# An Ensemble Learning and RUL Prediction Method Based on Bearings Degradation Indicator Construction
## 3 Methodology
### LSTM-AdaBoost Ensemble Learning and Prediction Model
After the training process, the trained model is used to predict the bearing RUL. ### Results and Analysis

To reflect the advantages of constructing the bearing degradation indicator set by using the three-stage feature selection method proposed in this paper, different bearings selection methods were applied to the bearings under three different working conditions to construct the bearing degradation indicator set. Each bearing in the test set was run 10 times; we obtained the average prediction accuracy of three bearings under the same operating conditions. Figure 12a-c depict the average prediction accuracy and feature selection of operating condition A, operating condition B, and operating condition C, respectively. There were three bearings in each condition. As shown in Figure 12, the proposed method extracts fewer features than the other two feature selection methods, and has relatively high accuracy. This is mainly because the proposed method conducts cross-operation on different subsets of degradation indicators, ensuring the robustness of the set of degradation indicators based on reducing feature dimensions. Figure 11: Features selected by the proposed method. The feature selection method proposed in this paper is based on the correlation and redundancy measurement, aiming to reduce the complexity of the model and ensure the sensitivity and high contribution rate of the features. mRMR is a method based on the correlation and redundancy measurement. Principal component analysis (PCA) is a dimensionality reduction method that also has a significant effect on reducing the data dimension, and FCBF\(+\)Markov Blanket has also been applied [36]. Therefore, these methods were compared with the proposed method in this study. Based on the bearings degradation indicator set constructed above, we used the LSTM neural network and LSTM-AdaBoost ensemble algorithm to predict the RUL of bearing 1_3, bearing 2_3, and bearing 3_3 under three operating conditions. Figure 13a,b reveal the results of predicting the RUL of bearing 1_3 using different feature selection methods and prediction models. The figure shows that in the early stage of prediction, the prediction result of all the three methods deviate considerably. The prediction results of the non-feature selection method deviates more from the real RUL value, indicating that feature selection is necessary for RUL prediction. The proposed method is the first to fit near the real curve. By comparing the prediction effects of different prediction models, we conclude that AdaBoost algorithm plays a role in improving the prediction accuracy. The prediction results of the other two bearings are shown in Figure 13c-f. The prediction results of the RUL of these two bearings are similar to those of bearing 1_3, further demonstrating that the method proposed in this paper is more robust and produces a better prediction effect under different operating conditions and degradation stages. The effectiveness of this method has been proven. 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.

The accuracy of model prediction is measured using the mean square error (MSE). Table 3 shows the comparison results of the MSE between no feature selection, PCA, mRMR method, FCBF + Markov Blanket method, and the proposed method. We predicted the bearings under different operating conditions in the test set 10 times, and calculated the mean value of the MSE of the three bearings under each operating condition to represent the predicted results under different operating conditions.