# Bridge Health Monitoring via Displacement Reconstruction-Based NB-IoT Technology
## 3 Bridge Health Monitoring Experiment
### Small-Scale Bridge with Vibration Induced by Passing Vehicle
#### 3.1.2 Level 1 Detection Using Frequency  
From 10 experiments of each scenario, statistics of the fundamental frequency are shown in Table 8. The fundamental frequency is calculated using the direct fast Fourier transform (FFT). Mean, Maximum, and Minimum among 10 experiments are presented. It is shown that frequencies are changed accordingly due to varied vehicle speeds and masses. The increasing vehicle can reduce the fundamental frequency while increasing vehicle mass tends to decrease fundamental frequency. In addition, the position of the vehicle also could affect the mass matrix of the entire bridge, resulting in a different frequency. For the current state, this study only reports the phenomena found in our small scale experiment; no further statement is concluded for other small scale or real bridge conditions. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Original Bridge**} & \multicolumn{4}{c}{**Stiffened Bridge**} \\ \hline \multirow{3}{*}{**Mode**} & \multicolumn{4}{c}{**Frequency Statistical Properties (Hz)**} & \multicolumn{4}{c}{**Frequency Statistical Properties (Hz)**} \\ \cline{2-9}  & **Max.** & **Min.** & **Mean** & **cov** & **Max.** & **Min.** & **Mean** & **cov** \\ \hline
1 & 3.733 & 3.733 & 3.733 & 0 & 3.867 & 3.867 & 0 \\
2 & 15.067 & 14.933 & 14.987 & 0.005 & 14.533 & 14.533 & 14.533 & 0 \\
3 & 32.000 & 29.600 & 30.800 & 0.037 & 31.867 & 30.667 & 31.493 & 0.015 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Bridge frequency for the first three modes. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Firequency Mode 1 Statistical Properties (Hz)**} \\ \cline{2-5}
**Scenario** & **Max.** & **Min.** & **Mean** & **cov** \\ \hline LVB0S1 & 4.027 & 3.973 & 4.002 & 0.004 \\ LVB0S2 & 3.978 & 3.822 & 3.9 & 0.021 \\ LVB0S3 & 3.927 & 3.293 & 3.58 & 0.073 \\ HVB0S1 & 4.069 & 3.997 & 4.02 & 0.008 \\ HVB0S2 & 3.964 & 3.809 & 3.871 & 0.021 \\ HVB0S3 & 3.894 & 3.622 & 3.821 & 0.031 \\ LVB1S1 & 4.057 & 4.003 & 4.035 & 0.005 \\ LVB1S2 & 3.994 & 3.864 & 3.97 & 0.01 \\ LVB1S3 & 3.931 & 3.84 & 3.883 & 0.01 \\ HVB1S1 & 4.086 & 3.908 & 3.979 & 0.011 \\ HVB1S2 & 3.956 & 3.801 & 3.816 & 0.013 \\ HVB1S3 & 3.925 & 3.623 & 3.847 & 0.029 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Fundamental frequency for each case. 3.1.3. Level 1 Detection Using Reconstructed Displacements  
This subsection introduces the results of the Level 1 detection using reconstructed displacements explained in Section 2.1. As described, both MEMS accelerometers and LVDT are used for measurement, as shown in Figure 10a; comparisons between two devices are conducted to validate the accuracy of the proposed approach. Figures 14 and 15 (top) shows the measured accelerations using MEMS for scenarios of LVB0S1 and LVB0S3, respectively. Figures 14 and 15 (bottom) shows the displacements from LVDT and reconstructed displacement using MEMS for scenarios of LVB0S1 and LVB0S3, respectively. It is shown that reconstructed displacement is almost identical to those of LVDT. Note that noise has been filtered out in the reconstructed displacements. Figure 13. Windowed FFT of LVB0S3. As shown in Figure 10, three accelerometers are attached to the bridge. To demonstrate the proposed approach, the mean value of _RMSD_s between original and stiffened bridges in the H1 direction is compared with those of the H2 direction. Figure 16 shows the mean _RMSD_s in H1 and H2 directions for (a) original (Cases 1 to 6) and (b) stiffened bridge (Cases 7 to 12). Points No. 1 and No. 5 represent the two ends of the test bridge, while points No. 2, No. 3, and No. 4 represent the sensor location at the first, second, and third quarters of the bridge. Figure 16 (top) clearly shows that the shapes created by the _RMSD_ value have no significant change between H1 and H2 directions since both plots have identical conditions (only the cart moving direction is opposite). Level 1 damage indicator between H1 and H2 directions is less than \(5\times 10^{-3}\).