GNAR-GARCH model and its application in feature extraction for rolling bearing fault diagnosis

Abstract

Given its simplicity of modeling and sensitivity to condition variations, time series model is widely used in feature extraction to realize fault classification and diagnosis. However, nonlinear and nonstationary characteristics common in fault signals of rolling bearing bring challenges to the diagnosis. In this paper, a hybrid model, the combination of a general expression for linear and nonlinear autoregressive (GNAR) model and a generalized autoregressive conditional heteroscedasticity (GARCH) model, (i.e., GNAR-GARCH), is proposed and applied to rolling bearing fault diagnosis. An exact expression of GNAR-GARCH model is given. Maximum likelihood method is used for parameter estimation and modified Akaike Information Criterion is adopted for structure identification of GNAR-GARCH model. The main advantage of this novel model over other models is that the combination makes the model suitable for nonlinear and nonstationary signals. It is verified with statistical tests that contain comparisons among the different time series models. Finally, GNAR-GARCH model is applied to fault diagnosis by modeling mechanical vibration signals including simulation and real data. With the parameters estimated and taken as feature vectors, k-nearest neighbor algorithm is utilized to realize the classification of fault status. The results show that GNAR-GARCH model exhibits higher accuracy and better performance than do other models.