# Midspan Deflection Prediction of Long-Span Cable-Stayed Bridge Based on DIWPSO-SVM Algorithm
## 4 Results and Discussion
### Prediction of Midspan Deflection by the DCWPSO-SVM Model  
The midspan deflection prediction was carried out using the DIWPSO-SVM model, which was developed and implemented using MATLAB 2016b software, operating on a test platform configured with specific hardware and software specifications. CPU: intel core i5 10400f; RAM: 16 GB; and system version: Windows 10. These hardware and software specifications ensured sufficient computational power to handle the complexity involved in training and validating the predictive models. To predict the midspan deflection, three different models were employed, including DIWPSO-SVM, PSO-SVM, and SVM, which were trained using sample data from June and subsequently utilized to forecast the midspan deflection for 1 July. A rigorous statistical analysis was conducted on the midspan deflection data collected hourly to validate the effectiveness of these prediction models. Each hourly mid-span deflection data point was subjected to probability density statistics to understand its distribution characteristics. The obtained probability density functions were fitted to a normal distribution. This step assumes that the deflection data follow a normal distribution, which is a common assumption in the statistical analyses of such data. The expected value of the normal distribution was selected as the data sampling point for comparison between measured and predicted values. The prediction results are visually presented in Figure 8, which compares the measured midspan deflection curves with those predicted by the DIWPSO-SVM, PSO-SVM, and SVM models. The SVM model shows the largest deviations from the measured data, while the PSO-SVM model demonstrates good prediction performance but with slightly higher deviations compared to DIWPSO-SVM, reflecting the benefits of PSO. The DIWPSO-SVM model, in particular, offers enhanced performance due to its optimized parameters derived from the improved DIWPSO algorithm. The DIWPSO-SVM model shows the closest alignment with the measured data, indicating high prediction accuracy. Figure 7: The deflection time–history curve for vehicle load. Table 1 presents the prediction errors of different models for midspan deflection. The SVM model optimized with DIWPSO exhibits a significantly better fit to the mid-span deflection data. This optimized model, DIWPSO-SVM, achieves a higher prediction accuracy, with an average error of approximately 1.43 mm and an RMSE of 2.05. The root-mean-square error (RMSE) as a primary metric was used to assess prediction accuracy, which inherently provides a measure of the average prediction error and, thus, is an indication of uncertainty. In contrast, the original SVM model, without optimized parameters, has an average error of around 5.29 mm and an RMSE of 5.62, indicating the lowest prediction accuracy among the models considered. However, the PSO-SVM model, while improving upon the original SVM model, falls short of the DIWPSO-SVM model in terms of prediction accuracy. This suggests that the parameter optimization provided by DIWPSO is more effective than that of PSO in enhancing the predictive capabilities of the SVM model. It is worth noting that the DIWPSO-SVM model requires additional computational time during the initialization stage to iterate the optimization process and determine the optimal parameter combinations for the SVM. Consequently, the total computational time for the DIWPSO-SVM model is higher than that of the original SVM model. However, when considering only the prediction time, it becomes evident that the optimized parameter combinations enable the SVM model to predict more efficiently. Therefore, despite the longer initialization phase, the DIWPSO-SVM model ultimately offers a much lower prediction time compared to the original SVM model. The DIWPSO-SVM model demonstrates superior performance in predicting mid-span deflection, achieving higher accuracy and efficiency through optimized parameter combinations.