Physics-informed probabilistic modelling of ship arrival time and fuel consumption under wave-induced uncertainty

Journal article, 2027

Reliable prediction of fuel consumption and estimated time of arrival (ETA) is essential for maritime operational decision support. However, added resistance due to waves is often treated as a deterministic correction, limiting the quantification of schedule delay risk and fuel consumption uncertainty under variable sea states. This study develops a physics-informed heteroscedastic Gaussian process regression (PhI-HGPR) framework for probabilistic prediction of added wave resistance and its propagation to ETA and fuel consumption uncertainty. A semi-empirical model is embedded as the Gaussian process mean function, while a non-parametric residual process and an input-dependent noise model capture model discrepancy, experimental scatter, and data sparsity in oblique wave conditions. A hybrid resampling strategy mitigates severe heading imbalance in 3081 towing tank records covering 52 ships and 288 experimental cases. The model is evaluated on five representative hulls and compared with a semi-empirical baseline and standard Gaussian process regression. Across oblique sea, it reduces prediction error relative to standard Gaussian process regression while preserving physically plausible curve shapes. The learned transfer function is embedded in a Bayesian sequential updating scheme using full-scale North Atlantic voyage data. Uncertainty in added wave resistance prediction is propagated through a fixed ship performance model, while observed leg-wise sailing times are used to update the posterior weights of candidate power profiles. Posterior distributions of ETA and fuel consumption are updated as observations are assimilated, enabling schedule reliability evaluation and fuel-exceedance risk assessment.