## 4 Monitoring Method Based on Influence Weight Optimization
### KPLS Monitoring Method Based on Influence Weight W Optimization  
Based on a data-driven algorithm, data feature is the direct information source of the monitoring model. Traditional data preprocessing cannot adapt to specific working conditions and cannot highlight the influence of different variables. According to the calculation of influence coefficients in Section 4.1, the influence coefficients of some variables obtained based on the historical data set of a certain rolling process are shown in Table 2. It can be found that due to the different orders of magnitude of different variables, their influence coefficient values often differ greatly. In the algorithm model, the difference in the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Index** & \(\mathbf{C_{H}}\) & \(\mathbf{C_{K}}\) & \(\mathbf{C_{S}}\) & \(\mathbf{C_{F}}\) & \(\mathbf{C_{q}}\) & \(\mathbf{C_{q}}\) \\ \hline Expression & \(\frac{1}{K_{n}+Q}\frac{\partial P}{\partial k_{0}}\) & \(\frac{1}{K_{n}+Q}\frac{\partial P}{\partial K}\) & \(\frac{K_{n}}{K_{n}  
order of magnitude of data becomes smaller after standardization, and thus the obtained influence coefficient cannot be directly used to distinguish the influence of variables. In this paper, the value of the influence coefficient is multiplied by the mean value \(\overline{\mathbf{X}}\) of the corresponding variable, which is used as the optimization weight \(\mathbf{W}\) of the follow-up monitoring model.  
\[\mathbf{W}=C\overline{\mathbf{X}}^{\overline{\mathbf{X}}} \tag{35}\]  
The overall optimization strategy is shown in Figure 7, and the training process of the monitoring model is shown on the left side of the figure. Firstly, input variable matrix \(\mathbf{X}\) and quality variable matrix \(\mathbf{Y}\) are selected from the historical sample database and standardized for use, respectively. A small section of variable samples and the corresponding rolling force were selected from the database to construct the influence weight \(\mathbf{W}\). Then, the normalized input matrix is reconstructed as \(\mathbf{X}_{W}\) through matrix dot product calculation. Finally, the monitoring model is trained by using the above input and output matrices according to the corresponding KPLS algorithm steps.  
In the figure above, the online monitoring process of the optimization model is shown on the right. The input sample \(\mathbf{x}_{\text{new}}\) of real-time monitoring should correspond to the input sample of the training model after preprocessing. Firstly, the new input samples are standardized according to the data characteristics of the input matrix in the training process. Then the influence weight matrix is used to reconstruct the new input samples to obtain \(\mathbf{x}_{\text{new}}^{\prime}\). Finally, the sample is kernel-mapped and centralized according to the online monitoring steps of the KPLS model. The trained monitoring model is used to complete the verification monitoring.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Index** & **Exit Velocity** & **Back Tension** & **Front Tension** & **Entry Thickness** \\ \hline Partial differential & 53,141.42 & 4.42 & 1.57 & 18,534.48 \\ Influence coefficient & 0.044 & \(3.70\times 10^{-6}\) & \(1.31\times 10^{-6}\) & 0.02 \\ Mean value & 5.78 & 18,829.54 & 15,846.74 & 0.28 \\ Influence weight & 0.254 & 0.070 & 0.021 & 0.004 \\ \hline \hline \end{tabular}
\end{table}
Table 2: An example of the influence coefficient of a course calculation.  
Figure 7: Monitoring model based on influence weight optimization.