## 5 Conclusions  
In this paper, a bearing RUL prediction method based on P-ResNet was proposed. During machine operation, the start prediction time was firstly determined by an RMS-based moving average method. Then, the time-frequency domain images of raw data were obtained by synchrosqueezed wavelet transform (SWT). To ensure the comprehensiveness of the bearing degradation information and improve the accuracy of the RUL prediction, the time domain features of bearing vibration signals and the time-frequency images were both used as the inputs of the parallel convolutional network model, which can learn those two types of features with two different series of convolutional operations in parallel. The residual network layers in the regression model enhance the learning ability. Finally, the KF algorithm is used to maintain the stability of the predicted results. In order to verify the performance of the proposed method, the IEEE PHM 2012 Data Challenge dataset was adopted for experimental study. The experimental results prove that the proposed method is effective for bearing RUL prediction. Compared with the other three methods, at least a 3% accuracy improvement proved that the proposed method has certain superiority. The advantages of the proposed methods are summarized as follows. (1) Synchrosqueezed wavelet transform (SWT), which overcomes the low time-frequency resolution of the traditional wavelet transform, was adopted to obtain time-frequency domain features of \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & & \multicolumn{2}{c}{**The Proposed**} & \multicolumn{2}{c}{**Time–Frequency**} & \multicolumn{2}{c}{**Time Domain**} \\  & & **Method** & **Features + CNN** & **Features + CNN** & **SVR** \\ \hline \multirow{2}{*}{Bearing1\_3} & MAE & 0.09 & 0.12 & 0.15 & 0.14 \\  & RMSE & 0.12 & 0.16 & 0.22 & 0.31 \\ \hline \multirow{2}{*}{Bearing1\_4} & MAE & 0.17 & 0.73 & 0.31 & 0.25 \\  & RMSE & 0.23 & 0.26 & 0.28 & 0.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Numerical prognostic performance comparisons of different methods. vibration signals. With both time-frequency domain features and time-domain features as training data, the comprehensiveness of bearing degradation information can be ensured. (2) A parallel deep residual convolutional neural network (P-ResNet) was used for training and RUL prediction. In the structure of P-ResNet, there are two parallel series of convolutional layers to learn time-frequency domain features and time-domain features, respectively, and residual layers to enhance the learning ability, which can obtain a more accurate trained model for RUL prediction. (3) The KF algorithm was adopted for smoothing the predicted results, which can effectively reduce the measurement noises and other uncertainties. In terms of practical application, the proposed method can be applied to the rolling bearing RUL prediction for equipment in the fields of automobile, metallurgy, petrochemical, and so on to reduce the probability of bearing failure, improve the reliability of equipment and finally reduce economic losses for enterprises. There are two directions for our further research on this work. First of all, to verify different components of the RUL prediction performance of the proposed method, more vibration signal datasets collected from different equipment components such as gear and worm must be used for training the proposed model, which adjusted the parameters. Secondly, in order to be applied to the RUL prediction of bearing under different working conditions, the proposed model will be improved with unsupervised domain adaptation. Conceptualization, X.W. and D.Q. ; methodology, X.W. ; software, K.H. and X.C. ; validation, X.W., K.H. and X.C. ; formal analysis, X.W. ; investigation, X.W. and D.Q. ; resources, X.W. ; data curation, X.W. ; writing--original draft preparation, X.W. and K.H. ; writing--review and editing, X.W. and Z.H. ; visualization, X.W. and K.H. ; supervision, X.W. and D.Q. ; project administration, X.W. ; funding acquisition, X.W.