# Automatic Identification of Bridge Vortex-Induced Vibration Using Random Decrement Method
## 3 Numerical Simulation
### VIV Identification Using RDT  
In order to obtain the dynamic responses of the system, the Gaussian white noise excitation with zero mean was applied to the three masses firstly, and then the acceleration response of the three masses was calculated. The sampling frequency was 100 Hz and the sampling time was 1300 s. Next, the periodic vortex-induced force was simulated by harmonic excitation, \(F=(5\)-\(7\times 10^{-4})\sin(2\pi f_{1}t)\). The harmonic excitation was changed every 200 s to simulate the change of wind speed. Applying the harmonic force on \(m_{2}\) and considering noise at the same time. The sampling time was 600s. Finally, the Gaussian white noise excitation with zero mean value was applied to each mass unit again. The sampling time was 4100 s. The three segments were combined to simulate the whole process of vortex vibration, which was 6000 s totally. The load information of the three stagesis listed in Table 1 and the acceleration signal is shown in Figure 6.  
Figure 5: Three-degree-of-freedom (DOF) system consisting of spring and damper. Figure 6: Time history of acceleration response at \(m_{2}\). In above figure, the signals of 0-1300 s and 1900-6000 s were the response signals caused by white noise excitation, and the signals from 1300 to 1900s were the response signals of \(m_{2}\) under the harmonic excitation with noise (0.03 SNR, signal-to-noise ratio). The overall data was divided into a series of segments, and the length of each segment has a length of 120 s. The parameter used in RDT was as follows: the interception \(A=1.0\times\sigma\), the length of RD is about 35 s (corresponding to 30 cycles). If the data length is too short, it is difficult to perform meaningful RDT; on the other hand, the false negative rate of detecting VIV will increase if the data length is too long. After applying RDT for each segment, the COV of peak value of processed data were then calculated. The result was shown in Figure 7. Based on the calculated COV of peak in each segment of buffeting responses, and the threshold value was determined as \(d_{\mathrm{c}}=0.1822\). When the COV was smaller than the threshold value, the signal was regarded as VIV. The COV for the data during 1320-1900 s was significantly less than the threshold, thus they were identified as VIV. The identification results of VIV were shown in Table 2. It was shown that the vibration type was correctly identified except for the data during 1200-1320 s. It can be seen from the Table 2 that since 100 s buffeting signal and 20 s VIV signal were contained in 1200-1320 s, the identification result was random vibration. During 1800-1920 s, which contained 100s VIV signal and 20 s buffeting signal, the identification result was VIV. The time interval can be appropriately adjusted, and the results of different time intervals can be combined to determine the VIV occurrence period. Since the SNR can influence the identification result, the harmonic excitation with different SNR was applied to this three-DOF system, and the segment of 1320 to 1920 s was selected to further study. The SNR was changed from 0.001 to 0.03, and the simulation was repeated 1000 times at each SNR level. The number of segments identified as vortex-induced vibration was then divided by 1000, and named as the identification ratio. It can be seen in Figure 8 that the identification ratio was lower than \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time** & **Actual Situation** & **Identification Results** \\ \hline
0–1200 s & R* & R \\
1200–1320 s & R-V & R \\
1320–1800 s & V* & V \\
1800–1920 s & V-R & V \\
1920–6000 s & R & R \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of identification results with actual situation.