Predicting Wind Loads on Container Ships in Harbor Environments through Multi-Fidelity Modeling
Authors: Matilde Fiore, Andrea Bresciani, Miguel Alfonso Mendez, Jeroen van Beeck
Organizations: Environmental and Applied Fluid Dynamics Department, von Karman Institute for Fluid Dynamics, Waterloosesteenweg 72, Sint-Genesius-Rode, B-1640, Belgium · Aero-Thermo-Mechanics Laboratory, École Polytechnique de Bruxelles, Université Libre de Bruxelles, Av. Franklin Roosevelt 50, Brussels, 1050, Belgium · Aerospace Engineering Research Group, Universidad Carlos III de Madrid, Av. de la Universidad 30, Leganés, 28911, Spain
Abstract
Modern container ships face higher wind loads due to increased windage areas, making accurate predictions of wind loads essential for mooring design. Existing empirical models, largely developed for container ships with smaller windage areas and simpler geometrical configurations than those of modern large-scale vessels, often lack accuracy and do not account for the influence of nearby structures. This study proposes a multi-fidelity surrogate modelling framework for the prediction of wind-load coefficients, combining empirical correlations with simplified and detailed CFD models for ships in open-sea and harbor environments. The approach relies on recursive co-kriging to consistently fuse information across fidelity levels, enabling accurate predictions at a reduced computational cost. A sensitivity analysis is used to identify the most influential geometric parameters, and the resulting reduced parameter space is explored through sequential sampling to efficiently construct the training database. The surrogate models are validated over a wide range of loading configurations and for two distinct harbor environments. The results demonstrate that the multi-fidelity approach significantly improves prediction accuracy compared to single-fidelity models, while substantially reducing the reliance on high-fidelity simulations. In particular, the proposed framework captures the dependence of wind loads on key geometric parameters and consistently outperforms traditional empirical correlations, providing a robust and efficient tool for engineering applications.
Accurate prediction of hydrodynamic performance is central to ship design, yet high-fidelity computational fluid dynamics remains prohibitively expensive for large-scale parametric exploration. This motivates the development of data-driven surrogate models that provide rapid approximations to hydrodynamic predictions at substantially reduced cost. We present ShipNet, a geometric deep-learning surrogate that predicts both hull-surface pressure distributions and far-field free-surface wave patterns directly from hull geometry and speed. The network employs a regularized dynamic graph convolutional backbone on hull point clouds, with a multi-head decoder for simultaneous near-body pressure and free-surface elevation outputs. Training data consist of 420 inviscid free-surface simulations generated using a potential-flow panel method for two parent yacht hulls, each parameterized into 70 variants and evaluated at three speeds. ShipNet predicts per-point pressure coefficient and two-dimensional wave elevation map using a composite loss that combines point-wise regression and image-structure terms. On a geometry-held-out test set, ShipNet achieves R^2=0.98 for hull pressure and R^2=0.91 for wave fields. Inference requires approximately 0.15s per case, yielding over a 550x speedup relative to the potential-flow solver on conventional hardware. Limitations include the restricted geometry and speed ranges and the inviscid training data, while future work will extend the model to high-fidelity viscous simulations with physics-informed regularization.
This study investigates supervised machine learning techniques for identifying ship hydrodynamic coefficients from CFD-generated data from free-running simulations. Specifically, ordinary least squares and regularized regression methods are applied to Abkowitz-type manoeuvring models. Training and validation datasets are derived from URANS simulations of zig-zag and turning circle manoeuvres, which are validated against experimental benchmark data. The analysis evaluates the effects of coefficient set size, minimum training length required for predictive model training, and manoeuvre combinations on model performance. Results demonstrate the suitability of large-angle zig-zag manoeuvres for hydrodynamic system identification, provided that multicollinearity is addressed through appropriate coefficient selection, regression models, or input data variability. Larger coefficient sets offer greater model flexibility for variable conditions but are more prone to multicollinearity. Regularized regression techniques effectively mitigate multicollinearity and notably enhance prediction accuracy, as does incorporating more diverse manoeuvring data. Among tested models, Ridge regression provided the best compromise between computational efficiency and prediction accuracy.
Multi-scale dynamic wake modeling and prediction are essential for the real-time control and optimization of floating offshore wind turbines (FOWTs). In this study, wakes of FOWTs under coupled surge and pitch motions across a range of Strouhal numbers (St), which can induce wake meandering, are modeled via two novel deep-learning frameworks: physics-informed neural networks (PINNs) and Fourier neural operators (FNOs). The high-fidelity dataset is obtained from large-eddy simulations with the actuator line model (LES-AL). The results demonstrate that the dominant large-scale dynamic structures, such as meandering, can be well modeled by both frameworks; however, FNOs exhibit significant advantages over the PINN model in terms of efficiency (8-fold computational speedup and 40-fold faster convergence), long-term predictive capability, and multi-scale coherent structural fidelity. Furthermore, the wakes predicted by the PINN model exhibit a smoothing effect that limits the resolution of high-frequency coherent structures and underestimates turbulent fluctuations in both the wake center and half-width. Spectral analysis reveals that FNOs resolve the primary meandering frequency (where Stp denotes the frequency induced by the coupled surge and pitch motions), its corresponding higher-order harmonics (2Stp, 3Stp), and the energy cascade. In contrast, the energy cascade in the PINN predictions dissipates more rapidly in the high-frequency regime (St > 1.0). Additionally, the pre-multiplied power spectral density indicates that the energy contained in meandering and the corresponding harmonic frequencies modeled by PINNs is relatively low compared to that in CFD and FNOs. These findings suggest that FNOs are promising for the high-fidelity, real-time modeling of FOWT wakes.