# Research on an ID-PCA Early Fault Detection Method for Rolling Bearings
## 4 Experimental Results and Analysis
### Simulation Results and Analysis of Rolling Bearing Rolling Body Faults  
#### 4.2.1 Rolling Bearing Rolling Body Faults Simulation Results  
Figure 4 depicts the first-level detection results of rolling element faults in rolling bearings based on the improved deep principal element analysis method. That is, the I-PCA method is used to detect the faults of the rolling elements of the rolling bearing. The red dot-dash line represents the control limit, and the blue solid line represents the statistic. It can be seen from Figure 4 that the early fault detection effect of rolling bearings based on the I-PCA method is not ideal, the missing detection rate is about 20%, and the false detection rate is about 50%. Although from the perspective of detection delay, it is almost 0, the detection effect is still not ideal.  
Figure 5 depicts one of the simulation results of \(T_{23}^{2}\) and \(SPE_{23}\) in the third-level detection results of rolling element faults of rolling bearings based on the DE-PCA detection method. The detection effect of this group is better in all the third-level detection results. However, 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 relatively large, exceeding 20%. There is a phenomenon of false positives. It is at about the 60 th sampling point that fault is detected; therefore, the detection delay is about 10 sampling points.  
Figure 4: Experimental results of the I-PCA fault detection method for the rolling bearing rolling body: (**a**) the result of \(T_{01}^{2}\); (**b**) the result of \(SPE_{01}\).  
Figure 6 depicts one of the simulation results of \(T_{24}^{2}\) and \(SPE_{24}\) in the third-level detection results of rolling element faults of rolling bearings based on the DV-PCA detection method. The detection effect of this group is better in all the third-level detection results. However, the results show that the method is not very effective in terms of false detection rate. The missing detection rate is about 20%. Although the detection delay is almost zero, the false detection rate is about 15%. Therefore, the detection effect is still not ideal.  
Figure 7 depicts the simulation results of \(T_{2j}^{2}\) and \(SPE_{2j}\) based on the ID-PCA method for the third-layer detection results of rolling element faults in rolling bearings. It can be seen from Figure 7 that the detection effect of the second layer of the early faults of the outer ring of the rolling bearing based on the ID-PCA method has a certain improvement compared with the improved PCA method. Among them, the false detection rate of \(SPE_{22}\), \(SPE_{23}\), and \(SPE_{24}\) is better in terms of false detection rate, the missing detection rate is within 5%, the false detection rate is also within 5%, and the detection delay is almost 0. Therefore, this method has good early fault detection performance for rolling  
Figure 5: Experimental results of DE-PCA fault detection method for the rolling bearing rolling body: (a) the result of \(T_{23}^{2}\); (b) the result of \(SPE_{23}\).  
Figure 6: Experimental results of DV-PCA fault detection method for the rolling bearing rolling body: (a) the result of \(T_{23}^{2}\); (b) the result of \(SPE_{23}\).