A novel interval prediction method with adaptive calibration for ship energy consumption prediction

Reliable Uncertainty Quantification for Ship Energy Consumption (SEC) is important for abnormality detection and energy efficiency management under complex operating conditions. Existing studies mainly estimate SEC as single deterministic values under different operating conditions, which cannot characterize uncertainty in complex maritime environments. Using operational data from a container ship, this study proposes a novel interval prediction method with adaptive calibration, named Gradient-resolved Adaptive Calibration for Energy consumption (GrACE). The method formulates SEC interval prediction as a multi-objective learning problem involving interval quality and interval width, and further introduces adaptive calibration to adjust the aggregated prediction intervals. The method was validated on five neural networks. Results show that GrACE consistently achieved the best interval quality. Under the best performing Convolutional Neural Network at the 90% confidence level, GrACE achieved a Prediction Interval Coverage Probability of 0.8976, and reduced the Mean Prediction Interval Width (MPIW) by 56.55% compared with classical LUBE. These results suggest that GrACE can provide useful uncertainty information for SEC prediction under complex operating conditions.