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The non-causal optimal control law for wave energy converters leads to a requirement of predicting waves and wave forces over a future horizon.  Using examples of generic body shapes and oscillation modes, we show through computations of the velocity reference trajectory how the length of prediction horizon required to reach the maximum power output depends on the level of dissipative losses in the conversion chain. The sensitivity to noise is discussed, and so is the use of filtering to improve performance when the available prediction horizon is short or predictions are inaccurate. Considerations are also made for amplitude constraints and other effects encountered in a real system.  With realistic assumptions for the level of dissipative losses, results indicate that the prediction horizon needed to approach the maximum achievable power output for real systems ranges from only a few seconds up to about half a wave period, which is shorter than has generally been assumed earlier.

Absorbing wave power from oceans for producing a usable form of energy represents an attractive challenge, which for the most part concerns the development and integration, in a wave energy device, of a reliable, efficient and cost-effective power take-off mechanism. During the various stages of progress, for assessing a wave energy device, it is convenient to carry out experimental testing that, opportunely, takes into account the realistic behaviour of the power take-off mechanism at a small scale. To successfully replicate and assess the power take-off, good practices need to be implemented aiming to correctly scale and evaluate the power take-off mechanism and its behaviour. The present paper aims to explore and propose solutions that can be applied for reproducing and assessing the power take-off element during experimental studies, namely experimental set-ups enhancements, calibration practices, and error estimation methods. A series of recommendations on how to practically organize and carry out experiments were identified and three case studies are briefly covered. It was found that, despite specific options that can be strictly technology-dependent, various recommendations could be universally applicable.

The experimental results of a 1:30 scaled wave tank experiment of a point-absorber in extreme sea states and intermediate water depth are studied. The effect of the PTO damping parameter and different non-linear phenomena in extreme wave conditions such as wave breaking and overtopping are investigated with the focus on the maximum line (mooring) force in the presence of an upper end-stop. In the comparison of different wave-type representations, i.e. irregular, regular, and focused waves, of the same sea state, not all the wave types necessarily yield to the same peak line force. Moreover, there exists an optimum damping value for each sea state in which the smallest peak force is achieved. Both end-stop spring compression and wave-breaking slamming result in peak line forces which may be compensated by overtopping water pressure. Large surge motion is obtained for waves with a long wavelength which can contribute to higher and more damaging line forces.

To achieve a high reliability and durability for wave energy technologies, the effect of extreme wave conditions on the system must be understood. Wave tank experiments are an essential tool to evaluate this, and provide also a foundation for validation of numerical and analytical methods. However, it is not straight-forward how to design such small scale experiments so that they realistically represent wave energy converters in the ocean. In this paper, wave tank experiments of a 1:30 scaled friction damping linear power take-off (PTO) and cylindrical buoy with ellipsoidal bottom are presented. The linear PTO includes a rod that moves vertically against a Teflon block which introduces friction damping. The damping can be adjusted by changing the spring length that provides the compressive force between the Teflon block and the rod. To study extreme forces and snap loads, two load cells measure the line force both directly beneath the buoy, and at the top of the PTO. The motion of the PTO and the buoy are measured with a wire draw line position sensor and Qualysis system, respectively, and a data acquisition system collects and synchronizes the data. The extreme wave conditions used in the experiments are sea states with 50 years return period at the Dowsing site, North Sea. The waves are modelled as regular, irregular and focused waves. Here, the experimental setup and dry testing experiments are presented, and results of the wave tank test experiment for extreme forces are evaluated and further compared with WEC-SIM, to evaluate the agreement of the numerical and experimental model.

To ensure a reliable operation over the life time of wave energy converters (WECs), a number of load cases need to be considered according to international standards for marine structures to determine an optimal design. This paper outlines the procedure of obtaining an environmental design load for the line force of a 1:30 scaled point-absorber WEC using an environmental contour with a 50-year return period for the Dowsing site in the North Sea. To obtain the response of the WEC during extreme conditions, a numerical WEC-Sim model is developed and calibrated with experimental wave tank tests to augment the data required for such design load analysis. The design load for the line force is estimated based on the full long-term extreme response computed from the full sea state approach by considering 180, 360, and 720 sea state samples as well as the contour approach for the sea state that gives the most extreme response. Further, a probabilistic approach is used to quantify the probability of failure for a critical mechanical component of the system such as shackle. The result shows that the numerical WEC-Sim model is able to sufficiently replicate the real response of the system during extreme irregular waves. The Bayesian theory with Monte-Carlo algorithm is found to be an excellent tool for identifying the degree of belief in the statistical models used for the short-term extreme response analysis. Considering the ultimate limit state, the design load for the 1:30 scaled system is calculated as 670.95 N (i.e. 18.11 MN for a full-scale system) after applying the partial load safety factor of 1.35 on the full long-term extreme response of the system for the 9.1 years return period (i.e. 50 years in a full-scale model).

