# An Alternative Procedure for the Description of Seismic Intensity Parameter-Based Damage Potential
## 3 Results and Discussion
### Testing the Multiple Regression Models  
As previously stated, to verify both models, a set of 30 records out of the 180 was used to test the prediction quality of the three Damage Indices. Considering that the utilized DIs have been thoroughly studied and numerically verified by various researchers [8; 16; 21; 49], the results of the non-linear time-history analyses are treated as a reference solution that is used in comparison with the values obtained by the generated predictive models. The test set comprises ground motion excitations that have induced all degrees of damage to the test frame. The accuracy of the predicted relative to the observed Damage Indices was tested, and the success rate in predicting the correct damage grade (minor, moderate, or severe) that the structure lies in for a given record. The accuracy and success rate of the two Model Sets for both the test and the training sets are shown in Figures 3 and 4, respectively. All cases presented an improvement in prediction accuracy and similar degrees of success in identifying the correct damage grade of the test structure. Figure 3: Prediction Accuracy (%) of the examined models per Damage Index. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **RMSE** & **RMSE** & **Adjusted–R\({}^{2}\)** & **Adjusted–R\({}^{2}\)** & **Adjusted–R\({}^{2}\)** & **Adjusted–R\({}^{2}\)** \\  & **Normalized** & **Maximum** & **Modified** & **Normalized** & **Maximum** & **Modified** \\  & **MISDR** & **Softening** & **Park–Ang** & **MISDR** & **Softening** & **Park–Ang** \\ \hline Model 1.1 & 0.1429 & 0.1191 & 0.1080 & 94.97\% & 94.04\% & 94.00\% \\ Model 2.1 & 0.1223 & 0.0771 & 0.1018 & 96.31\% & 97.50\% & 94.66\% \\ \hline Model 1.2 & 0.1433 & 0.1197 & 0.1121 & 94.94\% & 93.97\% & 93.52\% \\ Model 2.2 & 0.1225 & 0.0804 & 0.1027 & 96.30\% & 97.28\% & 94.57\% \\ \hline Model 1.3 & 0.1419 & 0.1181 & 0.1077 & 95.03\% & 94.13\% & 94.03\% \\ Model 2.3 & 0.1225 & 0.0765 & 0.1011 & 96.30\% & 97.54\% & 94.74\% \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Performance metrics of the statistical models. Model Set 1 presents a minimum of 80.572%, 86.834%, and 80.858% agreement in the Test Set with the Maximum Softening, Normalized MISDR, and Modified Park-Ang DIs computed from the non-linear dynamic analyses, respectively. Model Set 2 had a minimum of 89.803%, 87.564%, and 86.540% agreement with the Maximum Softening, Normalized MISDR, and Modified Park-Ang DIs, respectively. The Maximum Softening and Modified Park-Ang DIs were found to benefit the most concerning the degree of correctness in predicting the observed value. The minimum percentage of correctly identified damage grade in the Test Set were found to be 90.000%, 96.667%, and 93.333% for the Maximum Softening, Normalized MISDR, and Modified Park-Ang, respectively, for the Model Set 1, and 90.000%, 96.667%, 96.667%, respectively, for the Model Set 2. Both Model Sets provide similar levels of reliability in predicting the correct damage grade (minor, moderate, or severe). However, Model Set 2 presents the added benefit of improved accuracy with the same number of explanatory variables. An important observation regarding the case of utilizing the Forward Stepwise Selection is that it provides the same degree of accuracy in predicting both the Damage Index value and the damage grade in which the structure has entered, requiring only three or four predictors, depending on the Damage Index being predicted, allowing for damage potential predictions to be made with only a limited number of Intensity Measures. Figure 5 presents the standard deviation of prediction accuracy that Model Set 1 and Model Set 2 exhibit separately for the test and training subsets.