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Significant wave height is the most important parameter in feasibility studies and the design of wave energy converters. In this study, the novel nested artificial neural networks were developed and applied to predict significant wave height at twenty selected locations of the North Sea. A nested artificial neural network applies nonlinear machine learning models as transfer functions in the neurons of networks. Two input parameters comprising wind speed and wind direction were implemented to train the derived models. The results show that the derived nonlinear machine learning models are about 18.39% more accurate than the linear regression technique. The statistical indices confirm that the nested artificial neural network may increases the accuracy of traditional models by up to 34%. Among all applied models, the nested artificial neural network developed based on the integration of particle swarm optimization algorithm and adaptive neuro-fuzzy inference system, with RMSE = 0.525m and R 2 = 0.84, provides the most accurate prediction of wave heights. The high accuracy of the results indicates that if computational time is not a very critical factor for users, then the application of nested artificial neural networks may be recommended for the modeling of wave parameters and other complex problems. [ABSTRACT FROM AUTHOR]

Significant wave height (H s) is a critical parameter in the design, operation, and maintenance of nearshore and offshore wind and wave farms. In this study, the original pyramid neural network (PNN) was introduced and applied to predict H s for North Sea renewable energy farms. The performance of PNN was compared with state-of-the-art algorithms. The results show that the machine learning (ML) models trained by the network datasets can accurately predict Hs at any point of nearshore or offshore energy farms, significantly reducing wave monitoring costs. The PNN models predict H s with high accuracy. The results predicted by PNN, with SRMSE of 0.256 and R 2 of 0.873, are more accurate than the corresponding results obtained by the deep neural network (DNN) model, which show that PNNs with their far simpler structures and lower number of parameters are attractive alternatives for complex and time-consuming DNN models. The ensemble of regular models, with SRMSE of 0.247, is ranked as the most accurate method. The results also show that the applied state-of-the-art algorithms including MLR, SNN, DNN, ANFIS, and SVR models predict non-physical negative values of H s. The PNNs developed in this study predict H s with positive values. Moreover, the analysis shows that the scatter of the results obtained by the derived nonlinear models is less pronounced than the scatter of corresponding results obtained by other methods. The results also show that to evaluate the performance of nonlinear ML methods for large datasets, the analysis of standard statistical indices is not sufficient. For large datasets standard statistical indices provide inadequate or insufficient information and additional calculations, and statistical analysis are required. • The pyramid neural network (PNN) was introduced. • The performance of PNN was analyzed in predicting significant wave height (H s) for North Sea renewable energy farms. • The PNN with fewer unknown parameters has the potential to deliver results even superior to those of a deep neural network. • Even the trained models can predict the H s of neighboring farms. [ABSTRACT FROM AUTHOR]

In this study, multi-tracker optimization algorithm (MTOA), particle swarm optimization (PSO), and differential evolution (DE) algorithms were integrated with support vector regression (SVR) to predict energy dissipation downstream of labyrinth weirs (Δ E). In order to evaluate the performance of these methods, the results are compared with corresponding outcome obtained by applying two other methods, namely, multilayer perceptron neural network (MLPNN) and multiple linear regressions methods (MLR). The input parameters comprise the discharge, the upstream flow depth, the crest length of a single cycle of the labyrinth weir, the width of a single cycle of the labyrinth weir, the apex width, the number of labyrinth weir cycles, the sidewall angle, and the height of weir. The results indicate that the meta-heuristic algorithms substantially improve the performance of SVR. The results show that the integrative methods, SVR-MTOA, SVR-PSO, and SVR-DE, are more accurate than the MLPNN and the MLR. In average, the integrative methods provide 39.63% more accurate results than the MLPNN and 79.34% more accurate results than the MLR. The average RMSE and R2 for the integrative methods are 0.0054 m and 0.977, respectively. Among all integrative methods, the SVR-MTOA yields the best results, with RMSE = 0.0044 m and R2 = 0.986. [ABSTRACT FROM AUTHOR]

