## 4 Experiments
### Experimental Model and Damage Cases  
The performance of the EKF for damage identification was verified by a five-story steel frame experiment. Three different damage cases were considered with the corresponding experimental models shown in Figure 11. Case 1 represents the intact case with no damage occurred. However, in cases 2 and 3, certain extents of damages were introduced to the 5 th and 4 th stories, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**2\% Noise**} & \multicolumn{2}{c}{**5\% Noise**} & \multicolumn{2}{c}{**10\% Noise**} \\ \hline  & **Gaussian** & **Non-Gaussian** & **Gaussian** & **Non-Gaussian** & **Gaussian** & **Non-Gaussian** \\ \hline \(k_{1}\) & \(-0.008\) & \(0.024\) & \(-0.018\) & \(-0.360\) & \(0.554\) & \(0.744\) \\ \(k_{2}\) & \(-  
In the damage design, the stiffness reduction was simulated by reducing the cross section area of the columns. In terms of this steel frame, the story stiffness was composed by the lateral stiffness of 4 steel bars. Hence, the theoretical stiffness of each story can be calculated by the following equation:  
\[k_{i}=4\frac{12 EI}{l^{3}}(i=1,2,3,4,5) \tag{24}\]  
where \(k_{i}\) is the stiffness of \(i^{\text{th}}\) story; \(E\) is the elastic modulus of the bar and equal to 2.06 \(\times\) 10\({}^{5}\) N/mm\({}^{2}\); \(I\) is the moment of inertia and equal to \(bh^{3}/12\); \(I\) is the height of each story and equal to 350 mm.  
Columns with three different sizes were considered as shown in Figure 12, consistent with the three damage cases. Then, the damage case 2 was achieved by replacing the columns of 5 th story. The same action was made to the 4 th story to realize the damage case 3. Columns' parameters of theoretical and actual story stiffness are tabulated in Table 2. Considering the manufacturing error of the steel bars as well as the installing effect, the static test method was further developed to determine the actual story stiffness with steel bars of three different sizes. In each story, there were four columns and their sizes were assumed to be the same.  
For the intact case (case 1), all columns had the size of specification 1. Structural damage was then introduced by replacing the initial columns with the thinner columns (specification 2 or 3) so that the story stiffness was decreased. The details of the three damage cases can be found in Table 3. Actually, the damage degree, which was defined as the reduction extent of the story stiffness in this paper, of each case is 0%, 10.5%, and 22.7%, respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Specification** & **Size (mm)** & **Theoretical Story** & **Measured Actual Story** \\  & & **Stiffness (N/mm)** & **Stiffness (N/mm)** \\ \hline
1 & 350 \(\times\) 40 \(\times\) 4 & 49.20 & 47.17 \\
2 & 350 \(\times\) 36 \(\times\) 4 & 44.28 & 42.22 \\
3 & 350 \(\times\) 32 \(\times\) 4 & 39.36 & 36.48 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The parameters of the steel column bars and the story stiffness.  
Figure 12: Three specifications of the steel bars in the experiment.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Damage Cases** & **Initial Stiffness** & **Damaged Stiffness** & **Damage Location** & **Damage Degree (\%)** \\ \hline Case 1 & 47.17 & 47.17 & None & 0 \\ Case 2 & 47.17 & 42.22 & 5 th story & 10.5 \\ Case 3 & 47.17 & 36.48 & 4 th story & 22.7 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The details of damage cases.