Abstract
Wave energy converters (WECs) are devices that harness power from ocean waves with useful applications including powering remote communities and desalination plants. Oscillating surge WECs (OSWECs) are a promising sub-category of WECs because they can absorb power over a wide range of wave frequencies and rely less on resonance than other WEC archetypes. However, OSWECs can exhibit complex dynamics that can be difficult to accurately model without significant computational burden. Often, this results in either low-fidelity, potentially inaccurate linear models or high-fidelity numerical simulations that are too computationally expensive for operational use. Scaled experimental modeling can address these issues, however there are limitations when the scaled device does not achieve exact similarity to the full-scale system. When this occurs, data from the experiment may not be representative of the full-scale system and could cause errors when predicting device behavior and performance. This work explores data-driven and experimental methods that address these limitations. Specifically, we use data-driven algorithms that balance accuracy and computation speed to build accurate system models of OSWEC dynamics. We address realistic conditions such as noisy signals and nonlinear events, including wave overtopping. Additionally, we demonstrate experimental techniques that mitigate common scale effects using control, providing an efficient method to investigate and address hardware limitations.
To bridge the gap between model accuracy and computation speed, we propose the use of dynamic mode decomposition (DMD) as a purely data-driven technique that can generate an accurate and computationally efficient model of OSWEC dynamics. Specifically, we model and predict the behavior of an OSWEC in mono- and polychromatic seas without an equation of motion or knowledge of the incident wave field. We generate data with the open-source code WEC-Sim, then evaluate how well DMD can describe past dynamics and predict future behavior. We consider realistic challenges including noisy sensors, weakly nonlinear dynamics, and irregular wave forcing. Specifically, by using an extension of DMD we reduce the effect of noise on our system and significantly increase model accuracy outside the training region. Additionally, by introducing time delays we accurately describe weakly nonlinear dynamics, even though DMD is a linear algorithm. Finally, we use Optimized DMD (optDMD) to model OSWEC behavior in response to irregular waves. While optDMD accurately models training data, future prediction remains inaccurate, demonstrating the limits of modeling efforts without access to information about the incident wave field. These findings provide insight into the use of DMD, and its extensions, on systems with limited time-resolved data and present a framework for applying similar analysis to lab- or field-scale experiments.
Limitations of linear models are magnified in energetic seas where extreme events, such as overtopping and slamming, and large-amplitude motions can introduce significant nonlinearities in the dynamics. To address this, we use the sparse identification of nonlinear dynamics (SINDy) algorithm to build parsimonious reduced-order models of WEC dynamics from nonlinear experimental data. Specifically, we learn interpretable, nonlinear models to describe OSWEC dynamics in response to varying amounts of overtopping. The SINDy models are trained on experimental data from a laboratory-scale device operating in regular waves. These models describe the surge and heave forces acting on the OSWEC flap using only kinematic time series. While surge force is relatively unaffected by overtopping severity, heave force shows significant nonlinear behavior with increased overtopping. Regardless of complexity, SINDy generates accurate models of both surge and heave forces in tests ranging from no overtopping to severe overtopping, especially when compared to linear techniques. We explore how well these models generalize to other experiments and find that we can use a single model to describe surge force over the full range of overtopping, while heave force requires a continuum of models with varying degrees of nonlinearity to accurately describe the full range of dynamics. Overall, this work supports the use of SINDy to generate accurate models of WEC dynamics, especially when strong nonlinearities are present.
While scaled-model testing is a promising method for collecting high-quality data, scale effects can reduce result accuracy. Here, we identify, quantify, and mitigate scale effects of the same laboratory-scale OSWEC that would not be equally present in full-scale systems, including reduced buoyancy due to sensor weight and driveline friction. Specifically, after we characterize the buoyancy and friction torque profile, we use a servomotor to emulate additional buoyancy and offset friction using real-time position and torque feedback. We find that emulating additional buoyancy substantially improves system performance by adjusting the natural period of the device, essentially implementing phase control to operate closer to resonance. Because of this, sensor weight should be considered in scaled-devices to ensure performance is representative of the full-scale system. However, friction, while appreciable in comparison to the prescribed control torque, has a limited effect on system kinematics and performance. This is because the frictional torque is in phase with velocity and therefore acts as a damper in the same manner as the power takeoff. These examples demonstrate the importance of considering scale effects in experimental testing and introduces novel methods to address and mitigate these effects using feedback control, providing a low-cost and efficient method to investigate and address hardware limitations.
With this work, we aim to further WEC development by introducing data-driven and experimental methods that expand the existing WEC modeling tools and provide low-cost and efficient methods for accurate scale model testing.