## 1 Introduction
Due to the dependence of the time series, the sliding window method is typically used to reconstruct the data. To realize the process of mapping the previous time step tensor to the next required prediction time step, they are, respectively, provided to the nonlinear artificial intelligence algorithm for training. Therefore, the purpose is to explore the nonlinear relationship between the two tensors, and the reconstructed time series prediction is transformed into an artificial intelligence learning problem. For example, if a 30-day dam deformation dataset is used to train a model, and the purpose is to predict dam deformation the next day, which is called the prediction time, the time step needs to be first determined to generate samples. If the time step is five days, the first sample for the model training takes the dam deformation data from the first day to the fifth day as the input and the dam deformation data of the sixth day as the output. The next sample is inputted with the dam deformation data from the second day to the sixth day and outputs the dam deformation data from the seventh day. The sample generation process continues until the time corresponding to the output variable generated by the model is the 30 th day. The prediction time, which is one day in this case, is determined by the actual monitoring requirements. The time step size should be chosen depending on the characteristics of the data, and it is difficult to determine its value without any prior knowledge. Therefore, before using the artificial intelligence model to predict dam deformation, it is necessary to select the best time step in the model to capture the dependence between the original time series and improve the prediction accuracy. As one of the data-driven artificial intelligence models, the LSTM relies on the advantages of resisting noise in the time series without prior assumptions and is applied to solve nonlinear, high-dimensional, and large-sample problems [14]. Moreover, the LSTM has been widely used in the analyses of dam deformation and machinery. For example, [PERSON] et al. [15] proposed an improved LSTM model, which divides a variable into delay variables and no delay variables, for dam displacement prediction. [PERSON] et al. [16] obtained the residual stiffness related to the fatigue life of a blade under fatigue test conditions based on the LSTM and combined with historical fatigue data. However, the performance of the LSTM is significantly affected by the choice of the computational parameters employed in practice, such as the dropout rate used to avoid overfitting and the number of cell units in the hiding layers. However, there is no consensus on the optimal value selection. Furthermore, for a higher-precision dam deformation response, a high computational memory is required for training the model, making it challenging to use data-based sophisticated models for dam deformation prediction. Recently, as a variant of the LSTM, the gated recurrent unit (GRU) [17] has shown comparable performance to LSTM in many research fields, with its simpler structure and higher calculation speed [18]. However, the GRU network has drawbacks, such as overfitting and parameter tuning, which limit its application. In addition, it is more difficult to construct a model using a single algorithm because of the noise and heteroscedastic structure of time series data [19]. Combinatorial models have been developed to overcome this problem; the model built for predicting the target variable is sophisticated and is no longer a single-algorithm model but a diversified complex network. It makes full use of the effective information in each model by connecting each model with the weights to improve the model accuracy [20]. For instance, [PERSON] et al. [21] applied a hybrid model (CNN-LSTM) to capture the diversity of multimodal data at the sensor and feature level, which is conducive to emotion classification modeling. [PERSON] et al.