Seakeeping Calculation Workflow for Hull Form Optimisation

16th International Symposium on Practical Design of Ships and Other Floating Structures PRADS 2025 Ann Arbor, MI, USA, October 19th-23rd 2025 Seakeeping Calculation Workflow for Hull Form Optimisation Ruddy Kurnia*, Gaspard Ducamp, and Joy Klinkenberg Maritime Research Institute Netherlands (MARIN), Wageningen, The Netherlands Abstract. This paper focuses on a workflow of seakeeping calculations for the hull form optimisation of a wind assisted ship. The optimisation was performed for a bulk carrier and a cruise ship. From the reference vessels, hull variants of the bulk carrier and the cruise ship were generated. A robust workflow was developed to perform automatic seakeeping calculations for each hull form variant. The calculations focus on the motion Response Amplitude Operators (RAOs) and the surge drift force Quadratic Transfer Functions (QTFs). Before performing the full computations over the ship variants, validation against the model tests for the reference cruise ship with sail was conducted. Surrogate models of the RAOs and QTFs were developed to be used in the optimisation workflow. Verification of surrogate models was performed against the computational results, reasonably good results are obtained. Furthermore, evaluation of the surrogate model results over a systematic variation of design parameters was performed to study the trends of motion RAOs and drift force QTFs over a design parameter variation. Finally, an optimised hull is evaluated and compared to the reference hull. Key words: Seakeeping, optimisation, cruise ship, bulk carrier, surrogate model 1. Introduction In the OPTIWISE-EU project framework, an early-stage multidisciplinary design tool was developed. The tool is referred to as CREATOR which stands for Computational results-based Regression ship design methodology for Early Assessment of Total Operational performance including Routing. The CREATOR workflow is developed for the optimisation of a wind-assisted ship. In the workflow, CREATOR considers the following aspects: i) hull design and cargo capacity, ii) propulsion performance in calm water, iii) manoeuvring and iv) seakeeping performances, v) aerodynamic performance, and vi) weather routing (voyage simulations). M. Garenaux, M. Katgert and J. J. A. Schot. [2024] reported the CREATOR development and applied the holistic design and optimisation on a Newcastlemax bulk carrier. They found that the reference ship has the largest power savings per ton cargo*miles. A further detail optimisation was performed on the propeller design as described in [B. Schalk-Meijerink, E-J. Foeth, T. J. C. van Terswisga, 2025]. J. J. A. Schot., P. G. Barrena, R. Eggers [2025] applied the CREATOR optimisation workflow for an early design of cruise ship with wind propulsion. An optimised design was obtained by considering two objectives on the average required shaft power of the ship with and without wind propulsion. Some constraints were applied covering the weight distribution, the metacentric range for the ship stability and the main particulars limits. Performance of each design candidates was evaluated in voyage simulations with weather re-routing. This paper focuses on the seakeeping calculation workflow for the hull form optimisations of the bulk carrier and the cruise ship as used in [M. Garenaux, M. Katgert and J. J. A. Schot., 2024, J. J. A. Schot., P. G. Barrena, R. Eggers, 2025]. Verification and validation of the seakeeping calculations are presented. Furthermore, seakeeping performance evaluation of the optimized hull is discussed. The seakeeping calculations were performed using SEACAL, a 3D potential flow panel solver for zeroand forward-speed seakeeping calculations in the frequency domain. SEACAL is developed at MARIN under Cooperative Research Ship framework (CRS 1) [MARIN, 2024a,b]. SEACAL solves the boundary *Correspondence to: r[email protected] 1Cooperative Research Ships (CRS) was started in 1969 and focuses on hydrodynamics, structural and related problems of all kind of ship types from a fundamental, design and operational perspective. Today, the CRS consists of 24 member organizations and companies carrying out a joint work program. More information on http://www.crships.org 1 value problems of the double-body steady potential, radiation and diffraction potentials. For forward speed cases, the velocity potentials are obtained from the source distribution solutions of the boundary element solver with Rankine source over hull and free-surface domain. For zero-speed or relatively low-speed cases, Green-function method is applied with the source distribution only over hull domain. At forward