## 7 Conclusions  
This paper presents a performance evaluation of linear and nonlinear models in short-term forecasting of tropical-storm winds. The following conclusions can be obtained based on existing analyses and discussions:  
1. The artificial neural network-based models provide similar prediction errors in the one-step ahead forecasting of maximum wind speeds, while the SVR model offers the worst forecasting as the trained model cannot well represent the inherent general features of measured winds.
2. The forecasting errors of different models all increase with the augment of forecasting steps, but the error increment of the ARIMA model is the smallest. The SVR model still provides the worst prediction at different forecasting steps, and the difference in the errors of the BPNN, LSTM, and GRU models is small.
3. The errors of all the models in forecasting the mean wind speed are smaller than those in forecasting the maximum wind speed, which means high accuracy can be achieved when forecasting the wind speeds in the mean sense.
4. Among the investigated models, the ARIMA model provides the least forecasting error, and the error changes little when increasing the forecasting steps. Hence, the ARIMA model is suggested as an effective approach to forecast tropical-storm winds for the purpose of early warning.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Error**} & \multicolumn{6}{c}{**Forecasting Step**} \\ \cline{2-7}  & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline MAE (\%) & 19.8 & 18.9 & 18.6 & 18.2 & 18.7 & 20.4 \\ MRPE (\%) & 11.0 & 9.8 & 9.3 & 8.8 & 9.3 & 11.2 \\ RMSE (\%) & 22.7 & 20.9 & 20.8 & 20.6 & 20.7 & 21.9 \\ R\({}^{2}\) (\%) & 18.7 & 17.5 & 18.6 & 18.8 & 18.2 & 18.6 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Accuracy improvement of the ARIMA model.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & **Forecasting Steps** & **ARIMA** & **BPNN** & **LSTM** & **GRU** & **SVR** \\ \hline \multirow{4}{*}{Lekima} & 1 & 1.05 & 1.09 & 1.07 & 1.11 & 1.27 \\  & 3 & 1.09 & 1.26 & 1.15 & 1.38 & 1.33 \\  & 6 & 1.13 & 1.35 & 1.20 & 1.45 & 1.42 \\ \hline \multirow{4}{*}{Maria} & 1 & 0.52 & 0.52 & 0.52 & 0.55 & 0.57 \\  & 3 & 0.54 & 0.57 & 0.59 & 0.63 & 0.62 \\  & 6 & 0.54 & 0.62 & 0.64 & 0.64 & 0.71 \\ \hline \multirow{4}{*}{Ampil} & 1 & 1.10 & 1.10 & 1.11 & 1.12 & 1.14 \\  & 3 & 1.16 & 1.22 & 1.24 & 1.41 & 1.27 \\  & 6 & 1.14 & 1.20 & 1.25 & 1.35 & 1.32 \\ \hline \hline \end{tabular}
\end{table}
Table 5: MAE of different models in forecasting wind speeds.  
**Author Contributions:** Conceptualization, T.T. and H.W.; methodology, P.S. and T.T.; validation, T.T.; formal analysis, P.S., S.W. and L.Y.; writing--original draft preparation, P.S. and T.T.; writing--review and editing, T.T. and H.W.; supervision, T.T. and H.W.; project administration, T.T. and H.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Science Foundation of Jiangsu Province (Grant No. BK20190359) and the National Natural Science Foundation of China (Grant Nos. 51908125, 51978155).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** No new data were created or analyzed in this study. Data sharing is not applicable to this article.  
The authors would like to thank the Jiangsu Transportation Institute (JSTI) for providing the long-term monitored data of Sutong Cable-Stayed Bridge.  
The authors declare no conflict of interest.