## 5 Accuracy Evaluation  
The accuracy of the proposed tree-based models is deeper assessed in this section through performance metrics and Taylor diagrams.  
The most common performance metrics utilized for assessing the reliability prediction models are the \(R^{2}\)-score, \(R\), RMSE, MSE, MAPE, and MAE [51]. As could be seen in Equations (1)-(6), the mentioned parameters are all based on the difference between the predicted value and corresponding actual value.  
\[R^{2}=\frac{\sum\limits_{i}{(\hat{y}_{i}-\frac{1}{n}\frac{n}{1}y_{i})^{2}}}{ \sum\limits_{i}{(y_{i}-\frac{1}{n}\frac{n}{1}y_{i})^{2}}} \tag{1}\]  
\[R=\frac{\sqrt{\frac{\sum\limits_{i}{(\hat{y}_{i}-\frac{1}{n}\frac{n}{1}y_{i})^{ 2}}}{\sum\limits_{i}{(y_{i}-\frac{1}{n}\frac{n}{1}y_{i})^{2}}}}}{\sum\limits_{ i}{(y_{i}-\frac{1}{n}\frac{n}{1}y_{i})^{2}}} \tag{2}\]  
\[\text{RMSE}=\sqrt{\frac{1}{n}\frac{n}{1}\frac{n}{(\hat{y}_{i}-y_{i})^{2}}} \tag{3}\]  
\[\text{MSE}=\frac{1}{n}\frac{n}{1}{(\hat{y}_{i}-y_{i})^{2}} \tag{4}\]  
\[\text{MAE}=\frac{1}{n}\sum\limits_{1}^{n}\lvert\hat{y}_{i}-y_{i}\rvert \tag{5}\]  
\[\text{MAPE}=\frac{1}{n}\sum\limits_{1}^{n}\left\lvert\frac{\hat{y}_{i}-y_{i}} {y_{i}}\right\rvert \tag{6}\]  
Table 3 reports the performance metrics of the developed prediction models. As noted previously, the ultimate strain values predicted by the DT model (R\({}^{2}\) = 0.89) were slightly more accurate than those of the RF model (R\({}^{2}\) = 0.85). It should be explained that the RF method is claimed to lead to more reliable results compared to the DT model. However, this statement was concluded for when the same database is used for training and testing, whereas in this study, the training and testing databases were selected randomly. In other words, the training and testing datasets used for the DT and RF models were not the same and therefore caused the insignificant accuracy difference [52]. Briefly noted, both the DT and RF models demonstrated acceptable accuracy, with R\({}^{2}\) scores higher than 85%.  
In order to compare the R\({}^{2}\) scores and RMSE of the proposed prediction models more easily, they are shown in the Taylor diagram in Figure 8. It is worth stating that a Taylor diagram is a two-dimensional space in which predicted and actual values are positioned based on their coordination. The horizontal and vertical axes, circular lines, and radial lines reflect the standard deviation, RMSE, and R\({}^{2}\)-score, respectively. The distance of each mode to the actual value represents the model's accuracy [30]; the closer to the actual database a prediction model is, the more reliable it will be. According to the schematic illustration made in Figure 8, the DT model with the higher R\({}^{2}\)-score and standard deviation and lower  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & **R\({}^{2}\)** & **R** & **RMSE** & **MSE** & **MAE** & **MAPE** \\ \hline DT & 0.89 & 0.94 & 1.38 & 1.90 & 1.04 & 23.25 \\ \hline RF & 0.85 & 0.92 & 1.68 & 2.82 & 1.29 & 19.72 \\ \hline \end{tabular}
\end{table}
Table 3: Performance metrics for the prediction models.  
RMSE was positioned closer to the actual values (blue star) and thus was slightly more reliable than the RF model.