speeds, the Rankine method solves the free surface condition more accurately than the zero-speed Green-function method. The drift forces quadratic transfer functions (QTFs) are computed based on the direct pressure integration method for the quadratic part and based on the Pinkster approximation for the potential part [Pinkster, 1975]. A robust computation workflow was developed to perform automatic SEACAL calculations for each hull-form variants. SEACAL calculations were performed for the bulk carrier over 50 hull variants in ballast and scantling conditions, while for the cruise ship over 48 hull variants with four metacentric heights. Verification and validation of SEACAL results for the reference hulls were performed before the full computations over hull variants. SEACAL results for the reference cruise ship with wind propulsion were compared with model tests. The model test was performed at MARIN under the OPTIWISE project. Surrogate models of motion Response Amplitude Operators (RAOs) and surge drift force Quadratic Transfer Functions (QTF) were developed to be used in the CREATOR workflow. The surrogate models of the motion RAOs were used for the weather routing optimisation in the voyage simulation. While, the surrogate models of surge drift force QTFs were used for the ship powering optimisation related to added resistance in waves. The surrogate models were verified with the computational results from SEACAL. Furthermore, evaluation of the surrogate model results over a systematic variation of design parameters was performed to study the trends of motion RAOs and drift force QTFs. This paper is organised as follows. The design space is described in Section 2.. Description of the computational setup is presented in Section 3.. Surrogate modelling is described in Section 4.. SEACAL results are presented and discussed in Section 5.. Finally, Section 6. concludes this paper. 2. Design space Main particulars of reference ships are presented in Table 1. for the bulk carrier and the cruise ship. Based on the reference hulls, 50 hull variants of the bulk carrier and 48 hull variants of the cruise ship were generated. The hull variants are characterized with three design variables for the bulk carrier and five design variables for the cruise ship. These variables are systematically sampled using the Latin Hypercube Sampling (LHS) method McKay et al. [1979]. The design variables for the cruise ship are slenderness, block coefficient, relative LCB, beam-todraught ratio and displacement, as shown in Table 2.. The LCB is defined from amidship relative to the length overall submerged LOS with positive value being forward. Table 3. shows the design space for the bulk carrier consisting of the ship breadth (BW L), relative longitudinal centre of buoyancy (LCB) and the block coefficient (CB). The LCB is defined from the amidships relative to the ship length (Lpp) with positive being forward. The length of the ship variants is fixed as the reference vessel. These variations lead to the ship displacement variation of (71.2,96.9) kton for the ballast loading and (173.8,236.3) kton for the scantling loading. Table 1. Main particulars of the reference ships, bulk carrier and cruise ship. Particular Symbol Values Unit Bulkcarrier Cruise Length between perpendiculars LP P 294.47 - m Length overall submerged LOS -≈210 m Mean draught T18.5 ≈5.4 m Breadth moulded on waterline BW L 50 ≈25 m 2 Table 2. Design variable for the cruise ship. Design variable Symbol Range Unit Slenderness LOS ∇ 1 3 (6,10) Block coefficient CB(0.5,0.7) Relative LCB LCB Los (-5,3) % Beam-to-draught ratio B/T (2.4,6) Displacement ∆(15,30) kton Table 3. Design variables for the bulk carrier. Design variable Symbol Range Unit Breadth moulded on waterline BW L (40,50) m Relative LCB (fwd AP)LCB/Lpp (2.4,3.69) % Block coefficient CB(0.786,0.856) - 3. Computational setup This section describes SEACAL computational conditions and Grasshopper©Rhino©for SEACAL input generation. The calculations were performed with SEACAL v7.2.1. 