Interpretable Data-Driven Ship Dynamics Model: Enhancing Physics-Based Motion Prediction with Parameter Optimization

TL;DR

The paper tackles the need for accurate, ship-specific motion prediction for autonomous navigation by bridging physics-based models with data-driven adaptation. It introduces a grey-box model that preserves a physics-based 3-DoF dynamics core while optimizing 11 interpretable parameters via constraint nonlinear least squares to fit vessel data, ensuring physical consistency. The method is validated on two container ships using synthetic MMG-based data, showing substantial improvements in trajectory prediction accuracy and reliability over baseline physics-based models and maintaining interpretability of the fitted parameters. This approach enables vessel-specific, interpretable motion models suitable for safe and efficient autonomous operation across diverse conditions.

Abstract

The deployment of autonomous navigation systems on ships necessitates accurate motion prediction models tailored to individual vessels. Traditional physics-based models, while grounded in hydrodynamic principles, often fail to account for ship-specific behaviors under real-world conditions. Conversely, purely data-driven models offer specificity but lack interpretability and robustness in edge cases. This study proposes a data-driven physics-based model that integrates physics-based equations with data-driven parameter optimization, leveraging the strengths of both approaches to ensure interpretability and adaptability. The model incorporates physics-based components such as 3-DoF dynamics, rudder, and propeller forces, while parameters such as resistance curve and rudder coefficients are optimized using synthetic data. By embedding domain knowledge into the parameter optimization process, the fitted model maintains physical consistency. Validation of the approach is realized with two container ships by comparing, both qualitatively and quantitatively, predictions against ground-truth trajectories. The results demonstrate significant improvements, in predictive accuracy and reliability, of the data-driven physics-based models over baseline physics-based models tuned with traditional marine engineering practices. The fitted models capture ship-specific behaviors in diverse conditions with their predictions being, 51.6% (ship A) and 57.8% (ship B) more accurate, 72.36% (ship A) and 89.67% (ship B) more consistent.

Figures (6)

• Figure 1: Computational flow of a physics-based vessel motion prediction model, with the following key blocks: (a) "Control": input 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: Fitted ($\mathbf{p^*}$) vs baseline ($\mathbf{\tilde{p}}$) model curves for resistance, lift ($c_L$), and drag ($c_D$) coefficients for both vessels. Note that both ships have the same rudder type.
• Figure 3: Trajectory comparison for ship A with excellent accuracy improvement. Generated trajectory: $\bar{\xi}$ from the groundtruth data, $\tilde{\xi}$ from the baseline model and $\xi^*$ from the fitted model. MD$(\%)$ per dimension is: $x:90.6$, $y:56.4$, $\psi:86.9$, $u:13.0$, $v:13.1$, $r:52.2$, and cVDM$(\%)$ is 76.0.
• Figure 4: Trajectory comparison for ship B with remarkable accuracy improvement. Generated trajectories same as in \ref{['fig:Ship_A_good']}. MD$(\%)$ per dimension is: $x:75.7$, $y:-80.3$, $\psi:77.3$, $u:-25.9$, $v:61.2$, $r:80.9$, and cVDM$(\%)$ is 69.2.
• Figure 5: Trajectory comparison for ship A with increased accuracy and minor overshoot. Generated trajectories same as in \ref{['fig:Ship_A_good']}. MD$(\%)$ per dimension is: $x:36.3$, $y:22.1$, $\psi:43.9$, $u:34.5$, $v:23.5$, $r:31.9$, and cVDM$(\%)$ is 28.0.