Wave impact loads on maritime structures can cause casualties, damage, pollution of the sea and operational delays. Consequently, their extreme values should be accounted for in the design of these structures. However, this is challenging, as wave impact events are both rare and highly complex, requiring both high-fidelity simulations and long analysis durations to reliably quantify the associated design loads. Moreover, existing extreme value prediction methods are neither specifically developed nor adequately validated for wave impact phenomena. We therefore introduce the new Probabilistic Adaptive Screening (PAS) method for predicting extreme non-linear loads on maritime structures. The method integrates copula-based statistical dependence modelling with multi-fidelity screening and adaptive sampling. This framework enables efficient extreme value prediction by statistically mapping low-fidelity indicator variables to high-fidelity impact loads. The method allows for efficient linear potential flow indicators to be used in the low-fidelity stage, even for strongly non-linear load cases. The statistical framework of the method is validated against four weakly and strongly non-linear test cases, including non-linear waves, ship vertical bending moments, green water impact loads, and slamming loads. It is concluded that PAS with optimal settings accurately estimates both the short-term distributions and extreme values in these test cases, with most probable maximum (MPM) values within 2–15% of the reference brute-force Monte-Carlo Simulation (MCS) results. In addition, PAS achieves this performance very efficiently, requiring in the order of 1–3% of the high-fidelity simulation time needed for conventional MCS. These results demonstrate that PAS can reliably reproduce the statistics of both weakly and strongly non-linear extreme load problems, while significantly reducing the associated computational cost compared to MCS.

Predicting extreme values of strongly non-linear hydrodynamic responses (such as wave impact loads) is crucial for ensuring the safety and reliability of marine and coastal structures. However, this task is challenging due to the complexity and rarity of these responses. Existing methods are often limited to weakly non-linear responses or are very computationally expensive. This paper presents a new multi-fidelity method called ‘Adaptive Screening’, designed to efficiently predict extreme values of strongly non-linear wave-induced responses. These values are critical inputs for structural design and reliability analysis. Adaptive Screening combines elements of screening, multi-fidelity Gaussian Process Regression, and adaptive sampling. We validate its effectiveness through three applications: predicting the most probable maxima of second-order wave crests, vertical bending moments on a ferry, and green water impact loads on a containership. Our results demonstrate that Adaptive Screening outperforms conventional brute-force methods, achieving comparable accuracy in predicting extreme values while significantly reducing high-fidelity simulation times (especially for the most non-linear cases). Like many alternative methods, Adaptive Screening relies on a response-dependent low-fidelity indicator variable. We also show that the method performs well with realistic indicators for a range of applications. The test cases indicate that Adaptive Screening is very promising for the strongly non-linear responses it was designed for.

Floating marine litter is transported by several mechanisms, including surface waves. In studies of marine litter transport, the wave-induced drift is set to be equal to the Stokes drift, corresponding to the Lagrangian-mean wave-induced drift of an infinitesimally small tracer. Large-scale experiments are used to show how the wave-induced drift of objects of finite size depends on their size, density, and shape. We observe increases in drift of 95% compared to Stokes drift for discs with diameters of 13% of the wavelength, up to 23% for spheres with diameters of 3% of the wavelength, whereas drift is reduced for objects that become submerged such as nets. We investigate what these findings may imply for the transport of plastic pollution in realistic wave conditions and we predict an increase in wave-induced drift for (very) large plastic pollution objects. The different extrapolation techniques we explore to make this prediction exhibit a large range of uncertainty.

For the design of maritime structures in waves, the extreme values of responses such as motions and wave impact loads are required. Waves and wave-induced responses are stochastic, so such responses should always be related to a probability. This information is not easy to obtain for strongly non-linear responses such as wave impact forces. Usually class rules or direct assessment via experiments or numerical simulations are applied to obtain extreme values for design. This brings up questions related to the convergence of extreme values: how long do we need to test in order to obtain converged statistics for the target duration? Or, vice versa: given testing data, what is the uncertainty of the associated statistics? Often the test or simulation duration is cut up in ‘seeds’ or ‘realisations’, with an exposure duration of one or three hours based on the typical duration of a steady environmental condition at sea, or the time that a ship sails a single course. The required number of seeds for converged results depends on the type of structure and response, the exposure duration, and the desired probability level. The present study provides guidelines for the convergence of most probable maximum (MPM) wave crest heights and MPM green water wave impact forces on a ferry. Long duration experiments were done to gain insight into the required number of seeds, and the effect of fitting. The present paper presents part 1 of this study; part 2 [1] presents similar results for wave-in-deck loads on a stationary deck box.

