# Midspan Deflection Prediction of Long-Span Cable-Stayed Bridge Based on DIWPSO-SVM Algorithm
## 5 Conclusions  
This study presents the development and validation of the DIWPSO-SVM model for predicting the midspan deflection of large-span cable-stayed bridges. By integrating the Mallat wavelet transform algorithm to decompose deflection signals into temperature and vehicle load effects and employing the dynamic inertia weight particle swarm optimization (DIWPSO) to optimize SVM parameters, the model demonstrates significant improvements in prediction accuracy and efficiency. The key findings are summarized as follows:  
* The vertical deflection of the main girder exhibits a clear correlation with ambient temperature. As the temperature increases, the main girder shows an upward arching trend, reaching maximum deflection at around 16:00, followed by a gradual decrease. This change exhibits a hysteresis effect relative to temperature variations.
* The DIWPSO-SVM model achieves a high level of prediction accuracy, with an average error of 1.43 mm and a root-mean-square error (RMSE) of 2.05. This represents a significant improvement over the original SVM model, which had an average error of 5.29 mm and an RMSE of 5.62. The PSO-SVM model, while better than the original SVM, still falls short of the DIWPSO-SVM model, with an average error of 1.62 mm and an RMSE of 3.64. These results underscore the effectiveness of the DIWPSO algorithm in optimizing SVM parameters for enhanced prediction performance.
* Although the DIWPSO-SVM model requires additional computational time during the initialization phase for parameter optimization (a total time of 175.6 s compared to 45.5 s for the original SVM), the prediction time is significantly reduced (34.8 s for DIWPSO-SVM vs. 45.5 s for SVM). This improvement in prediction efficiency, combined with higher accuracy, makes the DIWPSO-SVM model a practical and effective tool for real-time bridge health monitoring.  
In conclusion, the DIWPSO-SVM model, enhanced by wavelet transform decomposition and dynamic inertia weight optimization, offers a robust and accurate approach for predicting midspan deflection in large-span cable-stayed bridges. Its ability to learn from monitoring data and adapt to varying conditions makes it a valuable tool for ensuring the safety and longevity of bridge structures.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Prediction Model** & **DIWPSO-SVM** & **PSO-SVM** & **SVM** \\ \hline Parameter & & & \\ combination & & & \\ (penalty factor and & & & \\ gamma parameter) & & & \\ \hline Total time/s & 175.6 & 193.6 & 45.5 \\ \hline Predicted time/s & 34.8 & 39.6 & 45.5 \\ \hline Average error/mm & 1.43 & 1.62 & 5.29 \\ \hline RMSE & 2.05 & 3.64 & 5.62 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The prediction errors of different models for midspan deflection.  
**Author Contributions:** Conceptualization, L.L., H.W. and W.W.; methodology, Q.H. and W.W.; formal analysis, Q.H. and W.W.; investigation, L.L., Q.H. and H.W.; data curation, Q.H. and H.W.; writing--original draft preparation, Q.H. and W.W.; writing--review and editing, L.L. and H.W.; supervision, L.L.; funding acquisition, L.L., H.W. and W.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the Natural Science Foundation of Jilin Province (20240101141)C and the Guangxi Science and Technology Plan Project-Scientific Research Project for Young Innovative Talents (AD21220121).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The original contributions presented in this study are included in the article. Further inquiries can be directed at the corresponding authors.  
**Conflicts of Interest:** Authors [PERSON], [PERSON] and [PERSON] were employed by the company Guangxi Transportation Science and Technology Group Co., Ltd. The remaining author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.