## 4 Experiment and Analysis
### Results and Analysis  
#### 4.3.1 Comparison of Point Prediction Results  
To reflect the advantages of constructing bearing DI set by the method proposed in this paper, different DI construction methods were applied to the bearings under three different working conditions. Each bearing in the test set was run 10 times; we obtained the average prediction accuracy of 3 bearings under the every operating condition. Figure 12\((a)-(c)\) depict the average prediction accuracy and the number of features in the DI set of operating condition A, operating condition B, and operating condition C, respectively. As shown in Figure 12, the proposed method extracts fewer features than the other feature selection methods, and has relatively high accuracy. This is mainly because the proposed method measures redundancy, correlation and monotonicity on the basis of dimension reduction, which ensures the sensitivity robustness of the degradation index set based on dimension reduction features.  
The median of TCNQR prediction result can be regarded as estimating the RUL of bearing as a certain value or at a certain point, in order to further quantify the effectiveness of the prediction results, we take MAE and RMSE as the evaluation indexes of the prediction results, the results were compared with the predicted results of TCNQR. We predicted the bearings under different operating conditions in the test set 10 times, and calculated the MAE and RMSE of the three bearings under each operating condition, compared the RUL prediction results based on the PCA construction method, SDAE construction method, de-redundant construction method and the DI construction method proposed in Table 3.  
According to the comparison results in Table 3, it is found that the proposed method has obvious advantages in the error of RUL deterministic prediction results under these three different working conditions, on the one hand, the feature selection method we proposed in the same prediction model has a lower error, which proves the effectiveness of the DI construction method proposed in this paper. On the other hand, under the same DI construction method, TCNQR prediction model has better prediction performance. The results show that the proposed method achieves the goal of optimizing the prediction model from the perspective of data analysis.  
Taking the bearing_3 of different conditions as case, taking the median of density function as the result of deterministic point prediction, and the influence of DI construction on the prediction results is considered. In order to increase the readability of the comparison graph, three sets of degradation indicators with fewer features were selected to compare the predicted results with the real RUL. The prediction results of TCNQR prediction model are shown in the Figure 13. Figure 13a-c are the deterministic prediction results of three different bearing _3 under working condition A, condition B, and condition C, respectively. It can be seen that the prediction results of the method proposed in this paper is closest to the real RUL value, this is more clearly shows the effectiveness of the DI method proposed in this paper.  
Figure 12: Cont.  
Figure 12: Average prediction accuracy and number of features selected under three operating conditions. (**a**) average prediction accuracy and the number of features selected under condition A, (**b**) average prediction accuracy and the number of features selected under condition B, (**c**) average prediction accuracy and the number of features selected under condition C.  
Figure 13: _Cont._  
Figure 13: Deterministic point prediction results based on different DI method. **(a)** deterministic point prediction results of bearing 3 under working condition A, **(b)** deterministic point prediction results of bearing 3 under working condition B, **(c)** deterministic point prediction results of bearing 3 under working condition C.