In this study novel clustered machine learning (CML) models were developed by applying different base learners including multi linear regression (MLR), adaptive neuro-fuzzy inference system (ANFIS), classification and regression trees (CART), least-squares boosting (LSBoost), and random forest (RF) to predict scour profile induced by the jet of a propeller. Moreover, the results of CML models were compared with regular ML algorithms. The results show that the tree-based ensemble models, RF and LSBoost, are more accurate than CART. The ANIFS has the worst performance compared with other regular nonlinear methods, RMSE = 17.414 mm. The performance of MLR is also weak, RMSE = 35.63 mm and R2 = 0.088. However, the implementation of CML drastically increases the performance of MLR, RMSE = 15.053 mm, and R2 = 0.871. The CANFIS with RMSE = 8.757 mm, R2 = 0.976, and SI = 0 is ranked as the most accurate model. The results show that CLM enhances the performance of regular ML by up to 59.90%. The application of clustered ML is recommended for other complex problems. Finally, the results show that the derived models trained by other datasets very well predict measured scour profiles which datasets were not used in the training process. • Novel clustered machine learning (CML) models are developed. • Several CML models were used to predict scour profile induced by the jet of a propeller. • The performance of CML were compared with regular models. • The results show that CLM drastically enhances the performance of regular ML. [ABSTRACT FROM AUTHOR]

Abstract An efficient semi-analytical solution to the problem of nonlinear water waves propagating at a constant depth is derived using parallel computing techniques. The approach is based on the assumptions of an irrotational flow of an inviscid and incompressible fluid. Velocity potential and free-surface displacement functions are represented in a form based on Fourier series satisfying a formulated initial boundary-value problem by a proper selection of time-dependent coefficients. The eigenfunction expansions are resolved by means of a Fast Fourier Transform technique and a higher-order time-stepping procedure to provide an efficient spectral collocation method of computation of wave-induced free-surface flows. The application of the Fourier transform qualifies the semi-analytical algorithm for efficient parallelization. Hence, the numerical model performance is improved using the computing capabilities of a GPU. The derived semi-analytical approach is easy to implement and may be straightforwardly extended to cover the generation of waves in a flume or a basin. The ability of the model to reproduce nonlinear phenomena is demonstrated in simulations of two- and three-dimensional instabilities of a modulated Stokes wave. The model can be used to solve standard as well as complex wave problems in large computational domains considerably faster than its CPU-based counterpart. [ABSTRACT FROM AUTHOR]

The problem of a solitary wave attack on a vertical seawall is investigated by applying two approaches. The first is a semi-analytical method in which the Euler equations of motion are solved under the assumption of a potential flow by employing an approach based on the fast Fourier transform technique and a numerical time-stepping scheme. The second approach employed to analyse the problem considered is the smoothed particle hydrodynamics (SPH) method, in which the equations are solved in the Lagrangian coordinates. The two methods are used to simulate solitary wave propagation in water of uniform depth, followed by a wave impact on a vertical wall. The simulations focus on the determination of the maximum run-up of the wave on the wall, the calculation of pressures exerted by water on the structure, and the evaluation of water velocities in the vicinity of the structure. The predictions of the two approaches are compared to identify wave regimes for which both methods give satisfactory results. The results of numerical simulations have shown that both proposed methods predict practically the same free-surface profiles for waves of small and moderate amplitudes. For higher waves, some discrepancies between the results of the two methods occur. The two models results have been also compared with empirical data known from the literature, showing good agreement with experimental measurements in terms of the maximum wave run-up and the wave crest residence time at a wall. [ABSTRACT FROM AUTHOR]

Laboratory experiments were conducted to investigate the interaction of gravity waves with a semi-submerged rectangular cylinder of elastic bottom. Laboratory investigations were conducted for a wide range of wave parameters and a structure of different drafts. The analysis of results focuses on wave transmission at the structure, wave-induced pressures excreted on the plate, plate deflections, etc. The results shows that the nonlinear pressure and plate deflection components arising from the interaction of incoming waves with the structure are often significant. The results show that the nonlinear components often exceed their linear counterparts even for waves of low steepness. This is an original and surprising outcome of significant practical importance as the large nonlinear pressure and plate deflection components may spark a resonance. The problem is serious because plate natural vibration frequencies are often lower than the frequency of fundamental waves or their nonlinear components and the vibration of a plate may be amplified by incoming waves or their nonlinear products. The occurrence of a resonance amplified by incoming waves may lead to the failure of a structure. This outcome is of significant practical importance because it may occur for a wide range of wave parameters. • Waves have substantial effects on the vibration of the elastic elements of submerged structures. • Wave-induced pressure and plate deflection co mponents are often significant. • Nonlinear components often exceed their linear counterparts even for waves of low steepness. • Large nonlinear pressure and plate deflection components spark resonance. [ABSTRACT FROM AUTHOR]

