# Tree Based Approaches for Predicting Concrete Carbonation Coefficient
## 4 Results and Discussion
In fact, the literature indicates that the concrete carbonation rate fundamentally depends on the CO2 diffusivity, which, besides depending on the concrete's porous structure and on its subsequent filling by other substances, particularly water, depends on the CO2 gradient from the concrete surface to carbonation front [23]. Performance indicators of the developed models, obtained from the testing samples, are shown in Table 4. The computational time to build the Model Tree (MT) is 0.08 s and 0.01 s to test the model, for Multi-Gene Genetic Programming (MGGP), the computational time is 14 min and 88 s, while for Random Forest (RF) the computational time is 40.5104 s. The performances of MT and RF are on par with the excellent performance of \(r=0.953\) and \(r=0.955\), respectively. MGGP, with \(r=0.936\), is close to, but below, the accuracy displayed by MT and RF, presenting simultaneously higher RMSE and MSE values. All these new models present lower RMSE values than those proposed in [11], developed using ANN and GP techniques. The former were developed with the purpose of overcoming the issue of having to consider two models when using the MLR technique, as in [23], due to the non-monotonic influence of \(RH\) in carbonation, as explained before. However, this use of two models, with \(RH\) playing the role of the splitting criterion, may be faced as a particular Model Tree. Thus, the performance indicators for the ensemble of the two MLR models proposed in [23] were computed, delivering values of \(r=0.867\), RMSE = 7.344 and MAE = 4.904. Therefore, MT, RF and MGGP models constitute an improvement concerning concrete carbonation coefficient prediction. \begin{table} \begin{tabular}{c c c c} \hline \hline  & **MT** & **RF** & **MGGP** \\ \hline Time required for modelling & Building the model: 0.08 s & \multirow{2}{*}{40.5104 s} & 14 min \\  & Testing the models: 0.01 s & & 88 s \\ \hline \(r\) & 0.953 & 0.955 & 0.936 \\ \hline RMSE & 3.871 & 3.584 & 4.453 \\ \hline MAE & 2.341 & 2.032 & 2.546 \\ \hline \hline \end{tabular}   
* The scatter plot for MT, RF and MGGP models in Figures 9–11 show a balanced scatter with no obvious under or over-prediction. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **MT** & **RF** & **MGGP** \\ \hline Time required for modelling & Building the model: 0.08 s & \multirow{2}{*}{40.5104 s} & 14 min \\  & Testing the models: 0.01 s & & 88 s \\ \hline \(r\) & 0.953 & 0.955 & 0.936 \\ \hline RMSE & 3.871 & 3.584 & 4.453 \\ \hline MAE & 2.341 & 2.032 & 2.546 \\ \hline \hline \end{tabular}  
* The scatter plot for MT, RF and MGGP models in Figures 9–11 show a balanced scatter with no obvious under or over-prediction.  
\end{table} 
Table 4: Performance indicators of the developed models. Figure 9: Scatter plot and hydrograph for MT model. Furthermore, the performance of the model developed using MGGP, MT and RF were compared with the model developed using Artificial Neural Networks, Genetic Programming and Multiple Linear Regression [11]. Tables 4 and 5 allow the comparison of the performance of the models, revealing that tree-based models display greater performance as compared to ANNs, GP and MLR. Standard Random Forest (SRF) is a powerful method for high-dimensional regression and classification. For Random Forest, SRF gives an accurate approximation of the conditional mean of a response variable, revealing that RF provides information about the full conditional distribution of the response variable, not only about the conditional mean. Further conditional quantiles can be inferred with quantile regression forests (QRF)--a generalisation of random forests. Thus, quantile regression forests give a non-parametric and accurate way of estimating conditional quantiles for high-dimensional predictor variables that can be further studied for better predictions and accuracy [43; 44]. The Gaussian  
Figure 11: Scatter plot and hydrograph for MGGP model. Figure 10: Scatter plot and hydrograph for RF model.