# A Data-Driven Model for Predictive Modeling of Vortex-Induced Vibrations of a Long-Span Bridge
## 5 Conclusions  
In this paper, we propose a machine learning-based model for predicting vortex-induced vibrations of a full-scale long-span suspension bridge. Different from previous research, this paper focuses on predicting the time history of the dynamic response, with which the characteristics of amplitude, phase and frequency can then be obtained. In the proposed model, gated recurrent unit neural network is selected as the basic module for its outstanding capacity to handle sequences. Fully connected neural networks are employed to generate the initial hidden-state vectors of the GRU neural network to enhance its generalization to structures with an arbitrary initial state. The Newmark-beta method is introduced into the model to utilize the relationship among acceleration, velocity and displacement to better manage the evolution of the dynamic response and enhance the interpretability of the proposed model. A novel weighted form of mean square error loss function is proposed and applied to help the model put more emphasis on the dynamic response of large amplitude, with which the trained model can predict the vortex-induced vibration of large amplitude more accurately.  
The proposed model is validated on the monitored VIV events of a long-span suspension bridge. The WMAPE and PCC of the trained model on the testing set indicate that the trained model can predict the amplitude and the phase of the dynamic response of the vortex-induced vibration accurately. Typical predictions of VIV events indicate that the trained model can make accurate predictions of VIV events of various shapes and amplitudes. Furthermore, an analysis of the physical meaning of the middle output and the effectiveness of WMSE is conducted. Middle outputs are convergent to certain patterns, but their physical meanings are deviated from the pre-designed roles, which demands the introduction of more knowledge about the underlying mechanism. WMSE is proven to be effective in training the proposed model. Future research is needed to enhance long-time prediction and interpretability.  
Conceptualization, Y.W., H.F. and S.L.; methodology, Y.W., H.F. and S.L.; software, H.F.; validation, Y.W., H.F., N.X., J.Z., Z.W., W.Y., Y.J. and S.L.; formal analysis, Y.W., H.F., N.X., J.Z., Z.W., W.Y., Y.J. and S.L.; investigation, Y.W., H.F., N.X., J.Z., W.Y., Y.J. and S.L.; resources, S.L.; data curation, H.F. and S.L.; writing--original draft preparation, Y.W., H.F. and S.L.; writing--review and editing, Y.W., H.F. and S.L.; visualization, Y.W., H.F. and S.L.; supervision, S.L.; project administration, S.L.; funding acquisition, S.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Key Research and Development Program of China (2022 YFC3005303), the Open Projects Foundation (BHSKL20-01-KF) of the National Key Laboratory of Bridge Intelligent and Green Construction, the National Natural Sciences Foundation of China (NSFC) (Grant No. 52178470), the Natural Science Foundation of Heilengjiang Province under Grant No. YQ2021E033, the Postdoctoral Scientific Research Development Fund of Heilongjiang Province under Grant No. LBH-Q20021, and Heilongjiang Touyan Team and Fundamental Research Funds for the Central Universities. The data presented in this study are available on request from the corresponding author. The data are not publicly available for confidentiality reasons. The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.