## 1 Introduction  
As a major component of water storage systems, dams play a significant role in water supply, flood control, power generation, and irrigation. However, the potential risk of dam failure increases due to a variety of reasons, including hydrology, geology, construction quality, material aging, and operational management. Additionally, in recent years, changes in extreme climate have adversely affected the dynamic behavior of dam structures and their interactions, thereby increasing the potential risk of dam failure [1]. In the event of a dam failure, the downstream area will be severely impacted. Therefore, the work of dam safety monitoring is particularly prominent and important [2, 3]. Displacement is a critical indicator of dam safety monitoring, as it can effectively reflect the degree of operational safety and structural integrity of dams [4, 5]. Analyzing measured data from dams and establishing displacement prediction models based on these data has become one of the primary focuses of dam health monitoring. Currently, the analysis and prediction of dam monitoring data principally utilize statistical, deterministic, or hybrid models to predict and monitor the dam behavior. Among these, statistical models based on multiple linear regression and its advanced forms have been extensively employed in dam health monitoring modeling to ascertain the reasonable behavior of the dam structure by comparing the observed structural response with the predicted values obtained from the mathematical model [6; 7]. In the field of statistical modeling, the regression models used include multiple linear regression (MLR) [8; 9], stepwise regression (SR) [10], regression models based on principal component analysis [11], partial least squares regression [12], etc. However, concrete dams are complex dynamic systems whose deformation values comprehensively reflect the dam's operating conditions. Due to the existence of a multitude of structural forms and the presence of complex external environmental factors, dam deformation is characterized by non-linearity, uncertainty, and time-variability. Traditional statistical models are essentially linear regression methods, which are unsuitable for modeling high-dimensional relationships. This limitation results in a decline in the predictive accuracy and robustness of statistical models. Recently, with the advancement of artificial intelligence, researchers have progressively combined machine learning models with dam deformation prediction models [13]. Owing to its capacity to handle nonlinear problems, prediction models formulated with machine learning algorithms exhibit substantial enhancements in terms of predictive accuracy and robustness. Machine learning methods, including but not limited to Relevance Vector Machines (RVMs) [14], Radial Basis Function Networks (RBFNs) [15], Support Vector Machines (SVMs) [16], Extreme Learning Machines (ELMs) [17], Stacked Gated Recurrent Unit Neural Networks (GRUs) [18], and Long and Short-Term Memory Neural Networks (LSTMs) [19], have been employed to address issues in dam health monitoring. Recent studies have indicated that artificial neural networks and SVM represent two machine learning algorithms that are utilized extensively in the context of dam safety monitoring. In comparison with artificial neural networks, SVM has clear advantages in solving problems involving small samples and high-dimensional and nonlinear problems due to its robust theoretical foundation [20; 21]. Least squares support vector machine (LSSVM) [22; 23] represents an enhanced SVM, whereby the inequality constraints are converted into equality constraints through the utilization of the quadratic programming method. The sum of squares of the loss function errors is then employed as the empirical loss of the training sample set, and the quadratic programming problems are transformed into linear equations. The prediction accuracy of LSSVM is contingent upon the reasonable setting of hyperparameters.