# An Attention-Based Method for Remaining Useful Life Prediction of Rotating Machinery
## 3 Model Verification and Comparison
### Experiment for Performance Evolution State Data Region Division
#### 3.2.2 Experimental Result  
In the clustered performance state classification process, the data are cut into multiple segments by a fixed-size window function; then, Fourier transform is performed separately so that each input sample has a dimension of 64. There are four types of data in the XJTU-SY dataset under working condition 2: healthy state, outer ring damage, inner ring damage, and cage cracks. As the degradation-begun stage and the degradation-intensified stage occur when the bearing evolves from the healthy state to a fault state, the number of clustering categories is set to 3, and the maximum number of iterations is set to 300 for the experiment. Figure 8 shows the clustering result of useful life data of five bearings under working condition 2. As the figure shows, the clustering method proposed herein achieves the classification of similar samples in the datasets from B2_1 to B2_5.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{No. of working conditions} & 1 & 2 & 3 \\ \multicolumn{1}{c}{Rotational speed (r/min)} & 2100 & 2250 & 2400 \\ \multicolumn{1}{c}{Radial force/KN} & 12 & 11 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Working conditions for accelerated life tests of bearings.  
Figure 6: Images of typical bearing failure types.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Working Condition** & **Dataset** & **Sum of Samples** & **L10** & **Actual Useful Life** & **Position of Faults** \\ \hline \multirow{5}{*}{2} & B2\_1 & 491 & & 8 h11 min & Inner ring \\  & B2\_2 & 161 & & 2 h41 min & Outer ring \\ \cline{1-1}  & B2\_3 & 533 & 6.789–11.726 h & 8 h53 min & Bearing cage \\ \cline{1-1}  & B2\_4 & 42 & & 42 min & Outer ring \\ \cline{1-1}  & B2\_5 & 339 & & 5 h39 min & Outer ring \\ \hline \hline \end{tabular}
\end{table}
Table 3: XJTU-SY datasets of bearings under working condition 2.  
To identify the correspondence relation between the cluster and the bearing performance states (healthy state, degradation-begun state, and degradation-intensified state), we find from Figure 7 that the healthy state lasts the longest in the whole life cycle of the bearing; therefore, the sample data at this stage take up the largest proportion among all samples, so the largest cluster amid the three clusters in Figure 8 is labeled as the \"healthy state\". Moreover, changes in the bearing performance state are progressive, and the damage worsens step by step. Therefore, when calculating the distance between the \"healthy state\" cluster and the other two clusters, the cluster closest to the \"healthy state\" cluster is labeled as the \"degradation-begun state\", whereas the cluster that is farthest is labeled as the \"degradation-intensified state\". All categories of data in Figure 8 post data region classification correspond accurately to the performance state stages of the bearings so that the attention-GRU model can assign different weights to the input data and the accuracy of attention to the data region in feature extraction can be increased.  
Figure 7: Time-domain data curves of bearing performance under working condition 2.