Sea State Characteristics Research Articles

Statistical Modeling and Applications of Joint Distributions for Significant Wave Height, Spectral Peak Period, and Peak Direction of Propagation: A Case Study in the Norwegian Sea

The estimation of long-term extreme response is a crucial task in the design of marine structures. The target extreme responses are typically defined by annual exceedance probabilities of 10−2 and 10−4. Various approaches can be employed for this purpose, with preference given to statistical long-term analysis, which involves aggregating the exceedance probabilities of all potential sea states contributing to the exceedance of the target extremes. A joint model encompassing important metocean parameters such as wind, waves, and current is often necessary. This study specifically focuses on waves and wave-induced responses. In characterizing short-term sea state conditions, significant wave height (Hs), spectral peak period (Tp) and peak direction of propagation (Φp) are identified as the most important sea state characteristics. The objective of this work is to present the results of the joint model for the three sea state parameters, i.e., Hs, Tp and Φp, at an offshore site in the Norwegian Sea. The conditional modeling approach is applied using long-term hindcast data, and different statistical models are discussed for fitting the marginal and conditional distributions. The fitted parameters for all directional sectors are provided, offering a comprehensive representation of the joint model for direct use in long-term response analysis. Two case studies are included to illustrate the application of the fitted joint model in long-term response analyses. The case studies identify the governing wave directions and the most important combinations of short-term sea state characteristics regarding the estimation of long-term extreme responses.

A novel geometry of an onshore Oscillating Water Column wave energy converter

This study aims proposing a novel geometry of the onshore Oscillating Water Column (OWC) device to increase its efficiency. A comparison between standard OWC's and the new proposal ones, in which the exterior front wall is inclined in opposite direction from that of the incident wave, is carried out. Simulations of 2D flows, with incompressible water and compressible air, are performed by means of the FLUENT® software, which is based on Reynolds-Averaged Navier-Stokes equations. The k-ϵ turbulence model and the Volume of Fluid method are employed. Analyses of the hydrodynamic and aerodynamic behavior, run-up/down on the exterior front wall, sloshing inside the chamber and the energy balance of OWC devices equipped with the Wells turbine and with different wall slopes (40° − 90° from horizontal) are carried out for incident regular waves with periods from 6 to 12 s and height of 1.5 m. The new proposal OWC's provide higher extracted energy than standard ones. The best performances are reached by wall slope of external front wall of 40° and internal wall slopes of 40° and 52°, although the more efficient solution depends on the sea state characteristics of the region where the OWC will be installed.

Automated detection of offshore wave power using machine learning techniques

BackgroundVarious statistical methods are used for estimating sea state and wave characteristics using digital wave models. Several machine learning techniques help to develop the computational difficulties of these methods. Materials and methodsThis study aims to estimate the wave power with Extreme Learning Machine (ELM), Regression, Restricted Boltzmann Machine (RBM), and RBM-ELM methods using nonlinear wave input parameters at different depths. Furthermore, the performance criteria are improved by applying the Relief feature selection algorithm to these methods. The input bias and input weights for the ELM have been determined using the RBM. ResultsIn the RBM-based presented method, the highest estimation values were obtained using Relief feature selection and without Relief as 96.96% and 94.02%, respectively. The highest accuracy rate based on ELM is 76.86% in the estimation of wave power without Relief. In the same way, the accuracy rate with Relief was calculated as 92.16%. These values were increased to 90.10% (without Relief) and 95.73% (with Relief) using the RBM-ELM method. ConclusionsThis study demonstrates that the performance of the presented methods with Relief feature selection was improved.

Joint spatial modeling of significant wave height and wave period using the SPDE approach

The ocean wave distribution in a specific region of space and time is described by its sea state. Knowledge about the sea states a ship encounters on a journey can be used to assess various parameters of risk and wear associated with this journey. Two important characteristics of the sea state are significant wave height and mean wave period. We propose a joint spatial model of these two quantities on the north Atlantic ocean. The model describes the distribution of the logarithm of the two quantities as a bivariate Gaussian random field, modeled as a solution to a system of coupled fractional stochastic partial differential equations. The bivariate random field is non-stationary and allows for arbitrary, and different, smoothness for the two marginal fields.The parameters of the model are estimated from data using a stepwise maximum likelihood method. The fitted model is used to derive the distribution of accumulated fatigue damage for a ship sailing a transatlantic route. Also, a method for estimating the risk of capsizing due to broaching-to based on the joint distribution of the two sea state characteristics is investigated. The risks are calculated for a transatlantic route between America and Europe using both data and the fitted model. The results show that the model compares well with observed data. It further shows that the bivariate model is needed and cannot simply be approximated by a model of significant wave height alone.

