Robust data-driven wave excitation force estimation for wave energy converters with nonlinear probabilistic modelling

Wave energy converters (WECs) require energy-maximising optimal controllers to improve efficiency and reliability. The wave excitation force (WEF) is necessary to align the WEC with the incoming wave field. The challenge arises from the unmeasurable properties of the WEFs, which necessitates its estimation. This study proposes a robust data-driven WEF estimation strategy based on a probabilistic model that integrates sparse identification of nonlinear dynamics (SINDy) and Gaussian process (GP) regression. The SINDy model captures the nonlinear dynamics of WEC systems, whereas the GP model estimates the unknown system dynamics and uncertainties. A Gaussian filter was constructed based on the designed probabilistic model to achieve the WEF estimation. This modern approach of incorporating first-principles models into a probabilistic framework provides improved robustness compared with computing estimates based on a parametric function representation. The means and covariances of the joint probabilities can be calculated directly based on analytic moment matching, enabling the reliable propagation of state-dependent uncertainty. The effectiveness of the model was validated using simulation results from the WaveStar WEC under various irregular wave conditions. The results demonstrated the accuracy and robustness of this data-driven WEF estimator, highlighting its potential for practical applications in WEC control and optimisation.