Abstract: Objectives To address the issues of insufficient prediction accuracy and the difficulty in quantifying uncertainties regarding the energy consumption of marine electro-hydrostatic actuators under complex operating conditions, this study proposes a novel interval probability prediction model based on an AE-Transformer-LSTM architecture and Adaptive Bandwidth Kernel Density Estimation. Methods Initially, a novel Transformer-LSTM time-series prediction architecture is constructed. This architecture utilizes the parallel computing mechanism and multi-head attention of the Transformer to extract global data features. Tailored to the characteristics of time-series tasks, the redundant decoder is discarded, and the original attention layers are replaced with Long Short-Term Memory layers to deeply capture dynamic temporal dependencies. Subsequently, the recently proposed Alpha Evolution algorithm is introduced for the fully automated optimization of hyperparameters, including the number of self-attention heads, LSTM hidden nodes, learning rate, and L2 regularization coefficient. This mitigates the risk of falling into local optima, accelerates the convergence rate, and generates highly accurate point predictions for energy consumption. Finally, based on the distribution of point prediction errors, the ABKDE method is employed to estimate interval probabilities. The Golden Section method is applied to efficiently search for the globally optimal bandwidth parameter, thereby accurately capturing the detailed variations of the probability density function. Results Experiments based on the actual operational data of a marine EHA demonstrate that the AE-optimized Transformer-LSTM model achieves a significant enhancement in point prediction accuracy. Compared to traditional baseline models, its Root Mean Square Error and Mean Absolute Percentage Error are reduced by 18.5% and 22.4%, respectively. Regarding interval prediction, under a 95% confidence level, the ABKDE optimized via the Golden Section method increases the Prediction Interval Coverage Probability by 5.3% while simultaneously shrinking the Prediction Interval Normalized Average Width by 14.6%. Conclusions The proposed hybrid prediction architecture effectively overcomes the limitations of traditional methods regarding temporal feature extraction and manual hyperparameter tuning. It achieves a highly accurate and robust interval probability prediction for energy consumption, providing solid scientific data support for the refined energy management and highly reliable operation of marine EHAs.