## 5 Experiment
### Case 2. Sulfur Recovery Unit  
To verify the effectiveness of the semi-supervised model SSCI-XGBoost and prove the ability of the unsupervised dynamic feature extractor to extract the dynamic information of unlabeled samples, the sulfur recovery industrial process dataset was selected for experimental verification. The sulfur recovery unit is an important device for dealing with industrial waste gas, which removes gases such as SO2 and H2S in acidic airflow. Its simplified industrial process flow is shown in Figure 9. The exhaust gas treated by the sulfur recovery unit still has residual SO2 and H2S. To avoid pollution, the concentrations of SO2 and H2S must be monitored before the exhaust gas is discharged into the atmosphere. The strong corrosion of acid gas requires the sensor to be removed and replaced frequently, so using a soft sensor to predict the gas concentration can reduce the monitoring cost. The sulfur recovery dataset [29] is described in Table 4. The dataset consists of five process variables (\(u_{1}\), \(u_{2}\), \(\ldots\), \(u_{5}\)) and two mass variables SO2 (\(y_{1}\)) and H2S (\(y_{2}\)). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Variable Description** & **Units** \\ \hline \(u_{1}\) & Gas flow MEA\_GAS & m\({}^{3}\)/s \\ \(u_{2}\) & Air flow AIR\_MEA & m\({}^{3}\)/s \\ \(u_{3}\) & Secondary air flow AIR\_MEA\_2 & m\({}^{3}\)/s \\ \(u_{4}\) & Gas flow in SWS zone & m\({}^{3}\)/s \\ \(u_{5}\) & Air flow in SWS zone & m\({}^{3}\)/s \\ \(y_{1}\) & Concentration of H2S & mol/m\({}^{3}\) \\ \(y_{2}\) & Concentration of SO2 & mol/m\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Variable description of the sulfur recovery unit. Figure 8: Features importance of XGBoost. The sulfur recovery dataset has a total of \(L\) = 10,081 samples. A sliding window is used to construct a sequence dataset on the dataset, and the sliding window size is \(T\) = 16. The number of samples \(L\) and the number of the sequence dataset \(N\) satisfy the relationship \(N=L-T+1\), so there is a total of \(N\) = 10,066 sequence samples. The sequence dataset is divided according to the rule of training set; validation set/test set = 7:1:2, and the number of samples in each part is 7046:1026:1994. In order to verify the effectiveness of the semi-supervised model, it is assumed that some quality variables are missing, and the quality variables of some samples in the training set are randomly erased. With some quality variables missing, the training samples of the sulfur recovery dataset are organized as shown in Figure 10 (\(T\) = 3 is assumed to simplify the representation, whereas \(T\) = 16 during the actual training process). The training set is divided into a labeled sample training set and an unlabeled sample training set, both of which can be used for training the unsupervised feature extractor, and the labeled sample training set is used for training the XGBoost regressor. Figure 10: Training set organization when missing partial quality samples. Figure 9: The flowchart of the sulfur recovery unit. Regarding the parameter setting of SSCI-XGBoost, referring to the parameter setting of SCI-XGBoost on the debutane column dataset and combined with the grid search algorithm and repeated experiments on this dataset, the final optimal hyperparameter table of SSCI-XGBoost on the sulfur recovery dataset is shown in Table 5.  
SS-SAE, XGBoost, and SCI-XGBoost were selected as comparison models. SS-SAE is a semi-supervised model, while XGBoost and SCI-XGBoost only use labeled samples for model training. On the sulfur recovery dataset, the input of the SS-SAE method refers to the paper [29], which provides the sulfur recovery dataset; the hyperparameter settings refer to the paper [20], which proposed the SS-SAE method and carried out the hyperparameter settings.