A BiLSTM-Based Hybrid Ensemble Approach for Forecasting Suspended Sediment Concentrations: Application to the Upper Yellow River

Accurately predicting suspended sediment concentrations (SSC) is vital for effective reservoir planning, water resource optimization, and ecological restoration. This study proposes a hybrid ensemble model—VMD-MGGP-NGO-BiLSTM-NGO—which integrates Variational Mode Decomposition (VMD) for signal decomposition, Multi-Gene Genetic Programming (MGGP) for feature filtering, and a double-optimized NGO-BiLSTM-NGO (Northern Goshawk Optimization) structure for enhanced predictive learning. The model was trained and validated using daily discharge and SSC data from the Tangnaihai Hydrological Station on the upper Yellow River. The main findings are as follows: (1) The proposed model achieved an NSC improvement of 19.93% over the Extreme Gradient Boosting (XGBoost) and 15.26% over the Convolutional Neural Network—Long Short-Term Memory network (CNN-LSTM). (2) Compared to GWO- and PSO-based BiLSTM ensembles, the NGO-optimized VMD-MGGP-NGO- BiLSTM-NGO model achieved superior accuracy and robustness, with an average testing-phase NSC of 0.964, outperforming the Grey Wolf Optimization (GWO) and Particle Swarm Optimization (PSO) counterparts. (3) On testing data, the model attained an NSC of 0.9708, indicating strong generalization across time. Overall, the VMD-MGGP-NGO-BiLSTM-NGO model demonstrates outstanding predictive capacity and structural synergy, serving as a reliable reference for future research on SSC forecasting and environmental modeling.