# Research on an ID-PCA Early Fault Detection Method for Rolling Bearings
## 4 Experimental Results and Analysis
### Simulation Results and Analysis of Rolling Bearing Outer Ring Faults  
#### 4.3.1 Rolling Bearing Outer Ring Fault Simulation Results  
Figure 8 depicts the first-level detection results of the outer ring faults of the rolling bearing based on the ID-PCA analysis method, that is, the detection results of the outer ring faults of the rolling bearing by the I-PCA method. It can be seen from Figure 6 that the early fault detection effect of rolling bearings based on the I-PCA method is not ideal, and the missing detection rate is about 40%. Additionally, \(SPE_{01}\) has almost no ability to detect the fault. Therefore, from the perspective of the false detection rate, \(T_{01}^{2}\) is the detection result for comparison, and the false detection rate is about 20%. Although the detection delay is almost 0, the detection effect is not ideal. Figure 9 depicts the simulation results of \(T_{22}^{2}\) and \(SPE_{22}\) in the third-layer detection results of the outer ring fault of the rolling bearing based on the DE-PCA detection method. This group of results has a better detection effect on the rolling element fault of the rolling bearing based on the DE-PCA method. It can be drawn from the figure that the early fault detection results of rolling bearing based on DE-PCA are obtained. The results show that the method is not very effective in terms of the false detection rate; the missing detection rate is about 15%, the false detection rate is about 40%, and the detection delay is about 15 sampling points. Figure 8: Experimental results of I-PCA fault detection method for the rolling bearing outer ring: (**a**) the result of \(T_{01}^{2}\); (**b**) the result of \(SPE_{01}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **I-PCA** & **DE-PCA** & **DV-PCA** & **ID-PCA** \\ \hline Missing detection rate & 18\% & 13.3\% & 16\% & 2\% \\ Fault detection rate & 48\% & 20\% & 18\% & 4\% \\ Detection delay & 0 & 9 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The performance comparison for rolling bearing rolling body. Figure 10 depicts the simulation results of \(T_{21}^{2}\) and \(SPE_{21}\) in the third-layer detection results of the outer ring fault of the rolling bearing based on the DE-PCA detection method. This group of results has a better detection effect on the rolling element fault of the rolling bearing based on the DE-PCA method. It can be drawn from the figure that the early fault detection results of rolling bearing based on DE-PCA are obtained. The results show that the method is not very effective in terms of false detection rate, the missing detection rate is about 15%, and the false detection rate is about 20%. Although the detection delay is almost 0, the detection effect is not ideal. Figure 11 depicts the simulation results of \(T_{2j}^{2}\) and \(SPE_{2j}\) based on the ID-PCA method for the detection results of the third layer of rolling bearing outer ring faults. From Figure 11, it can be concluded that the missed detection rate of \(T_{21}^{2}\), \(SPE_{23}\), and \(SPE_{24}\) is better in terms of the false detection rate; the missed detection rate is almost 0%, the false detection rate is also within 5%, and the detection delay is 0. In terms of the overall detection results, normal data and fault data can be clearly separated, and it has good early fault detection performance. Figure 10: Experimental results of DV-PCA fault detection method for rolling bearing outer ring: (**a**) the result of \(T_{21}^{2}\); (**b**) the result of \(SPE_{21}\). Figure 9: Experimental results of DE-PCA fault detection method for rolling bearing outer ring: (**a**) the result of \(T_{22}^{2}\); (**b**) the result of \(SPE_{22}\).