Onboard tuning of vessel seakeeping model parameters and sea state characteristics

It is essential for a safe and cost-efficient marine operation to improve the knowledge about the real-time onboard vessel conditions. This paper proposes a novel algorithm for simultaneous tuning of important vessel seakeeping model parameters and sea state characteristics based on onboard vessel motion measurements and available wave data. The proposed algorithm is fundamentally based on the unscented transformation and inspired by the scaled unscented Kalman filter, which is very computationally efficient for large dimensional and nonlinear problems. The algorithm is demonstrated by case studies based on numerical simulations, considering realistic sensor noises and wave data uncertainties. Both long-crested and short-crested wave conditions are considered in the case studies. The system state of the proposed tuning framework consists of a vessel state vector and a sea state vector. The tuning results reasonably approach the true values of the considered uncertain vessel parameters and sea state characteristics, with reduced uncertainties. The quantification of the system state uncertainties helps to close a critical gap towards achieving reliability-based marine operations.

On the distribution of maximum crest and wave height at intermediate water depths

We report new descriptions for the (probability) distributions of hourly maximum crest and wave height of water surface gravity waves for intermediate water depths. Estimated distributions are based on analysis of laboratory-scale measurements at the DHI wave basin. For a given sea state, the distribution of both hourly maximum crest and hourly maximum wave height, normalised by sea state significant wave height, is found to follow a generalised extreme value (GEV) distribution. Variation of the three parameters of the GEV distribution across sea states, is expressed in terms of a response surface model as a function of non-dimensional sea state Ursell number and wave steepness, and wave directional spreading angle. For inference, conventional Monte Carlo wave basin measurements are supplemented with measurements selected by means of a novel “pre-selection” sampling scheme using numerical simulations. This scheme effectively guarantees that extreme events from tails of distributions are produced, and reduces uncertainties associated with the estimated distributions. Estimation is performed using Bayesian inference, allowing uncertainties to be quantified, and providing estimates of posterior predictive tail distributions for sea states with arbitrary characteristics within the domain of sea state characteristics covered by the model.

Anti submarine Warfare Oceanography

Anti-submarine warfare (ASW) Oceanography has become an important and independent discipline, especially after World War II as the threat perceptions from hostile underwater platforms has been on a continuously rising trajectory worldwide. There is no doubt that till date, acoustic energy remains the only viable and most effective means to detect underwater objects. However, sound waves are highly susceptible to refraction, reflection, scattering, reverberation and absorption in the ocean medium. Among these, refraction is controlled by the 3D sound speed structure in the specific ocean region and reflection loss by the sea state and ocean bottom characteristics. Water quality parameters such as sediment concentration and suspended biological masses influence attenuation, scattering, reverberation and absorption. Oceanographic variability emerges from diurnal heating, seasonal changes, river discharges, etc. and are the most important environmental factors deciding the 3D sound speed structure in any given area in the ocean.

A novel spectral moments equivalence based lumping block method for efficient estimation of offshore structural fatigue damage

This paper provides a novel lumping block equivalence method, termed as spectral moments equivalence (SME) based method, to improve the efficiency of fatigue assessment in preliminary design stage. In the newly SME method, an equivalent equation of representative sea state’s spectral wave energy and original sea state’s spectral wave energy is set up in the fatigue equivalence viewpoint. The relations of wave parameters and wave spectral moments are introduced into the SME method to determine the equivalent significant wave height and up-crossing wave period of the representative sea state. A key feature of the SME method is that the effect of S-N curve’s slope and quantity of sea state in lumping block is incorporated into the equivalent formulae to make the method applicable to different lumping block partitions and fatigue curves. In addition, the SME method also has advantage of preserving the stochastic characteristics of sea states. Cumulative fatigue damage of fixed and floating offshore platforms are generated to verify the validity and applicability of the SME method. Numerical results indicate that the SME method not only yields the most accurate fatigue assessment but also has robustness to block partitions and offshore structures.

