## 1 Introduction  
Concrete dams are the most common types of dams for flood control, irrigation, and water supply. A dam in a safe state can significantly boost the national economy. The operation of dams is required not only to withstand various static and dynamic loads but also to avoid different impacts of harsh environmental conditions. Their service behavior is a nonlinear dynamic process [1]. Once a dam fails, it can cause unpredictable economic damage downstream. In order to ensure the safe operation of dams, it is essential to implement effective monitoring and analysis methods. Among these, dam deformation serves as a crucial indicator for monitoring the safe operation of the dam and can effectively reflect the working condition of a concrete gravity dam under complex environmental conditions. Therefore, scientific research on the deformation data can help to better understand and monitor the health of dams [2]. In the past few decades, researchers have proposed several effective mathematical models, including statistical, deterministic, and hybrid models, to forecast the deformation behavior of dams [3]. These models can describe and evaluate the deformation behavior of concrete dams by considering the effects of hydrostatic pressure, ambient temperature, and time on the deformation behavior [4; 5]. Among them, both deterministic and hybrid models require the solution of differential equations, for which closed-form solutions are difficult to obtain [6]. In comparison, the statistical model has a more straightforward formula and is faster to execute. However, the relationships between the structural response of a concrete dam and its influencing factors are nonlinear, while most of the existing statistical models are constructed using linear assumptions as their foundation, which limits the accuracy of the model fitting and thus cannot accurately capture the structural behavior of concrete dams [7]. In recent years, a variety of machine learning architectures have been used in the field of dam safety monitoring, such as the autoregressive integrated moving average (ARIMA) algorithm [8], the support vector machine (SVM) algorithm [9], the artificial neural network (ANN) algorithm [10; 11; 12], and the random forest (RF) algorithm [13; 14], etc. These algorithms can predict dam displacement with reasonable accuracy; among them, the ANN algorithm illustrates superior performance in dealing with nonlinear problems [15; 16]. [PERSON] et al. [17] used the long short-term memory (LSTM) model to predict the displacement of the arch dam. The results showed that the LSTM model can predict dam displacement well. However, the LSTM model has the problem of difficult hyperparameter selection. In order to alleviate this problem, [PERSON] et al. [18] proposed using an improved LSTM model to predict dam deformation and achieved good results. However, the relevant parameters need to be corrected within the iteration procedure, which makes it very expensive in terms of calculation time [19]. In comparison, dam displacement prediction models developed based on the SVM algorithm can avoid the shortcomings of ANN algorithms and remarkably improve computational efficiency. [PERSON] et al. [20] proposed using the SVM algorithm to predict dam deformation and achieved certain results. Regarding the SVM-based models, prediction accuracy and generalization ability are affected by the determination of model parameters, which narrows their application. The extreme learning machine (ELM) algorithm as a single hidden layer neural network is different from the traditional single hidden layer feedforward neural network. The ELM algorithm can randomly initialize the hidden layer bias and input layer weight; the whole learning is completed through a mathematical change without any iteration; there is only a need to set the number of hidden layer nodes, and in the process of algorithm implementation, there is no need to adjust the network input weight and hidden layer bias to generate the only optimal solution.