A Real-Time Detection System for the Onset of Parametric Resonance in Wave Energy Converters

Abstract

Parametric resonance is a dynamic instability due to the internal transfer of energy between degrees of freedom. Parametric resonance is known to cause large unstable pitch and/or roll motions in floating bodies, and has been observed in wave energy converters (WECs). The occurrence of parametric resonance can be highly detrimental to the performance of a WEC, since the energy in the primary mode of motion is parasitically transferred into other modes, reducing the available energy for conversion. In addition, the large unstable oscillations produce increased loading on the WEC structure and mooring system, accelerating fatigue and damage to the system. To remedy the negative effects of parametric resonance on WECs, control systems can be designed to mitigate the onset of parametric resonance. A key element of such a control system is a real-time detection system, which can provide an early warning of the likely occurrence of parametric resonance, enabling the control system sufficient time to respond and take action to avert the impending exponential increase in oscillation amplitude. This paper presents the first application of a real-time detection system for the onset of parametric resonance in WECs. The method is based on periodically assessing the stability of a mathematical model for the WEC dynamics, whose parameters are adapted online, via a recursive least squares algorithm, based on online measurements of the WEC motion. The performance of the detection system is demonstrated through a case study, considering a generic cylinder type spar-buoy, a representative of a heaving point absorber WEC, in both monochromatic and polychromatic sea states. The detection system achieved 95% accuracy across nearly 7000 sea states, producing 0.4% false negatives and 4.6% false positives. For the monochromatic waves more than 99% of the detections occurred while the pitch amplitude was less than 1/6 of its maximum amplitude, whereas for the polychromatic waves 63% of the detections occurred while the pitch amplitude was less than 1/6 of its maximum amplitude and 91% while it was less than 1/3 of its maximum amplitude.

Modelling of Parametric Resonance for Heaving Buoys with Position-Varying Waterplane Area

“…The active control methods utilise systems, such as the power-take off [39], variable inertia mechanisms [40] or a pressure relief valve, in an oscillating water column [41,42]. A real-time detection system for the onset of parametric resonance in WECs has also been developed to give early warning to such active control systems [43].…”

“…A finite set of basis functions is then fitted to the data as a function of the heave and pitch displacement and used to extend a conventional linear hydrodynamic model to include a time-varying restoring torque, which is demonstrated in a simulation to capture parametric resonance. Davidson and Kalmár-Nagy [43] utilise a model derived for a spar buoy [94][95][96] that describes the pitch-restoring torque as a function of the heave displacement and free surface elevation based on the instantaneous position of the centre of buoyancy.…”

Parametric excitation suppression in a floating cylinder via dynamic vibration absorbers: a comparative analysis

“…Hong et al [38] first introduced this case study, performing modelscale tests on the floating cylinder in a wave tank. Numerous authors then investigated various aspects relating to the dynamic instability and parametric excitation of the cylinder using numerical models [8,[39][40][41][42][43][44][45]. A schematic of the cylinder is shown in Fig.…”

Virtual Sensoring of Motion Using Pontryagin’s Treatment of Hamiltonian Systems

“…Zhao et al [ 31 ] very recently pursued the presently ubiquitous pursuit of optimality via stochastic artificial intelligence using particle swarm optimization genetic algorithm, while Anderlini et al [ 32 ] used real-time reinforcement learning. Sensing the ocean environment parallels the current emphasis in motion sensing, e.g., Davidson et al’s [ 33 ] parametric resonance technique for wave sensing and Sirigu et al’s [ 34 ] wave optimization via the stochastic genetic algorithm. Motion control similarly mimics the efforts of motion sensing and ocean environment sensing, e.g., Veremey’s [ 35 ] marine vessel tracking control, Volkova et al’s [ 36 ] trajectory prediction using neural networks, and the new guidance algorithm for surface ship path following proposed by Zhang et al [ 37 ].…”