A method for predicting the lifetime of rolling bearings based on composite multi-scale fractional order attention entropy and nonlinear Wiener stochastic process

This paper proposes a prediction method that integrates the Composite Multiscale Fractional Attention Entropy (CMFAE) and the Nonlinear Wiener Stochastic Process (NWSP). Firstly, the CMFAE is utilized to construct the Health Indicator (HI). During the calculation of the attention entropy, the concept of fractional order is introduced to capture the complex nonlinear features in the signal by adjusting the fractional-order parameters. Meanwhile, the composite multiscale analysis method is combined to extract features from multiple scales, forming a multi-dimensional feature matrix. The extracted multi-dimensional features are smoothed to reduce the influence of noise and outliers. Then, the TCN-Transform network is employed to reduce the dimension and fuse the multi-dimensional feature matrix to construct the health indicator. Finally, the Nonlinear Wiener Stochastic Process is used as a mathematical tool to describe random quantities for simulating and analyzing the life of rolling bearings. To verify the effectiveness of this method, the PHM2012 dataset is introduced for case analysis. The results show that the RMSE of the HI fitting is 0.031, the R^2 is 0.976, and the prediction error of the remaining life is controlled within about 3%. This method also quantitatively describes the uncertainty in life prediction using the probability density distribution function, providing a more accurate and reliable solution for the remaining life prediction of rolling bearings.