## 4 Experiment and Analysis
### Data Description
#### 4.2.2 Construction of Bearing Optimal Degradation Indicator Set  
In this paper, the SDAE feature compression method is used to compress and extract low dimensional features from 24 time-domain features and 26 frequency-domain features in horizontal and vertical directions. In this experiment, different output features are used to test. Before the original time-domain and frequency-domain features are input into the SDAE network, the input data are normalized to ensure the effectiveness of the compression [22]. It can be seen from Figure 7 that the decoding error decreases with the increase of the number of features. However, when the number of features is 35, the average decoding error of bearings from three working conditions tends to be flat. To retain decoding information as much as possible, the first 35 features are selected, that is, the network inputs 50-dimensional time domain and frequency domain vectors, and outputs 35-dimensional compressed time domain and frequency domain features. It is called the SDAE compression feature set \(F_{SDAE}\).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Feature** & **Feature** & **Time-Domain** & **Feature** & **Feature** & **Frequency-Domain** \\ (Horizontal) & **(Vertical)** & **Feature Parameters** & **(Horizontal)** & **(Vertical)** & **Feature Parameters** \\ \hline F0 & F25 & \(f_{0}=\frac{\sum_{i=1}^{N}x(n)}{N}\) & F12 & F37 & \(f_{12}=\frac{\sum\limits_{i=1}^{N}x}{K}\) \\ \(F1\) & F26 & \(f_{1}=\) & F  
Through SDAE compression, 35 features are first extracted and a feature set \(F_{SDAE}\) is constructed. Then the redundancy of 35 features under three working conditions are measured by using the MIC method. Taking the bearings of working condition A as an example, the MIC between features and features \(MIC_{FF}\) will be calculated to construct de-redundant feature subset \({}_{DE}MIC_{FF}\). Finally, we got 22 features as shown in the Figure 8. Figure 8 shows the average redundancy value of 22 features in the de-redundant feature subset \({}_{DE}MIC_{FF}\).  
Figure 8: The average \(MIC_{FF}\) values of the features in the subset \({}_{DE}MIC_{FF}\).  
Figure 7: Visualization of training process-SDAE.  
At last, the correlation and monotonicity of elements in feature subset \({}_{DE}MIC_{FF}\) are calculated, the correlation between features and degradation trend \(MIC_{FR}\), and the monotonicity \(Mon_{F-DT}\) between features and degradation trend obtained by monotonicity measurement method \(Mon_{F-DT}\). In order to get the optimal feature set \(Opt_{DI}\), the index \(Std_{DI}\) is used to select features, and 0.5 is taken as the threshold, as shown in Figure 9. Features higher than 0.5 will become members of the optimal feature set \(Opt_{DI}\), and features lower than 0.5 will not be retained. Therefore, there are 14 features in the final optimal feature set \(Opt_{DI}\). The \(MIC_{FR}\) value, \(Mon_{F-DT}\) value, and \(Std_{DI}\) value of the features in the final optimal feature set \(Opt_{DI}\) are shown in Figure 10.  
In the same process, the bearings degradation indicator set in working condition B and working condition C are constructed with the same method and the specific parameters of the features in the constructed optimal degradation indicator set are shown in Figure 11, in  
Figure 10: Features in the final optimal feature set \(Opt_{DI}\) under working condition A.  
Figure 9: The \(Std_{DI}\) calculation results of subset \({}_{DE}MIC_{FF}\).  
which Figure 11 represents the composition of the degradation indicator set under working condition B, and Figure 11 represents the composition of the degradation indicator set under working condition C.