# An Ensemble Learning and RUL Prediction Method Based on Bearings Degradation Indicator Construction
## 3 Methodology  
### Proposed Degradation Indicator Set  
The structure of the proposed bearing RUL prediction model is shown in Figure 3. The original data used for bearing RUL prediction include the bearing vibration signal. First, different features are extracted from the vibration signal data, including time-domain features and frequency-domain features. Secondly, a three-stage feature selection method is used to extract and reduce the sensitive features of the feature data to construct the indicator set for bearing degradation. Then, the most sensitive features selected in the degradation indicator set are input into LSTM-AdaBoost for RUL prediction. This section describes the procedure for construction of the proposed bearing degradation indicator set. As shown in Figure 3, the procedure is mainly composed of three stages: feature extraction, selection of sensitive features, and construction of the degradation indicator set. The characteristics of several subsets in a given data set can produce predictive models with similar performance, but the predictive power may be different. According to the algorithm's search strategy or sample bias, some features can be selected [40]. In general, features extracted by different feature extraction methods with similar performance are highly correlated. We assumed that the relevant features are separately calculated and extracted to ensure their independence in the search process. FCBF is a selection algorithm that uses correlation fast filter features. The feature ranking method is adopted to delete irrelevant or weakly correlated features. This method has low time complexity,  
Figure 3: A flowchart of the proposed bearing degradation indicator set. but it cannot remove redundant features. Some experts and scholars addressed this problem by using an approximate Markov blanket de-redundancy method based on the FCBF feature selection result using the MIC as the measurement standard [25]. In this study, the FCBF-AMB feature selection method [40] was used to construct the initial bearings degradation indicator subset. To ensure the independence of the initial bearing degradation indicator subsets, we used FCBF-AMB and the MIC algorithm to extract features and form different initial bearings degradation indicator subsets, respectively. First, the subset of relevant features is obtained and arranged in descending order to identify and delete the weak correlations with irrelevant features, and to add strong correlation features to the initial feature set \(F^{\prime}\) according to their SU with respect to the real RUL. The predominant feature \(f_{i}\) is selected from the feature set \(F\) and placed into subset \(F^{\prime}\). Next, let feature \(f_{i}\) become the first feature in this subset \(F^{\prime}\). By definition, feature \(f_{i}\) is a predominant feature for each of the remaining relevant features \(f_{j}\). Check whether \(f_{i}\) is an AMB for \(f_{j}\). If so, \(f_{j}\) is removed from the subset \(F^{\prime}\). Then, repeat the process until no predominant features remain in the feature set \(F^{\prime}\). Construct the initial bearings degradation indicator subset \(F^{*}\). The details are outlined in Algorithm 1. ```
0: Original feature set \(F=\{f_{1},f_{2},\cdots,f_{m},R\}\), real RUL values \(R\), \(SU\) threshold value \(\lambda\). 0: Initial bearing degradation indicator subset \(F^{*}\). 1:for\(f_{i}\in F\)do
2: Calculate the symmetric uncertainty \(SU(f_{i},R)\) between the features and real RUL values \(R\),
3:if\(SU(f_{i},R)>\lambda\)then,
4: Add feature \(f_{i}\) to feature subset \(F^{\prime}\) and rank it in descending order,
5:endif
6:endfor
7:for\(f_{i}\in F^{\prime}\)do
8:for\(f_{j}\in F^{\prime}\backslash\{f_{i}\}\)do
9:if\(f_{i}\) is an AMB for \(f_{j}\), then
10: Add \(f_{i}\) to \(F^{*}\), break;
11:endif
12:endfor
13: Remove predominant feature \(f_{i}\) from \(F^{\prime}\). 14:endfor
```  
**Algorithm 1** FCBF-AMB feature selection method.