Multivariate Accelerated Degradation Modeling and Reliability Assessment for Ball Screw Grease Based on Fractional Brownian Motion Process Model

Considering that the degradation of ball screw grease involves fractal characteristics, which exhibit long-term dependency and autocorrelation, a multivariate accelerated degradation modeling and reliability assessment method based on the fractional Brownian motion process model is proposed in this paper. Firstly, a nonlinear accelerated degradation model of grease is established using fractional Brownian motion, considering the heterogeneity of samples as well as the memory effect and long-term dependence in the deterioration process, and realizing parameter estimation. Secondly, a multivariate reliability evaluation model is established by considering multivariate performance indicators in combination with the Frank copula function. Finally, the effectiveness and potential engineering application value of this method are verified through actual degradation data of the grease.