Can Rogue Waves Be Predicted Using Characteristic Wave Parameters?

AbstractRogue waves are ocean surface waves larger than the surrounding sea that can pose a danger to ships and offshore structures. They are often deemed unpredictable without complex measurement of the wavefield and computationally intensive calculation, which is infeasible in most applications; consequently, there a need for fast predictors. Here we collate, quality control, and analyze the largest data set of single‐point field measurements from surface following wave buoys to search for predictors of rogue wave occurrence. We find that analysis of the sea state parameters in bulk yields no predictors, as the subset of seas containing rogue waves sits within the set of seas without. However, spectral bandwidth parameters of rogue seas display different probability distributions to normal seas, but these parameters are rarely provided in wave forecasts. When location is accounted for, trends can be identified in the occurrence of rogue waves as a function of the average sea state characteristics at that location. These trends follow a power law relationship with the characteristic sea state parameters: mean significant wave height and mean zero upcrossing wave period. We find that frequency of occurrence of rogue waves and their generating mechanism is not spatially uniform, and each location is likely to have its own unique sensitivities, which increase in the coastal seas. We conclude that forecastable predictors of rogue wave occurrence will need to be location specific and reflective of their generation mechanism. Therefore, given location and a sufficiently long historical record of sea state characteristics, the likelihood of occurrence can be obtained for mariners and offshore operators.

Ocean wave characteristics prediction and its load estimation on marine structures: A transfer learning approach

Statistical and stochastic approaches, commonly used to estimate wave induced loads in the marine and coastal structural analysis and design of offshore vessels and platform, require accurate sea state or wave characteristics, which are usually estimated using computationally intensive numerical wave models. While advances in machine learning helps to overcome the computational challenges of these approaches, they still need measurement of historic data at the region of interest to help prospective estimation of wave loads. This calls for deployment of sensors and allied resources for continuous monitoring and collection of streaming data. Transfer learning, on the other hand, provides a framework to derive representations from an existing region to estimate the characteristics in the region of interest. Deep Belief Networks are excellent candidates for latent representation of the relationship between the different sea state characteristics and the induced loads. In this paper, we first train a DBN based wave characteristic prediction model to predict the sea state characteristics (namely, significant wave height Hs, dominant or peak wave period Tp and average or zero crossing period Tz) using data from 12 stations at 3 geologically different regions (the Gulf of Mexico, the Korean Region and the UK region), using data between the period Jan 1, 2011 and Dec 31, 2014. We validate the model using data in these regions between Jan 1, 2015 and Aug 30, 2015. We then compute the effect of the wave characteristics, namely, the wave-drift force and moment on 12 different marine structures with both regular and irregular waves. Finally, we transfer the DBN representations to predict the sea state characteristics in Irish region for the same period. Evaluations against ground truth and comparisons with state-of-the-art methods show the superior transfer learning performance of the DBN and accurate computations of the wave drift force and moments.

Global ship accidents and ocean swell-related sea states

Abstract. With the increased frequency of shipping activities, navigation safety has become a major concern, especially when economic losses, human casualties and environmental issues are considered. As a contributing factor, the sea state plays a significant role in shipping safety. However, the types of dangerous sea states that trigger serious shipping accidents are not well understood. To address this issue, we analyzed the sea state characteristics during ship accidents that occurred in poor weather or heavy seas based on a 10-year ship accident dataset. Sea state parameters of a numerical wave model, i.e., significant wave height, mean wave period and mean wave direction, were analyzed for the selected ship accident cases. The results indicated that complex sea states with the co-occurrence of wind sea and swell conditions represent threats to sailing vessels, especially when these conditions include similar wave periods and oblique wave directions.

