## 1 Introduction
[22] verified the necessity of fully extracting sequence features when the CNN-LSTM model is used to predict PM2.5 concentration. These hybrid model-related studies demonstrated that owing to the extraction potential of the representative features of the CNNs and effective gated structure of multilayered LSTM or GRU, the model can more strongly express the temporal features in terms of the computational complexity and prediction accuracy, with the lowest error rate. Due to the particularity of the dam deformation monitoring data, although the commonly used dam deformation prediction methods can provide good prediction results, their comprehensive prediction performance is poor in the face of complex original observation datasets. The robustness of these methods is poor, and the long-term forecast will accumulate errors. Table 1 is a comparison table of the advantages and disadvantages of common dam deformation prediction methods. Notably, because of the many factors affecting dam deformation, existing methods have limited capabilities in modeling the multivariate correlation and high volatility of dam deformation, and to achieve the required accuracy, the final model architecture becomes complex and less universal. Therefore, the main method currently used is to strip out representative subcomponents from the observed dam deformation time series to reduce the modeling difficulty. For example, [PERSON] et al. [23] used multiple real-valued projections of signal to improve empirical mode decomposition (EMD) for the problem that it is difficult to find local extremum of the multivariate signal, and then remove noise from observations on dam safety. [PERSON] et al. [24] used wavelet analysis (WA) to decompose the localized waveforms of dam displacement time series for model construction. However, these methods have strict requirements on the assumption of the original sequence, and the denoising effect of white noise is poor, thereby decreasing the ability to reproduce abnormal values in certain tasks, and the application scope is not wide. The seasonal-trend decomposition based on loess (STL) is a mature filtering program that can split the original time series into several representative variation components for subsequent analysis. Owing to its strong reproducibility for outliers in the time series and its ability to generate robust subseries, the STL is recognized in many engineering fields involving dam deformation decomposition [25]. On the other hand, to deal with the problem of artificial intelligence parameter tuning, the sparrow search algorithm (SSA) has recently been proposed to deal with the parameter global optimization problem due to its advantages of simplicity of implementation, ease of expansion, and self-organization [26]. This paper proposes a hybrid model for dam deformation prediction and uses the SSA to perform global optimization of the model parameters. Taking a real-world parabolic variable-thickness double-curved arch dam in China as an example, the feasibility of the model is successfully verified. The main contributions of this paper can be summarized as follows: (i) The STL is used to decompose the complex dam deformation time series into several subcomponents, which makes data features in the dam deformation series more prominent and reduces the difficulty of subsequent modelling. (ii) For each subcomponent, the CNN-GRU model is used to identify the mapping relationship between impact factors and target variables, which can make the whole prediction process structured and broaden the application range of the model. (iii) The SSA method is used to identify the appropriate combination of the parameters to endow the model with optimization capability, accomplishing the pertinent modelling of dam deformation series at different measurement points. (iv) Compared with several conventional models, the proposed hybrid model provides better prediction accuracy, long-term stability, and robustness to abnormal sequences. The remainder of this paper is organized as follows.