## 4 Conclusions  
In this paper, a new factor set considering the hysteresis effect of temperature on displacement is proposed. The optimal factor set is formed by screening the main factors with the Reliefief according to the prediction accuracy of the PSO-LSSVM model as the index. The correlation between measurement points is then taken into account, and a MIMO displacement prediction model for concrete gravity dams is established by the LSSVM optimized by PSO, which achieves the synchronous prediction of the displacement of multiple measurement points. This process enables the establishment of a MIMO considering correlation and hysteresis prediction method for gravity dam displacement with interpretable functions. The feasibility and superiority of the method are verified by measured data of a concrete gravity dam in North China, and the main conclusions obtained are summarized as follows. 1. The specific times at which the temperature at different measurement points exhibits hysteresis effects on the displacement of gravity dams are determined through the utilization of the sliding match method and the cosine similarity calculation method. Figure 15: Comparison of the performance improvement rate of different prediction models. A factor set that considers the hysteresis effect of temperature on displacement is obtained, and the prediction accuracy of the PSO-LSSVM model is used as an index to compare with the other factor sets. This demonstrated the necessity to consider the hysteresis effect of the environmental factors on the displacement of gravity dams. 2. Through the Relieff feature selection method, the importance of each feature is found to be similar for the displacements at the measurement points in the same area, for instance, the influence of temperature on the dam displacement is greater in the non-overflow dam section, while the influence of hydraulic pressure on the dam displacement is greater in the overflow dam section. Furthermore, the implementation of a filtering process on the features of the factor set resulted in an enhancement of the model's prediction accuracy, thereby highlighting the significance of feature selection in the context of predicting dam displacements. 3. A MIMO synchronous prediction model, MIMO-PSO-LSSVM, that considers the potential spatial correlation between measurement points is proposed. Compared with the contrastive models, this MIMO-PSO-LSSVM model is able to take into account the potential spatial correlation between the displacement measured data, thereby improving the prediction accuracy. Furthermore, the model exhibits the advantage of being able to predict displacements at multiple measurement points simultaneously, resulting in a significant efficiency improvement over the single-output PSO-LSSVM model. The method proposed in this paper, with slight modifications, can be applied to predict other monitoring metrics of gravity dams, such as seepage, stress, and strain, as well as the relevant monitoring quantities of other types of dams, including arch dams and earth-rock dams. Concrete dams can be regarded as highly non-stationary systems, and the use of a static lag window to quantify the duration of lag presents certain limitations. Future research will investigate methods for dynamically calibrating lag times based on seasonal variations. Meanwhile, considering that the model treats all output dimensions equally during computation, assuming that each output contributes equally to the task without applying differential weights, future work will explore the introduction of an output weighting mechanism to assign different importance weights to different outputs. Future research will also explore the feasibility of using transfer learning, retraining, or retraining with fewer samples for the MIMO-PSO-LSSVM model. Additionally, the feasibility of applying the method proposed in this paper to strain prediction and damage detection in concrete structures will also be explored [59; 60]. Software, Y.Y. ; Validation, X.W., L.S., B.O. and Y.Z. ; Investigation, L.S., B.O.