Auxiliary Power Prediction for Underwater Vehicles Based on CEEMDAN–VMD–LSTM Multi-Stage Decomposition Framework

This study proposes a multi-stage decomposition framework for auxiliary power prediction of underwater vehicles to support energy management. Isolation Forest first removes outliers from the load record; Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) then decomposes it, and the modes are aggregated by Sample Entropy (SE) into high-, medium-, and low-frequency sub-sequences; Variational Mode Decomposition (VMD) further refines the highest-entropy sub-sequence; and Long Short-Term Memory (LSTM) networks predict each sub-sequence and sum the results. Validation on measured data adopts a leak-free protocol in which normalization, outlier detection, and decomposition never access future observations and all models are evaluated on the original, unmodified test targets; as the test segment’s mean load level is lower, bias-corrected metrics are reported alongside raw ones. The proposed method attains the best bias-corrected R2 (0.330) and NRMSE (0.109) among seven models, reducing NRMSE by 1.0% to 15.9% versus all benchmarks, while its MAPE (9.01%) stays within 0.71 percentage points of the best baseline; five-seed repetitions confirm that this advantage is not an artifact of a single training run, a capacity-matched comparison shows that it does not stem from the larger parameter count, and a 16-combination sweep indicates low sensitivity to the VMD hyperparameters. On the public Shifts vessel power dataset, the framework remains competitive (R2 = 0.885 ± 0.077 over three seeds), although the EMD–LSTM and direct baselines are superior there owing to richer exogenous features, delimiting the applicability of the decomposition cascade.