# A Novel Hybrid Model for the Prediction and Classification of Rolling Bearing Condition
Therefore, an effective time series forecasting model is the key to monitoring the condition of industrial equipment, which can uncover potential statistical patterns through exploring the functional relationships. Furthermore, such patterns can give a valuable early warning. However, it is a challenge to acquire reliable information in practical operations. For time-series analysis and modeling, ARMA is one of the most popular approaches, which has made considerable achievements in various fields in terms of forecasting, such as finance [24; 25], engineering [26], and many others [27; 28]. In addition, ARMA is more accurate than some other popular machine learning methods in prediction, such as multi-layer perceptron, SVM, and long short-term memory [29; 30]. Although ARMA has made great progress in coping with linear analyses based on the assumption that a linear functional relationship exists for current and past values and white noise, its limitations in nonlinear analysis hinder its application. Considerable research on ARMA has demonstrated that its performance is poor in modeling nonlinear real-world problems [31]. For nonlinear time series modeling, ANN is one of the most widely used algorithms [32; 33], while the ANN model alone can not give full consideration to both linear and nonlinear patterns simultaneously [31; 34]. In summary, any single model can not perform well in every situation. Consequently, considering the merits and drawbacks of ARMA in linear flexibility and ANN for nonlinear time series modeling, their synthetic prediction model, namely, ARMA-ANN, is constructed as a prediction model for subseries in this paper. The motivation for applying the hybrid model is demonstrated as follows [34]. First, instability and uncertainty are common in engineering applications. Second, the time series demonstrates complex characteristics in the real world. Third, each type of individual model rarely perform well compared to the hybrid technique, which combines the advantages of each type of model into an integration. Therefore, using the hybrid technique improves forecasting performance. Various measurement indicators were considered in vibration signal analysis and fault feature extraction [35; 36]. To comprehensively describe the condition information of the original signal, feature extraction plays an important role. Thus, the relevant studies have been widely studied [37; 38]. The multi-domain features extracted from the sensitive modes contain the main information of the original signal. The motivation for selecting sensitive IMFs is to avoid the interference of redundant information [39]. SVM is a promising method that can solve the classification problem of small samples [40; 41]. Therefore, SVM has been extensively used in mechanical fault classification based on its merits [39; 42]. This work proposes an effective hybrid condition monitoring strategy that achieves state-of-the-art performance, which makes predictive maintenance come true [43]. First, we apply VMD to decompose the original signals into several subseries and predict the IMFs by ARMA-ANN. Then, the time-frequency domain (T-F) features are extracted from the sensitive IMFs. Finally, a SVM classifier is used to identify the condition patterns of the rolling bearing based on the T-F features. The performance of our method is verified through experimental signals from the CWRU Laboratory. Our work mainly provides the following contributions:  
First, the key information can be sufficiently captured through VMD decomposing the original signal into subseries to improve the accuracy of feature extraction and classification. Then, the subseries are fed into the hybrid prediction model to provide a reliable trend of the original signal. Next, the excellent accuracy for pattern identification of rolling bearing is acquired based on the comprehensive T-F features. Finally, a sufficient comparable experimental analysis verifies that our method achieved excellent performance while simultaneously relieving time resource problems.