Research On Rotating Machinery Fault Condition Prediction Using Long-range Dependent Stochastic Model

This paper regards rolling bearing as the main research object and focuses on the condition trend prediction of equipment fault slow process which is applied rotating machinery vibration intensity as the characteristic parameter, the long-range dependent stochastic model—fractional Brown motion(FBM) and FARIMA model are proposed to evaluate and predict the health status of equipment. The vibration intensity parameters has the short range dependence property when rotating equipment is in normal operation condition, once the weak fault occurs, the weak fault characteristics will be gradually increased until a serious fault occurred in the running process, the slowly varying process has the long-range dependence characteristics, this paper presents the minimum entropy deconvolution theory to identify the weak fault characteristics of equipments. The main contents of this paper are the following four aspects:(1) Based on the introduction of long-range dependence(LRD) and self similarity’s theory and characteristic, several methods to estimate the degree of self similarity is proposed to describe the Hurst index, including implementation steps and performance evaluation of the algorithm. Because the long-range dependence model can more accurately describe the device weak fault vibration characteristic, by generating long range dependence time series simulation study is very important. Firstly, let Gaussian white noise through a linear filter, and the filter system autocorrelation function is in line with longrange dependence distribution and generates system function with the long range dependence structure. Thus, the output of the linear system is the stochastic sequence with LRD characteristics.(2) The long range dependence prediction model—FBM and FARIMA model are put forward. Firstly, the mathematical theory of Brownian motion to fractional Brownian motion is derived, and the stochastic differential equation driven by fractional Brownian motion is used as the random sequence prediction model. According to the characteristic of random sequence, the stochastic differential equation model parameters driven by FBM are estimated. On the basis of this, the convergence property is proved for the parameters of model using the maximum likelihood estimation; For FARIMA(p,d,q) model, the mathematical description of the FARIMA and how to generate and simulate the FARIMA(p, d, q) process are introduced. On this basis, verifing the FARIMA model can be used to fitting and forecasting with long range dependent time series.(3) Aimed at the advantages and disadvantages of these parameters of bearing kurtosis, sample entropy and the vibration intensity in the diagnosis of bearing early faults, fault type and location, the minimum entropy deconvolution theory to extract fault characteristic value of bearing is presented to determine fault point time. Firstly, the wavelet transform is introduced. By the comparison of combining the envelope spectrum extraction effect, the minimum entropy deconvolution combined with envelope spectrum is showed to accurate detection of weak fault. Finally, the vibration signal of the bearing is collected from the normal state to the fault, and the minimum entropy deconvolution diagnosis results are perfectly verified by calculating the vibration intensity and sample entropy.(4) The vibration intensity value of the rolling bearing is used as the prediction sample, and the intensity value analysis of collected data is to identify the weak fault point of the equipment. Data analysis found that the intensity value sequence of the slow process after the weak fault has LRD characteristics, so the LRD model—FARIMA model and fractional Brown motion model are proposed to predict the future intensity sequence. The experimental results verify the accuracy of the long-range dependent stochastic model prediction.