Accurate and reliable prediction of dam deformation (DD) is of great significance to the safe and stable operation of dams. In order to deal with the fluctuation characteristics in DD for more accurate prediction results, a new hybrid model based on a decomposition-ensemble model named VMD-SE-ER-PACF-ELM is proposed. First, the time series data are decomposed into subsequences with different frequencies and an error sequence (ER) by variational mode decomposition (VMD), and then the secondary decomposition method is introduced into the prediction of ER. In these two decomposition processes, the sample entropy (SE) method is innovatively utilized to determine the decomposition modulus. Then, the input variables of the subsequences are selected by partial autocorrelation analysis (PACF). Finally, the parameter-optimization-based extreme learning machine (ELM) models are used to predict the subsequences, and the outputs are reconstructed to obtain the final prediction results. The case analysis shows that the VMD-SE-ER-PACF-ELM model has strong prediction ability for DD. The model is then compared with other nonlinear and time series models, and its performance under different prediction periods is also analyzed. The results show that the proposed model is able to adequately describe the original DD. It performs well in both training and testing stages. It is a preferred data-driven model for DD prediction and can provide a priori knowledge for health monitoring of dams.

During the operation period, the deformation of an ultra-high arch dam is affected by the large fluctuation of the reservoir water level. Under the dual coupling of the ultra-high dam and the complex water level conditions, the traditional variational analysis method cannot be sufficiently applied to its deformation analysis. The deformation analysis of the ultra-high arch dam, however, is very important in order to judge the dam safety state. To analyze the deformation law of different parts of an ultra-high arch dam, the panel data clustering theory is used to construct a Spatio-temporal characteristic model of dam deformation. In order to solve the difficult problem of the fluctuating displacement of dam deformation with water level effect, three displacement component indexes (absolute quantity, growing, and fluctuation) are proposed to characterize dam deformation. To further optimize the panel clustering deformation model, the objective weight coefficient of clustering comprehensive distance is calculated based on the CRITIC (CRiteria Importance Through Inter-criteria Correlation) method. The zoning rules of the ultra-high arch dam are established by using the idea of the CSP (Constraint Satisfaction Problem) index, and the complex water level of the reservoir is simulated in the whole process. Finally, the dynamic cluster analysis of dam deformation is realized. Through a case study, three typical working conditions including the rapid rise and fall of water level and the normal operation are calculated, and the deformation laws of different deformation zones are analyzed. The results show that the model can reasonably describe the deformation law of an ultra-high arch dam under different water levels, conveniently and intuitively select representative measuring points and key monitoring parts, effectively reducing the analysis workload of lots of measuring points, and improve the reliability of arch dam deformation analysis.

Affected by various complex factors, dam deformation monitoring data usually reflect volatility and non-linear characteristics, and traditional prediction models are difficult to accurately capture the complex laws of dam deformation. A multi-scale deformation prediction model based on Variational Modal Decomposition (VMD) signal decomposition technology is proposed in this study. The method first decomposes the original deformation sequence into a series of sub-sequences with different frequencies, then the decomposed sub-sequences are modeled and predicted by Long Short-Term Memory neural network (LSTM) and Random Forest (RF) according to different frequencies. Finally, the prediction results of all sub-sequences are reconstructed to obtain the final deformation prediction results. In this process, it is proposed to use the instantaneous frequency mean method to determine the decomposition modulus of VMD. The innovation of this paper is to decompose the monitoring data with high volatility, and use LSTM and RF prediction, respectively, according to the frequency of the monitoring data, so as to realize the more accurate capture of volatility data during the prediction process. The case analysis results show that the proposed model can effectively solve the negative impact of the original data volatility on the prediction results, and is superior to the traditional prediction models in terms of stability and generalization ability, which has an important reference value for accurately predicting dam deformation and has far-reaching engineering significance.