Abstract
Modeling wave energy converter (WEC) systems and accurately predicting their behavior has been a challenge for the wave energy field since its conception, particularly in irregular sea states where the waves can exhibit nonlinear, nonstationary and stochastic behavior. WECs operating in irregular seas can, consequently, inherit behavior that is complex, non-periodic, and high-dimensional. This can result in significant error when using traditional modeling techniques that employ linear superposition to describe WEC dynamics, while making high-fidelity techniques such as CFD computationally expensive. This motivates the need for modeling tools that can describe and predict complex WEC behavior while remaining computationally efficient. One potential approach is using Sparse Identification of Nonlinear Dynamics (SINDy) to build reduced-order models (ROMs) that describe OSWEC behavior using only sensor data. SINDy is an equation-free, computationally efficient data-driven algorithm that uses sparse regression techniques to identify dominant nonlinear functions present in system state dynamics from a library of functions created from time series measurement data. The result is an ordinary differential equation (ODE) in time that relates a modeled variable to other system states, such as position, velocity, forces, and torques. SINDy produces parsimonious equations, meaning it uses a sparsity-promoting hyperparameter to find the minimum number of model terms necessary to capture dominant dynamics. Because of this, ROMs discovered by SINDy are interpretable, generalizable, and not overfit to data. SINDy can provide time series models and future state predictions of WEC dynamics, as well as give insights into which variables are critical in describing this behavior.
In this study, we use SINDy to describe the dynamics of a grid-scale oscillating surge WEC (OSWEC) operating in irregular seas. We generate the training data using the open-source modeling tool WEC-Sim, where we input a wave elevation time series from field measurements in the Pacific Ocean and output the OSWEC response. By using real wave elevation data, we aim to capture the complex phenomena present in real seas that may not be replicated by using a parametric wave spectra with equivalent statistics. We then employ SINDy to find a parsimonious ROM of OSWEC kinematics that accurately describes its behavior for a relatively short training period (60 s) and predicts future behavior. We show that not only can SINDy model time series behavior from the OSWEC in irregular waves with small error, in many cases, the model is generalizable to future sea states. This means that the SINDy model can be used on other data streams with similar wave conditions without having to retrain on new data. This work highlights a new tool for modeling high-dimensional, complex WEC behavior in response to irregular waves that does not require knowledge of the incident wave field. The results show promise in using this tool for future WEC modeling and is a first step in utilizing SINDy to model WEC behavior. For future work, we aim to expand this study to more modeled variables and test the tool on experimental data.