Nonlinear WEC modeling using Sparse Identification of Nonlinear Dynamics (SINDy)
Authors: Lydon Brittany , Polagye Brian , Brunton Steven 
Published: September 2023

Modeling oscillating surge wave energy converter (OSWEC) systems to accurately predict their behavior has been a notoriously difficult challenge for the wave energy field. This is particularly challenging in realistic sea states where nonlinear WEC dynamics are common due to complex fluid-structure interaction, breaking waves, and other phenomena. Common modeling techniques for OSWECs include using potential flow theory to linearize the governing equations and ease computations, or using CFD to solve the full Navier-Stokes equations coupled with rigid body motion. However, both of these options have significant limitations. Potential flow theory breaks down in realistic sea conditions where nonlinear WEC dynamics are present, and CFD is often too computationally expensive for many applications such as real-time state prediction and optimal control, two areas of active research in the wave energy field. In particular, OSWEC dynamics are dominated by diffractive and viscous forces, often making common assumptions and linearization approximations (including small-body approximations) unreasonable, and CFD computationally intractable.

To bridge this gap in modeling methods, we propose using Sparse Identification of Nonlinear Dynamics (SINDy) to build nonlinear reduced-order models (ROMs) that describe OSWEC behavior in response to large-amplitude regular waves. SINDy is an equation-free, data-driven algorithm that identifies dominant nonlinear functions present in system state dynamics using a library of nonlinear functions created from time series measurement data. The result is an ordinary differential equation (ODE) in time that can be solved from an initial condition to model and predict time behavior of the states. SINDy is parsimonious, meaning it uses a sparsity-promoting hyperparameter with the goal of only including the minimum number of terms to capture dominant dynamics, resulting in interpretable and generalizable results that are not overfit to the data. Using the discovered ROMs and integrating in time, not only can SINDy provide time series models and future state predictions of OSWEC dynamics, it can also give insights into which variables are critical in describing the underlying dynamics of the state. 

In this study, we use SINDy to describe the nonlinear dynamics of a lab-scale OSWEC in a wave tank subjected to large-amplitude regular waves. We use nonlinear simulation data to generate kinematic, force, and torque data and use it as input to SINDy to identify ODEs that describe the measurement variables in time. We then integrate the ODEs to recreate the time series as well as predict future system behavior. We directly compare the resulting time series to the original data input to assess the accuracy of the SINDy model. We also interpret the dominant terms in the ODEs to gain insight on underlying mechanisms of the observed nonlinearity.

Early results show SINDy is a promising tool for modeling nonlinear OSWEC dynamics. We are able to build ROMs for variables such as angular kinematics and the moment about the hinge that generate an accurate recreation of data measurements. We found strong dominance in cubic and quintic terms of the ROMs, suggesting higher-order nonlinearities in the system dynamics. These findings inspire future work in identifying underlying mechanisms driving nonlinearity.