation shows that multiple chaotic forecasting methods are accurate and feasible with all relative errors below 15%; the reliability of each step in the future can truly be described, and the prediction results for AMR over the same subseries show good consistency; dynamic monitoring of the health status of SPRB can be realized by the degree to which a BMOAS fails.