LAUSR

Abstract The accurate estimate of the Remaining Useful Life (RUL) of mechanical tools is a fundamental problem in Engineering. This prediction often implies the knowledge and application of sophisticated mathematical methods based on fractal and Long-Range Dependence (LRD) stochastic processes. However, the existing RUL prediction methods based on stochastic model cannot simultaneously consider the fractal and LRD characteristics of the equipment degradation process. This paper describes a new RUL prediction model based on the Generalized Cauchy (GC) process, which is a stochastic process with independent parameters. That is, the GC process uses the fractal dimension D and Hurst index H to describe the fractal and LRD characteristics of the degradation sequence, respectively. Then, the GC process is taken as the diffusion term, describing the uncertainty of the degradation sequence, to establish the GC degradation model, and the power law and exponential forms are used to describe the nonlinear drift of the degradation sequence. The stochastic volatility of the degradation sequence causes the equipment RUL unable to be predicted for a long time. This article uses the largest Lyapunov index to reveal the maximum prediction range of RUL. The analysis of actual equipment degradation verifies the effectiveness of the degradation model based on power law drift and GC process. The prediction results of the comparative case show that the prediction performance of the GC degradation model is better than Brownian motion, fractional Brownian motion, and long short-term memory neural network.