# A Data-Driven Model for Predictive Modeling of Vortex-Induced Vibrations of a Long-Span Bridge
## 3 Data Description  
The proposed model is validated using the monitoring data of a long-span suspension bridge. A comprehensive monitoring system is equipped on the investigated bridge, and the layout of the sensors for wind and girder vibration which are the main concern of our study is shown in Figure 3. To monitor the wind speed, three pairs of three-dimensional ultrasonic anemometers are installed on the 1/4, 1/2 and 3/4 span of the main span, where each pair consists of an anemometer installed at the upriver side and an anemometer installed at the downnriver side. The measurement range, resolution and sampling frequency of the anemometers are 0-60 m/s, 0.01 m/s and 32 Hz, respectively. To monitor the acceleration of the bridge deck, 4 sets of uniaxial accelerometers are installed on the 1/2 span of the side span and the 1/4, 1/2 and 3/4 span of the main span, where each set consists of an accelerometer at the upriver side monitoring vertical acceleration and two accelerators installed at the downnriver side monitoring vertical and lateral acceleration. The measurement range, sensitivity and sampling frequency of the anemometers are \(\pm\)2 g, 2.5 V/g and 50 Hz, respectively. Monitoring data from 2010 to 2015 are used to build a database of VIV events of a full-scale bridge. The investigated bridge has suffered from a number of vortex-induced vibration events during the last few years. The VIV events are identified with a clustering-based identification method [10; 27]. In the identified VIV events, different mode frequencies are observed, which are 0.18 Hz, 0.28 Hz, 0.33 Hz, 0.38 Hz, 0.44 Hz and 0.50 Hz. Among these different modes, the number of VIV events of 0.33 Hz is 31, while the numbers of VIV events of other frequencies are all less than 15. Therefore, to take the amount of data into consideration, the monitoring data of VIV events of 0.33 Hz are collected as the dataset to validate the proposed model. A typical VIV event is shown in Figure 4, where the blue color indicates the time series and the red color indicates the power spectrum density (PSD). Figure 3: The layout of equipped sensors for wind and girder vibration. As shown in Figure 4, the power spectrum of acceleration has only one significant frequency of 0.33 Hz, and the envelope of the time history of acceleration varies slowly with time. Compared to buffeting events, VIV events tend to have larger and slowly changing amplitude. As for wind speed, it can be found that the main trend of the wind speed component also varies with time, while certain wind fluctuations are contained. The wind fluctuations may influence the model's sensitivity to the change in the trend of wind speed. Therefore, the trend of wind speed is extracted using wavelet filtering, where a db5 wavelet is employed and the decomposition number is 10. In addition, acceleration data are filtered to eliminate other possible main frequencies other than 0.33 Hz. The collected data are then processed as follows. For the wind speed data, the instantaneous horizontal wind speed \(U\) and the angle of direction \(\theta\) at different sections are calculated from the monitored wind components of the corresponding anemometer as follows [12; 18]:  
\[U=\sqrt{u_{x}^{2}+u_{y}^{2}} \tag{16}\]  
\[U=\arcsin(u_{x}/U) \tag{17}\]  
where \(u_{x}\) and \(u_{y}\) are the x-direction and the y-direction wind components in the horizontal plane, respectively. It should be noted that the instantaneous wind speed and the corresponding angle of direction at the \(1/2\) span of the main span are not used because of the influence of the main cable, and only the wind characteristics at the \(1/4\) and \(3/4\) span of the main span are used. For the girder vibration data, the vertical acceleration, lateral acceleration and torsional acceleration of different sections are calculated from the monitored acceleration components of the corresponding accelerators.