# Midspan Deflection Prediction of Long-Span Cable-Stayed Bridge Based on DIWPSO-SVM Algorithm
###### Abstract
Previous research has focused on various methods for deflection assessment and prediction. Studies have utilized techniques such as the additional mass block mass normalization method, modal flexibility method, impact test data analysis, and finite element modeling to predict and analyze bridge deflection. [PERSON] et al. investigated the accuracy and engineering feasibility of the mass normalization method based on additional mass blocks and the modal flexibility method for predicting the modal deflection of bridges with the span of hollow plate girders as the research object [10]. [PERSON] et al. performed flexibility identification and deflection prediction on a three-span concrete box girder bridge based on impact test data with the predicted deflections in good agreement with the calculated deflections, and the experimental results verified the effectiveness of the method [11]. [PERSON] et al. proposed a deflection prediction method for post-tensioned concrete continuous box girder bridges based on ambient vibration tests and performed field tests on a three-span bridge to verify the performance and reliability of the proposed method [12]. While these methods have provided valuable insights, there is still room for improvement in terms of the accuracy of prediction and efficiency. Traditional methods for deflection prediction often rely on empirical models or finite element analysis, which may not fully capture the dynamic and nonlinear behavior of the bridge under varying load conditions. Accurately predicting and understanding bridge deflection is challenging due to the multitude of influencing factors and the nonlinear nature of their interactions. In recent years, machine learning algorithms have gained popularity in SHM due to their ability to model complex, nonlinear relationships, in which support vector machines (SVMs). in particular, have emerged as powerful tools for predicting bridge deflection [13; 14]. SVMs are well-suited for complex and nonlinear problems due to their robustness and generalization capability, making them ideal for modeling the behavior of large-span cable-stayed bridges [15]. However, the performance of SVMs heavily depends on the selection of their parameters, which can be a non-trivial task. To address this issue, optimization algorithms such as particle swarm optimization (PSO) have been employed to fine-tune SVM parameters [16]. PSO is a bio-inspired optimization technique that mimics the social behavior of birds flocking or fish schooling [17]. While PSO has been effective in various applications, it suffers from drawbacks such as slow convergence and the tendency to become trapped in local optima [18; 19]. To overcome these limitations, an improved PSO algorithm has been proposed, termed dynamic inertia weight PSO (DI-WPSO), which dynamically adjusts the inertia weight based on the swarm's aggregation degree, thereby balancing global exploration and local exploitation [20; 21]. Furthermore, the midspan deflection of a cable-stayed bridge is influenced by multiple load effects, primarily temperature and vehicle loads [22; 23]. These effects manifest at different time scales and frequencies, making it essential to separate them for accurate prediction. Wavelet transform, particularly the Mallat algorithm, was employed in this study to decompose the deflection signals into their constituent components [24; 25]. This decomposition allows for a more detailed analysis of the deflection behavior under different load conditions, thereby improving the prediction accuracy. The robustness of particle swarm optimization (PSO) is closely tied to its ability to balance exploration and exploitation in dynamic or complex problems. Traditional PSO exhibits limited performance in non-convex or multimodal optimization due to parameter sensitivity and premature convergence issues [26]. Studies have shown that the dynamic adjustment of the inertia weight (e.g., linearly decreasing strategies) or adaptive mechanisms (e.g., feedback based on swarm dispersion) can significantly enhance robustness.