Abstract
The deformation prediction of the dam in the initial stage of operation is very important for the safety of high dams. A hybrid model integrating chaos theory, support vector machine (SVM), and an improved Grey Wolf Optimization (IGWO) algorithm is developed for deformation prediction of dam in the initial operation period. Firstly, the chaotic characteristics of the dam deformation time series will be identified, mainly using the Lyapunov exponent method, the correlation dimension method, and the Kolmogorov entropy method. Secondly, the SVM-IGWO model based on phase space reconstruction (PSR) is established for deformation forecasting of the dam in the initial operation period. Taking SVM as the core, the deformation time series is reconstructed in phase space to determine the input variables of SVM and the GWO algorithm is improved to realize the optimization of SVM parameters. Finally, take the actual monitoring displacement of Xiluodu super-high arch dam as an example. The engineering application example shows that, compared with the existing models, the prediction accuracy of the PSR-SVM-IGWO model established in this paper is improved.
Highlights
Studies [5, 6] have shown that nearly 50% of dam failures occur in the first 5 years of operation, which emphasizes the necessity and importance of early statistical modelling methods for dam safety monitoring. e purpose of this paper is to propose a hybrid model based on chaos theory, support vector machine (SVM), and improved Grey Wolf Optimizer (GWO) (IGWO) algorithm and apply it to the deformation prediction of the dam in the initial operation stage
For the phase space reconstruction (PSR)-SVM-IGWO-based dam observation displacement prediction model, the relevant information is introduced as follows. e SVM is at the heart of this innovative combination model. e input variable is the reconstructed phase space of the measured displacement data sequence, and the IGWO algorithm is used to realize the parameter optimization of SVM
In order to better analyze the predictive performance of the PSR-SVM-IGWO model, the PSR-SVM and PSR-SVMGWO models that take the reconstructed phase space of the observed displacement data sequence as input variables are established, respectively
Summary
Where ξ+ and ξ− represent slack variables. e key is to establish the Lagrangian function. X(t + 1) Xp(t) − A · D, where t is the current iteration number, Xp(t) and X(t) represent the cur→rent positions of the prey and the wolf, respectively; and D is the distance between the wolf and the prey. (3) Calculate the objective function value of a single grey wolf individual and determine the best three individuals as Xα, Xβ, and Xδ, respectively. Crossover and competition operations are applied to retain better individual positions and generate new individuals, respectively. A hybrid model combining chaos theory and SVM is proposed, and the improved GWO algorithm is used to select optimal parameters for concrete dam deformation analysis and prediction. E Kolmogorov entropy estimate K2 is a finite positive value and the saturation of the correlation dimension indicates that the observed displacement time series has the chaotic characteristics. (5) Divide the data set into training data set and test data set, and normalize the data set
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