## 5 Measurement Equipment and Testing Setup
### The Building Strengthening and Upgrading Stages
This increase is caused by the upgrading, as the mass of the building significantly increases because of the addition of three new floors. Experimental values of the building natural vibration periods corresponding to the first four eigen modes are presented in Table 3. As mentioned above (Section 4), the eigen modes were obtained by the FFT of the recorded building's vibrations under the natural combination of different dynamic loads, like traffic, wind, etc. The dynamic loading vector is random and constantly changes its direction. In this case, the building response in the main direction corresponds to forced vibration under the external loading. Table 3 shows that experimental values of natural vibration periods are lower compared with the calculated ones (Table 2). This can be explained by the fact that the original building was constructed at a period when there was no seismic design code. There is no detailed design documentation of the building that would allow for the calculation of its exact stiffness. The stiffness of the structural elements was estimated according to modern codes. This means that the real stiffness may be higher (as it follows from the experimental data). Therefore, the numerical values of the building's dynamic parameters can be interpreted just as the qualitative ones, compared with experimental results. Correspondingly, the building's strengthening design as well as its upgrading should be based on experimental data. At the same time, based on the experimental results, the dominant natural vibration period increases in stage 1, compared with stage 0, and decreases from stage 1 to stage 5. After that, the dominant vibration period values increase, i.e., like in the case of numerical values, the tendencies are similar. This demonstrates the qualitative correspondence of the experimental and numerical results. A comparison of numerical and experimental values of the natural vibration periods is presented in Figures 6 and 7. As expected, the lowest values in the dominant natural vibration periods correspond to stage 5, representing the building with the highest \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Stage**} & \multicolumn{8}{c}{**Mode**} \\ \cline{2-10}  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline
0 & 0.574 & 0.569 & 0.362 & 0.167 & 0.162 & 0.115 & 0.092 & 0.089 & 0.068 & 0.067 \\
1 & 0.582 & 0.580 & 0.366 & 0.169 & 0.163 & 0.116 & 0.093 & 0.090 & 0.069 & 0.068 \\
2 & 0.521 & 0.498 & 0.346 & 0.159 & 0.154 & 0.113 & 0.089 & 0.086 & 0.068 & 0.067 \\
3 & 0.396 & 0.380 & 0.271 & 0.122 & 0.118 & 0.089 & 0.072 & 0.070 & 0.056 & 0.051 \\
4 & 0.281 & 0.268 & 0.197 & 0.099 & 0.093 & 0.074 & 0.070 & 0.066 & 0.054 & 0.028 \\
5 & 0.204 & 0.182 & 0.137 & 0.099 & 0.095 & 0.075 & 0.039 & 0.035 & 0.028 & 0.022 \\
6 & 0.216 & 0.186 & 0.133 & 0.054 & 0.049 & 0.037 & 0.027 & 0.025 & 0.020 & 0.020 \\
7 & 0.279 & 0.240 & 0.167 & 0.069 & 0.060 & 0.045 & 0.034 & 0.031 & 0.024 & 0.024 \\
8 & 0.341 & 0.292 & 0.205 & 0.087 & 0.075 & 0.057 & 0.043 & 0.038 & 0.029 & 0.028 \\
9 & 0.381 & 0.326 & 0.227 & 0.101 & 0.087 & 0.065 & 0.051 & 0.044 & 0.035 & 0.034 \\
10 & 0.432 & 0.369 & 0.252 & 0.109 & 0.094 & 0.070 & 0.055 & 0.048 & 0.038 & 0.037 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical values of natural vibration periods of the building, T\({}_{mm}\) [s]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Stage**} & \multicolumn{4}{c}{**Mode**} \\ \cline{2-5}  & **1** & **2** & **3** & **4** \\ \hline
0 & 0.315 & 0.260 & 0.167 & 0.123 \\
1 & 0.383 & 0.289 & 0.161 & 0.120 \\
2 & 0.360 & 0.261 & 0.184 & 0.124 \\
3 & 0.330 & 0.230 & 0.162 & 0.108 \\
4 & 0.298 & 0.221 & 0.171 & 0.101  
stiffness. The tendencies in varying natural vibration periods are similar for numerical and experimental data. Moreover, after completing the strengthening and upgrading, the experimental and numerical values of the dominant vibration period are similar (0.399 s and 0.432 s, respectively).