In the assessment of wave-in-deck loads for new and existing maritime structures typically model tests are carried out. To determine the most critical conditions and measure sufficient impact loads, a range of sea states and various seeds (realisations) for each sea state are tested. Based on these measurements, probability distributions can be derived and design loads determined. In air gap model testing usually only few, if any, impact loads occur per 3-hour seed. This can make it challenging to derive reliable probability distributions of the measured loads, especially when only a few seeds are generated. In addition wave impact forces, such as greenwater loading, slamming, or air gap impacts are typically strongly non-linear, resulting in a large variability of the measured loads. This results in the following questions: How many impacts are needed to derive a reliable distribution? How is the repeatability of individual events affecting the overall distribution? To answer these questions wave-in-deck model tests were carried out in 100 x 3-hour realisations of a 10,000 year North Sea sea state. The resulting probability distributions of the undisturbed wave measurements as well as the measured wave-in-deck loads are presented in this paper with focus on deriving the number of seeds and exposure durations required for a reliable estimate of design loads. The presented study is Part 2 of a combined study on guidance for the convergence and variability of wave crests and impact loading extreme values. The data set of Part 1 ([1]) is based on greenwater loads on a sailing ferry and the data set of Part 2 on wave-in-deck loads on a stationary deck box.

Green water and slamming wave impacts can lead to severe damage or operability issues for marine structures. It is therefore essential to consider their probability and loads in design. This is difficult, as impacts are both hydrodynamically complex and relatively rare. The complexity requires high-fidelity modeling (experiments or CFD), whereas a statistically sound analysis of rare events requires long durations. High-fidelity tools are too demanding to run a Monte-Carlo simulation; low-fidelity tools do not include sufficient physical details. The use of extreme value theory and/or multi-fidelity modeling is therefore required. The present paper reviews the state-of-the-art methods to find wave impact design loads, which include response-conditioning methods, screening methods, and adaptive sampling methods. Their benefits and shortcomings are discussed, as well as challenges for the wave impact problem. One challenge is the role of wave non-linearity. Another is the validation of the different methods; it is hard to obtain long-duration high-fidelity wave impact data.

Green water and slamming wave impacts can lead to severe damage or operability issues for marine structures. It is therefore essential to consider their probability and loads in design. This is difficult, as impacts are both hydrodynamically complex and relatively rare. The complexity requires high-fidelity modelling (experiments or CFD), whereas a statistically sound analysis of rare events requires long durations. High-fidelity tools are too demanding to run a Monte-Carlo simulation; low-fidelity tools do not include sufficient physical details. The use of extreme value theory and / or multi-fidelity modelling is therefore required. The present paper reviews the state-of-The-Art methods to find wave impact design loads, which include response-conditioning methods, screening methods and adaptive sampling methods. Their benefits and shortcomings are discussed, as well as challenges for the wave impact problem. One challenge is the role of wave non-linearity. Another is the validation of the different methods; it is hard to obtain long-duration high-fidelity wave impact data. A planned case study is introduced, where different techniques will be put to the test and these challenges will be addressed .

In order to validate numerical results or verify design choices using experiments, knowledge about the experimental variability is essential. This variability was evaluated for seakeeping tests at forward speed with a model in a steep wave condition over the long axis of a basin and in a less steep oblique wave condition, in a commonly applied test procedure. The incoming wave and response variability was evaluated using deterministic repeat tests. The results for incoming waves at some distance before the model have been published already; the present study discusses the model responses. Overall time trace similarity as well as the amplitude and timing variability of individual wave crests and response peaks were studied, after assessing the input uncertainties. The response variability increases with distance from the wave generator for the wave crest height and (relative) ship motion peaks. The variability of the impact loads on a deck structure is large with a lot of scatter. Small wave-induced currents may build up differences in wave propagation speed between the repeat runs, which means that the seakeeping variability partly depends on previous wave conditions. A proportional relation could be identified between most response peaks and the corresponding incoming wave peaks. The timing variability of the response peaks follows from that of the incoming wave crests. Unfortunately, there is no direct relation between the response amplitude variability and that of the corresponding wave crest. The presented results can be used as reference for the typical variability of free-sailing seakeeping experiments.

Design loads for extreme wave events on ships, such as slamming and green water, are hard to define. These events depend on details in the incoming waves, ship motions and structure layout, which requires high-fidelity tools such as CFD or experiments to obtain the correct loads. These tools (presently) do not have the capability to fully resolve the long-term statistics of rare events in all metocean conditions over the ship's lifetime. The idea of ‘screening’ is to use lower-fidelity numerical methods to identify the occurrence of extreme load events based on an indicator. A good indicator has a strong correlation to the design load, but is easier to calculate. A high-fidelity tool can then be used to find the loads in these events. The low-fidelity statistics and the high-fidelity loads can be combined to define a design load and its probability. The present study compares different numerical screening indicators for green water loads on a containership against experiments. The quality of the identification of the critical events and the required computational time served as comparison metrics. This showed that screening both with potential flow tools and with coarse mesh CFD tools is feasible, provided the indicator, grid, time step and wave input settings are well chosen. The results from coarse mesh CFD are slightly better than from potential flow, but the computational costs are much higher. The results also show that the peaks and steepness of the relative wave elevation around the bow are suitable green water load indicators, as well as the undisturbed wave crests at the bow. Fine mesh CFD calculations were done for the identified events based on an example indicator, which resulted in a green water load distribution very close to that of the experiments. This study shows that screening could potentially reduce the required high-fidelity modelling time with up to ∼90% compared to common practice.

