Extreme wave impacts can damage ships and pose a risk to those on board. An extreme wave impact can be green water: a wave impact on a ship's deck or superstructure, or slamming: a ship's underside slamming on a wave. To prevent serious accidents these green water and slamming impacts need to be minimized. Predicting the probability and impact pressures can make minimizing impacts possible. Extreme wave impacts are challenging to predict as they are multiphase, nonlinear, turbulent and rare. The rarity, complexity and variety of impacts have resulted in limited studies into the statistics of extreme wave impacts, causing questions about the probability, distributions and ranges in which impacts occur. To predict extreme wave impacts answers to these questions would be helpful.

The goal of this thesis is to study the statistics of extreme wave impacts. To fulfill this goal a large data set of extreme wave impacts is collected. A new testing facility is created to collect data by adding a wave maker to an existing recirculating tank. In the test facility water and waves flow past the model, allowing for long testing times. Three large experimental data sets with a ship with forward velocity in head waves are collected. The collected data is in total 246 hours of experimental data over 23 test cases, representing over 2766 hours of continuous sailing at full scale.

From the first experimental data set the probability of occurrence of green water and the expected maximum pressures during green water events are identified. The data set contains green water events in different sea states, forward speeds and drafts. Two proposed methods to estimate the probability of green water occurrence are compared. One method is based on the probability of water exceeding the deck and one on a ship’s freeboard and the significant wave height, the former being in better agreement with the data, the latter being more practical for designers. The maximum pressures caused by green water are distributed according to the Fréchet distribution, also called extreme value distribution II. With the newly identified distribution, an equation to calculate the probability of a pressure limit being exceeded for a ship in operation is formulated. This first data set shows that the distribution of the time between green water occurrences is exponential, indicating that when green water occurs is independent of the time since the last occurrence.

The second set of experiments is aimed at identifying the influence of surge on green water and slamming. Long-running experiments with forward velocity and irregular waves are repeated with and without surge. Surge is found to increase the probability of green water events, but the impact pressures on deck and the probability of a green water event reaching the deck box decreases when the ship is free to surge. In this second data set green water and slamming events turn out to not occur independently as both event types cluster. The clusters occur for large probabilities of occurrence, which is why the first data set did not show these dependent clusters. Clusters are caused by large pitch motions. Larger pressures on deck are found for clustered events.

The conditions under which green water occurs and the relation between water exceeding the deck and green water are investigated. The relation is not direct and a difference between green water and exceedance that does not develop into a flow on deck is identified. A proposed prediction method follows from the difference between green water and exceedance. Pitch is identified as an important indicator for green water as green water events consistently occurred with large forward pitch motion, while exceedance also occurred with neutral pitch.
A prediction method of probability is proposed that implements separate limits for the motions and wave elevation that occur simultaneously, thus including the phase difference between the motions and wave elevation.

Design variations with different drafts and freeboards at the bow are tested in the third set of tests. A large set of 3263 green water events in irregular waves with forward velocity is experimentally obtained for six different bow designs. The data demonstrates that both freeboard and draft at the bow affect the probability of green water. Increasing the draft at the bow increases the swell-up, reducing the effective freeboard and in turn, increasing the probability of green water.

Increasing the freeboard results in a decrease in the probability of green water, as expected. However, the probability is not reduced equally for different green water impact pressures. The joint probability of green water occurrence and pressures shows that increasing the freeboard only decreases the probability of low-pressure events. Increasing the freeboard increases the probability of high-pressure events. These results highlight the importance of statistics when designing for green water.

The large experimental data sets have been combined with a machine learning method: SINDy. The models are trained to predict the acceleration of heave and pitch with the parameters heave, pitch, velocity of heave and pitch and the wave elevations along the hull. As a first step, a model is trained on fictitious data. The data is based on empirical response amplitude operators. The resulting model represents a damped mass-spring system with external forcing. The identification of the damped mass-spring system with external forcing is sensitive to random noise in the input data. Models have also been trained on the experimental data available. The models trained on experimental data did not result in the expected damped mass-spring system with external forcing model. The likely cause is noise in the experimental data.@en

The original goal of the present research is to investigate the influence of surge on green water and slamming. Long-running experiments with forward velocity and irregular waves were repeated with and without surge. Surge is found to increase the probability of green water events, but the impact pressures on deck and the probability of a green water event reaching the deck box decreases when the ship is free to surge. Green water and slamming events turned out to not occur independently as both event types cluster for large probabilities of occurrence. Clusters are caused by large pitch motions. Larger pressures on deck are found for clustered events.@en

Green water is an extreme event that impacts ships and poses a risk to those on board. Conventional methods of screening assume a direct relation between exceedance and green water. This article demonstrates that the relation is not direct and identifies a difference between green water and exceedance that does not develop into a flow on deck. A proposed prediction method follows from the difference between green water and exceedance identified from analysing a big data set. The big data set is from experiments modelling 1945 full-scale hours and includes 409 green water events and 729 exceedance events which did not become green water. Pitch was identified as an important indicator for green water as green water events consistently occurred with large forward pitch motion, while exceedance also occurred with neutral pitch. A prediction method of probability is proposed that implements separate limits for the motions and wave elevation that occur simultaneously, thus including the phase difference between the motions and wave elevation. The result is a method for the prediction of the occurrence of green water on the deck of a ship with different forward velocities and in different sea states.

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Green water is a rare and complex wave impact event that can affect the safety of the ship and those aboard. During the design process, the risks that these events pose have to be mitigated, preferably by minimizing the probability of a high impact pressure. As green water events are rare and complex it is difficult to get a statistically representative dataset and thus previous work has mostly compared design variations through a limited number of events, instead of comparing the probabilities. The present study will use probabilities to compare design variations with different drafts and freeboards at the bow. A large set of green water events in irregular waves with forward velocity was experimentally obtained for six different bow designs. The dataset represents 57 hours of sailing per bow design and 3263 green water events. The data demonstrates that both freeboard and draft at the bow affect the probability of green water in a complex way. Increasing the draft at the bow increases the swell-up, reducing the effective freeboard and in turn, increasing the probability of green water. Increasing the freeboard results in a decrease in the probability of green water, as expected. However, the probability is not reduced equally for different green water impact pressures. The joint probability of green water occurrence and pressures shows that increasing the freeboard only decreases the probability of low-pressure events. Counter-intuitively, increasing the freeboard increases the probability of high-pressure events. These interesting results show the value of using statistically representative datasets when designing for green water.@en

This article proposes a method to quantify, first, the probability of occurrence of green water and, second, the expected maximum pressures during green water events using their statistical distribution for ships at forward speed. A large green water data set which represents 1945 hours of continuous sailing on full scale with different sea states, forward speeds and drafts was obtained with model test experiments in a wave–current tank. The data of the experiment are available as open data through https://doi.org/10.4121/21031981. With the large data set obtained, the distribution of the time between green water occurrences is identified as exponential, indicating that when green water occurs is independent of the time since the last occurrence. Two methods were compared to estimate the probability of green water occurrence. One method is based on the probability of water exceeding the deck and one on a ship’s freeboard and the significant wave height, the former being in better agreement with the data, the latter being more practical for designers. The maximum pressures caused by green water are distributed according to the Fréchet distribution, also called extreme value distribution II. With the newly identified distributions, finally, an equation to calculate the probability of a pressure limit being exceeded for a ship in operation is formulated.@en