Multi-step energy consumption prediction of underwater gliders based on the hybrid deep learning model

Accurate energy consumption prediction for underwater gliders is critical for long-endurance ocean missions. However, the non-stationary and nonlinear characteristics of energy consumption data make it difficult for conventional physical models or single-step methods to provide reliable multi-step forecasts. To address this, we propose a hybrid framework integrating Variational Mode Decomposition (VMD), Bidirectional Long Short-Term Memory (BiLSTM), and an Improved Grey Wolf Optimizer (IGWO). VMD adaptively decomposes the raw energy signal into physically meaningful modes; BiLSTM captures bidirectional temporal dependencies in dive-climb cycles; and IGWO globally optimizes network hyperparameters. The model is validated using sea-trial data from a self-developed UG platform. Systematic comparisons with long short-term memory (LSTM), gated recurrent unit (GRU), and Transformer variants under identical conditions show that VMD-BiLSTM-IGWO outperforms all benchmarks across MAE, RMSE, MAPE, MSE, and R 2 . Specifically, it reduces MAE by 14.1% and RMSE by 12.3% versus VMD-BiLSTM-PSO, and improves R 2 from 0.934 to 0.968 versus VMD-LSTM-IGWO. Multi-step forecasts maintain R 2 greater than 0.95 up to 4 steps and R 2 greater than 0.84 up to 10 steps, with CPU-only inference latency below 2 ms, which is three orders of magnitude faster than the UG re-planning cycle. These results confirm that the proposed framework offers an accurate, real-time deployable solution for UG energy management in long-duration ocean observations.