Abstract: The main objective of the Conscience project was to develop and test concepts, guidelines and tools for the sustainable management of erosion along the European coastline, based on the best available scientific knowledge and on existing practical experience. Four concepts are potentially capable of providing the nexus between scientific knowledge and management: coastal resilience, coastal sediment cell, favourable sediment status and strategic sediment reservoir. The project has tested the use of these concepts and found that they are useful, provided that they are positioned and linked within a logical structure that we shall call the Conscience “Frame of Reference”, defined in time and space and supported through data and monitoring. Practical experience in six coastal sites in Europe has shown that the use of this Frame of Reference together with these concepts can make management objectives explicit and transparent. It can therefore support the design of an appropriate, resilience based coastal erosion management practice. [Copyright &y& Elsevier]

Abstract: A theoretical approach is applied to predict the propagation and transformation of nonlinear water waves. A semi-analytical solution was derived by applying an eigenfunction expansion method. The solution is applied to analyze the effect of wave frequencies and wave steepness on the propagation of nonlinear waves. The main attention is paid to the wave profile, the wave energy spectrum, and the changes of wave profile and energy spectrum due to the interaction of wave components in a wave train. The results show that for waves of low steepness the nonlinear wave effects and effects associated with the interaction of water waves in a wave train are of secondary importance. For waves of moderate steepness and steep waves the effects associated with the interactions between waves in a wave train are becoming significant and a train of initially sinusoidal waves may drastically change its form within a short distance from its original position. The evolution of wave components has substantial effects on the wave spectrum. A train of initially very narrow-banded waves changes its one-peak spectrum to a multi-peak one in a fairly short period of time. Laboratory experiments were conducted in a wave flume to verify theoretical approaches. The free-surface elevation recorded by a system of wave gauges was compared with the results provided by the semi-analytical solution. Theoretical results are in a fairly good agreement with experimental data. A reasonable agreement between theoretical results and experimental data is observed often even for relatively steep waves. [Copyright &y& Elsevier]

The analytical solution to the problem of the diffraction of second-order surface waves by a horizontal rectangular cylinder founded on a low rubble base was derived. The solution is based on the assumption that the pressure underneath the cylinder is linearly dependent on the horizontal space coordinate. The approach is basically valid for a small rubble base height to cylinder beam ratio and is recommended especially for cylinders founded on low and very low rubble bases for which other methods are difficult to apply. The solution was applied to investigate wave loads on a cylinder founded on a low rubble base. The results show that low rubble bases have significant effect on a nonlinear wave load on a cylinder. In general, the load increases with increasing cylinder width and increases with decreasing rubble base height. This implies that even thin rubble bases have to be included in the analysis of wave loads on a founded cylinder. Moreover, the results show that the nonlinear component of wave load is a dominant contribution to the wave load for a wide range of wave frequency. Laboratory experiments were conducted to verify theoretical results. The second-order component of vertical force and the vertical force correct up to second-order were compared with corresponding experimental data. The comparison show a fairly good agreement for both amplitudes and phases. [Copyright &y& Elsevier]

