# A Novel Hybrid Model for the Prediction and Classification of Rolling Bearing Condition
## 5 Conclusions  
In this paper, an effective condition monitoring scheme is designed for rolling bearings. First, the original signal can be sufficiently described by IMFs obtained by VMD. Next, each IMF is forecasted through the hybrid prediction model ARMA-ANN. Moreover, the sensitive IMFs, which contain over 90% of the energy of the original signal, are selected to provide downstream feature extraction and classification processing. Then, the T-F features, which can represent the comprehensive condition characteristics of the rolling bearing, are extracted and normalized. Finally, the normalized T-F features are fed into the SVM classifier to identify the operating patterns of the rolling bearing. The performance of the proposed condition monitoring method is verified by the motor-bearing data set of the CWRU laboratory.  
Note that the scheme of the original signal first decomposed by VMD into a subseries provides the sufficiency and convenience of analyzing the operating condition. Secondly, the hybrid prediction model enhances the accuracy of prediction. Thirdly, the condition patterns are identified accurately using a SVM classifier based on the T-F features. Additionally, the proposed method balances the performance and time resources equally well. Thus, it can be concluded that our proposed method under the hybrid framework has some potential value for monitoring machinery condition.  
Conceptualization, A.W.; methodology, A.W.; software, A.W. and B.X.; validation, A.W. and B.X.; formal analysis, A.W.; investigation, A.W.; data curation, A.W. and B.X.; writing--original draft preparation, A.W. and B.X.; writing--review and editing, Y.L., Z.Y., C.Z. and Z.G.; funding acquisition, Y.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the LiaoNing Revitalization Talents Program XLYC1903015.  
Not applicable.  
Data Availability StatementData available in a publicly accessible repository that does not issue DOIs Publicly available datasets were analyzed in this study. This data can be found here: ([[https://engineering.case.edu/bearingdatacenter](https://engineering.case.edu/bearingdatacenter)]([https://engineering.case.edu/bearingdatacenter](https://engineering.case.edu/bearingdatacenter)), accessed on 5 April 2022).  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} VMD & Variational mode decomposition \\ IMFs & Intrinsic mode functions \\ ARMA & Autoregressive moving average \\ ANN & Artificial neural network \\ \end{tabular}  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Operating Condition** & **Method** & **RMSE** & **MAPE** & **MAE** \\ \hline \multirow{2}{*}{Inner Race} & LSTM & \(5.5412\times 10^{-2}\) & \(7.0271\times 10^{-1}\) & \(4.1816\times 10^{-2}\) \\  & ARMA-ANN & \(5.2744\times 10^{-3}\) & \(3.0023\times 10^{-1}\) & \(4.1815\times 10^{-3}\) \\ \hline \multirow{2}{*}{Normal} & LSTM & \(1.2815\times 10^{-2}\) & \(4.5444\times 10^{-1}\) & \(9.6361\times 10^{-3}\) \\  & ARMA-ANN & \(5.3683\times 10^{-3}\) & \(3.1319\times 10^{-1}\) & \(4.2680\times 10^{-3}\) \\ \hline \multirow{2}{*}{Ball} & LSTM & \(2.8762\times 10^{-2}\) & \(4.0346\times 10^{-1}\) & \(2.1655\times 10^{-2}\) \\  & ARMA-ANN & \(5.2354\times 10^{-3}\) & \(3.0846\times 10^{-1}\) & \(4.1308\times 10^{-3}\) \\ \hline \multirow{2}{*}{Outer Race} & LSTM & \(1.0495\times 10^{-1}\) & \(1.3158\times 10^{0}\) & \(7.7409\times 10^{-2}\) \\  & ARMA-ANN & \(5.1080\times 10^{-3}\) & \(3.0283\times 10^{-1}\) & \(4.0719\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparison of performance criteria of prediction results for ARMA-ANN and LSTM.