The increasing size of cargo vessels poses significant challenges for ports in ensuring safe mooring, as larger ships result in higher mooring forces.
Most existing port infrastructure and mooring equipment were designed for smaller ships, making accurate estimation of mooring line forces increasingly critical.
Metamodels, machine learning models trained on numerically simulated data, offer a promising alternative to traditional, computationally expensive simulation-based methods by enabling rapid predictions with a useful level of accuracy.
This study proposes a metamodeling approach for the numerical Dynamic Mooring Analysis (DMA) to predict mooring line forces from input parameters that describe environmental conditions, mooring systems, and ship characteristics.
The methodology is demonstrated in a case study involving a 333-meter container vessel moored at a berth in the Port of Rotterdam.
A total of 11,520 scenarios were simulated using the DMA model aNySIM and used to train and test two candidate metamodels: Linear Regression (LR) and Multilayer Perceptron (MLP).
After evaluating both models on predictive accuracy, efficiency in terms of prediction speed and development effort, and interpretability, the MLP was selected as the preferred DMA metamodel.
It achieved high predictive performance, with an RMSE of 10 kN and an R² of 0.996, while offering prediction times measured in microseconds. This is more than seven orders of magnitude faster than the numerical DMA, thereby enabling large-batch predictions.
The metamodel revealed that pretension is clearly the most dominant feature for predicting the mean mooring line force, followed by MBL. For the maximum mooring line force, the most influential features were identified as pretension, windvelocity, and wind direction.

Moored vessels are subject to wave forces and moments at different frequencies, which induce motions of the body and can be transferred to the mooring lines and fenders. Under extreme forces and vessel motions, dangerous line breaking accidents can occur or the ship movements can be simply too large to continue the loading/unloading process, causing downtime of the port. An accurate modelling of the waves in the harbour and the response of moored ships is of prime importance to determine the safety and workability of the berths.

In Royal HaskoningDHV, a time domain conventional work flow (MIKE 21 BW - Harberth) is used for years. In this project the combination of the wave model SWASH and the frequency domain 3D diffraction model DIFFRAC to compute wave forces acting on moored ships is investigated, this proposed approach using the SWASH wave model comes as a possible alternative to the current practice of Royal HaskoningDHV, who experienced a sequence of numerical issues while simulating extreme incident waves with an operational Boussinesq-type model.

The objectives of the study leads to the following research question: To which extent can the SWASH wave model and the DIFFRAC model be combined in order to accurately compute wave forces acting on moored ships?

To answer this research question, the coupling tool to combine SWASH and DIFFRAC is developed with 'Full FFT' method and 'Partial Overlapping FFT' method. The coupling tool developed to combine the SWASH and DIFFRAC models proved to be consistent for the simplified tested conditions. The first-order forces computed using SWASH and DIFFRAC are generally well predicted, while larger deviations can occur for the second-order forces. This is mainly because the simplification of waterline geometry made by DIFFRAC in the computation of second-order forces.

The proposed approach using the SWASH and DIFFRAC models, combined with the developed coupling tool, is validated against model test data of waves and forces acting on a restrained ship (including regular, irregular long-crested and irregular short-crested waves in open water case and basin case). Based on the result from validation, this new developed frequency domain approach has been proven competitive with respect to the current time domain approach in both accuracy and time consuming , and can be applied to future projects.