# Tree Based Approaches for Predicting Concrete Carbonation Coefficient
## 4 Results and Discussion  
This section presents the developed models and their performance in testing (i.e., for 30% of the unseen data) and discusses the results. The number of rules (equations) developed for MT is 6. Figure 4 displays the decision tree of the model and the identification of the leaves' equations, with these being presented in Equation (1). \[ \begin{split} k=2.0647\times w/b-0.0317\times fc-0.1763\times RH+3. 7078\times CO-0.4215\times X+18.2778\\ \text{LMnum}:2\\ k=1.1429\times w/b-0.1064\times fc-0.0014\times RH+1.4393\times CO-0.4 215\times X+9.3049\\ \text{LMnum}:3\\ k=-0.0584\times fc+0.0051\times RH+1.9178\times CO-1.3093\times X+8. 3759\\ \text{LMnum}:4\\ k=-0.2653\times fc-0.4663\times RH+0.0849\times CO-0.1624\times X+60. 371\\ \text{LMnum}:5\\ k=4.8709\times w/b+44.1425\times fc-0.0335\times RH+0.0536\times CO-0. 1624\times X+3102.7607\\ \text{LMnum}:6\\ k=6.4793\times w/b-0.0291\times fc-0.0335\times RH+0.0536\times CO-0. 1624\times X+35.0456\\ \text{Numberofrules}:6\\ \end{split}  \tag{1}\] \begin{table}
\begin{tabular}{c c} \hline
**MGGP Parameters** & **Parameter Settings** \\ \hline Population size & 500–900 \\ Number of generations & 200–500 \\ Selection method & Tournament \\ Tournament size & 13–15 \\ Cross-over rate & 0.78–0.84 \\ Mutation rate & 0.14–0.20 \\ Termination criteria & 500 generation or fitness value less than 0.00 \\  & whichever is earlier. \\ Maximum number of genes and tree depth & 4–5 \\ Mathematical operations & +, \(-\), \(\times\), /, sin, cos, exp, \(\surd\), \(\parallel\) \\ \hline \end{tabular}
\end{table} 
Table 2: Parameter setting for MGGP. Concerning the MT model, when new data are presented, the first step is to analyse the CO\({}_{2}\) content, i.e., to check whether \(CO\) is \(\leq\)3 or \(>\)3. If \(CO\) is \(>\)3, the next branch is selected, and it is again determined whether the \(CO\) value is \(\leq\)15 or \(>\)15. If it is \(\leq\)15, the LM 4 equation can be used for the prediction of \(k\). Each variable at each node is analysed by estimating the expected decrease in error. The variable that is selected for separating maximises the expected error reduction at that node. The decision criteria rely on CO\({}_{2}\) levels, \(w/b\) ratios and compressive strength, corresponding to their higher significance. Furthermore, despite the empirical/statistical nature of the model, it is interesting to notice a positive association of \(k\) with \(w/b\) ratio and with CO\({}_{2}\) content, while the association between k and \(RH\) is varying, which is in tune with the fundamental knowledge on concrete carbonation. In general, the negative influence of \(X\) and \(fc\) is observed through their negative coefficients. Random Forest (RF) has the unique characteristic of splitting the data randomly and building decision trees and further bagging or averaging the values. This feature of RF stands out in these models' families and can be also stated as non-linear modelling technique. Random Forest displays the output in terms of the regression trees developed. Random Forest has a unique characteristic of splitting the data randomly and building decision trees and further bagging or averaging the values. This feature of RF stands out in these models' families and can be also stated as a non-linear modelling technique. The splitting starts with the randomly selected parameters and determines which parameter value would lead to the \"best split\" i.e., the least MSE (mean squared error) as its objective or cost function, which needs to be minimised--in this case MSE. The output values at the end of each tree are subjected to averaging. Such a regressor can be useful for a set of equally well-performing models in order to offset their individual weaknesses and can also be called ensemble prediction. RF has the characteristic of the selection of parameters that are highly influential in predicting the output. The permutation feature importance is defined as the reduction in a model result when a single variable value is arbitrarily rearranged.