# Midspan Deflection Prediction of Long-Span Cable-Stayed Bridge Based on DIWPSO-SVM Algorithm
###### Abstract  
With the increasing emphasis on the safety and longevity of large-span cable-stayed bridges, the accurate prediction of midspan deflection has become a critical aspect of structural health monitoring (SHM). This study proposes a novel hybrid model, DIWPSO-SVM, which integrates dynamic inertia weight particle swarm optimization (DIWPSO) with support vector machines (SVMs) to enhance the prediction accuracy of midspan deflection. The model incorporates wavelet transform to decompose deflection signals into temperature and vehicle load effects, allowing for a more detailed analysis of their individual impacts. The DIWPSO algorithm dynamically adjusts the inertia weight to balance global exploration and local exploitation, optimizing SVM parameters for improved performance. The proposed model was validated using real-world data from a long-span cable-stayed bridge, demonstrating superior prediction accuracy compared to traditional SVM and PSO-SVM models. The DIWPSO-SVM model achieved an average prediction error of 1.43 mm and a root-mean-square error (RMSE) of 2.05, significantly outperforming the original SVM model, which had an average error of 5.29 mm and an RMSE of 5.62. These results highlight the effectiveness of the DIWPSO-SVM model in providing accurate and reliable midspan deflection predictions, offering a robust tool for bridge health monitoring and maintenance decision-making. dynamic inertia weight (DIW); particle swarm optimization (PSO); support vector machine (SVM); long-span cable-stayed bridge; midspan deflection prediction; inertia weight; convergence +
Footnote †: journal: Applied sciences  
1 Guanggi Transportation Science and Technology Group Co., Ltd., Nanning 530207, China 12 Guanggi Bridge Monitoring and Reinforcement Technology Innovation Center, Nanning 530025, China 2  
Footnote †: journal: Applied sciences  
1 Guanggi Transportation Science and Technology Group Co., Ltd., Nanning 530207, China 1  
Footnote 1: Guanggi Transportation Science and Technology Group Co. Therefore, the detection and monitoring of bridge performance, providing a scientific and reasonable assessment and maintenance decision-making, has become a current research hotspot around the world. The main girder is a very important part of the bridge, and its performance is always a concern. The performance of the main girder will be affected by the environment, load, and other impacts that make the bridge's structural material performance degrade and decline [6]. Failure to detect this in time may shorten the service life of the bridge and increase the cost of bridge maintenance as its performance deteriorates, and in severe cases, may lead to sudden ruptures and serious traffic accidents. Large-span cable-stayed bridges are more vulnerable to corrosion and fatigue damage as they are subjected to higher tensile forces during long-term use. The vertical deflection of the main bridge girder is a pivotal indicator of its structural health and is one of the most important items of structural safety and applicability in SHM [7]. Vertical deflection refers to the linear displacement of the bridge deck axis in the direction perpendicular to the deck, which is caused by factors such as non-uniform temperature changes, automobile loads, and other external forces. The accurate prediction of midspan deflection can help in the early detection of potential structural issues, thereby preventing catastrophic failures [8]. However, predicting midspan deflection is challenging due to the complex interplay of various factors, such as ambient temperature, vehicle load, and material properties. Long-span cable-stayed bridges are particularly susceptible to deflections due to their complex structural configuration and the significant forces involved. Deflection monitoring is, thus, a crucial aspect of bridge maintenance and safety assessment [9]. It allows for the early detection of potential issues, enabling timely interventions to prevent more severe structural damage.