## 5 Experiment
### Case 1. Debutane Column Process
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Variable Description** & **Units** \\ \hline \(u_{1}\) & Top temperature & \({}^{\circ}\)C \\ \(u_{2}\) & Top pressure & kg/cm\({}^{2}\) \\ \(u_{3}\) & Reflux flow & m\({}^{3}\)/h \\ \(u_{4}\) & Flow to next process & m\({}^{3}\)/h \\ \(u_{5}\) & 6 th tray temperature & \({}^{\circ}\)C \\ \(u_{6}\) & Bottom temperature A & \({}^{\circ}\)C \\ \(u_{7}\) & Bottom temperature B & \({}^{\circ}\)C \\ \(y\) & Butane concentration & \% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Descriptions of the variables in the debutanizer column. In order to verify the effectiveness of the SCI-XGBoost model, ANN, XGBoost, LSTM, SLSTM, and SCINet were selected as comparison models. For the non-sequential models, ANN and XGBoost, the model's input is the data after one-dimensional expansion of the sequence data to increase their dynamic learning ability. The network structure of ANN is [128-64-16-1], and the activation function is Relu. For both LSTM and SLSTM, the number of hidden layer neurons is set as 100, the input sequence length is the same as the input window length T of SCI-XGBoost, the learning rate is 0.01, and the number of iterations is 100. Under the above hyperparameter settings, the prediction curves of various models on the test set of the debutane column are shown in Figure 6, and the evaluation metrics of the models are shown in Table 3. When only the sequence data of \(k\)-4 and its previous time are used to predict the quality variable at time \(k\), the predicted value of SLSTM has a large deviation from the true value at some peak moments, and the prediction performance is not as good as LSTM and SCINet. LSTM has worse prediction performance than SCINet at some peak moments. SCI-XGBoost has better performance than SCINet, which indicates that even if the dynamic features are extracted through SCINet, it is difficult to achieve the regression accuracy of the ensemble model only through the fully connected layer, which proves the strong generalization ability of XGBoost. Compared with XGBoost, the predicted value of XGBoost is significantly deviated from the true value at the peak time, indicating that XGBoost has insufficient ability to capture the dynamic characteristics of the process. Therefore, SCI-XGBoost has strong dynamic feature capture ability and better generalization performance, so the prediction effect is better than that of other models. For further comparison, the boxplot comparisons of absolute prediction errors on the testing dataset are shown in Figure 7 for these six models. Compared with other models, SCI-XGBoost has the narrowest box, and the bottom is also the closest to zero. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Hyperparameter** & **Value** \\ \hline  & Length of sliding window & 16 \\  & Maximum depth of subsample & 3 \\ Dynamic & Rxpansion of hidden layer & 3 \\ Feature & Dize of the convolution kernel & 3 \\ Extractor & Initial learning rate & 0.01 \\  & Maximum number of iterations & 100 \\  & Optimizer & Adam \\  & Scrivation function & Tanh \\ \hline  & Number of ensemble trees & 100 \\ XGBoost & Maximum depth of the tree & 2 \\  & Learning rate & 0.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Hyperparameters of the SCI-XGBoost model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline ANN & 0.0652 & 0.0815 & 0.8381 \\ SLSTM & 0.0891 & 0.1179 & 0.6619 \\ LSTM & 0.0409 & 0.0474 & 0.9451 \\ XGBoost & 0.0335 & 0.0413 & 0.9583 \\ SCINet & 0.0315 & 0.0393 & 0.9623 \\ SCI-XGBoost & 0.0295 & 0.0367 & 0.9672 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evaluation metric of the model on the test set. Figure 6: Prediction curve of the model on the test set, (**a**) ANN, (**b**) SLSTM, (**c**) LSTM, (**d**) SCINet, (**e**) XGBoost, and (**f**) SCI-XGBoost. Figure 7: Box of absolute prediction errors for different Models.