Recurrence quantification analysis: Nonlinear wave dynamics in the Kuramoto-Sivashinsky equation, Response of the Tri-pendulum and FlanSea WEC and Extreme Events

Nonlinear transitions and associated dynamics are an important aspect of many natural, physical and engineering systems and are most certainly relevant to ocean engineering. In this paper, the method of recurrence plots (RP) and recurrence quantification analysis (RQA) is shown to be a suitable method for the identification of nonlinear evolution in dynamical systems, by first analysing the Kuramoto-Sivashinky (KS) wave equation. The KS equation is chosen as a candidate for analysis, among many nonlinear partial differential equations, since it describes rich nonlinear evolution and shows the propagation of wave structures that possess qualitative and quantitative similarities to ocean waves and response of wave-energy-conversion devices and wave tank experiments. It captures facets of complexity such as dissipation, dispersion and nonlinearity and their interplay.After establishing the utility of the RQA for nonlinear transitions in wave dynamics via the KS equation, the heave motion of a moored buoy, treated as a 1-D second order system in a “Brownian ocean the response of a tri-pendulum wave energy conversion device and that of the point-absorber type FlanSea WEC are studied using RQA. An RQA based control strategy is postulated. Finally, NDBC buoy 42040's significant wave height data in the year of hurricane Katrina and the next year have their RP/RQA signature created, as an introductory measure to pursue this analysis to create predictive tools in the future.