## 5 Correlation Analysis of \(C_{y}\) and \(T\) on the \(S_{d}\) Ranking
### Analysis of \(S_{d}\) Ranking under Different \(T\) and Same \(C_{y}\) Condition  
When the \(C_{y}\) is constant, the correlation analysis of the \(S_{d}\) ranking under different \(T\) conditions is analyzed, and the calculated results are shown in Figure 5. The ordinate is the correlation coefficient, and the following conclusions can be obtained from the results in the diagram:  
1. In the short-period range (\(T\) < 0.5 s), the correlation coefficients of \(S_{d}\) rankings under different \(C_{y}\) condition is less than 0.8. Especially when the change of \(C_{y}\) is large, the correlation is poor. In the medium- and long-period ranges (\(T\geq 0.5\) s), the correlation coefficient of the \(S_{d}\) ranking under different \(C_{y}\) conditions is higher, and the correlation is very good. When the \(C_{y}\) changes, the \(S_{d}\) values will change, but the variation of the \(S_{d}\) rankings is small. It can be concluded that the damage potential rankings in the short-period range are more sensitive to the change of \(C_{y}\) than that in the medium- and long-period. 2. When the change of \(C_{y}\) is smaller, the larger the correlation coefficient of the corresponding \(S_{d}\) rankings is, the smaller the variation of \(S_{d}\) ranking is. On the contrary, when the difference between the \(S_{d}\) rankings under different \(C_{y}\) conditions is larger, the smaller the correlation coefficient of the corresponding \(S_{d}\) rankings is. Correlation Analysis of the \(S_{d}\) Ranking under Different \(T\) and Same \(C_{y}\) Condition  
When the \(C_{y}\) is constant, the correlation analysis of \(S_{d}\) ranking under different \(T\) conditions is analyzed, and the calculated results are shown in Figures 6 and 7, in which abscissa and ordinates are both \(T\), and different colors represent the value of the \(\rho\). The following conclusions can be drawn from the results:  
1. The variation law of the \(S_{d}\) ranking at different \(T\) is the same. When the \(\Delta T\) of the two periods is small, the \(\rho\) of the corresponding \(S_{d}\) rankings is larger, and the variation of the damage potential ranking is small. On the contrary, when the \(\Delta T\) of the two periods is larger, the \(\rho\) of the corresponding \(S_{d}\) ranking is smaller. Figure 5: Correlation analysis of \(S_{d}\) rankings under different \(C_{y}\) conditions. (**a**) Bilinear model, (**b**) modified Clough model. 2. The \(S_{d}\) rankings are more sensitive to the change of \(T\) in the short-period compared with the medium- and long-period. More periods need to be selected for research in short-period. Comparative Analysis of the Damage Potential Ranking under Specific \(C_{y}\) and \(T\) Condition  
The effect of different \(C_{y}\) and \(T\) on the damage potential ranking is analyzed in detail in this paper, and the degree of influence is mainly reflected by the correlation coefficient of \(S_{d}\) rankings. Based on the two hysteretic models, this section selects the specific \(S_{d}\) ranking results under 12 conditions of different \(C_{y}\) and \(T\) for comparative analysis, and the size of  
Figure 6: Correlation analysis of \(S_{d}\) rankings at different periodic points (Bilinear model). Figure 7: Correlation analysis of \(S_{d}\) rankings at different periodic points (modified Clough model). Figure 9: Comparison of displacement response rankings under different \(C_{g}\) with a constant \(T\). (**a**) Bilinear model (\(T=0.2\) s), (**b**) modified Clough model (\(T=0.2\) s), (**c**) bilinear model (\(T=2.0\) s), (**d**) modified Clough model (\(T=2.0\) s). 1. According to the results of Figure 8 and Table 2, when the \(T\) is equal to 0.8 s and 1.0 s, respectively, with a constant \(C_{y}\) value of 0.6, the corresponding \(\Delta T\) is smaller, and the corresponding damage potential rankings of ground motions have a strong correlation and a smaller discreteness.