## 5 Analysis of Results
For the MAE, which mainly measures the performance of the machine learning, the error was reduced by more than 50% when three variables were used instead of one variable in the SVM and ANN models. Compared with the linear regression, there was no significant difference between the SVM and ANN with one variable (P-wave velocity). Thus, more types of ultrasonic velocities, rather than the predictive method, can provide a more accurate prediction. Relative comparisons between the SVM and ANN showed a 4.13% improvement in the MSE when three variables were used. Figure 9 shows the correlation between the actual and predicted strengths. Both SVM and ANN can make good predictions, also the SVM was more highly correlated with the actual strength than the ANN, and it was more concentrated on the equality line. Figure 10 shows the ratio of the predicted value to the actual value. The data from the SVM model was closer to a ratio of 1 than that of the ANN model, and the data was highly concentrated. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Method**} & \multicolumn{2}{c}{**SVM**} & \multicolumn{3}{c}{**ANN**} \\ \hline
**Input Variable** & **Vp** & **Vp, Vs** & **Vp, Vs, Vr** & **Vp** & **Vp, Vs** & **Vp, Vs, Vr** \\ \hline Correlation coefficient(R) & 0.985 & 0.991 & 0.994 & 0.984 & 0.989 & 0.993 \\ MAE & 1.581 & 1.218 & 1.072 & 1.666 & 1.359 & 0.987 \\ MRE & 0.044 & 0.033 & 0.029 & 0.048 & 0.037 & 0.027 \\ MSE & 3.864 & 2.404 & 1.719 & 4.071 & 2.832 & 1.790 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: SVM and ANN model prediction accuracy. Figure 9: Correlation of predicted to measured concrete strength using the SVM and ANN models. (a) SVM; (b) ANN. The accessibility of predicted strength by SVM and ANN into the target strength is presented in Figure 11, and there was less data variance for the SVM model than the ANN model. Understanding the nonlinearity of the predicted model was difficult owing to the lack of data in the 50-60 MPa range. The predicted and measured strengths exhibited abrupt changes above 50 MPa, and thus, the ability of the model to simulate the nonlinearity at normal and high strengths is important. In Figure 12, the empirical cumulative distribution function provided by MATLAB was applied to the predicted data, and a \(\pm\)25% deviation was plotted. First, it was confirmed that below 50 MPa, the data were below the distribution curve, and above 50 MPa, they were above this curve. This was because the velocities of the ultrasonic waves changed significantly from 50 MPa because of the change in the mechanical properties between the normal and high strengths. The convergence efficiency and prediction accuracy of the ANN method for the data variables are shown in Figure 13. It was confirmed that convergence was faster, and the MSE (performance) decreased as the number of ultrasonic velocity types increased. Although the prediction accuracy for the validation and test data sets is large due to the limited number of data and nonlinearity of concrete, the differences of prediction in validation and test data sets are greatly reduced and the accuracy is greatly increased with Vp, Vs, and Vr. Figure 11: Tracking of measured concrete strength by SVM and ANN. (**a**) SVM; (**b**) ANN. Figure 10: Distribution of predicted strength to test strength ratios. (**a**) SVM; (**b**) ANN. This study analyzed the performances and accuracies of the SVM and ANN models with three types of ultrasonic velocities. As in previous studies, the SVM was more accurate than the ANN because of the inherent drawbacks of the ANN, such as the slow convergence, less generalizable performance, tendency to find only local minima, and over-fitting problems. The generalization of the developed model was difficult owing to the nonlinearity in the normal- and high-strength concrete,  
Figure 12: Predicted data distributions by SVM and ANN within a \(\pm\)25% deviation from the empirical cumulative distribution curve of the test data. (**a**) SVM; (**b**) ANN.