## 5 Results and Discussion
Figure 9: KPLS monitoring of sample 1. Online monitoring simulation for monitoring sample 2 is shown in Figures 12-15. From the monitoring results of the following four methods for sample 2, the recognition rate of the W-KPLS monitoring model in fault sample points is greatly improved compared with the traditional algorithm. As shown in Figure 15, W-KPLS monitoring is used to reduce the missing rate of sample points. The feasibility of W-KPLS is verified by monitoring two  
Figure 11: W-KPLS monitoring of sample 1. Figure 10: W-PLS monitoring of sample 1.  
samples with four methods. By fusing the mechanism model, the accuracy of traditional monitoring methods is improved. Figure 12: PLS monitoring of sample 2. Figure 13: KPLS monitoring of sample 2. Figure 14: W-PLS monitoring of sample 2. Figure 15: W-KPLS monitoring of sample 2. The detailed fault detection rate statistics of the monitoring model based on the four algorithms for the two groups of monitoring samples are shown in Table 5. When the monitored sample exceeds one of the \(T^{2}\) or \(\boldsymbol{SPE}\) control lines, an early warning will be generated. An alarm indication will be issued if it exceeds two control limits at the same time. According to the control limit, the overall fault detection rate of the W-PLS algorithm is improved compared with that of the PLS algorithm, but it cannot meet the monitoring requirements. The data points of the W-KPLS algorithm whose \(T^{2}\) and \(SPE\) monitoring indexes simultaneously exceed the limit account for 75% and 68%, respectively, which are the highest among the four algorithms. At the same time, compared with the KPLS algorithm before optimization, the detection rate of the W-KPLS algorithm is increased by about 20 percentage points. The proportion of data points reaching the early warning limit is also increased to over 95%. The over-limit monitoring index is analyzed using the traditional contribution plot and relative contribution plot based on a linear algorithm and the contribution plot based on a nonlinear algorithm. Results for the first group of monitoring samples are shown in Figures 16-18, and results for the second group of monitoring samples are shown in Figures 19-21. Figure 8:0 Traditional contribution plot of sample 2. Figure 8:1 Relative contribution plot of sample 1. Figure 8:2 Nonlinear contribution plot of sample 1. The fault of monitoring sample 1 is caused by rolling mill drive system fluctuation. Both linear contribution plots show that variable 5 (roll gap value) has the largest contribution value, followed by variable 2 (exit speed). However, the contribution plot diagnosis results of the nonlinear algorithm show that variable 2 (exit velocity) is the main fault variable, and variable 5 (roll gap value) is the secondary fault variable. The quality fluctuation of sample 2 was caused by the uneven thickness of incoming material. The traditional contribution plot shows that the most contributing fault variables are variable 2 (outlet speed) and variable 5 (roll gap value). While the relative contribution plot shows that variable 1 (inlet speed) is the main fault variable, and the influence of variable 7 (incoming material thickness) is the second. The contribution plot based on the nonlinear algorithm shows that variable 7 (entry thickness) is the main influencing variable. Data related to the quality fluctuation of actual production status were collected and verified by the diagnostic method in this paper. By analyzing the contribution plot above, it can be seen that the diagnosis result based on a nonlinear contribution diagram is consistent with the on-site fault diagnosis result. Figure 8:3 Nonlinear contribution plot of sample 2. Figure 8:4 Relative contribution plot of sample 2.