# An Ensemble Learning and RUL Prediction Method Based on Bearings Degradation Indicator Construction
## 3 Methodology
### LSTM-AdaBoost Ensemble Learning and Prediction Model
XJTU-SY bearing datasets were provided by the Institute of Design Science and Basic Component at Xi'an Jiaotong University (XJTU), Shaanxi, China, and the Changxing Sumyoung Technology Co., Ltd. (SY), Zhejiang, China. The data sets contained complete run-to-failure data of 15 rolling element bearings that were acquired by conducting many accelerated degradation experiments. This testbed was designed to conduct the accelerated degradation tests of rolling element bearings under different operating conditions (different radial forces and rotating speeds). The tested bearings were type LDK UER204. This platform can conduct accelerated degradation tests of bearings to provide real experimental data that characterize the degradation of bearings during their whole operating life. To acquire the run-to-failure data of the tested bearings, two type PCB 352C33 accelerometers were horizontally and vertically mounted on the bearing to monitor its vibration. The sampling frequency was set to 25.6 kHz. As shown in Figure 5, a total of 32,768 data points (i.e., 1.28 s) were recorded for each sampling, and the sampling period was 1 min. Detailed information about the platform and experiments can be found in [41]. As tabulated in Table 1, 15 rolling element bearings were tested under three different operating conditions. Among them, the first two bearings in every operating condition were regarded as a training set and the others were used as a testing set. Figure 6 shows the vibration signal of test bearing 1-1 during its whole life cycle. The amplitude of vibration signal increases with time, which indicates that vibration signal plays an important role in bearing performance degradation assessment. Figure 4: Bearing testbed. Figure 5: Sampling setting for vibration signals. ### Experiment

#### 4.2.1 Data Preprocessing and Feature Extraction

Because the vibration signal collected by the sensor contains important degradation information, appropriate transformation of the vibration signal can reflect the degradation state of the bearings. To avoid information loss, multiple features in the time and frequency domains are extracted to form feature set for selection. In addition, to accelerate the convergence of the prediction model and improve the prediction accuracy, all the features are normalized. The data preprocessing details are as shown in Algorithm 4. ```
0: Data sample \(S=\{s_{1},s_{2},\cdots,s_{n}\}\), \(n\) is the number of samples. 0: Original feature set \(F\) after data preprocessing. 1:for\(s_{i}mS\)do
2: Calculate each feature in the time and frequency domains, the calculated features are normalized and set between [0,1] to form the original feature set \(F=\{f_{1},f_{2},\cdots,f_{m}\}\), and \(m\) is the number of features. 3:endfor
```

**Algorithm 4** Data preprocessing

When the bearings in mechanical equipment fail, the amplitude and probability distribution of the time-domain signal change. Signal frequency components, energy of different frequency components, and the position of the main energy spectrum of the spectrum change, which can effectively characterize the state of bearing health, provide the information about the noise in the bearing vibration signal [6; 42]. Some features are useless, so choosing the appropriate time-domain and frequency-domain features is the key to effectively predicting the bearing RUL. To obtain more DI and fully reflect the running state of bearings, the feature parameters in the time and frequency-domain are comprehensively used here. Each of these vibration signals is processed to extract 12 time-domain features, such as mean, variance, and kurtosis. A total of 13 frequency-domain features characterize the degradation of bearing performance, as shown in Table 2. In this study, the time-domain feature and frequency-domain features were calculated using the feature parameters listed in Table 2[43].