# Exploration of Multi-Scale Reconstruction Framework in Dam Deformation Prediction
## 1 Introduction  
So far, there are approximately 98,000 dams in China, which play a significant role in flood control and power generation. Once the dam bursts, it will cause irreversible damage to the environment, society and economy [1, 2]. Generally, the collapse of the dam is caused by the long-term deformation. Therefore, it is the primary task to accurately predict the deformation of the dam at present. Furthermore, how to improve the prediction accuracy is an important issue in the field of the dam's safety monitoring [3]. From the perspective of the current relevant research, the common dam deformation analysis and prediction models are mainly divided into the following three categories: the statistical model [4, 5, 6], the deterministic model [7, 8], and the mixed model [9, 10, 11]. Based on the regression theory, the statistical model is usually applied to output the linear relationship between the influencing factor and the target variable. [PERSON] et al. [12, 13] have conducted more comprehensive research in this area, and their findings have been widely utilized. However, the dam deformation is usually affected by factors such as temperature and water level. These influencing factors present a strong nonlinear relationship, which can be quantified by the long-term persistence (LTP). The global scale analysis reveals that there is long-term persistence in all the above factors [14]. Hence, the existence of these LTP factors makes the deformation of the dam exhibit strong volatility, which increases the difficulty to accurately predict the deformation of the dam. Although the regression model can establish a nonlinear relationship between variables, itsgeneralization ability is weak. Based on mechanical assumptions, the deterministic model simulates the working process of the dam through the finite element method and calculates its displacement and stress [15]. However, this method requires a heavy workload and there is a strong nonlinear relationship between dam deformation and influencing factors, so that it can only implement qualitative analysis. In recent years, with the development of artificial intelligence, machine learning has made breakthroughs in data mining, especially the neural network models represented by BP, ARIMA, SVM, ELM, etc. Many scholars applying neural network to dam deformation prediction have achieved good results [16; 17; 18], which has further improved the processing of nonlinear problems in comparison with the regression model. The ARIMA model can capture processes with strong volatility, while it requires a large number of parameters when the process exhibits long-range dependence [19]. It makes the model complicated and difficult to handle. However, multivariate forecasting models usually only consider environmental factors and ignore the time dependence of the deformation sequence itself. When the deformation sequence has strong volatility, the above methods have poor robustness and generalization ability. In order to solve the shortcomings of the above models, many scholars have proposed to adopt the LSTM [20] model to solve the problem of the dam's deformation prediction. Due to a long-term memory function, LSTM possesses a unique advantage in time series prediction. [PERSON] et al. [21] proposed employing LSTM to predict import and export. They found that LSTM can effectively simulate the uncertainty trend in the data. [PERSON] et al. [22] applied LSTM to predict ship motion and proved that this approach has better performance. [PERSON] et al. combined LSTM with the attention mechanism, so that the model could attach great importance to other more important factors in the time dimension [23]. Through the analysis of the results, it is found that although the model has made great improvements in the overall prediction accuracy, the extreme value prediction is still insufficiently accurate when the data's volatility is large. In this case, this study proposes a multi-scale dam deformation prediction model based on signal decomposition.