A hierarchical Bayesian approach for the modelling of ice force peaks on ship hull considering ice Thickness, concentration and floe size

Ships navigating in Polar areas are exposed to significant ice loads, characterized by stochasticity stemming from highly variable ice conditions. Accurate prediction of the ice loads is important for ensuring structural integrity and operational safety. A critical aspect of ice load prediction involves establishing reliable relationships between ice conditions and the resulting ice loads. However, inherent uncertainties in ice condition measurements significantly impact the precision of ice load predictions, and the quantitative assessment of this uncertainty remains challenging. This paper introduces a Hierarchical Bayesian Model (HBM) designed to probabilistically model ice force peak distributions as a function of ice thickness, concentration and floe size, accounting for the uncertainties associated with the covariate measurements. The model’s core framework treats the parameters of the ice force distribution as random variables that follow their own probability distributions, allowing uncertainty to be fully propagated through the model’s hierarchical structure. A Generalized Nonlinear Model (GNLM) is also introduced for a comparison purpose. The data from the 2018–2019 Antarctic voyage of S.A. Agulhas II is used to train the models. Results show successful HBM convergence and strong posterior predictive fits to both training and testing data, demonstrating robust generalization. While the GNLM is also evaluated, the comparative analysis shows it provides a poorer fit to the data, particularly for high-magnitude ice forces. In contrast, the HBM provides a robust framework for probabilistic ice force modelling, enhancing predictions under diverse ice conditions to support safer ship design and polar navigation.