Empirical models based on linear and nonlinear potential theory that determine the forces on Wave Energy Converters (WECs) are essential as they can be used for structural, mechanical and control system design as well as performance prediction. In contrast to empirical modelling, Computational Fluid Dynamics (CFD) solves the mass and momentum balance equations for fluid domains. CFD and linear potential theory models represent two extreme in terms of capturing the full range of hydrodynamic effects. These are classified as white box models and the structure of these models is completely derived from first principles understanding of the system. In contrast black box models like a Artificial Neural Networks and Auto-Regressive with, Exogenous Input (ARX), map input and output behaviour of a system without any specific physics based structure. Grey box models do not strictly follow a first principles approach but are based on some observations of relationships between the hydrodynamic effects (e.g. buoyancy force) and system state (e.g. free surface height). The objective of this thesis is to propose a data driven grey box modelling approach, which is computationally efficient compared to high fidelity white box models and still sufficiently accurate for the purpose of determining hydrodynamic forces on heaving WECs.

In this thesis, a unique data driven approach that combines features from existing works in modelling of WEC and application of nonlinear hysteretic systems is developed. To that end a CFD based Numerical Wave Tank that could provide the data needed to populate the new modelling framework is used. A hull which hydrodynamically represents a Self Reacting Point Absorbers (SRPAs) with heave plate is subjected to pan-chromatic wave fields and is forced to oscillate concomitantly. The results provide evidence that a SRPA with heave plate exhibits nonlinear relationships with motion parameters including relative position, velocity and acceleration. These parameters show causal relationships with the hydrodynamic force. A simulation methodology to establish confidence in the components of a model framework is developed and the hydrodynamic forces on SRPAs with heave plate and bulbous tank have been analyzed and compared. Two sets of numerical simulation were conducted. Firstly, the WECs were restricted to all degrees of freedom and subjected to monochromatic waves and later the WECs were oscillated at various frequency in a quiescent numerical tank. These results were validated against existing experimental data.

Earlier attempts by other authors to develop a data-driven model were limited to simple hulls and did not include rate dependent nonlinearities that develop for heave plates. These studies laid the foundation to current work. The model framework developed in this thesis accounts for the nonlinear relationship between force and parameters like velocity and acceleration along with hysteretic relationship between force and velocity. This modelling framework has a nonlinear static, a hysteresis (Bouc-Wen model) and a dynamic (ARX model) block. In this work the Bouc-Wen model is employed to model the hysteresis effect. Five different models developed from this modelling framework are analyzed;​ two are state dependent models, while the other three required training to identify dynamic order of model equations. These latter models (Hammerstein, rate dependent Hammerstein and rate dependent KGP models) have been trained and validated for various cases of fixed and oscillating HP cylinder. The results demonstrate significant improvement (max 39%) in prediction accuracy of hydrodynamic forces on a WEC with heave plate, for the model in which a rate dependent hysteresis block is coupled with Hammerstein or KGP models.