Forecasting Gate-Front Water Levels Using a Coupled GRU–TCN–Transformer Model and Permutation Entropy Algorithm

Abstract

Water level forecasting has significant impacts on transportation, agriculture, and flood control measures. Accurate water level values can enhance the safety and efficiency of water conservancy hub operation scheduling, reduce flood risks, and are essential for ensuring sustainable regional development. Addressing the nonlinearity and non-stationarity characteristics of gate-front water level sequences, this paper introduces a gate-front water level forecasting method based on a GRU–TCN–Transformer coupled model and permutation entropy (PE) algorithm. Firstly, an analysis method combining Singular Spectrum Analysis (SSA) and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is used to separate the original water level data into different frequency modal components. The PE algorithm subsequently divides each modal component into sequences of high and low frequencies. The GRU model is applied to predict the high-frequency sequence part, while the TCN–Transformer combination model is used for the low-frequency sequence part. The forecasting from both models are combined to obtain the final water level forecasting value. Multiple evaluation metrics are used to assess the forecasting performance. The findings indicate that the combined GRU–TCN–Transformer model achieves a Mean Absolute Error (MAE) of 0.0154, a Root Mean Square Error (RMSE) of 0.0205, and a Coefficient of Determination (R2) of 0.8076. These metrics indicate that the model outperforms machine learning Support Vector Machine (SVM) models, GRU models, Transformer models, and TCN–Transformer combination models in forecasting performance. The forecasting results have high credibility. This model provides a new reference for improving the accuracy of gate-front water level forecasting and offers significant insights for water resource management and flood prevention, demonstrating promising application prospects.