## 1 Introduction
Compared with traditional mathematical models, machine learning models can better handle complex nonlinear relationships and learn the patterns and laws between deformation and various influencing factors from a large amount of measured data [25; 26]. [PERSON] et al. [27] developed a neural-network-based dam deformation modeling system that can adapt to the dynamic changes in the dam observation data by updating the algorithm parameters in real time and effectively improving the adaptive nature of the model. This can reduce the influence of artificial parameters on model accuracy while ensuring the timeliness of parameter selection. [PERSON] et al. [28] used adaptive theory to optimize the artificial bee colony algorithm and combined it with a back propagation (BP) neural network model to accurately predict the deformation sequences of high arch dams and provide a safety state analysis of dam structures with [PERSON]'s [29] combined singular spectrum analysis and ANNs to study the influencing factors of dam displacement, and they achieved good results. [PERSON] et al. [30] considered the influence that complex nonlinearities in the residual sequence would have on the prediction accuracy in the modeling process of deformation prediction, and they proposed a combined prediction model, which integrated wavelet decomposition, neural networks, and integrated moving average autonomy on the basis of traditional statistical models. [PERSON] [31] used a GNSS to analyze the deformation of the Eleonora DArborea dam and demonstrated that GNSS technology could reflect the displacement of the dam in both time and space. For the highly nonlinear problem of temperature factor, based on the deformation prediction model constructed using radial basis neural network technology, the kernel principal component analysis method was introduced to reduce the dimensionality of the temperature effect quantity, and the effectiveness of the model was verified in engineering applications. However, neural network methods are prone to fall into local optimal solutions in the prediction process due to the gradient-descent-based training [32; 33], and their generalization ability still needs to be improved. For this reason, [PERSON] et al. [34], [PERSON] et al. [35], and [PERSON] et al. [36] applied the extreme learning machine (ELM) model to the dam deformation prediction. The ELM model uses the least squares method for the model solution, which avoids the impact of iterative computation on network accuracy. The effectiveness and superiority of the extreme learning machine model were demonstrated by comparing it with statistical models and conventional artificial neural network methods and by validating it in engineering examples [37; 38]. In summary, a combined MHA-ConvLSTM (Multi-Head Attention-ConvLSTM) model that takes the environmental volume lag into account is suggested. By including lag variables to strengthen the explanation of the prediction model and by merging the attention mechanism and convolution technique, they seek to boost the performance of the prediction model in memorization, depiction, and mining features. Finally, by comparing and assessing the prediction effect with other models or benchmark models for actual engineering data, the viability of introducing the lag component and the efficacy of the combined prediction model are confirmed. The remainder of this essay is structured as follows. The deformation hysteresis quantification algorithm's fundamental principles and implementation procedure are covered in Section 2. The proposed hybrid prediction model for dam deformation, MHA-ConvLSTM, is also provided along with its creation method. Section 3 gives a full examination of the findings from each of the three validation procedures for the model, including the feasibility validation of the hysteresis factor addition, the ablation validation, and the validity and generalization validation. Section 4 concludes the entire essay and presents a plan for more research.