Predicting wave impact design loads is crucial for ensuring safety and performance of maritime structures, but it is challenging due to the complexity and rarity of these events. Existing methods are mainly suitable for prediction of weakly non-linear responses, or are very computationally expensive. Highly nonlinear responses require a fidelity level that can only be achieved with expensive CFD or experiments, leading to sparsely populated exceedance distributions. A new event-based multi-fidelity method called ‘adaptive screening’ therefore combines elements of screening, multi-fidelity Gaussian Process Regression and adaptive sampling, to more efficiently predict highly non-linear loads. It is applied at the level of the response peak exceedance probability distributions. A simplified case study using second-order wave data validates the effectiveness of the method in accurately predicting short-term design loads. The new method predicts more accurate MPM results than the conventional method recommended by class societies and the ITTC, while also significantly reducing the required HF simulation time. The new method has a deviation of only 0.3–3.5% from the true 1-hour MPM over all test cases, compared to the conventional method’s deviation of 5.2–6.7%. The HF simulation time required to do this is 91 times shorter with the new method (0.033 versus 3 hours per sea state). The new method is not very sensitive to input noise as long as HF samples are selected properly, and the application of the method to the exceedance distributions works.@en

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.

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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.

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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.

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Catamarans are popular in the offshore sector as they combine good transverse stability and ample deck space with low wave resistance. However, their slender hull shape results in low restoring qualities in heave and pitch motions. The large motions in rough weather can often result in water impacting the underside of the deck connecting the two hulls, a phenomenon called wet deck slamming. The impulse excitation from wet deck slamming can then produce a transient hydroelastic response of the structure called whipping. Whipping excites mode shapes that would not normally be present in the response, as their natural frequencies are significantly higher than the wave encounter frequency. This results in detrimental contributions to fatigue life through high-amplitude cyclical bending moments. Both the calculation of slamming loads and the prediction of resulting structural responses have been a challenge for several decades. The highly nonlinear and three-dimensional character of the phenomenon, combined with the strongly coupled fluid-structure interaction means that it is unpredictable, and even the definition of slamming events has been a matter of disagreement among researchers. Experiments are still a vital part of these investigations, for validating ever-improving numerical techniques. An essential issue with experiments is the extent to which mode shapes and natural frequencies can be emulated in model scale. Traditional hydroelastic models are segmented and use either a flexible backbone or flexible joints to introduce stiffness. This often results in an excellent description of the 2-node bending mode, but an increasing error for higher modes leads to stress inaccuracies. In this investigation, a continuous model of a catamaran is designed and produced for hydroelastic experiments. The advantages and limitations of the concept are identified, the verification against structural models is presented, and the calibration of the measurements is discussed.

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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 .

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To examine the reliability or performance of marine systems related to dynamic time-varying responses, time domain simulation may be required. But for long durations, brute-force simulation is clearly not feasible from a computational point of view to examine converged extreme value statistics. An additional challenge is defining a set of mutually exclusive and exhaustive wave excitation records which excite the desired extreme response(s). To address these challenges, this work develops a non-linear Design Loads Generator (NL-DLG) process which links wave profiles targeted for extreme responses generated via response-conditioning wave techniques to a probabilistic framework which examines the possible correlation or mutual exclusivity between those wave profiles. The end result is an ensemble of short targeted wave profiles which excite converged extreme value return-period statistics of a defined response that may be excited by multiple correlated processes. The method of the NL-DLG process is explained by applying it towards rare wave groups, where the result is an ensemble of short wave profiles which contain extreme occurrences of different wave groups targeted for the defined exposure duration. These generated wave excitation profiles are compared to physical data from the Pt. Reyes buoy and then numerical simulations are employed to consider rarer events.

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Very large waves, such as rogue waves, can be dangerous for ships and offshore structures. There is no consensus on the theoretical occurrence probability of these rogues and ocean measurements containing rogue waves are rare. This paper addresses the long-term occurrence probability of rogue waves using time-extreme (TE) and space–time extreme (STE) statistical wave models, evaluated with a significant amount of historical directional wave data from Monterey Bay, California, USA. A novel understanding of these models is obtained by exploring the area size for which the STE models estimate a higher rogue wave occurrence probability compared to the TE models. For four rogue wave and crest heights the return periods until a 95% rogue wave occurrence probability are estimated. To illustrate an application of this statistical analysis, the risk of rogue waves to a spar-type floating wind turbine is evaluated. Based on both the dynamic response and the long-term occurrence probability of the rogue wave, this research presents a new and advanced approach for a risk analysis of rogue waves to floating offshore structures.

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This paper examines the performance of 6 stiffened ship panel designs in different operational profiles. The main question of interest is: which sea states will lead to the worst panel performances in terms of reliability? As stiffened panel collapse is governed by combined lateral and in-plane loading effects (non-linear functions of the wave environment) this is not a simple problem and does not easily fit into the confines of traditional analyses. Interesting sea states for stiffened panel collapse are identified by a low-order design contour method which uses order statistics and extreme value theory. The resulting multimodal design contours pinpoint areas of interest and the panel performances are confirmed using a higher-order reliability analysis: the non-linear Design Loads Generator process. Such results have impact for creating and interpreting environmental and design contours, as well as assumptions about which operational profiles will lead to the worst system responses.

