# Inter-Story Drift Ratio Detection of High-Rise Buildings Based on Ambient Noise Recordings
## 4 Results and Analysis
### Results and Analysis of Deflection Function Fitting  
The obtained data set of \(\Delta\theta_{1}\) and the height of the corresponding station were imported into MATLAB in order to fit the derivative function of the deflection function, and its corresponding expression was determined as follows:  
\[f(x)=7.795\times 10^{-9}x^{3}-7.453\times 10^{-7}x^{2}-2.106\times 10^{-6}x+2.584 \times 10^{-6} \tag{6}\]  
where \(x\) is the distance from the ground to the calculation point and \(f(x)\) is the derivative of the deflection function.  
The deflection function expression can be obtained by integrating its derivative function, as shown below:  
\[\rho(x)=1.949\times 10^{-9}x^{4}-2.484\times 10^{-7}x^{3}+1.053\times 10^{-6}x^{ 2}-2.584\times 10^{-6}x \tag{7}\]  
where \(x\) is the distance from the ground to the calculation point and \(\rho(x)\) is the function of deflection. Its curve is shown in Figure 7.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Floor** & \(\Delta\theta_{1}\)\({}^{c}\) & **Height/m** & \(\Delta\theta_{1}\) \\ \hline
0 & 0 & 0 & 0 \\
13 & \(-\)0.054757 & 56 & \(-\)0.00096 \\
16 & \(-\)0.09 & 70 & \(-\)0.00157 \\
17 & \(-\)0.07 & 74 & \(-\)0.00122 \\
18 & \(-\)0.020511 & 78 & \(-\)0.00036 \\
20 & \(-\)0.032471 & 88 & \(-\)0.00057 \\
21 & \(-\)0.021921 & 92 & \(-\)0.00038 \\ \hline \end{tabular}
\end{table}
Table 1: Results for the polarization parameters.  
In Figure 7, the overall deflection was close to 0 at floors near the ground, increasing rapidly in the middle floors and slowing down in the high-rise floors. The maximum drift occurring at the 21 st floor was 0.06 m. The deflection curve is consistent with the theoretical model of the building's horizontal deformation under a wind load.  
As described in Section 2, generally, the analyzed structure is a frame structure with a viscous damping support system [18]. Its idealized deformation has the following characteristics [19]: (1) the deformation is small near the ground; (2) the deformation grows rapidly in the middle floors; and (3) the deformation increases slowly at high-rise floors and peaks at the highest point. The deflection curve in Figure 7 satisfies this description. However, at high-rise floors, although the deflection curve had a trend to slow down, it was still growing rapidly. This is because the structure of the Zhonghe Building is not completely the same as the ideal structure proposed by [PERSON]. In the Zhonghe Building, the flexural deformation is unignorable, maintaining the growth of the upper floor's drift according to the angular slope of the lower floors, even at high-rise floors. Therefore, the fitted deflection curve can be considered consistent with the result of current mainstream theoretical models for the structure of the Zhonghe Building.  
In Figure 7, the change in the growth rate of deflection represents the change in IDRs. If IDRs increase, the calculated floor will be more inclined than the floor below, making the deflection growth rate increase quickly. If IDRs decrease, the calculated floor will be only slightly more inclined than the floor below, making the deflection growth rate increase slowly. However, deflection always increases as long as IDRs are positive. With these conclusions, Figure 7 shows that the deflection grew rapidly at floors 1-15, so the IDRs will increase in this range; the deflection grew slowly at floors 16-21, so the IDRs may decrease in this range.  
In addition, the total drift was 0.06 m from the 21 st floor to the ground with a height of 98 m, so the total IDR between the 21 st and ground floors can be calculated as \(6.122\times 10^{-4}\). The IDR limit in the Technical Specification for Concrete Structures of Tall Building of China (JGJ3-2010) [4] is 1/550 and approximately \(1.818\times 10^{-3}\), which is obviously larger than the  
Figure 7: Diagram of deflection curve.  
total IDR. The structural health of the Zhonghe Building is preliminarily qualified through the examination of the total IDR.