# An Ensemble Learning and RUL Prediction Method Based on Bearings Degradation Indicator Construction
## 3 Methodology
### LSTM-AdaBoost Ensemble Learning and Prediction Model
To more clearly determine the prediction effects of different methods, taking bearing 1_3 as an example, we selected the prediction results for 12 moments of the bearing, which was the average values obtained by the prediction model running 10 times. We compared the different methods and list the absolute error\(=|Predicted\)\(RUL-Real\)\(RUL|\). Table 4 provides the details of the predicted results. In Tables 3 and 4, the MSE and absolute error of non-feature selection method were the largest because irrelevant and redundant data existed in the original data set, even noise. If no feature selection process or filtering process is applied, some outliers also contribute to the prediction model, which leads to significant deviation of the prediction model and reduces the prediction accuracy. Figure 13: RUL prediction resultsusing three different features selection methods for three bearings. This further proves that feature selection is critical during bearing RUL prediction process. The two tables show that PCA and mRMR do not perform well either because, at the initial stage of bearing degradation, the prediction model learning the degradation characteristics is not complete, resulting in a large error. When the prediction model learns the degradation characteristics, it is affected by the low indicators or weak contribution rate of degradation characteristics to some extent. The prediction error of the method based on FCBF + Markov Blanket is higher than our proposed method. This shows that the more comprehensive the comprehensive features, the more accurate the prediction results. Compared with the results of the two prediction models, the error is significantly reduced for the proposed model, which proves that the LSTM-AdaBoost ensemble prediction method provides improved prediction accuracy. The proposed method can approximate the real RUL curve of bearings because the method is more robust and avoids the single feature selection method, which may lead to feature sensitivity bias and make the contribution rate of some features larger or smaller under certain measurement standards. The AdaBoost algorithm is a robust lifting algorithm that further guarantees the generalization ability of the prediction model. The experimental results showed that the proposed method has good practical value for bearing RUL prediction. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Operating Condition**} & \multirow{2}{*}{**Feature Selection Method**} & \multicolumn{2}{c}{**Prediction Results (MSE)**} \\ \cline{3-4}  & & **LSTM** & **LSTM-AdaBoost** \\ \hline \multirow{4}{*}{Condition A 2100 rpm} & No feature selection & 471.28 & 317.43 \\  & PCA & 359.44 & 244.06 \\ \cline{1-1}  & mRMR & 221.64 & 162.90 \\ \cline{1-1}  & FCBF + Markov Blanket & 82.96 & 67.09 \\ \cline{1-1}  & Proposed method & 19.68 & 10.02 \\ \hline \multirow{4}{*}{Condition B 2250 rpm} & No feature selection & 322.81 & 263.26 \\ \cline{1-1}  & PCA & 206.92 & 141.32 \\ \cline{1-1}  & mRMR & 186.46 & 127.24 \\ \cline{1-1}  & FCBF + Markov Blanket & 46.62 & 41.18 \\ \cline{1-1}  & Proposed method & 13.29 & 7.06 \\ \hline \multirow{4}{*}{Condition A 2400 rpm} & No feature selection & 419.36 & 179.02 \\ \cline{1-1}  & PCA & 143.52 & 97.21 \\ \cline{1-1}  & mRMR & 193.77 & 102.06 \\ \cline{1-1}  & FCBF + Markov Blanket & 64.27 & 28.64 \\ \cline{1-1}  & Proposed method & 21.49 & 15.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of prediction accuracy of LSTM and LSTM-AdaBoost at motor speeds of 2100, 2250, and 2400 rpm using different feature selection methods.