## 3 DATA Preparation for the Developed Model  
Three data files were generated and used to develop the final ML model. Each data file is described below. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & **Variables** & **Mean** & **Median** & **Dispersion** & **Min.** & **Max.** \\ \hline \multirow{8}{*}{Independent} & \(f_{c}\) (MPa) & 60.8 & 56 & 0.568 & 11.6 & 145.1 \\ \cline{2-7}  & _h/w_ & 1.96 & 2 & 0.407 & 1 & 3 \\ \cline{2-7}  & Shape (1) & 2.14 & 2 & 0.41 & 1 & 3 \\ \cline{2-7}  & \(S_{\text{max}}\) & 0.805 & 0.8 & 0.0977 & 0.457 & 0.95 \\ \cline{2-7}  & \(R\) & 0.180 & 0.118 & 0.795 & 0.0143 & 0.667 \\ \cline{2-7}  & \(f\) (Hz) & 8.46 & 5 & 2.70 & 0.0625 & 150 \\ \hline Dependent & Log\(N\) & 5.10 & 3.55 & 0.537 & 0.699 & 6.78 \\ \hline \hline \end{tabular} (1) Since shape is a categorical variable, the statistical features expressed in the table may not be meaningful.  
\end{table} 
Table 1: Statistical features of original data. 1. ORIGINAL DATA. These are data used in [PERSON]'s paper, directly collected by the authors from papers [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. The full-data spreadsheet is available in the Supplementary Materials. These are used as the reference data for this study. A total of 1298 data were collected, and statistical features such as the mean, median, dispersion, minimum, and maximum values of independent and dependent variables are summarized in Table 1. The ORIGINAL DATA were grouped by the same input variable value. 2. DATA Excluding OUTLIERS. If there are outliers in the group, these are the data created after removing them. These data are used as a basis for determining the average value after removing the outliers. A total of 1252 data were generated. Statistical features such as the mean, median, dispersion, minimum and maximum values of independent and dependent variables are summarized in Table 2.
3. AVERAGE DATA Excluding OUTLIERS. These are the data created by averaging the grouped data after excluding outliers from among the grouped data. In this process, the total number of data was reduced to 310. Statistical features such as the mean, median, dispersion, minimum and maximum values of independent and dependent variables are summarized in Table 3.  
Tables 1-3 illustrate the statistical analysis of variables, showing the numerous mathematical descriptions of the input and output values for each data set. Tables 4-6 describe the data process in which parts of the data from reference [5] are used to illustrate the process more clearly as an example. Table 4 represents a part of the grouped data in which data sets with the same input variable value, but with different output variable values, are grouped together. Table 4 consists of two groups. Group 1 is a data set with an\(f_{c}\) value of 56 MPa, _h/w_ value of 1, shape value of 1, \(S_{\text{max}}\) value of 0.85, R value of 0.3, and f value of 4 Hz, but with different output values \(N\). Group 2 is a data set with an\(f_{c}\) value of 56 MPa, _h/w_ value of 1, shape value of 1, \(S_{\text{max}}\) value of 0.85, R value of 0.3, and \(f\) value of 1 Hz, but with different output values \(N\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & **Variables** & **Mean** & **Median** & **Dispersion** & **Min.** & **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}  & \(R\) & 0.180 & 0.118 & 0.794 & 0.0143 & 0.667 \\ \cline{2-6}  & \(f\) (Hz) & 8.48 & 5 & 2.70 & 0.0625 & 150 \\ \hline Dependent & Log\(N\) & 5.05 & 3.51 & 0.523 & 0.699 & 6.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistical feature of data excluding outliers. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & **Variables** & **Mean** & **Median** & **Dispersion** & **Min.