Towards Real-World Validation of a Physics-Based Ship Motion Prediction Model

Abstract

The maritime industry aims towards a sustainable future, which requires significant improvements in operational efficiency. Current approaches focus on minimising fuel consumption and emissions through greater autonomy. Efficient and safe autonomous navigation requires high-fidelity ship motion models applicable to real-world conditions. Although physics-based ship motion models can predict ships' motion with sub-second resolution, their validation in real-world conditions is rarely found in the literature. This study presents a physics-based 3D dynamics motion model that is tailored to a container-ship, and compares its predictions against real-world voyages. The model integrates vessel motion over time and accounts for its hydrodynamic behavior under different environmental conditions. The model's predictions are evaluated against real vessel data both visually and using multiple distance measures. Both methodologies demonstrate that the model's predictions align closely with the real-world trajectories of the container-ship.

Figures (13)

• Figure 1: Computational flow of a physics-based vessel motion prediction model, with the following key blocks that are specific to ship maneuvering models: (a) "Control": control commands of the rudder and the propeller, (b) "Environment": environmental effects from the wind, waves, and sea currents, (c) "Force calculation": computation of forced using the outputs of (a) and (b) along with hydrodynamic forces and the current ship state, and (d) "Equations of motion": dynamics equations and integration over time to produce the next ship state.
• Figure 2: The body-fixed coordinate system of the vessel is ${y_s-x_s}$, while the earth-fixed coordinate system is ${y-x}$. The position $O_S$ and heading $\psi$ of the vessel, and the direction of the sea current $\omega$ are depicted in terms of an earth-fixed coordinate system ${y-x}$. Surge speed $u$, sway speed $v$, total speed $U$ and yaw rate of turn $r$ are depicted in terms of a body-fixed coordinate system ${y_s-x_s}$. Also, the drift angle of the vessel is depicted as $\beta$ and the rudder angle as $\delta$.
• Figure 3: Visual comparison of trajectories from FAM (our model) and an MMG model as described and reported in (Figure 3 in suyama2024parameter). N.B. The ship icons depict the heading of the FAM model. There is no actual trajectory of the real SUZAKU vessel in this plot, just a comparison between two models. The size of the vessel has been scaled for visual purposes and does not represent the actual size of the vessel.
• Figure 4: Error explanatory scenarios. Case Study 1. All dimensions are very close between actual trajectory and FAM.
• Figure 5: Error explanatory scenarios. Case Study 2. In this trajectory there is close distance in terms of $x, y$ but not as good in terms of heading $\psi$ and yaw rate of turn $r$.