## 3 Results and Discussion  
### Predictive Performance of the Initialized Model  
The selection of hyper parameters has a significant influence on the predictive performance of machine learning models. However, there is currently no relevant theoretical support for hyper parameter selection, and the adjustment process of hyper parameters is usually extremely cumbersome. The main hyper parameters that need to be adjusted for the XGB model and their meanings are shown in Table 7. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Metric** & **Equation** & **Performance Criteria** \\ \hline MSE & \(\frac{1}{n}\sum\limits_{i=1}^{n}{(g_{i}-y_{i})^{2}}\) & The smaller the MSE value, the higher the prediction accuracy of the model. The value range of MSE is [0, +\(\infty\)]. \\ RMSE & \(\sqrt[2]{\frac{1}{n}\sum\limits_{i=1}^{n}{(g_{i}-y_{i})^{2}}}\) & RMSE is the arithmetic square root of MSE. The value range of RMSE is [0, +\(\infty\)]. \\ MAE & \(\frac{1}{n}\sum\limits_{i=1}^{n}{[g_{i}-y_{i}]}\) & equal to 0. The greater the error, the greater the MAE, and the value range of MAE is [0, +\(\infty\)]. \\ R2 & \(\frac{\sum\limits_{i=1}^{n}{(g_{i}-\overline{y})^{2}}}{\sum\limits_{i=1}^{n}{(g _{i}-\overline{y})^{2}}}\) & it is to 1, the stronger the model’s ability to explain the predicted object. The closer it is to 0, the worse the fit of the model. \\ \hline \hline \end{tabular} \({}^{1}\)\(\hat{y}_{i}\) is the predicted value, \(y_{i}\) is the true value and \(\overline{y}\) is the average of the true values.  
\end{table} 
Table 6: Description of evaluation metrics \({}^{1}\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Meaning** \\ \hline max\_depth & Depth of decision tree \\ n\_estimators & Number of weak learners \\ eta & Learning rate \\ min\_child\_weight & Sum of minimum sample weights required by leaf nodes \\ gamma & The drop value of the minimum loss function required for node splitting \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Hyper parameters of XGB and their meanings. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Features** & **Count** & **Mean** & **Std** & **Min** & **25\%** & **50\%** & **75\%** & **Max** \\ \hline \(\varphi\)\({}^{1}\) & 34,584 & 0.262 & 0.250 & 0 & 0.053 & 0.225 & 0.374 & 1 \\ Speed & 34,584 & 0.467 & 0.411 & 0 & 0.000 & 0.400 & 1.000 & 1 \\ Torque & 34,584 & 0.450 & 0.315 & 0 & 0.188 & 0.394 & 0.728 & 1 \\ Power & 34,584 & 0.409 & 0.287 & 0 & 0.164 & 0.371 & 0.608 & 1 \\ FS\({}^{2}\) & 34,584 & 0.397 & 0.270 & 0 & 0.177 & 0.366 & 0.559 & 1 \\ CA \({}^{3}\) & 34,584 & 0.500 & 0.289 & 0 & 0.250 & 0.500 & 0.750 & 1 \\ \hline \hline \end{tabular} \({}^{1}\) Excess air coefficient; \({}^{2}\) fuel consumption; \({}^{3}\) crank angle.  
\end{table} 
Table 5: Data description after preprocessing. First, the predictive performance of the initialized XGB was analyzed. The five hyper parameters of the model, max_depth, n_estimators, eta, min_child_weight, and gamma, were set to 2, 100, 0.1, 3, and 0.1, respectively. Figure 4 shows the results of the regression analysis of the initialized model, in which the blue scatter points represent the results of prediction for the training set, the orange scatter points represent the results of prediction for the test set, and the black straight line represents the 45\({}^{\circ}\) line where the predicted values are equal to the test values. The number of samples in the training set is 27,667 and the number of samples in the test set is 6917 according to the data set division ratio described in Section 2.3.2. It can be seen in Figure 4 that the prediction performance of the initialized model is poor, and the prediction results for samples with larger values are extremely inaccurate.