## 5 Experiment
### Case 1. Debutane Column Process  
In this section, experiments are carried out on the debutane column's industrial process to prove the effectiveness of the feature transfer. In this process, there is a complex coupling relationship between samples, which has strong process dynamics. Figure 5 shows the schematic diagram of the debutanizer. The description and units of primary process and quality variables are listed in Table 1. Process variables (\(u_{1}\), \(u_{2}\), \(\ldots\), \(u_{7}\)) and quality variable (butane concentration, \(y\)) are collected every 15 min. Butane concentration must be analyzed using a gas chromatograph, which takes 30 min. Therefore, the acquisition time of the quality variable lags the process variable by 45 min. This lag prevents the production process from obtaining real-time feedback information in a timely manner, affecting the subsequent process's control. Figure 5: The schematic diagram of the debutanizer. The acquisition of the quality variable time lags behind the process variables by four time steps, and a soft sensor model is needed to measure butane concentration in real time. Fortuna developed a nonlinear autoregressive moving average (NARMA) model as shown in (11) [28]. At the \(i\) moment, only the butane concentrations at the \(i\)-4 moment and the moment before are available from the database. Butane concentrations at \(i\)-3 to \(i\) are obtained by iteration of the model prediction, which leads to larger errors. \[ \begin{array}{l}\hat{y}(i)=f[u_{1}(i),u_{2}(i),u_{3}(i),u_{4}(k),u_{5}(k),u_ {5}(i-1),\\ u_{5}(i-2),u_{5}(i-3),(u_{6}(i)+u_{7}(i))/2,\\ \hat{y}(i-1),\hat{y}(i-2),\hat{y}(i-3),y(i-4)]\end{array}  \tag{11}\]  
where \(\hat{y}\) represents the predicted value of the soft sensor model. To avoid this accumulation of iterative errors, SCI-XGBoost predicts butane concentration at time \(i\) using only historical data, including time \(i\) and its predecessor, as follows. \[ \begin{array}{l}\hat{y}(i)=f[u_{1}(i),u_{2}(i),u_{3}(i),u_{4}(k),u_{5}(k),u_ {5}(i-1),\\ u_{5}(i-2),u_{5}(i-3),(u_{6}(i)+u_{7}(i))/2,y(i-4)]\end{array}  \tag{12}\]  
The debutane column dataset has a total of \(L=2394\) samples. A sliding window is used to construct a sequence dataset on the debutane column dataset, and the data are sliced by sliding from front to back in the time dimension. It is known that the step length of quality variable lag \(P=4\), and sliding window size \(T=16\); then, the number of samples \(L\) and the number of the sequence dataset \(N\) satisfy the relationship \(N=L-T-P+1\), so there is a total of \(N=2375\) 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 1662:238:475. Regarding the hyperparameters of the SCI-XGBoost model, the optimal values of some parameters are determined by a grid search algorithm and multiple attempts. Parameters such as the size of the convolution kernel in the convolutional layer of the feature extractor, the multiple of the extended dimension of the hidden layer, and the maximum depth of downsampling are used to determine the optimal parameters through several trials. An adaptive learning rate adjustment strategy improves the neuron weights during training. The learning rate will be reduced slightly if the training loss does not decrease after five consecutive iterations. Additionally, training can be halted to prevent overfitting when the model's loss stabilizes and shows little to no decrease, even if the maximum number of iterations has not yet been reached. The grid search method is also used to determine the critical parameters of the parameter setting of the XGBoost regressor. After many trial experiments, the model trained in Table 2 performs best on the validation set.