## 5 Results and Discussion  
In order to illustrate our point of view further, we use the simulation data that come from the rolling production data of a 2800 mm cold rolling mill. The process variables included: roll gap value, roll bending force, entry speed, exit speed, incoming material thickness, front tension and back tension. Mass variable is the pass exit thickness of the strip. A total of 1200 sets of production data samples were collected, among which 800 sets of normal operation data were used for training the offline model. The other 400 sets of data were used for the online monitoring model. Monitoring sample 1 included 100 sets of normal samples and 100 sets of fault samples, among which the default fault source was the transmission system fluctuation of the rolling mill. Monitoring sample 2 contains 100 groups of normal samples and 100 groups of fault samples, among which the default fault source is the uneven thickness of incoming materials. The cumulative variance contribution rate is calculated using the sample data, as shown in Table 3. In order to pursue calculation efficiency and take into account the accuracy of the model, the variance contribution of nearly 90% can be obtained when the number of principal components is set as 4. The monitoring model is trained according to the modeling process of the PLS algorithm. The projection direction matrix \(\mathbf{R}\) of training is used to project each group of monitoring samples to obtain a new principal component and residual component. Statistical index \(T^{2}\) and \(\mathbf{SPE}\) are constructed, respectively. The online monitoring simulation diagram of the monitoring model based on the PLS algorithm is finally obtained. Radial basis function is used to carry out simulation monitoring based on the KPLS algorithm, and cross-validation was used to determine the kernel parameter \(\sigma=3.5\). The influence weight coefficient of strip thickness monitoring simulation based on optimization model as shown in Table 4. W-KPLS is used for online monitoring of sample 1 and compared with other methods. The simulation results of online monitoring are shown in the figure. As shown in Figure 8, using the traditional PLS method for monitoring, the monitoring index of sample 1 exhibits an obvious overrun phenomenon in the fault sample number 101-140 with a high detection rate. However, there is a lack of fault point monitoring around 140-200. For the monitoring results of KPLS in Figure 9, the fault detection rate of this method is significantly higher than that of PLS, but there are still a few missing points. In order to improve the fault detection rate, the monitoring method based on influence weight optimization is used for monitoring, and the results are shown in Figures 10 and 11. We can see that the optimized monitoring method is better than the traditional monitoring method. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Index** & **Entry Velocity** & **Exit Velocity** & **Front Tension** & **Back Tension** & **Roll Gap** & **Roll Bending Force** & \begin{tabular}{c} **Entry** \\ **Thickness** \\ \end{tabular} \\ \hline Partial & 4494.08 & 7166.41 & 11.13 & 19.52 & - & - & 123,513.80 \\ \begin{tabular}{c} Influence \\ coefficient \\ \end{tabular} & 0.08 & 0.01 & \(2.04\times 10^{-5}\) & \(3.52\times 10^{-5}\) & 0.014 & \(4.80\times 10^{-6}\) & 0.22 \\ \
\begin{tabular}{c} Mean value \\ \end{tabular} & 10.58 & 13.57 & 15,828.13 & 18,820.76 & 0.72 & 146.36 & 0.28 \\
\begin{tabular}{c} Influence weight \\ \end{tabular} & 0.85 & 0.14 & 0.32 & 0.66 & 0.01 & 0.007 & 0.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation calculation of influence weight. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Component Number** & **1** & **2** & **3** & **4** & **5** & **6** & **7** \\ \hline Variance contribution rate \% & 39.02 & 61.87 & 80.67 & 89.93 & 95.69 & 99.38 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calculation of cumulative variance contribution rate. Figure 8: PLS monitoring of sample 1.