# An Ensemble Learning and RUL Prediction Method Based on Bearings Degradation Indicator Construction
## 1 Introduction
A feature that does not contain information about the bearing DI is considered insignificant and therefore unnecessary for the prediction task. Removing such features can improve the prediction model and speed up the learning algorithm. Conversely, the relevant features are those that can reflect bearing DI. To minimize the prediction error, it may not be necessary to select all relevant features, but instead only select the feature subset with the highest contribution rate and the strongest prediction ability. Feature subsets with these properties may not be unique due to redundancy effects. Redundancy is usually measured by feature correlation; if the values of two features are relevant, then they are redundant. With the feature selection method, the representative feature subset is selected, the features with a high contribution rate and sensitivity that are favorable for prediction are retained, and the complete set is replaced to construct and train the learning model. Experts and scholars have studied this field, especially based on artificial intelligence and statistical methods, using feature compression methods or similar monotonic methods [6; 10]. The optimal feature selection method should not only reduce data dimensions, but also eliminate redundant and irrelevant features. Therefore, considering correlations in feature selection plays a crucial role in reducing data dimensions [29]. However, in the construction of feature subsets, only relying on a single correlation or sensitivity measurement method will bias the calculation results to some extent, which will reduce the robustness of the feature subsets. Therefore, we aimed to use the three-stage feature selection method to extract sensitive features and construct a bearing degradation indicator set. Based on two different feature extraction methods, the initial subsets of bearing degradation indicators were constructed, and the cross-operation of these subsets was applied to obtain the robust set that can fully reflect bearing degradation information. In the deep learning model establishment and prediction stage, scholars introduced a bearing RUL prediction method based on a recurrent neural network (RNN). However, for practical problems,gradient disappearance occurs. [PERSON] et al. [30] proposed a long short-term memory (LSTM) model in 1997 to overcome the RNN problem of gradient disappearance. Some experts have proposed using the LSTM neural network to predict bearing RUL based on the bearing degradation bottleneck feature, waveform entropy (WFE) indicator, time factor, or based on the deep feature representation method [26, 31, 32, 33]. Compared with the previous artificial intelligence algorithms, the predictive ability of the LSTM significantly improved. The above research used a single artificial intelligence algorithm to predict bearing RUL; however, the single artificial intelligence algorithm has weaker generalization and low robustness. The bearing RUL cannot be predicted well outside the sample. To address this problem, we wanted to enhance the LSTM neural network prediction model using the AdaBoost algorithm. To overcome the aforementioned shortcomings, we propose an ensemble robust prediction method to predict bearing RUL based on the construction of a bearing degradation indicator set. The main contributions of this paper are summarized as follows:  
1. To reveal the state of bearing degradation more fully, we integrated the selected high contribution rate and sensitive features to form a more representative and robust feature set, defined as the bearing degradation indicator set. 2. To ensure the robustness of the constructed set of bearing degradation indicators, a new framework for three-stage feature selection is proposed for bearing RUL prediction, which more comprehensively considers the correlation between features and bearing degradation state. 3. The AdaBoost algorithm is proposed to enhance the prediction ability, the prediction accuracy, and the generalization ability of the LSTM prediction model.