Modeling wave energy converter (WEC) systems to accurately predict their behavior has been a notoriously difficult challenge for the wave energy field, particularly in polychromatic sea states. A key challenge is that accurate, physics-based WEC modeling has too high a computational cost to be used for future-state prediction and optimal control, two areas of active research in the wave energy field. One promising technique to combat these issues is the dynamic mode decomposition (DMD). DMD is a data-driven modal decomposition technique that has been valuable for modeling and predicting the behavior of complex dynamical systems, such as fluid flows, as well as for creating robust and computationally efficient models for optimal control. The algorithm works by taking time-resolved data as input, and the output is a set of spatial modes with associated eigenvalues that describe the oscillation frequency and growth/decay rates of those modes. A weighted sum of modes and corresponding eigenvalues can then be used to approximate the continuous time signal of each state and forecast this into the future. DMD is an established and powerful method in other fields including robotics, video processing, and finance, but has yet to be used in the wave energy field. In this field, the known limitations of linearity and sensitivity to sensor noise will be important to study and carefully characterize.
In this study, we use DMD to develop a linear model of a grid-scale Oscillating Surge WEC (OSWEC) operating in polychromatic seas. Our goal is to generate a purely data-driven model that can predict the behavior of the OSWEC for use in optimal control schemes, such as model predictive control (MPC), without requiring an infeasible computational cost or sacrificing accuracy. To generate the training data for the DMD model, we use a validated semi-analytical model developed by Renzi et al.  that describes OSWEC behavior in the open ocean, as well as WEC-Sim. From these models, we calculate kinematic (angular displacement and velocity) and dynamic (hydrodynamic torque and flap pressure) responses of the OSWEC to represent the state of this system. Using the output from the models as training data, we use DMD to create linear models of each state variable. We then compare the time series from the DMD model directly to the original time series and evaluate its accuracy for both modeling the training data (i.e., a hindcast) and future time performance (i.e., a forecast). Critically, this future prediction does not require knowledge of future sea states.
We show that by using DMD, we can accurately model and predict OSWEC behavior, even when considering signal noise, weakly nonlinear hydrodynamics, and irregular sea states. Results indicate that model accuracy depends on both the length of training data as well as the number and the rank of the reduced data matrix.
These findings provide insight on the use of DMD on systems with limited time-resolved data and presents a framework for applying similar analysis to experiments, high-fidelity simulations, or data from operating OSWECs.