Generalized Cauchy Degradation Model With Long-Range Dependence and Maximum Lyapunov Exponent for Remaining Useful Life

TLDR: In this paper, a new long-range-dependent degradation model is described based on the generalized Cauchy (GC) process, which describes local irregularities and global correlation characteristics of the data time sequence by the Hurst parameter $H$ and fractal dimension $D$.

Abstract: A new long-range-dependent (LRD) degradation model is described based on the generalized Cauchy (GC) process. The GC process is a two-parameter model, which describes local irregularities and global correlation characteristics of the data time sequence by the Hurst parameter $H$ and fractal dimension $D$ . Compared with the fractional Brownian motion (fBm) with linear relationship $H=2-D$ , two parameters of the GC process are independent of each other. The GC process is taken as the diffusion term to describe the LRD characteristics and uncertainty of the degradation process, and the degradation model is established in the form of power law and exponential drift. The Gaussian assumption of the GC process allows us to use linear system theory and statistics to derive its incremental distribution for obtaining the difference iteration form of the GC degradation model. Besides, the dimensionless factors, the principal component analysis (PCA), and the iterative method are used to eliminate the interference of noise on the degradation data. Then, the maximum prediction range of the GC degradation model in the degradation sequence is obtained by the reciprocal of the maximum Lyapunov exponent. Finally, the GC degradation model was applied for prediction of the remaining useful life (RUL) of rolling bearing. The validity of the GC degradation model is verified.