# An Alternative Procedure for the Description of Seismic Intensity Parameter-Based Damage Potential
## 3 Results and Discussion
### Comparison of the Proposed Methodology with Predictions Obtained Through Compound IM  
The validity verification of the proposed methodology is carried out by comparing Model Set 2 with models that utilize Compound IMs (CIMs) generated using Canonical Correlation Analysis (CCA) [19]. An analytical discussion on the method of CCA-generated CIMs can be found in the cited literature [19]. The CIM for the 10 selected IMs is calculated through CCA for each DI (Normalized MISDR, Maximum Softening, and Modified Park-Ang). Since the CIM is related to only one DI at a time, to enable direct comparison with the proposed methodology, it is evident that the compound Engineering Demand Parameter (EDP) coincides with the DI of choice, i.e., the Normalized MISDR, the Maximum Softening, and the Modified Park-Ang DIs. After the Canonical Correlation Analysis in the logarithmic scale, the CIM and the DI are reverted to the original scale. A conventional regression analysis is carried out to obtain a relationship between the CIM and the DI in the same form as the proposed methodology, i.e., \"DI = a \(\cdot\) CIM\" (hereby referenced as the CCA Model). The calculated prediction equations for the Normalized MISDR, Maximum Softening, and Modified Park-Ang DIs are shown in Equations (9)-(11).  
\[\text{NMISDR}=0.00760519\cdot\text{IM}_{\text{CCA}} \tag{9}\]  
\[\delta_{\text{M}}=1.39787\times 10^{10}\cdot\text{IM}_{\text{CCA}} \tag{10}\]  
Figure 5: Standard deviation of the prediction accuracy (%) of the examined models per Damage Index.  
\begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline \hline \multirow{3}{*}{**Model**} & \multirow{3}{*}{**Average Prediction Accuracy: Test Set**} & \multicolumn{3}{c}{**Average of Success Rate of Correctly Identified Damage Grade: Test Set**} & \multicolumn{3}{c}{**Average of Success Rate of Prediction Accuracy: Test and Training Sets**} \\  & & & **Average** & **Success Rate of Correctly Identified** & **Average** & **Success Rate of Prediction Accuracy: Test and Training Sets** \\  & & **Prediction Accuracy: Test Set** & **Average** & **Success Rate of Correctly Identified** & **Success Rate of Correctly Identified** & **Success Rate of Correctly Identified** & **Success Rate of Correctly Identified** \\  & & **Accuracy: Test Set** & **Training Set** & **Damage Grade: Test Set** & **Damage Grade: Training Set** & **Test and Training Sets** & **Damage Grade: Test and Training Sets** \\ \hline Model 1.1 & 83.05\% & 78.73\% & 94.44\% & 92.22\% & 80.89\% & 93.33\% \\ Model 2.1 & 88.59\% & 82.46\% & 94.44\% & 93.56\% & 85.53\% & 94.00\% \\ \hline Model 1.2 & 84.06\% & 78.39\% & 94.44\% & 91.56\% & 81.22\% & 93.00\% \\ Model 2.2 & 87.97\% & 81.58\% & 96.67\% & 91.56\% & 84.77\% & 94.11\% \\ \hline Model 1.3 & 83.01\% & 78.81\% & 94.44\% & 92.44\% & 80.91\% & 93.44\% \\ Model 2.3 & 88.26\% & 82.37\% & 94.44\% & 93.33\% & 85.32\% & 93.89\% \\ \hline \hline \end{tabular}
\end{table}
Table 10: Averages of prediction accuracy and successful categorization in the correct damage grade.  
It can be observed that Model Set 2 provides better structural damage grade prediction. Especially in the case of Maximum Softening, the difference in prediction accuracy and success rate is significant. This difference can be attributed to various factors, such as the nature of the specific DI and the differences in the two approaches. Thus, Model Set 2 utilizes a linear combination of modified IMs to predict the damage grade directly; in contrast, the CCA Model utilizes a single Compound IM to relate to the observed damage.