# Exploration of Multi-Scale Reconstruction Framework in Dam Deformation Prediction
## 1 Introduction
The model decomposes the original deformation sequence into a finite number of sub-sequences with a variety of frequencies, which can greatly reduce the model's nonlinearity with the potential to improve the model's prediction accuracy and robustness. The traditional signal decomposition techniques mainly include Fourier transform, Wavelet Decomposition (WD) and Empirical Mode Decomposition (EMD) which are frequently applied to decompose the dam deformation sequence [24]. Fourier transform can realize the mutual conversion from time domain to frequency domain, while its conditions are relatively harsh, and there is no Fourier transform for considerable useful signals; WD has a certain priority, while it is difficult to choose the basis function and decomposition scale. Furthermore, its practical application is more complicated [25]; EMD does not need to set a basis function, which is capable to be adaptively decomposed into a finite number of modal functions. However, it is prone to modal confusion and lacks the support of mathematical theory [26; 27]. Aiming at solving the above problems, this paper introduces a new adaptive signal decomposition method--Variational Modal Decomposition (VMD) [28]. In contrast to the above decomposition method, it is a more accurate mathematical model, which can decompose the original data into a set of eigenmode functions (IMFs) fluctuating around the center frequency [29; 30; 31], with a better decomposition effect as well as higher robustness [9; 32]. However, the decomposition effect of VMD is affected by the decomposition modulus, and too many or too few subsequences will affect the decomposition effect [33; 34]. In order to solve this problem, this paper proposes the instantaneous frequency average method to analyze the decomposition modulus K so as to avoid the modal confusion caused by excessive modulus or insufficient decomposition due to too small modulus. In summary, this paper proposes a multi-scale dam-deformation prediction model based on VMD-LSTM-RF, which greatly reduces the complexity of the original sequence. In this model, the original sequence is first decomposed into sub-sequences with various frequencies and residuals. The LSTM is suitable for dealing with complex nonlinear problems with good long-term memory capabilities; it has the following characteristics: its results are reliable in predicting weak volatility series; the model is stable; it is not prone to overfitting, and the model performance is robust. Therefore, LSTM is applied to predict high-frequency components and residuals, and the low-frequency components are input to RF for prediction. Finally, the prediction results of the two parts are superimposed and reconstructed to obtain the final prediction results, which can not only avoid the inaccurate prediction problem caused by too large volatility of LSTM, but can also reduce the workload to a large extent, and effectively improve the accuracy of dam prediction. In order to verify the superiority of the proposed model, the most commonly applied methods are selected as benchmark methods, and the three quantitative evaluation indicators are utilized to evaluate the prediction performance of the proposed model. The main contributions of this paper are as follows:  
1. The VMD decomposition technology is introduced, and the instantaneous frequency average method is adopted to determine the decomposition modulus K, and the dam displacement and deformation data with strong volatility are decomposed into periodic and stable sub-sequences. 2. On the basis of LSTM and RF, the high and low frequency sub-sequences are modeled and predicted, respectively. The analysis indicates that this approach can accurately capture the nonlinear characteristics of the dam deformation. 3.