## 3 Results
### Test of MLA Trained with All Training Dataset (Case-1)  
After training the MLA using the 2991 training dataset, the algorithm was tested with a 1288 testing dataset (Case-1). The verification results were summarized using the analysis method introduced in Section 3.1 and are presented in Table 2. Figure 3 shows the relationship between the ratios of the measured value to the predicted value (ratio of \(f^{\prime}_{c,meas}\) to \(f^{\prime}_{c,pred}\), hereinafter \(\gamma\)) and the measured value. The mean (\(m\)) and CV of the data were found to be 1.00 and 0.28. However, as shown in the graph, there was a linear relationship where \(\gamma\) increased with \(f^{\prime}_{c,meas}\). To analyze this tendency in detail, it was classified into different compressive-strength ranges, and the \(m\), CV, RMSE, MAPE, and MAE of each range are presented in Table 2. The m and CV of \(\gamma\) and RMSE, MAPE, and MAE in the range of 7-20 MPa are 0.7, 0.22, 10.23 MPa, 8.76 MPa, and 51.0%, respectively. \(m\) increases as the \(f^{\prime}_{c,meas}\) range value increases, and the m of \(\gamma\) at 30-40 MPa was 0.96, which was the closest to 1, followed by the m of \(\gamma\) in the 40-60 MPa range (\(m=1.09\)). The RMSE, MAPE, and MAE of the 30-40 MPa range were 8.86 MPa, 7.58 MPa, and 20.96%, respectively. Among the different strength ranges, this range had the smallest RMSE and MAPE. The RMSE, MAPE, and MAE of the 40-60 MPa range were 9.54 MPa, 7.99 MPa, and 16.52%, respectively; this range had the best MAE index among the different \(f^{\prime}_{c,meas}\) ranges. These ranges had the highest accuracy because 51% of the training dataset were included in them. Based on only the analysis result from Case-1, the results indicate that the algorithm estimates \(w_{i}\) values with priority given to the range having the largest number of training datasets in the regression analysis. Figure 4 presents the normal distribution \(\gamma\) based on the mean \(m\) and \(\sigma\) calculated based on all the training datasets (Case-1). As shown, the frequency increased as \(\gamma\) approached 1, indicating that there were many cases in which the error between the measured and predicted values was small. The \(\gamma\)-value of the 95% confidence interval was 0.45-1.55. This suggests that if the MLA is trained using all the training datasets, the predicted values with an error rate of approximately 55% will be included in 95% of the result values. The \(\gamma\)-value of the 90% confidence interval was 0.53-1.47. The error rate was approximately 47%. The \(\gamma\)-value of the 80% confidence interval was 0.63-1.37, and the error rate was approximately 37%. Therefore, if the MLA is trained using a wide range of training datasets, the accuracy and reliability of the prediction can be reduced. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **All Data** & \multicolumn{6}{c}{**Range of \(f^{\prime}{}_{c,meas}\)**} \\ \hline  & **4279** & **7–20 MPa** & **20–30 MPa** & **30–40 MPa** & **40–60 MPa** & **60–80 MPa** & **80–100 MPa** \\ \hline Training & \multirow{2}{*}{2991} & 189 & 675 & 680 & 842 & 420 & 185 \\ dataset & & (6.3\%) & (22.6\%) & (22.7)\% & (28.2\%) & (14.0\%) & (6.2\%) \\ \hline Test dataset & \multirow{2}{*}{1288} & 86 & 297 & 282 & 348 & 183 & 92 \\  & & (6.7\%) & (23.1\%) & (21.9\%) & (27.0\%) & (14.2\%) & (7.1\%) \\ \hline mean (\(m\)) & 1.00 & 0.70 & 0.77 & 0.96 & 1.09 & 1.21 & 1.36 \\ \hline \(\sigma\) & 0.28 & 0.15 & 0.16 & 0.23 & 0.22 & 0.23 & 0.22 \\ \hline CV & 0.28 & 0.22 & 0.21 & 0.23 & 0.20 & 0.17 & 0.16 \\ \hline RMSE (MPa) & 12.30 & 10.23 & 10.32 & 8.86 & 9.54 & 15.32 & 25.00 \\ \hline MAE & \multirow{2}{*}{9.98} & \multirow{2}{*}{8.76} & \multirow{2}{*}{9.28} & \multirow{2}{*}{7.58} & \multirow{2}{*}{7.99} & \multirow{2}{*}{12.95} & \multirow{2}{*}{22.45} \\ (MPa) & & & & & & & \\ \hline MAPE (\%) & 25.2 & 51.00 & 36.6 & 20.96 & 16.52 & 18.43 & 24.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Analysis accuracy of ML trained with \(f^{\prime}{}_{c,meas}\) in all ranges.