Ship fuel consumption plays a crucial role not only in understanding ships’ energy efficiency but also in gaining insights into their emissions. However, enhancing the accuracy of these predictions poses significant challenges due to data limitations and the methods employed. Due to these factors, such as data variability and equipment characteristics, ship fuel consumption exhibits certain fluctuations under specific conditions. Previous fuel consumption prediction methods primarily generate a single specific value, making it difficult to capture the volatility of and variability in fuel consumption. To overcome this limitation, this paper proposes a novel method that integrates Gaussian process prediction with quantile regression theory to perform interval predictions of ship fuel consumption, providing a range of possible outcomes. Through comparative analyses with traditional methods, the possibility of using the method is verified and its results are validated. The results indicate the following: (1) at a 95% confidence level, the proposed method achieves a prediction interval coverage probability of 0.98 and a prediction interval normalized average width of 0.123, which are significantly better than those of the existing backpropagation neural network (BPNN) and gradient boosting decision tree (GBDT) quantile regression models; (2) the prediction accuracy of the proposed method is 92% for point forecasts; and (3) the proposed method is applicable to main datasets, including both noon report and sensor datasets. These findings provide valuable insights into interval predictions of ship fuel consumption and highlight their potential applications in related fields, emphasizing the importance of accurate interval predictions in intelligent energy efficiency optimization.

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.