Experimental or numerical analysis of the response of ships and other floating structures starts with correct environmental modelling. The capabilities of numerical tools are rapidly expanding, but presently the evaluation of extreme events in waves (such as slamming, green water, air-gap exceedance) still requires a combination of experiments and different levels of numerical tools. The present paper describes recent efforts within the Maritime Research Institute Netherlands (MARIN) to improve experimental and numerical wave modelling and especially their combination. The ultimate objective is to be able to reproduce any wave condition from a basin or from sea in numerical tools and vice versa, including a sound treatment of basin effects, numerical effects and statistical variability. The aspects that are of importance in both types of wave modelling are first introduced, after which a number of examples of recent projects is discussed. It can be concluded that important steps were made towards linking experimental and numerical wave modelling, but there are some challenges common to all wave reproductions. Some future planned studies focussing on how to deal with them are discussed as well.

The amount of green water and the associated loads that an ocean-going vessel may encounter during its service life are important aspects to consider in the vessel's design and classification. As green water is typically a highly non-linear phenomenon, commonly the maritime industry relies on model tests to predict green water loads and their occurrence. In recent years, however, a lot of progress with Computation Fluid Dynamics (CFD) has been made in predicting non-linear flows and associated loads at a high level of accuracy. Especially in the field of wave impacts on (moored) offshore structures at zero speed, significant progress has been made and documented using CFD. A natural extension of this progress is to expand the obtained confidence in the applicability of CFD for simulating extreme wave events to applications involving vessels at forward speed. To that end, this paper presents a validation study towards the prediction of green water loading on a (typical) container vessel at forward speed by CFD. For validation, two extreme green water events were selected from a model test campaign carried out at MARIN within the context of the CRS (Cooperative Research Ships) working group 'green water dynamics'. In these tests a KRISO Container Ship (KCS) is sailing in head seas when encountering severe green water. As CFD tool, the Cartesian-grid based Volume-of-Fluid CFD solver ComFLOW was selected. Furthermore, a deterministic approach is taken for the validation, by reconstructing the non-linear incoming wave in a high amount of detail and imposing the 6 degrees of motion of the vessel using the wave basin measurements. Time traces of the green water flow on deck and local- and global impact loads on the breakwater are presented and compared against the experimental data. Detailed visualizations of the CFD results are presented to further illustrate the obtained match with the model test results and emphasize the additional value of complementing model tests with deterministic CFD analysis.

Experiments with a flat plate in oblique waves at different speeds, wave conditions, headings and drift speed were done to evaluate non-linear wave run-up along a sailing ship. Both the incoming and diffracted part of the run-up were highly nonlinear in all test conditions. The run-up was larger at 135 than at 150 deg heading, the influence of speed was small, wave steepness increased run-up up to the point of breaking and a drift speed decreased the run-up. Most of the observed differences were larger than the seed and basin variability. (Semi-) linear diffraction methods are not sufficient to predict the highest runup crests, but applying them to screen for critical events could be further studied. CFD is able to accurately predict the nonlinear run-up in such selected events. Combining different levels of tools seems the most efficient way to predict extreme wave events such as green water due to run-up.

Numerical seakeeping codes for ships at forward speed in waves are often validated or tuned based on experiments, which makes knowledge about the experimental variability essential. This variability was evaluated using repeat tests during a state-of-the-art seakeeping campaign. A steep wave condition over the longitudinal basin axis (waveA) and a less steep oblique wave condition (waveB) were studied. Overall similarity as well as individual crest height, steepnesses and timing variability are discussed, because ship response is not equally sensitive for every point in the wave time series. The variability of the measured incoming wave crests and their timing increases with distance from the wave generator for waveA. The crest height variability for waveB is lower and more constant over the basin length (because the propagation distance to the model is constant in oblique waves and wave breaking is less likely). It was shown that only a small part of the variability close to the wave generator is caused by input uncertainties such as the accuracy of the wave generator flap motions, measurement carriage position, their synchronisation and measurement accuracy. The rest of the variability is caused by wave and basin effects, such as wave breaking instabilities and small residual wave-induced currents from previous tests. The latter depend on previous wave conditions, which requires further study.