## 5 Experiment
### Case 2. Sulfur Recovery Unit
To overcome the process dynamics, the network structure of SS- SAE is set as [20-16-12-6-1], the pre-training learning rate is 0.1, the number of pre-training iterations is 10, the fine-tuning learning rate is 0.01, and the number of fine-tuning iterations is 60. For the training set, it is assumed that there are three cases for the proportion of labeled samples: 33%, 50%, and 67%. Under the above hyperparameter settings and different proportions of labeled samples, SSCI-XGBoost and other models are trained, respectively, and the experimental results of each model on the test set are shown in Table 6.  
From Table 6, it can be seen that the performance of SCI-XGBoost is better than XGBoost in the case of three different proportions of labeled samples, indicating that the proposed model can fully extract process dynamic information. This result is consistent with the experimental results in the previous section to verify the effectiveness of feature extraction using the debutane tower dataset, which once again verifies the effectiveness of feature transfer. SSCI-XGBoost performs better than SCI-XGBoost trained only with labeled samples under different proportions of labeled samples, which indicates that the \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Proportion** & **Model** & **MAE** & **RMSE** & \(\mathbf{R^{2}}\) \\ \hline \multirow{4}{*}{33\%} & XGBoost & 0.0142 & 0.0306 & 0.6983 \\  & SCI-XGBoost & 0.0141 & 0.0291 & 0.7283 \\  & SS-SAE & 0.0188 & 0.0306 & 0.6722 \\  & SSCI-XGBoost & 0.0137 & 0.0281 & 0.7447 \\ \hline \multirow{4}{*}{50\%} & XGBoost & 0.0135 & 0.0290 & 0.7287 \\  & SCI-XGBoost & 0.0133 & 0.0282 & 0.7428 \\  & SS-SAE & 0.0180 & 0.0289 & 0.7088 \\  & SSCI-XGBoost & 0.0132 & 0.0274 & 0.7582 \\ \hline \multirow{4}{*}{67\%} & XGBoost & 0.0124 & 0.0231 & 0.8271 \\  & SCI-XGBoost & 0.0123 & 0.0221 & 0.8420 \\ \cline{1-1}  & SS-SAE & 0.0137 & 0.0206 & 0.8521 \\ \cline{1-1}  & SSCI-XGBoost & 0.0118 & 0.0195 & 0.8774 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance metrics of the models on the sulfur recovery test set. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Hyperparameter** & **Value** \\ \hline \multirow{3}{*}{Dynamic Feature Extractor} & Length of sliding window & 16 \\  & Maximum depth of subsample & 3 \\  & Expansion of hidden layer & 3 \\  & Size of the convolution kernel & 3 \\ \hline \multirow{3}{*}{XGBoost Learning rate} & Number of ensemble trees & 200 \\  & Maximum depth of the tree & 3 \\  & Learning rate & 0.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The hyperparameters of the SSCI-XGBoost model. unsupervised dynamic feature extractor can capture the hidden dynamic information in unlabeled samples as a supplement. In the case of 33% and 50% labeled samples, the performance of XGBoost is better than SS-SAE, indicating that the ensemble model has stronger generalization ability when the number of labeled samples is small. The performance of the semi-supervised model SS-SAE is not as good as SSCI-XGBoost, which indicates that the dynamic feature extractor is more capable of capturing the process dynamic information. In order to more intuitively represent the performance improvement brought by SSCI-XGBoost using unlabeled samples, the RMSE broken lines of the three models XGBoost, SCI-XGBoost, and SSCI-XGBoost are shown in Figure 11. In the case of three different proportions of labeled samples, the RMSE values of SCI-XGBoost are smaller than those of XGBoost, which indicates that the feature transfer is effective. The performance of SSCI-XGBoost is better than SCI-XGBoost, which proves that the feature extractor captures the hidden information of the unlabeled samples. Combining the dynamic feature extraction ability of a sequential model and the generalization performance of an ensemble model, the semi-supervised soft sensor model SSCI-XGBoost, based on unsupervised dynamic feature extraction, can fully capture the hidden dynamic information in unlabeled samples to maximize the model performance.