## 3 Results
### Stacking Model Combination Performance Analysis  
To verify the rationality of the abovementioned single-model combination method, and due to the small sample, the input of the metamodel is obtained through eight cross-validations to prevent overfitting. There is a significant gap in the prediction effect of the ensemble model obtained by combining different single models. To further verify the influence of base learner selection in the stacking ensemble learning model on the prediction results, Table 10 and Figure 11 show the prediction results of different combination methods on the test set. The combination method Stacking_1 selects the model combination method with the greatest correlation, and the result of the ensemble model is worse than the prediction effect of the single model linear regression and SVM. The stacking model has an \(R^{2}\) of 0.8796, and MAE and RMSE of 0.0607 and 0.0784, respectively. This is because the first-layer model contains the most relevant random forest, ExtraTrees, GBDT, and XGBoost, which causes the data to be repeatedly trained, resulting in overfitting, which reduces the accuracy of the model. Figure 10: MIC model correlation analysis. The combination methods Stacking_2 and Stacking_3 choose random combination models, which are both higher than the optimal single model prediction accuracy. The \(R^{2}\) of Stacking_2 model is 0.9415, and MAE and RMSE are 0.0441 and 0.0546, respectively. The \(R^{2}\) of Stacking_3 model is 0.9445, and MAE and RMSE are 0.0435 and 0.0532, respectively. The combination method Stacking_4 chooses the combination method that meets the minimum correlation on the basis of having stronger models (linear regression, SVR, KNN, CatBoost) to make the best use of the advantages of different algorithms to observe data from different data spaces to ensure prediction accuracy, effectively improving the generalization performance of the fusion ensemble model and showing the best predictive effect. The \(R^{2}\) of Stacking_4 model is 0.9702, and MAE and RMSE are 0.0304 and 0.0389, respectively. The experimental results show that it is necessary to analyze the correlation of each model before constructing the stacking ensemble learning model. It is difficult to achieve the best prediction effect by randomly selecting a model to build a stacking model. MIC can \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Stacking Model**} & \multirow{2}{*}{**Base Model Combination**} & \multicolumn{3}{c}{**The Evaluation Index**} \\ \cline{3-5}  & & **R2** & **MAE** & **RMSE** \\ \hline \multirow{2}{*}{Stacking 1} & GBDT, Random Forest, XGBoost, ExtraTrees, GBDT & 0.8796 & 0.0607 & 0.0784 \\ \hline \multirow{2}{*}{Stacking 2} & SVR, XGBoost, Random Forest, GBDT, CatBoost & 0.9415 & 0.0441 & 0.0546 \\ \hline \multirow{2}{*}{Stacking 3} & SVR, XGBoost, ExtraTrees, Random Forest CatBoost & 0.9445 & 0.0435 & 0.0532 \\ \hline \multirow{2}{*}{Stacking 4} & Linear Regression, KNN, SVR, CatBoost & 0.9702 & 0.0304 & 0.0389 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Prediction results of different stacking models. Figure 11: Comparison of prediction errors of different stacking models: (**a**) Stacking model 1 builds the most relevant ensemble learning model; (**b**) Stacking model 2 builds the ensemble learning model randomly; (**c**) Stacking model 3 builds the ensemble learning model randomly; (**d**) Stacking model 4 builds a minimum correlation ensemble learning model. The ordinate of 28-day compressive strength is logarithmically processed. effectively analyze the linear and nonlinear correlation of the model, which provides strong support for the model selection when constructing the stacking ensemble model. Compared with the stacking 2 ensemble model and stacking 3 ensemble model constructed by random selection, the most differentiated stacking model has an average increase of 2.72% in \(R^{2}\), an average reduction of 1.34% in MAE, and an average reduction in RMSE of 1.5%.