Closed Form Modelling and Identification of Banking Effects in Confined Waters

TL;DR

This work tackles banking effects that arise for vessels navigating in confined waters by developing a closed-form, first-principles model of bank suction and cushioning. The authors identify model coefficients from physics-informed regression on towing-tank data and validate the banking terms with Shapley-value analysis, demonstrating the significance of bank-induced sway and yaw terms. A nondimensional formulation is derived for the banking coefficients, enabling cross-scale application provided geometric similarity is preserved. The results support real-time estimation and control applications, including bank-warning and trajectory planning in canal environments.

Abstract

Vessels navigating in confined waters are subject to banking effects, which are hydrodynamic forces and moments arising from pressure differentials between the vessel sides, significantly affecting manoeuvrability and safety. Existing numerical approaches such as computational fluid dynamics (CFD) can accurately capture these effects but are computationally expensive and unsuitable for real-time control or estimation. This paper presents a closed-form, first-principles model of banking effects. The model coefficients are identified using physics-informed regression on towing tank experiment data for a scaled container vessel. Validation through Shapley value analysis confirms the significance of the banking terms in reproducing the measured forces and moments. Lastly, the derived coefficients are shown to be non-dimensional, making the model applicable across different scales that preserve vessel geometry.

Figures (9)

• Figure 1: Model ship trajectories, forces, and moments for test scenario A, B and C from Eloot2016RunningPurposes.
• Figure 2: Banking scenario top and back view.
• Figure 3: $\delta$\ref{['eq:Delta_1']} as a function of vessel deviation from centre of canal $y$ with parameters taken from the experiments $W=7$ and $B=0.572$ (blue), and with boundary layer effect (red). Green area is the scope of the $y$ experiment data.
• Figure 4: Starboard and port side midship hull clearance with non-zero heading $\psi$. The blue line indicates the equivalent aligned canal.
• Figure 5: $\delta(y,\psi)$ with varying transverse positions and headings.