3.1. Computational conditions 3.1.1. Cruise ship The following conditions are applied for SEACAL computations on the cruise ship. The wave frequency ranges from 0.05 to 2.4 rad/s, wave direction ranges from 0 to 180 deg with step of 15 deg, ship speeds of 0, 6, 12, 15 and 17 knots, metacentric heights GMTof 1, 3, 5, and 8 m. The choice of the maximum wave frequency is selected to be correspond to the minimum wavelength equal to a half of the minimum breadth. Frequency steps are selected to be finer in the peak frequency and coarser in the tail frequencies, i.e. 0.02 rad/s in the frequency interval between 0.3 and 0.7 rad/s, 0.2 rad/s in the frequency interval between 1.6 and 2.4 rad/s. SEACAL with Green-function method (without free surface panels) is used for the computations of the ship sailing at speeds of 0 and 6 knots. In those computations, the lid panels were added to the hull mesh for the irregular frequencies removal. For higher speeds, SEACAL computes the Rankine source over the hull panels and free surface panels. Over 48 hull variants, see Table 2., full computations were performed only with GMT= 3 m. For the other GMTvalues, restart calculations were performed by recomputing the added mass, damping coefficient, excitation forces, motion RAOs and drift forces QTFs. The same source distribution over the panels, as computed in the full computation, were reused in the restart computations. The ship’s particular data, CoG and radius of gyration were updated following the hull characteristics. The radius gyration is computed as kxx = 0.424B−7.10−4B2,kyy =kzz = 0.266Lpp −3.1−5L2 pp. This regression was derived from an existing database of similar ships. The input file is then updated in the Grasshopper©script, as described in Section 3.2.. 3.1.2. Bulk carrier The following conditions are applied for SEACAL computation for the bulk carrier. The wave frequency ranges from 0.05 to 1.6 rad/s, wave direction ranges from 0 to 180 deg with step of 15 deg, ship speeds of 0, 8, 11 and 13 knots for the scantling loading and of 8, 12 and 16 knots for the ballast loading. 3 Depending on the hull form variants, the input file is updated in the Grasshopper©script, Section 3.2.. The radius of gyration was obtained by a regression from an existing database, where kxx = 0.35B, kyy =kzz = 0.25Lpp. Mesh sensitivity study was performed before running the full computations. The full computations were then performed over 50 hull form variants, for each of the two loading conditions. 3.2. Grasshopper©Rhino©for SEACAL input generation A workflow in Grasshopper® Rhinoceros® has been developed to provide a consistent mesh file and a parameter input file (.xml) for each hull form. The workflow starts by reading a hull form file (.3dm), a hydrostatic file (.lis) and a template of SEACAL input file (.xml). The main ship particulars are taken from the hydrostatic file. The hydrostatic file is used for computing the centre of gravity (CoG) position. Longitudinal and transversal position of CoG are obtained from the centre of buoyancy, the vertical position (VCG) is obtained from the KM value and the GMTinput. In the bulk carrier case, the VCG is directly computed to be 50% of the depth of the vessel in ballast condition and 55% in scantling condition. A SEACAL input file (.xml) is then created containing the main particulars, CoG position, radius of gyration, wave directions, wave frequencies, ship speeds and other numerical setting. The main particular data and the ship hull form are used for re-computing hydrostatics in the Grasshopper® and obtaining a waterline curve. This curve is then used for trimming the hull form to get underwater hull form. The trimmed hull form is split into several surfaces, i.e. bow, mid-hull and stern surfaces. Those surfaces are panelled and then save to a .vtk file. In the Grasshopper® Rhinoceros® with MARIN’s plugins, the Gen tool is used to create unstructured mesh on the split surfaces. For each grid, a fixed grid size can be specified. So this approach is suitable for a large change in the hull form variants. A strategy in defining the grid size is needed so that the mesh has a sufficient total panel to obtain an efficient computation. The grid size at the mid ship is defined as ∆x=λmin/9where the minimum wavelength equals to the half breadth, λmin =B/2. A grid refinement is applied to the bow and stern surfaces. This approach fixes the grid size for the hull variants with the same breadth. This leads to finer panels for more slender hulls or smaller breadth hulls. Figure 1. shows the meshes for the cruise ship variants, ship 3 for the smallest displacement, ship 33 for the largest displacement, ship 9 for the smallest slenderness and ship 2 for the largest slenderness. Figure 2. shows the meshes for the bulk carrier variants, ship 34 for the minimum breadth and ship 2 for the maximum breadth. Figure 1. SEACAL meshes for the cruise ship variants: the largest and smallest displacements variants, and the largest and smallest slenderness variants from the top to bottom plots respectively. 4 Figure 2. SEACAL meshes for the bulk carrier variants: the smallest breadth variant, ship 34, and the largest breadth variant, ship 2, for the scantling draft. From top to bottom are ship 34 (side view), ship 2 (side view), ship 34 (top view) and ship 2 (top view), respectively. 