Hierarchical Bayesian propulsion power models - A simplified example with cruise ships

Mathematical models for ships’ consumption are in a central role in assessing the CO2 emissions of marine traffic. Moreover, such models are needed when optimizing the ways the vessels are operated (e.g. routing). Nowadays, many ships are equipped with data collection systems, enabling data-based calibration of the models. Typically this calibration is done independently for each ship. In this paper, we demonstrate a hierarchical Bayesian approach, where we fit a single model over many vessels, with the assumption that the parameters of vessels of similar characteristics are likely close to each other. The benefits of such an approach are two-fold; (1) we can borrow information about parameters that are not well informed by the vessel-specific data using data from similar ships, and (2) we can use the hierarchical model to predict the behavior of a vessel from which we have no data, based only on its characteristics. In this paper, we discuss the basic concept and present a simple version of the model using cruise vessels. We apply the Stan modeling tool for the fitting and use real data from 64 ships collected via the commercial Eniram platform. The prediction accuracy of the model is compared to an existing data-free method. We demonstrate that the accuracy of such an approach can improve upon the classical resistance calculation-based methods.