## 1 Introduction
Advancements in monitoring technology have led to an increase in the scale of monitoring sensors and the amount of data collected on dam behavior. Consequently, with the objective of enhancing prediction efficiency, displacement-based dam health monitoring is transitioning from single-point independent modeling to multi-point synchronous modeling [48]. [PERSON] et al. [49] proposed a method for spatio-temporal clustering and health diagnosis of ultra-high concrete arch dams based on multi-point displacement data. [PERSON] et al. [50] proposed a spatial association-coupled double objective SVM prediction model for diagnosing the displacement behavior of high arch dams. Recently, a new data modeling technique based on multiple linear regression, termed multi-target regression [51], has been proposed. This technique is capable of multiple-input multiple-output (MIMO) mapping, with the objective of predicting multiple targets simultaneously and sharing relevant information across targets. In the event of there being a correlation between the targets, each predictor variable can benefit from the others, thus improving the prediction accuracy of the model [52]. Multi-target regression algorithms have been extensively utilized in a range of multi-output prediction problems. [PERSON] et al. [53] proposed a mathematical approach, termed Multiple Correlation-based Structural Stack Test (MCSST), for the synchronous prediction of multiple displacement responses in arch dams. This approach integrates a target stacking strategy with a correlation-based feature selection framework. [PERSON] et al. [54] utilized an integrated Bayesian approach and multi-output SVM to analyze the displacement of rocky slopes. [PERSON] et al. [55] proposed a MIMO machine learning paradigm based on SVM for synchronous modeling and prediction of multi-point displacements from different blocks of dams. Considering the advantages of LSSVM in solving small sample, high-dimensional, and nonlinear problems, this paper elects to integrate the multi-target regression algorithm with LSSVM to formulate a model for dam displacement prediction. For ease of viewing, the abbreviations are summarized in Table 1.  
In summary, this paper proposes a factor set that considers the hysteresis effects of temperature on the displacement of gravity dams. Feature selection is carried out by the Relieff, which analyses the importance of the feature factors on the displacements of different measurement points and screens the main factors in the factor set to obtain a unified factor set for measurement points in the same area. After considering the spatial correlation between the measurement points, a multi-output prediction model is established using an LSSVM optimized by PSO. This approach achieves the synchronous prediction of displacements at multiple measurement points of gravity dams, thus demonstrating the efficacy of the proposed methodology. The main contributions of this study are as follows. 1. A new factor set that considers the hysteresis effects of temperature on displacement is proposed by calculating the specific hysteresis times with the sliding match method and the cosine similarity calculation method. This factor set considers the hysteresis effects of temperature on displacements, emphasizing that the hysteresis effects of environmental factors on displacements are significant and providing a new factor set for prediction models to be investigated. 2. The Relieff is utilized to rank the importance of the features from each group of measurement points. This enables an analysis to be conducted of the impact of feature factors on the displacement of measurement points at varying locations. Thereafter, the features are entered into the prediction model by their importance, from the most significant to the least significant. The optimal factor set is obtained by comparing the prediction accuracy. It is demonstrated that feature selection can effectively identify important features in the input factor sets for different measurement points, reduce