Accurate and computationally efficient models for wave energy converters (WECs) are critical for design and control development. Often, these models are based in linear potential flow theory, which has low computational cost, but may require restrictive assumptions that cannot account for complicated hydrodynamics. High fidelity tools, such as computational fluid dynamics (CFD), do not face such limitations, but their computational cost can be too high for real-time control or design iteration. These issues are magnified in energetic seas, where nonlinear hydrodynamics, such as overtopping and slamming, can drive design loads. Data-driven algorithms are attractive to bridge this gap by replacing the full solution to the Navier-Stokes equation with reduced-order models. One option is Sparse Identification of Nonlinear Dynamics (SINDy) - an equation-free, data-driven algorithm that identifies dominant nonlinear functions present in system state dynamics from time series data. SINDy is parsimonious, meaning it uses a sparsity-promoting hyperparameter with the goal of including the minimum number of terms to capture dominant dynamics, resulting in interpretable and generalizable results that are not overfit to the data. In this study, we use SINDy to generate nonlinear reduced order models of an oscillating surge WEC (OSWEC) experiencing varying degrees of overtopping (when the crest of the wave passes over the top of a surface-piercing flap). Overtopping can occur in energetic seas where the flap experiences large rotations or interacts with large waves. While this behavior can significantly affect the structure and magnitude of the loads on the WEC, especially in the heave direction, it can be difficult to account for with common modeling techniques. With SINDy, we use experimental data to build a reduced order model of the heave force as a function of flap kinematics, with the goals of drawing connections between overtopping severity and the resulting dynamics, as well as better understanding the role nonlinearity plays in these complex events. We collected experimental data using a laboratory-scale OSWEC that was tested in the wave tank at the National Renewable Energy Laboratory. We tested the OSWEC in regular waves and measured flap kinematics (position, velocity, and acceleration) as well as loads acting at the rotation axis, including three-dimensional forces and torques. The tests encompassed a wide range of overtopping and we chose three tests to model using SINDy that ranged from no overtopping to significant overtopping. All three SINDy models accurately describe the heave force experienced by the flap. While the model for the test with no overtopping shows a linear relationship between heave force and flap velocity, higher-order terms are required to accurately describe both the structure and magnitude of the heave force as overtopping increases. We were able to generalize the SINDy models to other tests with similar amounts of overtopping, but no single model could accurately represent the entire testing range. Overall, this shows that SINDy can generate accurate system models of complex WEC dynamics with limited computational cost and that the interpretation of the reduced order model can illuminate connections between physical phenomena and the model mathematics.
Lydon et al. (Mon,) studied this question.