An innovative block partition and equivalence method of the wave scatter diagram for offshore structural fatigue assessment

The fatigue assessment plays an increasing role for the offshore structural safety. Many fatigue assessment methods have been developed for this purpose. Among those methods, the time domain method is regarded as the most accurate method but less adopted in practice due to time consuming. In order to improve the efficiency of the time domain method, an innovative block partition and equivalence method of the wave scatter diagram is developed for offshore structural fatigue assessment. After the wave scatter diagram is partitioned into several blocks, the newly developed method, involves determination of the equivalent wave height, wave period and occurrence probability of the representative sea states based on modified energy equivalent principle. The equivalent wave period of the representative sea state is calculated via the spectral moment formula in which the equivalent spectral moments of zero and second order are obtained based on the weighted averaging principle. Combining with the determined wave period, the equivalent significant wave height can be determined by reversing the wave spectrum integral formula, where the equivalent wave energy of a divided block of the wave scatter diagram is modified by introducing a factor to compensate the effect of low- and high-amplitude cycles fatigue damage. The equivalent occurrence probability is equal to the summation of the original sea states’ occurrence probability within the divided block. The developed method has the advantage of preserving the stochastic characteristics of the short term sea states within the divided block during determining the representative sea state. At the same time the newly developed method has no limitation on block partition and can be applied on different offshore structure. Two structural models, a fixed mono-pile platform and a floating semi-submersible platform, are demonstrated in the numerical examples. Results indicate that the newly developed method is robust, computationally affordable, and accurate within engineering expectations.

Extreme Wave Condition at Doggerbank

In design of offshore wind turbines, extreme wave conditions are of interest. Usually, the design wave condition is taken as the sea state corresponding to an annual exceedance probability of 2 × 10−2, i.e., a return period of 50 years. A possible location for a future wind farm, consisting of bottom fixed wind turbines, is the Doggerbank area. The water depth in this area varies from about 60 m in the north to about 20 m in the south. The hindcast database NORA10 provides sea state characteristics from 1957 to present over a domain covering Doggerbank. Regarding the deeper areas just north of Doggerbank, this hindcast model is found to be of good quality. Larger uncertainties are associated with the hindcast results as we approach shallower water further south. The purpose of the present study is to compare sea state evolution over Doggerbank as reflected by NORA10 with the results of the commonly used shallow water hindcast model SWAN. The adequacy of the default parameters of SWAN for reflecting changes in wave conditions over a sloping bottom is investigated by comparison with model test results. Extreme wave conditions for two locations 102.5 km apart in a north–south direction are established using NORA10. This is done using both, an all sea states approach and a peak over threshold (POT) approach. Assuming the extremes for the northern position to represent good estimates, the wave evolution southward is analyzed using SWAN. The extreme condition obtained from NORA10 in the northern position is used as input to SWAN and the results from the two hindcast models are compared in the southern position. SWAN seems to suggest a somewhat faster decay over Doggerbank compared to NORA10.

Sea state conditions for marine structures' analysis and model tests

The study reviews, based on the state-of-the-art findings, some uncertainties associated with wave data and models currently used in design and operation procedures of ship and offshore structures. Although the same basic principles prevail for hydrodynamic loads on ships and offshore structures, actual problems and methods for assessing these loads in the design and operation stage are not the same. Different wave data and models are used for specifying design and operational criteria for these two types of platforms and different uncertainties are related to them. Wave data and models used to define sea state characteristics are discussed and particular attention is given to the associated sources of uncertainties. Some weaknesses of wave input used in design and operational procedures for marine structures are pointed out. Focus is also given on uncertainties related to model tests as tank testing is an important supporting tool for design and operation. Impact of some selected uncertainties on wave description and wave loads is demonstrated by examples.

On the Capability of Hybrid-Polarity Features to Observe Metallic Targets at Sea

In this paper, target at sea detection is addressed using hybrid-polarity (HP) synthetic aperture radar (SAR) architecture. Wave polarimetry concepts are used to define HP features that are used to observe targets at sea. The sensitivity of HP features to both targets and the surrounding environment is analyzed through a novel objective norm, namely the Relative Sensitivity for Polarimetric Features (RSPolF) index. Detection performance is evaluated by the novel Dependency of Sea state and Target (DoST) surface characteristics metric, and by the well-known Figure of Merit (FoM). Experiments undertaken on HP measurements emulated from Radarsat-2 and ALOS-PALSAR full-polarimetric actual SAR data demonstrate the effectiveness of the proposed HP approach and the different sensitivity of HP features to targets and background sea characteristics. Following those results, a ranking of the HP features performance is proposed which mainly highlights that HP features complement each other in the detection process. Finally, a constant false alarm rate (CFAR) approach is proposed to exploit two HP features for target detection in an unsupervised way.

