## 5 Numerical Validation
If focusing on the criteria between the results from vRTHS and the reference solution, namely the global errors (\(J_{4}\), \(J_{5}\), and \(J_{6}\)) and relative peak errors (\(J_{7}\), \(J_{8}\), and \(J_{9}\)), it can be seen that most of them are less than 5%. This demonstrates that the proposed KF-ADC method enables the RTHS to reliably assess the structural performance under different dynamic loads. Furthermore, it can also be observed that with the increase in the sensitivity of different partitioning schemes, both the global errors and relative peak errors generally tend to increase. However, the maximum value of the criteria \(J_{4}\) to \(J_{9}\) is still acceptable. This indicates that the proposed KF-ADC strategy enables RTHS to obtain reliable results when the partitioning configuration is in the moderately and slightly sensitive regions. To further investigate the robustness of the KF-ADC strategy proposed in this study, the mean and standard deviation of the evaluation criteria for the 240 perturbed vRTHSs are shown in Tables 6 and 7, respectively. By comparing the mean of the nine criteria from the perturbed vRTHSs in Table 6 and those from the nominal vRTHSs in Table 5, similar trends can be observed. The maximum value of the criteria for \(J_{4}\) to \(J_{9}\) is less than 15%. Moreover, based on the standard deviation presented in Table 7, the less sensitive partitioning scheme is preferred in order to obtain more robust RTHS results. However, the standard deviation of the evaluation criteria of each partitioning configuration and load case is generally less than 2% and no more than 3%, which demonstrates that the proposed KF-ADC method exhibits good robustness when uncertainties are considered in the control plant. Figure 12: Evolutions of the estimated system model parameters. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Earthquake Record**} & \multirow{2}{*}{**Case**} & \multicolumn{8}{c}{**Evaluation Criteria**} \\ \cline{3-10}  & & \(J_{1}\) & \(J_{2}\) & \(J_{3}\) & \(J_{4}\) & \(J_{5}\) & \(J_{6}\) & \(J_{7}\) & \(J_{8}\) & \(J_{9}\) \\ \hline \multirow{4}{*}{El Centro} & Case 1 & 0.20 & 1.10 & 1.42 & 3.77 & 2.81 & 3.36 & 3.37 & 2.09 & 2.06 \\  & Case 2 & 0.20 & 1.06 & 1.59 & 3.51 & 2.05 & 3.15 & 3.17 & 1.76 & 1.74 \\  & Case 3 & 0.20 & 0.78 & 1.28 & 4.50 & 3.32 & 4.41 & 4.41 & 3.04 & 3.09 \\  & Case 4 & 0.20 & 0.93 & 1.18 & 5.70 & 3.18 & 5.40 & 5.42 & 2.79 & 2.78 \\  & Case 1 & 0.20 & 1.15 & 1.24 & 2.81 & 1.92 & 2.52 & 2.52 & 1.50 & 1.50 \\  & Case 2 & 0.20 & 1.04 & 1.15 & 3.53 & 2.27 & 3.35 & 3.35 & 1.97 & 2.00 \\  & Case 3 & 0.20 & 1.03 & 1.17 & 3.28 & 2.19 & 3.23 & 3.22 & 1.99 & 1.99 \\  & Case 4 & 0.20 & 1.03 & 1.20 & 4.37 & 2.54 & 4.23 & 4.23 & 2.46 & 2.46 \\  & Case 1 & 0.20 & 1.20 & 1.14 & 3.13 & 2.69 & 2.80 & 2.81 & 2.29 & 2.29 \\  & Case 2 & 0.00 & 1.19 & 0.90 & 2.96 & 2.29 & 2.65 & 2.66 & 1.72 & 1.71 \\  & Case 3 & 0.00 & 1.12 & 0.91 & 3.15 & 1.75 & 3.06 & 3.07 & 1.61 & 1.59 \\  & Case 4 & 0.20 & 0.93 & 1.04 & 4.77 & 4.13 & 4.55 & 4.57 & 3.91 & 3.89 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: vRTHS evaluation criteria for nominal cases.