Reliability Analysis Of Roller Bearings Based On Generalized Cauchy Process

This paper takes roller bearings as the research object.As the degradation process of bearings from normal to failure is a slowly-varying trend,a long-range dependence(LRD)model,fractional Brownian motion model(FBM)is proposed to predict the remaining useful life of bearings.The main research contents are as follows:(1)Analyze the characteristics of LRD,heavy-tailed distribution,and self-similarity.LRD and heavy-tailed distribution are different manifestations of the long-range dependence process in the time domain and the probability,distribution domain,respectively.Both selfsimilarity and LRD are expressed by Hurst index,but the relationship between the two is not equivalent.The estimation methods of two key parameters of FBM fractal dimensions and Hurst index are given.(2)Fractional Brownian motion(FBM)and fractional Gaussian noise(f Gn)of the LRD model with 1/f process properties are analyzed.It is pointed out that the fractal dimension and the Hurst index in the two models have a linear relationship.The description of the LRD process can only be described by a parameter of the Hurst index,which limits the scope of expression.(3)A GC process is proposed to describe the LRD process.First,the definition and properties of the GC process are given.The fractal dimension and the Hurst index of the GC process are independent,and the influence of two parameters on the autocorrelation function is analyzed.According to the fractal linear system theory,the impulse function is generated from the autocorrelation function of the GC process,and the time series of the GC process is obtained by convolution with white noise.(4)The stochastic differential equation of the GC process is deduced,and a degradation model based on the GC process is established.The maximum likelihood method is used to estimate the parameters in the model.For the problem that the model has randomness in prediction and the closed-form expression of the probability density function is difficult to obtain for the nonlinear model,Monte Carlo method is used to obtain an approximate probability density function through a large number of numerical simulations,and the function is used to predict the remaining useful life.(5)Aiming at the problem that the inner race fault characteristics are not obvious,the inner race fault characteristics are extracted through the variational mode decomposition(VMD).The monotonicity,robustness and trendability are used to evaluate the characteristic features of the inner race fault,and the feature component with the highest comprehensive score is selected as the feature sequence that reflects the bearing inner race degradation trend for prediction.(6)The inner race fault data of the NSF I/UCR Intelligent Maintenance System Center(IMS)was used for prediction,and the accuracy of the GC process model was verified by the a-l accuracy method.The validation of the bearing outer race fault experimental data of Xi'an Jiaotong University shows the validity of the GC process model in outer race fault prediction.