Offshore wind farms play a crucial role in generating renewable marine energy. Therefore, a suitable design of the associated wind turbine is required to enhance the performance, longevity, and cost efficiency. Thus, in this work, we consider multiple horizontal porous rings attached to a bottom-mounted impermeable cylinder that resembles a wind turbine and study the wave diffraction problem. The wave action on the cylinder is studied by using linear water wave theory and solved by using the matched eigenfunction expansion method in the cylindrical coordinate system. The fluid domain is divided into multiple subregions with different vertical eigenfunctions in the respective regions. The eigenvalues obtained in the porous regions are complex numbers which satisfy the complicated dissipative-dispersion relation. The solution to this relation corresponds to locating the wavenumbers for which a non-trivial solution exists for a homogeneous system of equations, the order of which depends on the number of porous rings considered in the problem. For an incoming wave, the diffraction problem is then solved by using these eigenvalues and their associated eigenfunctions. The wave forces acting on the impermeable cylinder and the porous rings are evaluated by integrating the pressure difference. Finally, after validation of the considered model, numerical results are presented to observe the effect of the porosity, radii and draft of the rings and also of the water depth on different hydrodynamic coefficients. For numerical computation, three rings are considered. The key finding of this analysis is that a suitable choice of porosity distribution pattern to reduce the wave impact mainly depends on the radii of the porous rings and also of the impermeable cylinder. The wave run-up predominantly increases when the rings are placed very near to each other. • Multiple horizontal porous rings attached to a bottom-mounted impermeable cylinder are considered. • The structure resembles a wind turbine and we study the wave diffraction problem. • Complex eigenvalues in the porous regions satisfy the 'dissipative-dispersion' relation. • A sophisticated numerical algorithm is adopted to find those eigenvalues. • The effect of the parameters of the rings on different hydrodynamic coefficients is shown numerically. [ABSTRACT FROM AUTHOR]

A theoretical approach is applied to investigate wave-induced mixing. The problem is formulated to describe evolution of temperature in a layer of fluid and is solved by applying eigenfunction expansions. The derived semi-analytical solution is applied to predict temperature changes and evolution of temperature profiles due to mechanically generated waves in a closed flume. The results show that water waves modify the temperature distribution in space and time. The analysis shows that the changes occur in the whole layer of fluid. The results indicate that time is a more important factor in a process of wave-induced mixing than expected. Mixing processes depend on a wave height. The rate of change of temperature distribution is more pronounced for higher waves. Another important parameter in mixing processes is the wavelength. The mixing effects are more distinct for deep water waves. The sensitivity analysis implies a need to conduct more theoretical studies and experimental investigations on wave-induced mixing. the model is verified in the course of the original laboratory experiments that were conducted in the insulated flume. A reasonable agreement between predicted and measured temperature profiles proves the applicability of the present approach even for relatively high gradients of temperature distribution over water depth. • An original theoretical approach to the problem of wave-induced mixing is derived. • The analytical model is applied to predict the effect of wave-induced mixing. • Novel laboratory experiments are conducted to verify theoretical results. • The experimental data confirm theoretical results even for high waves. • The effect of wave-induced mixing is more pronounced for deep water waves. [ABSTRACT FROM AUTHOR]

• A new methodology is derived to determine sediment particle velocities over a sandy rippled bed. • The analysis shows that the derived method nearly perfectly predict observed wave-induced sediment particle velocity. • The results indicate that the ANFIS and CART methods are more accurate than regression equations. • SPBO as a training method is more accurate and PSO. The physics and quantification of sediment transport are still a challenge for scientists and engineers. Measurements of wave-induced sediment velocities may be conducted only in selected laboratories and require weeks of pre-tests and a very experienced team. In this study, student psychology-based optimization (SPBO) algorithm was applied to develop new integrated machine learning methods for the determination of wave-induced non-cohesive sediment particle velocities over a rippled bed by incorporating the outcome of particle image velocimetry. Easily measurable data comprising sediment characteristics, bedform details, and hydrodynamic conditions were used to train the machine learning models. The developed techniques determine well the sediment particle horizontal velocity over a horizontal profile. The analysis shows that the derived models nearly perfectly predict observed data. The proposed methodology provides insight into the physics of sediment processes and may also be applied to interpret measurement data and verify sediment transport models. [ABSTRACT FROM AUTHOR]

