# A Data-Driven Model for Predictive Modeling of Vortex-Induced Vibrations of a Long-Span Bridge
## 3 Data Description
It should be noted that vertical vibration is the main form of vortex-induced vibration of the investigated bridge, and the relationship among the amplitudes of vertical acceleration of different sections is similar to the modal shape of the investigated bridge. Therefore, only vertical accelerations of \(1/2\) span of the main span are used. The corresponding vertical velocities and displacements of different sections are calculated by integration in the frequency domain. In addition, to make the time resolution of the wind speed data consistent with that of the acceleration data, both wind speed data and acceleration data are down-sampled to 2 Hz. After the preprocessing, a dataset that consists of 31 VIV events of 0.33 Hz for validating the proposed model is built. The specifics of the dataset can be summarized as follows. The built dataset contains both wind characteristics and vibration characteristics. The wind  
Figure 4: A typical VIV event: (**a**) x-direction wind component at the \(1/4\) span of the main span; (**b**) y-direction wind component at the \(1/4\) span of the main span; (**c**) time history of the vertical acceleration of \(1/2\) span of the main span; (**d**) power spectrum of the vertical acceleration of \(1/2\) span of the main span. characteristics consist of wind speeds and angles of direction at \(1/4\) and \(3/4\) span of the main span, and the vibration characteristics consist of vertical acceleration, velocity and displacement of \(1/2\) span of the main span. The time resolution of the wind characteristics and vibration characteristics is the same, which is \(0.5\) s. The summary of statistics of the 31 events is shown in Table 1. A wind rose plot of 31 VIV events is shown in Figure 5 (the red line is the axis of the investigated bridge), where the blue color indicates the wind characteristics and the red color indicates the bridge. Histograms of the duration time and amplitude of VIV events are shown in Figure 6.  
As shown in Table 1 and Figure 5, in these 31 events, the angle of direction of the wind is mostly perpendicular to the axis of the investigated bridge. It can also be seen that VIV \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Duration** & **Mean Wind Speed** & **Angle of Direction** & **Maximum Amplitude** \\
**(min)** & **(m/s)** & **(\({}^{\circ}\))** & **(cm)** \\ \hline
48.39 & 9.67 & 137.07/315.47 & 6.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The summary of statistics of the 31 events. Figure 5: Wind rose plot of VIV events. Figure 6: Histograms of duration time and amplitude of VIV events: (**a**) histogram of duration time; (**b**) histogram of amplitude. events can happen under wind scenarios of either direction. The range of mean wind speed is between 8 and 12 m/s, and most mean wind speed is concentrated around 10 m/s. As shown in Table 1 and Figure 6a, the range of duration times of VIV events is between 20 to 160 min, and the duration time of most VIV events is less than 80 min. As shown in Table 1 and Figure 6b, the range of amplitudes of VIV events is between 2 to 12 cm. Both VIV events of large amplitude and those of small amplitude are possible to happen. It can be concluded that the processed dataset contains VIV events of various wind characteristics and various vibration characteristics. The data that are used to validate the proposed model consist of 31 monitored VIV events of 0.33 Hz. The dataset is randomly split by VIV event to guarantee the continuity of individual events that can have various lengths. The training set consists of 18 VIV events (97,200 data points in total), the validation set consists of 6 VIV events (50,400 data points in total) and the testing set consists of 7 VIV events (32,400 data points in total). Four different metrics are employed to evaluate the trained model. Three of them, which are mean absolute error (MAE), root-mean-square error (RMSE) and weighted mean absolute percentage error (WMAPE), are employed to evaluate the point-to-point error.