To avoid over-designing wave energy converters (WECs), their reliability and survivability aspects need to be accurately addressed. The most common failure modes are: instantaneous failure due to high instantaneous loads, and fatigue failure due to the accumulated damage in the structure during years of operation. Here, we present a fatigue analysis of a point-absorber WEC in sea states corresponding to a 50-year environmental contour from the Dowsing site, UK. The data for this analysis is generated by a WEC-Sim model that is calibrated with a 1:30 scaled WEC from a wave tank experiment. In this study, the partial damage in each 1-hour sea state sample is calculated using the rainflow counting and Palmgren-Miner rule. Then, considering the joint probability density function of the sea states, the equivalent two-million cycle load is 2.42 MN for the full-scale system considering the accumulated damage in 50 years of operation. In a comparison of the fatigue limit state (FLS) and ultimate limit state (ULS), it was found that the ULS is the governing limit state in the design of the WEC system here.

One strategy for the survivability of wave energy converters(WECs) is to minimize the extreme forces on the structure by adjusting the system damping. In this paper, a neural network model is developed to predict the peak line force for a 1:30 scaled point-absorber WEC with a linear friction-damping power take-off (PTO). The algorithm trains over the wave tank experimental data and enables an update of the system damping based on the system state (i.e. position, velocity, and acceleration) and information on the incoming waves for the extreme sea states. The results show that the deep neural network (DNN) developed here is relatively fast and able to predict the peak line forces with a correlation of 88% when compared to the true (experimental)data. Then, the optimum damping for survivability purposes is found by minimizing the peak line force. It is shown that the optimum damping varies depending on the system state in each zero up-crossing episode.

The survivability of wave energy converters (WECs) is one of the challenges that have a direct influence on their cost. To protect the WEC from the impact of extreme waves, it is often to over-dimension the components or adopt survivability modes e.g. by submerging or lifting the WEC if it is applicable. Here, a control strategy for adjusting the system damping is developed based on deep neural networks (DNN) to minimize the line (mooring) force exerted on a 1:30 scaled WEC. This DNN model is then implemented in a control system of a numerical WEC-Sim model to find the optimal power take-off (PTO) damping for every zero up-crossing episode of surface elevation which minimizes the peak line force. The WEC-Sim model was calibrated based on a 1:30 scaled wave tank experiment that was designed to investigate the WEC response in extreme sea states with a 50-year return period. It is shown that this survival strategy reduces the peak forces when compared with the response of a system that has been set to a constant PTO damping for the entire duration of the sea state.

To determine the optimal design of the wave energy converter (WEC) that can withstand extreme waveconditions, the short- and long-term extreme responses of the system need to be determined. This paper focuses on the extreme peak force distribution of the mooring force for a 1:30 scaled point absorber WEC. The basis of this analysis is the mooring force response obtained from a WEC-Sim model calibrated by wave tank experimental data. The extreme sea states have been chosen from a50-year environmental contour. Here, first, the long-term extreme response using the full sea state approach is obtained for three constant damping cases of the power take-off (PTO) system. Then, using a contour approach, the expected value of the extreme peak line (mooring) force distribution is computed for the sea states along an environmental contour. Further, for the most extremesea state, the extreme peak line force distribution is also computed where a survivability control system, based on a deep neural network (DNN), changes the PTO damping to minimize the peak mooring force in each zero up-crossing episode of surface elevation. The results show that in the absence of a control system, the zero PTO damping case is a conservative choice in the analysis of the long-term response and the design load. For the most extreme sea state along the environmental contour, the survivability control system slightly reduces the expected value of the extreme peak force distribution when compared with lower constant PTO damping configurations.

To tune the wave energy converter (WEC) controller parameters such as damping to reduce the line force during extreme wave conditions, future knowledge of the line force is required.To achieve this, the incoming wave and system state should be predicted for a few seconds in the future. It is rather an arduous task to predict the future knowledge of waves and the system's dynamic when dealing with breaking and steep waves, and the system is subject to various nonlinear forces. The classical model-based control strategies often rely on linear assumptions to estimate the WEC dynamics for the sake of simplicity. Unlike the model-based, the data-driven approaches are free from modeling errors and the algorithms are trained over the true and noisy data to predict non-linear system behaviors.Using data-driven approaches, we are able to model nonlinear dynamics. However, new questions emerge on the accuracy of the future wave and system state predictions, and how this uncertainty propagates into the final prediction of the line force. As incorrect damping may lead to excessive line force and detrimental damage to the system, these are the knowledge gaps that need to be addressed.The main purpose of this paper is to answer these questions through a survivability strategy for wave energy converters by providing a realistic perspective on the implementation of the neural network approaches by accounting for the errors in the input data. For this purpose, a series of neural networks is designed that first predicts the surface elevation for 0.36 s ahead, i.e. corresponding to 2 s in the full-scale WEC. This future knowledge of the wave elevation is then used to predict the system state (i.e. power take-off (PTO) translator position) for the same prediction horizon based on the PTO damping. This information is then fed to a convolutional neural network (CNN) that predicts the peak line force 0.36 s ahead. Further, the sensitivity of the peak line force prediction to the uncertainties in the input data and the prediction horizon is analyzed. The neural network models are trained over the experimental data subjected to the extreme sea states for a point absorber wave energy converter. The results present a thorough analysis of the NN models’ performance.The results suggest that the accuracy of the surface elevation prediction has an insignificant independent effect on the peak force prediction model. However, these uncertainties reflect in the PTO translator position prediction, and the model is considerably sensitive to the accuracy of this prediction. This sensitivity nonetheless is less notable for higher PTO damping values. The prediction accuracy of the peak forces dropped by only about 7\% when the predicted input was used in the lower damping cases here, whereas, a larger drop was seen for the higher damping case.