## 7 Experimental Verification
### Bearing Reliability Modeling  
The initial feature parameter set consists of high-dimensional feature vectors, which can be challenging to directly incorporate into reliability models for solving reliability problems, potentially even leading to the curse of dimensionality. In this study, the PacMAP algorithm is employed to perform dimensionality reduction on the degradation feature parameter set. Based on the characteristics of bearing degradation data, 2D is selected as the target dimensionality for reduction. This choice not only better preserves both local and global structures of the data but also provides more intuitive spatial visualization effects.  
Figure 10: The 12-dimensional feature parameter set.  
Figure 11 illustrates the relationship between the dimensionality reduction levels (from 1D to 5D) and both the variance retained and relative computation time. The left vertical axis represents the variance retained, while the right vertical axis shows the relative computation time. Through cumulative variance contribution rate analysis, it was found that 2D reduction retains approximately 91.24% of the original information, 3D retains about 92.31%, 4D retains around 93.43%, and 5D retains approximately 93.67%. As shown in the figure, the computation time increases nonlinearly with higher dimensions (5D requires about 2.5 times the computation time of 2D). Selecting higher dimensions does not significantly improve the variance contribution rate but substantially increases computational complexity. Therefore, this study opts to reduce the data to two dimensions.  
Additionally, T-Distributed Stochastic Neighbor Embedding (t-SNE) and Principal Component Analysis (PCA) are also used to perform dimensionality reduction on the data. The dimensionality reduction results of the three algorithms are shown in Figure 12.  
Figure 11: Variance retention rate and computation time vary with dimension.  
Figure 12: Dimensionality reduction results of the three algorithms. **(a)** t-SNE; **(b)** PCA; **(c)** PaCMAP.  
As shown in the figure, the dimensionality reduction results of t-SNE, PCA, and PaCMAP all exhibit a certain degree of overlap, with data points from different stages crossing over significantly, making it less effective in distinguishing the operational cycles of the bearings. In contrast, the PaCMAP algorithm performs better in segmenting the operational cycles of the bearings. Its dimensionality reduction results more clearly illustrate the separations between the three cycles, with the data points from each stage being more distinctly separated. This indicates that the dimensionality reduction results of the PaCMAP algorithm are more effective in reflecting the degradation conditions of the bearings.  
Based on the bearing 3-1 degradation feature set obtained after dimensionality reduction, a model for reliability assessment can be constructed. This study employs an intuitive logistic regression model for the reliability assessment of the bearing. By selecting the three-dimensional feature vector set obtained after dimensionality reduction by PaCMAP as the degradation feature information, and using it as the input for the logistic regression model, the regression coefficients of the logistic regression model are calculated as follows: \(\varepsilon_{0}=2.486\), \(\varepsilon_{1}  
model for the bearing and observing its reliability curve, one can effectively characterize the trend of changes throughout the bearing's entire life cycle, thereby analyzing the bearing's operational status.