## 5 Conclusions  
In this paper, a new wind speed prediction model with a new scheme of real-time decomposition is proposed to predict wind speed near cross-sea bridges. Specifically, a scheme of real-time decomposition that combines truncated real-time decomposition and multi-resolution is proposed, which discards the part of input influenced by the end effect and collects corresponding high-resolution data to compensate for the information loss. Further, a prediction model that combines the proposed scheme of real-time decomposition and neural networks is proposed, where two gated recurrent unit (GRU) neural networks are used to extract features from multi-resolution data, and a multi-layer perceptron (MLP) is employed to utilize extracted features to make predictions. The proposed model is validated on the monitoring wind speed data of two long-span cross-sea bridges, and the superiority of the model is illustrated through comparisons. The reason for the superiority of the proposed model is as follows. Firstly, the GRU neural network is more suitable for extracting features from time series than from convolutional neural networks (CNN) and shallow models, such as extreme learning machine (ELM). Secondly, data decomposition can enhance the predictability of wind speed by effectively eliminating the unpredictable noise. Thirdly, the proposed scheme is superior to existing schemes of real-time decomposition for its ability to discard the influenced part of input and compensating relevant information. In summary, the proposed scheme provides a new approach to conduct real-time decomposition, and the proposed model can utilize the proposed scheme to make wind speed predictions with higher accuracy.  
The major limitation of the proposed model is that only the trend of wind speed is predicted and the uncertainty of wind speed is not considered. The uncertainty of wind speed is mainly reflected in the unpredictable noise, which is eliminated by data  
Figure 11: The comparison between the models with different schemes of real-time decomposition: (a) MAE; (b) RMSE.  
decomposition to promote the prediction accuracy of the model. The quantification of the uncertainty of wind speed by interval prediction or distribution prediction can enhance the reliability of the prediction of the trend. To this end, future work should extend the proposed model to probabilistic prediction and solve this major limitation.  
Conceptualization, H.F. and S.L.; methodology, H.F. and S.L.; software, H.F.; validation, H.F. and S.L.; formal analysis, H.F. and S.L.; investigation, H.F., S.L., Y.J., S.L., F.H. and W.X.; resources, S.L., Y.J., S.L., F.H., W.X. and Z.L.; data curation, H.F.; writing--original draft preparation, H.F. and S.L.; writing--review and editing, H.F. and S.L.; visualization, 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 Funds for the National Natural Sciences Foundation of China (NSFC) (grant no. 51878230 and 52178470), Natural Science Foundation of Heilongjiang Province (grant no. YQ2021E033), Postdoctoral scientific research development fund of Heilongjiang Province (grant no. LBH-Q20021), and was supported by the Department of Science and Technology of Guangdong Province (grant no. 2020B1212030001), Heilongjiang Touyan Team and Fundamental Research Funds for the Central Universities, and by field observations and research based for long-term performance of sea-crossing bridge in transportation industry.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
The authors declare no conflict of interest.