## 5 Analysis of Results  
The optimum parameters were obtained for the SVM and ANN regression algorithms using an optimum search approach corresponding to the best generalized performance for the trained model based on measured performance criteria, such as the mean square error, as listed in Table 10.  
For the SVM, the model was built using all the data (three types of ultrasonic velocities), and the errors with the target values (core strength) were analyzed for accuracy evaluation. For the ANN, 70% of the total data was used to construct the model, 15% was used for data verification, and 15% was used for testing. The ANN model constructed in this manner was compared with the SVM for the entire data set for comparative evaluation. The prediction accuracies of the SVM and ANN models were evaluated using the correlation coefficient (R), mean absolute error (MAE), mean relative error, and mean squared error (MSE), defined as follows:  
\[\mathrm{R}=\frac{n\sum_{i=1}^{n}y_{i}\cdot\hat{y}_{i}-\left(\sum_{i=1}^{n}y_{i }\right)\left(\sum_{i=1}^{n}\hat{y}_{i}\right)}{\sqrt{\sum_{i=1}^{n}y_{i}^{2}- \left(\sum y_{i}\right)^{2}}\sqrt{\sum_{i=1}^{n}\hat{y}_{i}^{2}-\left(\sum\hat {y}_{i}\right)^{2}}} \tag{14}\]  
\[MAE=\ \frac{1}{n}\sum_{i=1}^{n}\left|y_{i}-\hat{y}_{i}\right| \tag{15}\]  
\[MRE=\ \frac{1}{n}\sum_{i=1}^{n}\frac{\left|y_{i}-\hat{y}_{i}\right|}{y_{i}} \tag{16}\]  
\[MSE=\frac{\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2}}{n} \tag{17}\]  
where y\({}_{i}\) is the target value, \(\hat{y}_{i}\) is the predicted value, and the n is the number of data. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**SVM**} & \multicolumn{2}{c}{**ANN**} \\ \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Bias & 42.75 & Hidden Layers & 1 \\ Box constraint & 9.4885 & Hidden Neurons & 50 \\ Epsilon & 0.9489 & Training function & trainlm \\ Number of & 64 & Epoch & 5 \\ iterations & Kernel & Gaussian & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Optimum parameters of support vector machine (SVM) and ANN models with P-wave velocity. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Div.**} & \multicolumn{3}{c}{**Regression Method**} & \multicolumn{3}{c}{**Mean Square Error**} \\ \cline{2-9}  & **Estimation** & **Estimation** & **Estimation** & **Core** & \multicolumn{3}{c}{**Strength**} \\  & **by Vp** & **by Vs** & **by Vr** & **(MPa)** & **(MPa)** & **by Vp** & **by Vs** & **by Vr** \\ \hline S24D210 & 26.65 & 28.00 & 27.89 & 26.23 & 0.17 & 3.13 & 2.74 \\ S27D400 & 25.00 & 22.59 & 24.20 & 29.44 & 19.73 & 47.02 & 27.52 \\ S30D270 & 32.99 & 34.27 & 34.39 & 31.66 & 1.79 & 6.85 & 7.46 \\ S30D300 & 31.50 & 35.17 & 34.11 & 30.43 & 1.13 & 22.40 & 13.53 \\ S35D210 & 38.47 & 35.20 & 37.62 & 38.81 & 0.12 & 13.02 & 1.42 \\ S35D240 & 35.14 & 36.79 & 36.79 & 37.07 & 3.72 & 0.08 & 0.08 \\ S50D210 & 55.20 & 51.92 & 54.85 & 57.82 & 6.85 & 34.84 & 8.83 \\ S50D240 & 52.65 & 52.98 & 54.13 & 51.71 & 0.88 & 1.62 & 5.87 \\  & & & avg & 4.30 & 16.12 & 8.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Mean squared error of regressions for P-, S-, and R-wave velocities. For the comparison, the SVM and ANN models were constructed with different input variables: (a) P-wave velocity, (b) P- and S-wave velocities, and (c) P-, S-, and R-wave velocities. The output variable was the actual core strength for all the models. After training with the 72 test sample data, all the samples in the testing data set were used to examine the model prediction accuracy. The model prediction results are summarized in Table 11.  
As summarized in Table 11, the correlation did not increase significantly as the number of input variables increased from one to three. However, as the number of variables increased, the prediction accuracy improved more than the correlation. Overall, the SVM and ANN models with three input variables (P-, S-, and R-wave velocities) yielded the best prediction results in terms of the MAE, MRE, and MSE.