## 1 Introduction
However, the primary challenges that must be addressed include the avoidance of overfitting, the selection of appropriate regularization constants, and the choice of the optimal kernel function and related parameters. Optimization algorithms can be utilized to facilitate the adaptive search for the optimal hyperparameters of the model, thereby enabling the construction of combined prediction models that exhibit superior performance. Examples of such algorithms include Genetic Algorithm (GA) [24], Fruit Fly Optimization Algorithm (FOA) [25], White Shark Optimizer (WSO) [26], Grasshopper Optimization Algorithm (GOA) [27], and Particle Swarm Optimization Algorithm (PSO) [28]. Among them, the PSO, due to its simplicity and ease of understanding, has been widely applied in the field of engineering structural health monitoring. Numerous research achievements have successfully integrated PSO, GA, FOA, and other intelligent optimization algorithms with various models for predictive analysis [29; 30]. The hyperparameters of the LSSVM are adjusted through PSO. The optimized PSO-LSSVM model demonstrates a high degree of accuracy in prediction; thus, it is widely applied in dam displacement prediction [31; 32]. Dam deformation can be influenced by various environmental factors, including hydraulic pressure and temperature. Hydraulic-Seasonal-Time (HST) and Hydraulic-Temperature-Time (HTT) models are fundamental statistical models for selecting input variables to predict dam displacement [33; 34]. Building on the HTT model, [PERSON] et al. [35; 36] proposed a long-term air temperature-based Hydraulic-Air temperature-Time (HT\({}_{\text{A}}\)T) model to achieve more accurate predictions of dam behavior. However, the hysteresis effect between dam deformation and changes in environmental factors is often observed [37; 38; 39]. Therefore, the hysteresis effect of dam deformation on temperature must be taken into account in the analysis process. [PERSON] et al. [40] proposed the Hydraulic-Hysteresis-Seasonal-Time (HHST) model, which considered the hysteresis effect of environmental factors. [PERSON] et al. [41] introduced a hysteresis quantification algorithm to estimate the hysteresis days of environmental factors affecting deformation. In order to enhance the performance and prediction accuracy of the model, it is necessary to utilize feature selection for variable screening to select appropriate input variables for dam health monitoring by comparing the magnitude of importance of different variables. [PERSON] et al. [42] utilized the Principal Component Analysis (PCA) method to identify the primary factors, thereby further optimizing the model. [PERSON] et al. [43] employed the Random Forest (RF) algorithm to predict the displacements and analyze the significance of the variables on the displacements. [PERSON] et al. [44] applied the mRMR algorithm and the Lasso algorithm for feature selection to obtain the optimal factor sets. [PERSON] et al. [45] utilized the ReliefF algorithm, an extension of the Relief algorithm, as a feature weighting method. The ReliefF algorithm assigns different weights to features based on the relevance of the different features and categories and then removes the features whose weights are less than a certain value. It has been demonstrated that the ReliefF algorithm is characterized by simplicity in operation, high efficiency in execution, the capacity to select features exhibiting strong relevance to the category, and the ability to reduce the complexity of subsequent algorithms by decreasing the original feature vectors from high dimensions to low dimensions [46]. This renders it a reliable feature selection method. In the past, the majority of prediction methods have been modeled for a single measurement point, which disregards the potential spatial correlation between different displacement measurement sites [47]. Essentially, these methods belong to the multiple-input-single-output model, which can only approximate the mapping from a multivariate input space to a univariate output space.