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Response-conditioning wave techniques are a rational way to link wave excitation environments with return-period extreme loading responses. By retaining the wave excitation which leads to a design response, these techniques can also define extreme combined loading scenarios. For complex or novel hull forms, combined loading may be relevant for evaluating structural reliability or adequacy. But using combined loading scenarios as inputs to high-fidelity structural or dynamic modeling tools implies that such load scenarios are realistic for the defined return-period. This paper investigates three response-conditioning wave techniques: a modified Equivalent Design Wave method, a modified Conditioned Random Response Wave method, and the Design Loads Generator, to evaluate how well they reproduce combined loading statistics for a 1000-hr return-period as compared to stochastic brute-force simulations. The investigation is carried out for extreme combined loading scenarios on a 110 m trimaran hull. The Design Loads Generator produces the most realistic extreme combined loading statistics as compared to the brute-force approach with a significant reduction in computation time based on combined load conditional probability density functions, cumulative density functions, and individual stochastic load vectors.

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Evaluating marine system reliability requires considering the interaction of a limit state with the stochastic ocean excitation. Given a range of operational profiles, a relevant question is which sea states lead to the worst-case system responses, considering the effects of short and long-term variability. If the identified subset of operational profiles indeed leads to the worst-case system responses, it is possible to assess lifetime system performance without unnecessary computational effort via this directed set of conditions. Environmental contour methods identify rare sea states assumed to excite rare responses but generally do not include response dynamics when choosing these sea states. For systems with limit states involving combined loading or with multiple failure modes, rare environmental conditions may not exclusively lead to rare responses. In this case, the response cannot be severed from the identification of relevant sea conditions but should instead drive that identification. This paper illustrates a way to construct response-based reliability contours that identify sea states most relevant for analyzing rare responses of marine systems. These sea states are compared with sea states identified by environmental contours, showing the effect on perceived system risk levels when system dynamics, short-term response variability, and long-term environmental variability are considered.

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The evaluation of marine system reliability requires the definition of the most extreme loading that a vessel is expected to experience. To quantify the risk levels associated with a full ship lifetime, some decisions must be made about which vessel scenarios are worth analyzing, i.e. the worst-case vessel scenarios. The problem is further complicated when considering extreme combined loading on a novel hull form such as a trimaran. To evaluate structural compliance with given acceptance criteria many classification societies suggest defining simultaneous load combination cases by an Equivalent Design Wave (EDW) method for use in a finite element model. This paper examines whether the EDW approach defines realistic lifetime combined loading scenarios specifically for a novel hull form like a trimaran.

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With harshening ocean environments and the push to extend the service life of vessels and platforms, lifetime structural design performance is an increasingly important factor to differentiate between design options. But despite many advancements in structural modeling, reliability analysis may still be too time consuming and computationally expensive to be employed for local design choices. Reliability analysis for stiffened ship panels is additionally complicated as the collapse mechanism is due to combined stochastic lateral and in-plane loading effects [1]. This paper employs the non-linear Design Loads Generator (NL-DLG) process [2] to efficiently estimate the probability of stiffened ship panel collapse while retaining the wave profiles which lead to lifetime responses. This information allows a direct comparison between panel options and highlights critical panel parameters which are strongly related to design robustness. The resulting ensemble of short NL-DLG wave profiles lead to similar statistical characteristics of the panel designs as do brute-force Monte Carlo Simulations, but reduce the required simulation time by a factor of nearly 87,000 for the same number of simulations. These directed wave profiles offer naval architects the opportunity to efficiently examine rare complex structural responses by linking high-fidelity structural and hydrodynamic models. The potential of the NL-DLG process is that relevant information about complex marine structures, even those with limit surfaces excited by combined non-Gaussian loading, can be obtained efficiently and in earlier stages of the design process via low-order surrogate models.@en

A theoretical basis for the occurrence of rare wave groups is developed. The work is not limited to a successive threshold crossing criteria, only that a derived Gaussian process, based on the wave elevation, has a maximum value in a given exposure time. The theory is compared with numerical Monte Carlo simulations in addition to physical oceanographic data. The wave groups, in run length, shape, and amplitude, are shown to be dependent on the wave spectrum and its spectral moments, a prescribed exposure time, and a pre-selected mean wavegroup period.@en

This paper addresses the existence of rare wave groups by examining time series data from the Pt. Reyes buoy. The buoy is operated by the Coastal Data Information Program (CDIP), University of California San Diego. The definition of rare wave groups, as defined by Kim and Troesch, used in this paper differs from the more commonly used wave group definition based on threshold crossings. With the time series data from the Pt. Reyes buoy, these rare wave groups are shown to be a naturally occurring phenomenon. The essential features of the data are examined, as well as the analysis methods and findings. By sifting through 17 years of wave elevation data from the Pt. Reyes buoy, this preliminary work addresses not only the question to what extent rare wave groups exist in nature but also what their probability of occurrence is.@en