## 3 DATA Preparation for the Developed Model
** & **Max. ** \\ \hline \multirow{6}{*}{Independent} & \(f_{c}\) (MPa) & 60.7 & 56 & 0.570 & 11.6 & 145.1 \\ \cline{2-6}  & _h/w_ & 1.97 & 2 & 0.406 & 1 & 3 \\ \cline{2-6}  & Shape & 2.14 & 2 & 0.41 & 1 & 3 \\ \cline{2-6}  & \(S_{\text{max}}\) & 0.805 & 0.8 & 0.0988 & 0.457 & 0.95 \\ \cline{2-6}  & \(R\)  
To designate whether there are outlier data in each group, four commonly used outlier detection methods [70,71] were performed. If three or more of them were designated as an outlier, they were excluded from the data. The four methodologies are as follows:  
1. Outlier detection method using [PERSON]'s criterion;
2. Outlier detection method using [PERSON]'s criterion;
3. Outlier detection method using Thompson-Tau criterion;
4. Outlier detection method using IQR (inter quartile range) criterion. We performed all four of these methodologies on each group of data to determine which values were detected as outliers. All four of these outlier detection methodologies detected the N value of 22,570 (see Table 4) as an outlier for the Group 1 data. On the other hand, for the data in Group 2, the N value of 1571 (see Table 4) was detected as an outlier only by the Thompson-Tau methodology, but was not detected as an outlier by the other three methodologies. Table 5 represents the grouped data in which the data set with an N value of 22,570 is removed from Group 1. Even after removing outliers, the values of different output variables are recorded as experimental values in the same input variable values. With these data, it is difficult to make an accurate prediction model as long as the current input variables are maintained. One must suppose that the user predicts a function of \(y=\sin(x)\). If several different values of the y experimental value for the \(\sin(x)\) value are matched when x = 30, it will be difficult to create an ML model that predicts the \(\sin(x)\) function. Therefore, in the case of grouped data having the same input variable value and different output variable values to eliminate this situation, the average value of all other output variable values is obtained. One average value is used as the output value for the same specific input variable value. This should provide more reasonable data for creating predictive ML models. Table 6 represents the average grouped data in Table 5.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Group** & \(f_{\epsilon}\) **(MPa)** & _h/w_ & **Shape** & \(S_{\max}\) & \(R\) & \(f\) **(Hz)** & \(N\) \\ \hline
1 & 56 & 1 & 1 & 0.85 & 0.3 & 4 & 8411 \\ \hline
1 & 56 & 1 & 1 & 0.85 & 0.3 & 4 & 821 \\ \hline
1 & 56 & 1 & 1 & 0.85 & 0.3 & 4 & 2485 \\ \hline
1 & 56 & 1 & 1 & 0.85 & 0.3 & 4 & 1660 \\ \hline
1 & 56 & 1 & 1 & 0.85 & 0.3 & 4 & 13,020 \\ \hline
1 & 56 & 1 & 1 & 0.85 & 0.3 & 4 & **22,570** \\ \hline
1 & 56 & 1 & 1 & 0.85 & 0.3 & 4 & 9521 \\ \hline
1 & 56 & 1 & 1 & 0.85 & 0.3 & 4 & 4192 \\ \hline
1 & 56 & 1 & 1 & 0.85 & 0.3 & 4 & 170 \\ \hline
1 & 56 & 1 & 1 & 0.85 & 0.3 & 4 & 1578 \\ \hline
1 & 56 & 1 & 1 & 0.85 & 0.3 & 4 &Figure 1 depicts the relative frequency distributions of the six input variables and one output variable. The shape variable is not only a numerical variable, but also a categorical variable. In the model, shape = 1 is represented as a cube, shape = 2 as a prism, and shape = 3 as a cylinder. Since the numbers are meaningful in determining the category, (d) in Figure 1 can be changed to (e), which is more suitable for normal distribution. The \(f\) variable appears to be unsuitable for normal distribution, since some high-frequency values of 10 Hz exist in the data. The \(f\) variable appears to be unsuitable for normal distribution, since some high-frequency value of 10 Hz exist in the data. If these high-frequency data are removed, the rest of the data are much more suitable for normal distribution in Figure 1.  
The relationships between various independent variables and log\(N\) are plotted in Figure 2. Although not strong, one linear relationship is identified in Figure 2a (log\(N\) vs. \(S_{\text{max}}\)).