Probabilistic modeling of directional and linear characteristics of wind and sea states

The analytic wind and wave climate modeling is important for a variety of ocean engineering applications. Usually, the probabilistic description of the wind and wave regime is confined to the linear characteristics of sea states and wind conditions, i.e., the significant wave height, wave period and wind speed. Rapidly emerging applications, such as offshore wind and wave energy utilization, are largely dependent on the accurate description of the directional wind and wave characteristics of the areas under study. In this work, two analytic bivariate probability models for the joint distributions of: (a) significant wave height–wave direction, (b) wind speed–wind direction and (c) wave direction–wind direction are presented, discussed and applied in detail. The proposed models, which take into consideration the dependence of the corresponding variables and are defined by closed-form relations, are theoretically sound and tractable. Numerical results are provided for three locations along the US coasts, which are characterized by different characteristics of wind and wave climate. The proposed joint distributions elucidate the probabilistic structure of the wind and wave climate patterns and, furthermore, they allow the assessment of the special and important cases of aligned and opposing wind and sea states.

Real-Time Heave Motion Estimation using Adaptive Filtering Techniques

Active heave compensation (AHC) systems require an accurate estimate of the vertical vessel motion in order to decouple the offshore crane's lift operation from the motion of the vessel. In this work, the heave motion is estimated based on measurements from an inertial measurement unit (IMU) using an adaptive heave filter whose parameters are adapted online. A standard double integrating heave filter introduces large phase errors resulting in large estimation errors for real-time applications. This work presents three modifications of a standard heave filter in order to reduce those phase errors. The error composition of each proposed filter is analyzed. The results are used to derive error functions which are minimized in order to obtain the optimal filter parameters. Furthermore, sea state characteristics, such as the mean heave height and the dominant heave frequency are determined online and utilized for parameter adaptation. The real-time estimation accuracy improves significantly when applying the phase correction algorithms to the filters. This is evaluated using measurement results from the Liebherr AHC test bench.

Euler characteristics of oceanic sea states

We present an application of a novel Variational Wave Acquisition Stereo System (VWASS) for the estimation of the wave surface height of oceanic sea states. Specifically, we show that VWASS video technology combined with statistical techniques based on Euler Characteristics of random fields provides a new paradigm for the prediction of wave extremes expected over a given area of the ocean.

Complexity assessment of human–computer interaction

A quantitative complexity theory of human–computer interaction is presented and validated by means of laboratory experiments. Based on the seminal work of Grassberger in theoretical physics, a complexity measure is introduced. The measure is termed the Effective Measure Complexity and has three main advantages. First, it relies solely on information-theoretic quantities, which are intimately connected with the concept of complexity and not randomness. Second, it is model independent and can be estimated efficiently from data. Third, the estimates can be derived from behavioural patterns in terms of observable interaction events alone. Subjective ratings or psychophysiological measurements can be included but are not mandatory. In order to explain the theory, a simple and easy to generalise example in mobile human–computer interaction is presented. Furthermore, the external validity of the complexity measure is studied in laboratory experiments. The experimental task was to search for multiple targets on an electronic chart display and information system (ECDIS). ECDIS is an integral component of modern ship bridge concepts and therefore the experiments were carried out in a marine simulator. Thirty users participated. The platform motion (with or without motion) and the workplace illumination (800 lux or 30 lux) were varied systematically and the complexity effects were studied. The results show that the complexity of the visual search processes is significantly lower when the simulator is put in sea state characteristics and the users are facing straining motion forces. In addition, interaction complexity is significantly lowered when illuminance is reduced from the daylight level of 800 lux to the twilight level of 30 lux. Therefore, the complexity measure seems to be a valid for the quantitative assessment of human–computer interaction.

Simulation of the mean zero-up-crossing wave period using artificial neural networks trained with a simulated annealing algorithm

The aim of this work was to develop a predictive model to forecast the mean zero-up-crossing wave periods (T z ) for 3-hourly sea states at a location in the Pacific using artificial neural networks (ANNs). Seven multilayer ANNs were trained with a simulated annealing algorithm. The output of each trained ANN was used to estimate each of the seven parameters of a new distribution called the hepta-parameter spline proposed for the conditional distribution of T z , given some mean zero-up-crossing wave periods and significant wave heights. After estimating the parameters of the distribution, the model was used to simulate and predict future values of T z . Forecasting a sea state and developing the joint distribution of sea state characteristics with the help of the simulated characteristics are also discussed in this article.