# An Alternative Procedure for the Description of Seismic Intensity Parameter-Based Damage Potential
## 3 Results and Discussion
### Training the Multiple Regression Models
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Intensity Measure** & **Model 1.1** & **Model 1.2** & **Model 1.3** & **Model 2.1** & **Model 2.2** & **Model 2.3** \\ \hline Housner Intensity & \(-0.00315\) & \(-0.00396\) & \(-0.00327\) & \(-0.03584\) & \(-0.03541\) & \(-0.03617\) \\ \(\mathrm{S}_{\rm a,avg}\) & 2.14631 & 2.27422 & 2.09444 & 1.61169 & 2.01052 & 1.60807 \\ Specific Energy Density & \(-3.55\times 10^{-7}\) & - & - & 0.00082 & 0.00079 & 0.00088 \\ Velocity Spectrum Intensity & \(-0.00046\) & - & - & \(-0.02279\) & \(-0.06588\) & - \\ \(\mathrm{PGV}\) & 0.00101 & 0.00147 & - & 0.06651 & - & - \\ \(\mathrm{S}_{\rm v,T1}(5\%)\) & 0.00207 & - & 0.00172 & \(-0.03221\) & - & - \\ \(\mathrm{S}_{\rm a,T1}(5\%)\) & 1.28091 & - & - & \(-9.87011\) & - & \(-9.96924\) \\ \(\mathrm{S}_{\rm d,T1}(5\%)\) & \(-0.04399\) & - & \(-0.00987\) & 3.02685 & - & 3.03894 \\ Sustained Maximum & \(0.00210\) & 0.00317 & 0.00214 & \(-0.36318\) & - & \(-0.36436\) \\ Velocity RMS & 0.00644 & - & 0.00881 & 0.18342 & - & 0.19688 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Regression model coefficients for the Maximum Softening Damage Index. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Intensity Measure** & **Model 1.1** & **Model 1.2** & **Model 1.3** & **Model 2.1** & **Model 2.2** & **Model 2.3** \\ \hline Housner Intensity & \(-0.00233\) & \(-0.00388\) & \(-0.00277\) & \(-0.01671\) & - & - \\ \(\mathrm{S}_{\rm a,avg}\) & 2.56422 & 2.43042 & 2.45724 & 1.66802 & 1.18412 & 1.18412 \\ Specific Energy Density & \(0.00000\) & \(4.30\times 10^{-6}\) & 3.91\(\times\)\(10^{-6}\) & 0.00925 & 0.00826 & 0.00826 \\ Velocity Spectrum Intensity & \(-0.00133\) & 0.00119 & - & 0.00560 & - & - \\ \(\mathrm{PGV}\) & 0.00100 & - & - & 0.01069 & - & - \\ \(\mathrm{S}_{\rm v,T1}(5\%)\) & 0.00361 & - & 0.00226 & 0.00840 & - & - \\ \(\mathrm{S}_{\rm a,T1}(5\%)\) & 11.08590 & - & - & 2.94016 & - & - \\ \(\mathrm{S}_{\rm d,T1}(5\%)\) & \(-0.30221\) & - & \(-0.01104\) & \(-0.81300\) & - & - \\ Sustained Maximum & \(0.00011\) & - & - & \(-0.26576\) & \(-0.14961\) & \(-0.14961\) \\ Velocity RMS & 0.00282 & - & - & 0.12614 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Regression model coefficients for the NMISDR Damage Index. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Intensity Measure** & **Model 1.1** & **Model 1.2** & **Model 1.3** & **Model 2.1** & **Model 2.2** & **Model 2.3** \\ \hline Housner Intensity & \(-0.00084\) & - & - & 0.06351 & 0.04842 & 0.07174 \\ \(\mathrm{S}_{\rm a,avg}\) & 0.84262 & 0.48282 & 1.09999 & 0.29184 & - & - \\ Specific Energy Density & \(0.00001\) & \(0.00001\) & \(0.00001\) & \(0.00119\) & \(0.00136\) & \(0.00129\) \\ Velocity Spectrum Intensity & \(-0.00196\) & - & \(-0.00180\) & \(-0.28076\) & \(-0.08295\) & \(-0.20725\) \\ \(\mathrm{PGV}\) & 0.00014 & - & - & 0.08743 & - & - \\ \(\mathrm{S}_{\rm v,T1}(5\%)\) & 0.00330 & - & 0.00277 & 3.16888 & - & 2.70311 \\ \(\mathrm{S}_{\rm d,T1}(5\%)\) & \(-11.95520\) & - & \(-0.36320\) & \(-51.95980\) & - & \(-45.04080\) \\ \(\mathrm{S}_{\rm d,T1}(5\%)\) & 0.29622 & - & - & 46.97820 & - & 40.80560 \\ Sustained Maximum & \(0.00199\) & \(0.00207\) & \(0.00212\) & \(0.02463\) & - & - \\ Velocity RMS & 0.00099 & - & - & \(-0.04007\) & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Regression model coefficients for the DI\({}_{\rm PA}\) Damage Index. The calculation time is nearly instant in both Model Sets; hence, the computational efficiency of the proposed Model Set 2 is considered on par with that of the conventional Model Set 1. While both Model Sets present comparable computational costs in terms of computation time, the proposed models provide increased accuracy in the numerical value of the predicted DI (accuracy of prediction) and comparable results in the predicted value being within the limits of the correct damage grade (success rate in damage grade identification).