Citation :

Lakshmi. N. Sridhar, "Artificial Intelligence-Guided Bifurcation Control and Reduced-Order Modeling of Nonlinear Wave Energy Converter Dynamics," International Journal of Thermal Engineering, vol. 12, no. 2, pp. 1-18, 2026. Crossref, https://doi.org/10.14445/23950250/IJTE-V12I2P101

Abstract

This study offers a reduced-order model, bifurcation analysis, and optimal control framework for a nonlinear floating wave-energy converter interacting with an incompressible free-surface fluid. Starting with a potential-flow formulation of wave-structure interaction, a Galerkin projection is used to create a low-dimensional nonlinear dynamical system. This system retains the main hydrodynamic mechanisms, such as resonance effects, radiation damping, nonlinear restoring forces, and modal coupling with secondary hydrodynamic interactions. The resulting model provides a workable representation of a complex fluid-structure system suitable for stability and control analysis. Bifurcation analysis of the reduced system is carried out using numerical continuation. This process reveals a Hopf bifurcation at the trivial equilibrium state. The first Lyapunov coefficient calculated is negative. This confirms a supercritical bifurcation that leads to stable limit-cycle oscillations. These self-sustained oscillations reflect the relevant dynamics between waves and the buoy, resulting from the balance of hydrodynamic forcing, nonlinear damping, and restoring effects. The appearance of bounded periodic solutions shows how nonlinearities help regulate energy transfer and create stable operating conditions for wave-energy conversion. An optimal control formulation is created to maximize energy harvesting through the power take-off mechanism while managing oscillatory behavior. The control input is integrated directly into the nonlinear oscillator dynamics. A soft stability constraint is added to control the system’s distance from the Hopf bifurcation boundary. Numerical results indicate that stability-aware control improves performance. This suggests that controlled nonlinear dynamics lead to better energy extraction. The findings demonstrate that bifurcation-informed control strategies can significantly impact wave-energy converter performance. They balance resonance exploitation with nonlinear stability constraints. The proposed framework combines reduced-order modeling, nonlinear dynamical systems theory, and optimal control into a single approach for analyzing and optimizing wave-energy systems in strongly nonlinear conditions.

Keywords

Wave Energy Conversion, Nonlinear Dynamics, Hopf Bifurcation, Reduced-Order Modeling, Optimal Control.

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