The present study aimed to predict the maximum seasonal wave height by new integrative data driven methods. For this purpose, two data-driven techniques, that are, the Adaptive Neuro-Fuzzy Inference System (ANFIS) and the Support Vector Regression (SVR), were applied, and a BWO algorithm was used as an integrated method (ANFIS-BWO and SVR-BWO). In addition, the Particle Swarm Optimization (PSO) algorithm was used as a method integrated with SVR and ANFIS (SVR-PSO and ANFIS-PSO) to compare the performance of the newly developed methods (ANFIS-BWO and SVR-BWO). The wave data were collected in different seasons by a buoy station deployed in the southern Baltic Sea by the Institute of Hydro-Engineering of the Polish Academy of Sciences. Seasonal simulations were performed to investigate the effect of seasons on the maximum wave height. The wave data constituted an unevenly spaced time series. The maximum wave height was modeled using the maximum wave height period (T max), the significant wave height (H s), the significant wave period (T s), and time steps (Δt). The results showed that the application of BWO and PSO algorithms increased the accuracy of ANFIS and SVR by about 18.45%. Moreover, the results show that PSO increased the accuracy of ANFIS and SVR by about 17.98% and 21.59%, respectively. The results of different runs indicated that the BWO is more stable to reach the global solution than PSO. The results also show that show that SVR-BWO is the most accurate model. • The obtained results indicated that the BWO and PSO algorithms increased the accuracy of ANFIS and SVR. • The results indicate that the BWO acted better in SVR than the PSO. • The performance of the models was poorer in summer than in the other seasons. • The models can predict the maximum wave height for winter more accurately than other seasons. [ABSTRACT FROM AUTHOR]

Based on the potential flow theory, a second-order Higher-Order Boundary Element Method model is developed to simulate hydrodynamic loads and pressure on a stationary cylindrical-type oscillating water column (OWC) wave energy converter. Quadratic pneumatic damping and additional viscous damping are introduced to simulate the effects of the power take-off and the viscous dissipation inside the chamber, respectively. The proposed model is verified against a carefully instrumented scaled experiment. The effects of the chamber geometry and the wave environment on the hydrodynamic loads of the OWC device are then explored using the validated model. The resonance excited by the second-order wave component is observed with the fundamental frequency being half of the natural frequency. This resembles a sloshing mode and leads to a significant increase in hydrodynamic pressure and surge force as well as pitch moment. The effects of the second-order waves cannot be ignored under the action of the low-frequency long waves. In addition, the surge force and the pitch moment are not sensitive to the variation in the orifice opening ratios, while the heave force increases with the opening ratio at a resonant heave frequency. • Nonlinear wave dynamic on a stationary cylindrical-type OWC device was investigated. • A second-order time-domain HOBEM model for OWC dynamics was developed. • A second-order sloshing resonance is observed inside the OWC chamber. • The effects of the opening ratio on the OWC device are discussed. [ABSTRACT FROM AUTHOR]

A breakwater consisting of three pontoon-type wave energy converters equipped with Power Take-Off (PTO) systems to extract wave energy from pitch and heave motions is proposed. The proposed integrated system has the potential to reduce the cost of the wave energy conversion system by sharing the essential infrastructure with the floating breakwater. In the model, the eigenfunction expansion matching method and technique of variables separation are used. The effects of the geometrical parameters (including pontoon width, draft and spacing) on the hydrodynamic performance characterized by the wave energy conversion efficiency, transmission and reflection coefficients are investigated, respectively. It is found that the effective bandwidth (transmission coefficient K T < 0.5 and hydrodynamic efficiency C w > 0.3) and the peak efficiency are enhanced when the pitch and heave motions are considered simultaneously, compared with the single DoF motion system. The effective bandwidth increases with the decrease of width and draft of the front pontoon. And the variation of pontoon spacing affects significantly the distribution of the efficiency due to the Bragg-type reflection. Additionally, it is found that the variation of the geometrical parameters of the front pontoon on wave transmission is limited by changing the geometrical parameters of the front pontoon only. • Hydrodynamics of triple dual-DoF-motion pontoons is analytically investigated. • Hydrodynamic efficiency is enhanced when pontoons allowed both pitch and heave motions, compared with single DOF motion. • The smaller the width and draft of front pontoon, the larger the effective bandwidth. • The distribution of efficiency with wave frequency is obviously affected by the pontoon spacing. [ABSTRACT FROM AUTHOR]