4. Surrogate modelling This section discusses the methodology for developing and evaluating the surrogate models. 4.1. Surrogate model development A systematic approach was applied in the development of surrogate models. A wide range of models, from simple white-box models, such as linear regression, to black-box models, such as neural networks and ensemble methods (as those implemented in Scikit-Learn in [Pedregosa et al., 2011] and XGBoost [Chen and Guestrin, 2016]), was considered. Before training any model on the dataset, a series of preprocessing steps was applied to make the input data as informative as possible. Several strategies were considered: • Normalization 2, which scales the features to a common range and can improve the convergence and stability of many learning algorithms. • Polynomial feature combinations 3, to allow models to learn potentially more complex, non-linear relationships between variables. In order to compare the models in a systematic and fair manner, 5-fold cross-validation was employed 4. As illustrated in Figure 3., this technique splits the dataset into five subsets. At each iteration, one subset is held out for model evaluation, while the remaining four are used for training. This process is repeated five times so that each subset serves as the test set once. Although more computationally expensive, this approach offers two major advantages: 2Scikit-learn on standardization 3Scikit-learn on polynomial features 4Scikit-learn on cross-validation 5 • It helps to mitigate or at least detect overfitting by ensuring that the model is evaluated on unseen data during each iteration. • It enables a more robust comparison between different models by reducing the variance associated with a single train/test split. Figure 3. Illustration of 5-fold cross-validation. The dataset is split into five equal parts (folds), and the model is trained five times, each time using a different fold as the test set (in green) while the remaining four folds are used for training (in blue). This approach ensures that every data point is used for both training and evaluation, providing a more robust assessment of model performance. All combinations of models, preprocessing strategies, and cross-validation configurations were then systematically evaluated to identify the best-performing models. Each configuration was assessed using standard performance metrics—such as mean squared error (MSE), R² score, or others depending on the problem formulation. This quantitative evaluation allowed us to objectively compare the different approaches and select those offering the best balance between accuracy, robustness, and computational efficiency. Separate models were trained for each individual component of force and motion transfer functions, in order to reduce the complexity of the learning task. This approach also allowed us to identify and select the most suitable model for each output, giving us the flexibility to focus on the most challenging cases when needed. 4.2. Surrogate model evaluation In the case of the bulk carrier, the most effective models were ensemble methods. In particular, algorithms such as Random Forest and Extra Trees Regressor demonstrated strong predictive capabilities, likely due to their robustness to noise, ability to model non-linear relationships, and limited requirement for hyperparameter tuning. These tree-based ensembles are particularly well-suited to tabular datasets with moderate dimensionality and perform well even with relatively small training sets. However, when applied to the cruise ship case, these ensemble models proved insufficient, especially for predicting roll motion. We attribute this to two main factors: • The roll response is inherently complex and non-linear, which makes it difficult to capture with ensemble methods that tend to model variable interactions in a relatively rigid and piecewise manner. • The training dataset for the cruise ship exhibited greater variability in term of design parameters while still being relatively limited in size. To address this, a fully connected neural network was used, whose structure and parameters are listed in Table 4.. The rationale behind this choice is the flexibility and adaptability of neural networks, which can approximate complex, non-linear mappings between inputs and outputs, provided that the architecture is well-tuned and regularized. In this context, the neural network outperformed the ensemble methods and delivered significantly better results for the cruise ship case, particularly in predicting roll. 6 Table 4. Neural network architecture and training parameters. Parameter Value Network size [64,64] Activation ReLU Optimizer Adam Learning rate 1e-3 Nr. of epochs 500 5. Results and analysis This section presents SEACAL computational and surrogate model results and analysis. The results are presented for the cruise ship and bulk carrier. 