## 4 Application of Record Selection Model
When the _MSE_ results are compared in terms of 2D and 3D selection, it can be said that the _MSE_ values determined for 2D analysis models are generally lower than those for 3D models. This situation may be due to stricter constraints in 3D selection. When the average of four sets, as calculated in the right side of Table 2, are  
Figure 11: Selection of three components simultaneously according to the TBEC and soil classes of ZC and ZD (**left**: SRSS spectrum of horizontal GMs; **right**: mean spectrum of selected records in the vertical direction). evaluated it can be said that the \(MSE\) values of vertical sets are lower than 0.09% while the \(MSE\) values of horizontal sets are lower than 1.24%. Comparisons are also made for further investigation for buildings with \(T=0.5\) s considering the different seismic codes using four GM sets, and the \(MSE\) values are computed and provided in Table 3. It can be seen in Table 3 that the maximum \(MSE\) value is 1.321% for the horizontal direction obtained for 3D analysis considering the ZC soil class for EC8. The maximum \(MSE\) value for the vertical direction is 0.349%, which is obtained from 3D analysis considering the ZD soil class for EC8. Similar to \(T=1.0\) s results, the \(MSE\) values determined for 2D analysis models are generally lower than those for 3D models. Considering the diverse period ranges, soil type, spectral shapes, and the stochastic nature of the process used in the solution algorithm, it is expected that the \(MSE\) values will vary for different building periods. Nevertheless, when the \(MSE\) values for \(T=1.0\) s and \(T=0.5\) s are compared, it can be concurrently said that the \(MSE\) values are generally close. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{**Seismic Codes**} & \multicolumn{2}{c}{**1. Set**} & \multicolumn{2}{c}{**2. Set**} & \multicolumn{2}{c}{**3. Set**} & \multicolumn{2}{c}{**4. Set**} & \multicolumn{2}{c}{**Mean**} \\ \cline{2-11}  & **Hor.** & **Ver.** & **Hor.** & **Ver.** & **Hor.** & **Ver.** & **Hor.** & **Ver.** & **Hor.** & **Ver.** \\ \hline TBDY\_2D\_ZC & 0.143 & 0.036 & 0.162 & 0.033 & 0.054 & 0.034 & 0.178 & 0.052 & 0.134 & 0.039 \\ \hline TBDY\_3D\_ZC & 0.126 & 0.036 & 0.232 & 0.033 & 0.177 & 0.048 & 0.131 & 0.069 & 0.166 & 0.046 \\ \hline EC8\_2D\_ZC & 0.607 & 0.068 & 0.279 & 0.045 & 0.860 & 0.083 & 0.310 & 0.063 & 0.514 & 0.065 \\ \hline EC8\_3D\_ZC & 1.566 & 0.070 & 1.417 & 0.060 & 0.843 & 0.069 & 1.113 & 0.050 & 1.235 & 0.062 \\ \hline TBDY\_2D\_ZD & 0.226 & 0.053 & 0.117 & 0.018 & 0.148 & 0.013 & 0.166 & 0.020 & 0.164 & 0.026 \\ \hline TBDY\_3D\_ZD & 0.262 & 0.039 & 0.062 & 0.014 & 0.193 & 0.037 & 0.298 & 0.028 & 0.204 & 0.029 \\ \hline EC8\_2D\_ZD & 0.454 & 0.071 & 0.231 & 0.078 & 0.310 & 0.130 & 0.123 & 0.088 & 0.280 & 0.091 \\ \hline EC8\_3D\_ZD & 0.990 & 0.047 & 0.614 & 0.059 & 1.251 & 0.127 & 1.488 & 0.069 & 1.086 & 0.076 \\ \hline \end{tabular}
\end{table} 
Table 2: The \(MSE\) values (units in percentage) of the sets for \(T=1.0\) s.  
Figure 12: Selection of three components simultaneously according to EC8 and the soil classes of B and C (**left**: SRSS spectrum of horizontal GMs; **right**: mean spectrum of selected records in the vertical direction). Although the calculated _MSE_ values in earlier examples are low, it should be reminded that the standard deviation (or record-to-record variability) of selected GMs was not considered (Figures 9-12) for uni- and bi-directional selection since compatibility between the individual spectra of selected GMs and the target spectra was ignored in code-based selection. Accordingly, record-to-record variability is obvious [6, 20, 37, 59]. On the other hand, the proposed model can control the variability of the records in both directions even for code-based target spectra. As can be seen in Figures 13 and 14, individual spectra are between considered constraints (e.g., 2- and 0.5-times the target spectra) within the predefined period range.