## 5 Numerical Simulations
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Earthquake** & **Control Case** & \(J_{1}\) & \(J_{2}\) & \(J_{3}\) & \(J_{4}\) & \(J_{5}\) & \(J_{6}\) & \(J_{7}\) & \(J_{8}\) & \(J_{9}\) \\ \hline \multirow{2}{*}{A1} & Passive-max & **0.88** & 0.92 & **0.61** & 1.00 & 1.40 & **0.63** & **0.70** & 1.29 & 0.85 \\  & SHFLC & 0.94 & **0.90** & 0.70 & **0.96** & **1.26** & 0.69 & 0.83 & **1.10** & **0.79** \\ \hline \multirow{2}{*}{A2} & Passive-max & **0.95** & 1.00 & 0.75 & 1.08 & **0.89** & **0.65** & **0.83** & **0.79** & **0.85** \\  & SHFLC & 0.98 & **0.94** & **0.72** & **0.94** & 0.98 & 0.64 & 0.86 & 0.92 & **0.85** \\ \hline \multirow{2}{*}{A3} & Passive-max & **0.83** & **0.93** & **0.41** & 1.29 & 0.99 & 0.66 & **0.46** & 0.92 & 0.84 \\  & SHFLC & 0.88 & 0.95 & 0.62 & **0.95** & **0.93** & **0.66** & 0.65 & **0.81** & **0.89** \\ \hline \multirow{2}{*}{A4} & Passive-max & **0.61** & **0.68** & **0.35** & 1.14 & 1.74 & 0.57 & **0.54** & 1.46 & 0.76 \\  & SHFLC & 0.79 & 0.76 & 0.47 & **1.09** & **1.30** & **0.39** & 0.66 & **1.21** & **0.77** \\ \hline \multirow{2}{*}{B1} & Passive-max & 0.82 & 0.85 & **0.67** & 1.14 & 1.31 & 0.89 & **0.72** & 1.13 & **0.89** \\  & SHFLC & **0.72** & **0.75** & 0.81 & **1.07** & **1.16** & **0.89** & 0.81 & **0.95** & 0.81 \\ \hline \multirow{2}{*}{B2} & Passive-max & **0.94** & 0.94 & **0.54** & **0.95** & 1.52 & 0.81 & **0.63** & 1.36 & 0.60 \\  & SHFLC & 0.95 & **0.95** & 0.54 & **0.95** & **1.02** & **0.68** & 0.66 & **0.91** & **0.64** \\ \hline \multirow{2}{*}{B3} & Passive-max & 0.98 & 1.01 & 0.63 & **1.14** & 0.97 & **0.67** & **0.70** & 0.81 & **0.82** \\  & SHFLC & **0.89** & **0.89** & **0.62** & **0.94** & **0.81** & 0.78 & 0.83 & **0.66** & 0.78 \\ \hline \multirow{2}{*}{B4} & Passive-max & **0.96** & **0.97** & **0.52** & **1.00** & 1.33 & 0.85 & 0.66 & 1.12 & 0.45 \\  & SHFLC & 0.99 & 0.99 & **0.52** & 1.07 & **1.20** & **0.53** & **0.62** & **1.01** & **0.59** \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance indices for various control cases under pulse-type near-fault earthquakes. Figure 9: Peak base displacement of controlled base-isolated structure subjected to earthquakes. Although the SHFLC also increases the peak floor acceleration with respect to the uncontrolled structure under most of the earthquakes, the SHFLC can successfully limit the increase in peak floor accelerations for the selected earthquakes. For example, for A4, B2, C2, and D2 earthquakes, maximum passive operation of PFD increases peak floor acceleration (\(J_{5}\)) by 74%, 52%, 29%, and 37%, respectively, while SHFLC increases these responses by 30%, 2%, 3%, and 14%. Additionally, the SHFLC case can lead to obvious decreases in RMS floor acceleration (\(J_{8}\)) for most of the selected earthquakes. In addition, it can be seen that the SHFLC case can reduce peak and RMS base displacements for most of the selected earthquakes, which indicates the effectiveness of the proposed control strategy subjected to different types of earthquakes. According to the definition of performance indices, \(J_{3}\), \(J_{5}\), \(J_{7}\) and \(J_{8}\) for the uncontrolled base-isolated structure are equal to 1. In order to graphically compare the control effectiveness of maximum passive control case and the developed SHFLC case with the uncontrolled case for peak and RMS base displacements and floor accelerations, Figures 10 and 11 show the difference between the performance indices \(J_{3}\), \(J_{5}\), \(J_{7}\) and \(J_{8}\) for control cases and the performance index 1 for uncontrolled case. The vertical coordinate of these figures is the difference between the performance indices and 1, a negative value indicates that the structural response is reduced relative to the uncontrolled structure, and a positive value illustrates that the structural response is amplified relative to the uncontrolled structure. The absolute value of the vertical coordinate is the proportion of the reduction or amplification.