# A Data-Driven Model for Predictive Modeling of Vortex-Induced Vibrations of a Long-Span Bridge
## 1 Introduction  
With the rapid development of the economy, long-span bridges as important traffic-connection links receive more and more recognition and become a developing trend in the field of transportation. With the increasing span, the structure of the bridge is of increasing flexibility and is more and more sensitive to the wind environment [1, 2, 3]. A long-span bridge can undergo different kinds of wind-induced loadings under various wind environments [4, 5, 6, 7, 8, 9, 10]. One typical wind-induced vibration is vortex-induced vibration (VIV). When the frequency of the vortex shedding generated by the wind passing through the bridge girder is close to a certain natural frequency, the vortex-excited force that is of the same frequency can stimulate the resonance of the bridge girder. VIV events have been observed on several long-span bridges, such as the Volgograd Bridge in Russia [11], the Trans-Tokyo Bay Crossing Bridge [6] in Japan and so on. Compared to the buffeting, the amplitude of the dynamic response of VIV is usually larger [9]. Although vortex-induced vibration does not necessarily lead to catastrophic consequences, it will seriously affect the fatigue life of the structure and may also lead to the loss of the expected functionality of the structure [12]. Therefore, it is of great importance to conduct research on the vortex-induced vibration of a bridge girder. Researchers have proposed semi-empirical methods to describe vortex-induced vibrations where aerodynamic parameters are introduced to represent aerodynamic stiffness andaerodynamic damping. Typical semi-empirical theoretical models are the wake oscillator model [13; 14] and the single-degree-of-freedom model [15; 16]. The wake oscillator model takes the motion of the structure and the wake flow into consideration at the same time in the form of a pair of coupled equations. The single-degree-of-freedom model, on the other hand, models the vortex-induced load as the aeroelastic term in the dynamic equation, by which the corresponding expression is more intuitive and practical [17]. However, as a complex phenomenon of wind-bridge interaction, vortex-induced vibration is difficult to be modeled comprehensively using semi-empirical approaches [18]. As a complicated aerodynamic phenomenon, modeling VIV events involves modeling aerodynamic forces and the wind-bridge interaction. To predict the VIV response of a full-scale bridge using a physical model, modal and aerodynamic characteristics and the corresponding wind field are needed, which are difficult to obtain. Further, modal characteristics obtained with the finite element model can be inaccurate because of the modeling error, and aerodynamic characteristics obtained with wind-tunnel tests can be inaccurate when the real wind field is a nonuniform and has a larger Reynolds number. Therefore, physical models can have high computational demand and have difficulty in obtaining accurate predictions. Advanced data-driven methods, on the other hand, can be an alternative. Advanced data-driven methods such as neural networks model the dynamic mechanism of the system by mining the relationship embedded in the data of the input and output [19; 20]. Without the limitation of various assumptions, data-driven methods can be more flexible and more easily capture the complex mechanism such as seismic demand [21], vehicle-bridge interaction [22] and the aerodynamic system [23; 24; 25; 26]. Some research has been conducted in the field of parameter identification. [PERSON] et al. [27] used the standard Scanlan linear single-degree-of-freedom aerodynamic equation for modeling the vortex-induced vibration of a bridge girder. [PERSON] et al. [28] obtained the modal characteristics and aerodynamic characteristics of the structure by minimizing the negative log-likelihood function method. However, little research has been conducted on the prediction of dynamic responses of VIV events of full-scale bridge girders, which can aid the management of the bridge. [PERSON] et al.