# Mechanical Performance Prediction Model of Steel Bridge Deck Pavement System Based on XGBoost
## 4 Predictive Modeling
### Model Evaluation Metrics  
The parameters in a machine learning model play a crucial role in the performance of the model. By optimizing the parameters, the best-performing parameters of the machine learning model on the dataset can be obtained, thus improving the performance of the model. In this study, a combination of the grid search method and the five-fold cross-validation method is used to optimize the parameters of the machine learning model. The grid search method is an exhaustive search method used by setting up a combination of \(n\) parameters and training the model \(n\) times. The optimal combination of parameters is the one that performs the best in these \(n\) training sessions [30]. The five-fold cross-validation method first divides the dataset into five mutually exclusive subsets of similar size by \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Level**} & \multicolumn{6}{c}{**Factors**} \\ \cline{2-7}  & \(E1\) (MPa) & \(E2\) (MPa) & \(H1\) (mm) & \(H2\) (mm) & \(T\) (mm) & \(D\) (mm) \\ \hline
1 & 1000 & 1000 & 20 & 20 & 12 & 3000 \\
2 & 2000 & 2000 & 25 & 25 & 14 & 3500 \\
3 & 3000 & 3000 & 30 & 30 & 16 & 4000 \\
4 & 4000 & 4000 & 35 & 35 & 18 & \\
5 & 5000 & 5000 & 40 & 40 & 20 & \\
6 & 6000 & 6000 & 45 & 45 & & \\
7 & 7000 & 7000 & & & & \\
8 & 8000 & 8000 & & & & \\
9 & 10,000 & 10,000 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Influencing factors and level taking of the test. stratified sampling and selects the concatenated set of four of these subsets as the training set without repetition, and uses the remaining one as the test set, so that five different combinations can be obtained by selecting five times, and the final result is the average of the results of these five combinations [31]. The combination of the grid search method and the cross-validation method is to evaluate all \(n\) parameter combinations in the grid search using five-fold cross-validation, and the generalization of the model can be effectively improved using the cross-validation method [31]. The prediction of the mechanical performance index of the steel deck pavement system is a regression problem, and the evaluation indexes in the regression problem are usually root mean square error (_RMSE_), mean absolute error (_MAE_), and coefficient of determination (\(R^{2}\)), as shown in Equations (1)-(3). The smaller the _RMSE_ and _MAE_, the better the model performance. \(R^{2}\) reflects the degree of linear correlation between the sample prediction and the sample true value, and the closer \(R^{2}\) is to 1, the stronger the linear correlation is. Where \(M\) is the number of samples in the dataset, \(y^{\prime}_{j}\) is the true value of the sample, \(y_{j}\) is the predicted value of the sample, and \(\overline{y}\) is the mean of the predicted value of the sample. \[RMSE=\sqrt{\frac{\sum\limits_{j=1}^{M}\left(y^{\prime}_{j}-y_{j}\right)^{2}}{ M}} \tag{1}\]  
\[MAE=\frac{\sum\limits_{j=1}^{M}\left|\left(y^{\prime}_{j}-y_{j}\right)\right|}{ M} \tag{2}\]  
\[R^{2}=1-\frac{\sum\limits_{j=1}^{M}\left(y^{\prime}_{j}-y_{j}\right)^{2}}{ \sum\limits_{j=1}^{M}\left(y_{j}-\overline{y}\right)^{2}} \tag{3}\]