## 3 Numerical Simulation
### Results of Numerical Simulation
To realize the second purpose of the simulation, three different cases of reduced structural stiffness were selected, which are outlined as follows: (1) 30%, 30%, and 65% reductions in stiffness on the first, second, and third floors, respectively (case 6); (2) 30%, 65%, and 65% reductions in stiffness on the third, fourth, and fifth floors, respectively (case 7); (3) 65%, 30%, and 65% reductions in stiffness on the fifth, sixth, and seventh floors, respectively (case 8). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Damaged Floor** & **Health Index** & **Evaluated Health Index** & **Error (\%)** \\ \hline
1F & & 1 & 0.996 & 0.4\% \\ \hline
2F & & 1 & 0.958 & 4.2\% \\ \hline
3F & ✓ & 0 & 0.006 & 0.6\% \\ \hline
4F & ✓ & 0 & 0.004 & 0.4\% \\ \hline
5F & & 1 & 0.835 & 16.5\% \\ \hline
6F & & 1 & 0.977 & 2.3\% \\ \hline
7F & & 1 & 0.997 & 0.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Diagnosis result of damage for the third floor and the fourth floor (case 3). Figure 10: Health index of damage from the fourth floor to the seventh floor. Figure 9: Health index of damage from the first floor to the third floor. * The case of low damaged floors: the stiffness of the first, second, and third floors was reduced to 70%, 70%, and 35%, respectively. The results for case 6 are detailed as follows: The damage conditions were set as irregular because the stiffness loss was assumed to be 30%, 30%, and 65%. The evaluated HI appeared to be close to the target value (Table 9). Furthermore, the ANN-based algorithm could appropriately estimate the HI (Figure 11). Only an 18.1% error was observed for the second floor. * The case of middle damaged floors: the stiffness of the third, fourth, fifth floors are reduced to 70%, 35%, and 35%, respectively. The results for case 7 are detailed as follows: The evaluated HI values appeared to be close to the target values (Table 10). The HI values for all floors were close to the target values (Figure 12). * The case of high damaged floors: the stiffness of the fifth, sixth, seventh floors are reduced to 35%, 70%, and 35%, respectively. The results for case 8 are detailed as follows: The maximum error observed for this case was only 4.4% and others are even minor. (Table 11) Therefore, the system successfully identified the damage. (Figure 13) In summary, the results obtained from the assessment of SHM system reliability reveal that the system has certain sensitivity to detect the location and level of damage. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Stiffness Reduction** & **Health Index** & **Evaluated Health Index** & **Error (\%)** \\ \hline
**1F** & k & 1 & 0.984 & 1.6\% \\ \hline
**2F** & k & 1 & 1.044 & 4.4\% \\ \hline
**3F** & k & 1 & 0.988 & 1.2\% \\ \hline
**4F** & k & 1 & 1 & 0\% \\ \hline
**5F** & k*35 & 0.35 & 0.371 & 2.1\% \\ \hline
**6F** & k*0.7 & 0.7 & 0.689 & 1.1\% \\ \hline
**7F** & k*0.35 & 0.35 & 0.361 & 1.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Diagnosis result of damage on the high floors (case 8). Figure 11: Health index of damage on the low floors. Figure 12: Health index of damage on the middle floors.