5.1. Cruise ship 5.1.1. SEACAL results for the reference ship Before performing the full computations over ship hull variants, comparison between SEACAL and model test were performed for the reference ship. The computational results were compared to the model test with sail. For the comparison against the model test with sail, the roll RAO from SEACAL were tuned to the model test. Figure 4. shows the motion RAOs for the ship sailing at 12 knots in stern-quartering seas in 17 knots True Wind Speed (TWS) and 90 deg True Wind Angle (TWA). A reasonably good agreement in the motion RAOs between SEACAL and the model test is achieved. Figure 4. Comparison of the motion RAOs between SEACAL (dashed-line) and the model test data (+) for the ship sailing at 12 knots in stern-quartering seas (30 deg) and in wind conditions of 17 knots TWS and 90 deg TWA. 7 5.1.2. SEACAL results for the ship variants Figure 5. shows the motion RAOs over 48 hull variants. The result shows a clear variation of motion RAOs, particularly in the heave, roll and pitch RAOs. This large variation in the motion RAOs represent a large variation in the particulars of the hull variants. Furthermore, a large variation is also shown in the surge drift force QTFs, see Figure 6.. The peak QTF magnitude varies from 100kN/m2to 400kN/m2. Large variation in the design variables makes it difficult to study trends of RAOs and QTFs from the computational results. The trends can be studied in a later section from evaluation of surrogate models that have been developed from these dataset. Figure 5. Motion RAOs results over 48 hull variants at 12 knots. From top to bottom plots are surge, heave and pitch in head seas, 180 degree heading (left column) and sway, roll and yaw in stern quartering seas, 45 degree heading (right column). Figure 6. Surge drift force Quadratic Transfer Functions (QTFs) over 48 hull variants at 12 knots in head seas (180 degree heading) 8 5.1.3. Verification of surrogate models Surrogate models have been developed with the model training over 48 ships. The reference ship was not included in the training. In this section, the results of the surrogate models are compared to the SEACAL data for the reference ship. Figure 7. shows the roll motions RAOs and surge drift force QTFs for the reference ship sailing at 12 knots. The contour RAOs are quite well reconstructed by the surrogate models with some discrepancies in the magnitude. Further improvement of the surrogate model prediction might be needed but the predicted trend over ship variation contributes more in the hull form optimisation process as discussed in the next section. Figure 7. Comparison between SEACAL (left) and the surrogate model (middle) for the roll motions RAO (top) and surge drift force QTF (bottom). The differences are shown at the right column. 5.1.4. Surrogate model results for a systematic variation of the design parameters The density plots over a systematic variation of design parameter while keeping constant for the other parameters, are shown in Figure 8. for the heave and roll RAOs, and the surge drift force QTFs. The drift force QTFs are shown for the ship sailing at 12 knots in head seas (180 deg) while the motion RAOs at the same speed in beam seas (90 deg). The heave RAO over the displacement variation shows that the natural frequency is shifted to a lower frequency for increasing displacement. The trend over relative LCB is similar as the trend over the displacement but to a lesser extend. Conversely, the slenderness variation shifts the natural frequency to a higher frequency for more slender ships. The trend is similar as in the variation over CB. The roll RAOs over the variation of B/T or displacement show a similar trend. The peak frequency is shifted to the lower frequency for increasing B/T or displacement. It is clear that a larger ship with larger displacement or larger B/T gives a smaller response in the roll RAO. Conversely, the increasing slenderness or CB increases roll RAO. The roll RAO shows small variation over the variation of relative LCB . The surge drift force QTF over the variation of displacement shows that the peak frequency is shifted to the lower frequencies for the ship with a larger displacement. The trends over the variation of B/T or relative LCB are similar, the magnitude at the peak is larger for a larger value of B/T or for a more forward LCB position. The peak QTF does not change over the CB variation. The drift force magnitude decreases for a more slender ship. 9