Dynamic prediction of slope displacement using Vmd decomposition with collaborative lssvm-lstm optimization

With the in-depth implementation of China's "National Strategy for Building a Strong Transportation Network," the scale of expressway construction has continued to expand. As a result, the number of high-fill and deep-cut subgrade projects under complex geological conditions has increased significantly, leading to a surge in landslide-related issues. Consequently, accurate prediction of slope displacement is of critical importance for early warning and prevention of landslide disasters. This study proposes a hybrid prediction model, VMD-MPA-LSSVM-LSTM (VMLL), which integrates Variational Mode Decomposition (VMD), Marine Predators Algorithm (MPA), Least Squares Support Vector Machine (LSSVM), and Long Short-Term Memory (LSTM) networks. Using monitoring data from the high-fill embankment slope at Hongtuyao as the research subject, the VMLL model is employed to predict slope displacement based on small-sample data. The objective is to provide a more accurate method for early warning of slope displacement. Firstly, the original monitoring data are decomposed into trend displacement components and fluctuation displacement components using Variational Mode Decomposition (VMD). Subsequently, the trend component and the fluctuation component are predicted using Least Squares Support Vector Machine (LSSVM) and Long Short-Term Memory (LSTM) networks, respectively. Finally, the Marine Predators Algorithm (MPA) is employed to optimize the hyperparameters of the predictive models. Based on this framework, a VMLL-based slope displacement prediction model is constructed. To verify the superiority of the VMLL model, a comparative analysis was conducted against LSSVM, LSTM, and the VMD-LSSVM-LSTM models. The results demonstrate that the VMLL model achieves the highest prediction accuracy, with a Mean Absolute Percentage Error (MAPE) of 0.4022%, a Mean Absolute Error (MAE) of 0.016 mm, a Root Mean Square Error (RMSE) of 0.0206 mm, a coefficient of determination (R²) of 94.08%, and a Variance Accounted For (VAF) of 96.5%. Compared with the other three models, the VMLL model reduces the MAPE, MAE, and RMSE by 30.41-67.62%, 30.38-67.40%, and 27.32-71.00%, respectively. Meanwhile, it improves the R² and VAF by 5.95-217.51% and 0.38-11.48%, respectively. These improvements clearly demonstrate that the VMLL model outperforms the other models, indicating its significant advantage over single prediction models. Furthermore, three additional datasets were used to evaluate the model's performance. The average values of the performance evaluation metrics for these datasets were 0.6207% (MAPE), 0.0238 mm(MAE), 0.0273 mm(RMSE), 90.33%(R²), and 96.81%(VAF), respectively. These results demonstrate the high accuracy and strong robustness of the proposed model in predicting both horizontal displacement and vertical settlement of slopes, providing a reliable methodological framework for slope stability assessment and landslide disaster early warning.