## 4 Implementation of RUL Prediction Based on Proposed Method  
### Dataset Description  
To verify the effectiveness of the proposed method, the IEEE PHM 2012 public dataset [38] was employed for validation. This dataset was collected from the Pronostia experimental platform developed by the FEMTO-ST Institute, and the structure of the test rig is shown in Figure 8. The experimental platform is functionally divided into three main components: the rotation unit, the loading unit, and the measurement unit. Rotation unit: This section primarily consists of an asynchronous motor, a gear reducer, couplings, and a drive shaft. The asynchronous motor has a rated power of 250 W and a rated speed of 2830 rpm. The motor's rotational motion is transmitted to the supporting bearings through the gearbox, couplings, and shaft. The rotational speed and direction of the motor can be adjusted via a control interface to accommodate different experimental conditions with varying rotational speeds. Loading unit: This unit is composed of a pneumatic cylinder, pressure regulator, force sensor, and lever arm. The force generated by the pneumatic cylinder is amplified through the lever arm and applied to the outer ring of the bearing, imposing a high radial load to accelerate bearing degradation and failure. The pressure regulator allows for the adjustment of the applied force to meet different load condition requirements. Measurement unit: This section includes a set of sensors and a  
Figure 8: Pronostia experimental platform. data acquisition card to monitor and record the operational state of the bearing, thereby capturing its degradation process. The acceleration sensor used is a DYTRAN3035B, with a measurement range of 50 g and a sensitivity of 100 mV/g. The temperature sensor is a platinum RTD100 (PROSENSOR), with detailed specifications available in reference [38]. The experiment recorded horizontal and vertical vibration signals throughout the degradation process of the bearings. When the amplitude of the measured vibration signal continuously exceeded 20 g, the bearing was considered to have reached complete failure, and the experiment was terminated. The sampling frequency was 25.6 kHz, the sampling duration was 0.1 s, and the sampling interval was 10 s. The experimental dataset includes three different operating conditions and a total of 17 rolling bearings. Detailed information is provided in Table 2. The first bearing under Condition 1 is denoted as B1-1, and the remaining bearings are labeled accordingly. Three groups of experiments were conducted in this study, and the detailed division of the training and testing sets is shown in Table 3. Each training or testing set contains the full life cycle data of the corresponding bearing. According to the findings of reference [39], horizontal vibration signals carry richer information; therefore, horizontal vibration signals were selected for subsequent analysis. A sliding window approach was adopted to convert the optimal feature sequences into sample data, as illustrated in Figure 9. In the figure, \(x_{1}\) denotes the multidimensional feature vector at the first time point in the bearing life cycle, and \(y_{1}\) represents the corresponding RUL label at that time. The sliding window length defines the number of data points included in a single sample, and the step size specifies the interval between two adjacent windows. To maximize data utilization, the step size was set to 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Working Condition** & **Rotational Speed (rpm)** & **Radial Load (kN)** & **Bearing Data** \\ \hline
1 & 1800 & 4 & Bearing 1-1, Bearing 1-2, Bearing 1-3, Bearing 1-4, Bearing 1-5, Bearing 1-6, Bearing 1-7 \\
2 & 1650 & 4.2 & Bearing 2-1, Bearing 2-2, Bearing 2-3, Bearing 2-4, Bearing 2-5, Bearing 2-6, Bearing 2-7 \\
3 & 1500 & 5 & Bearing 3-1, Bearing 3-2, Bearing 3-3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data of PHM2012.