Stochastic Response Determination of U-Oscillating Water Columns in Severe Seas by a Statistical Linearization Scheme

Abstract U-Oscillating Water Columns (U-OWCs) are fixed wave energy converters that are becoming increasingly popular. Indeed, a full-scale prototype was installed recently at the port of Civitavecchia (Rome, Italy), while another U-OWC integrated breakwater is currently under construction at the port of Salerno (Italy). The dynamics of these systems is governed by a system of nonlinear integro-differential equations with no known exact solution. Various solution methodologies have been proposed ranging from purely numerical ones to approximate semi-analytical schemes, such as those based on statistical linearization. The latter was shown to exhibit satisfactory accuracy in determining response statistics vis-à-vis Monte Carlo data. However, significant discrepancies may arise in severe sea states, because the U-OWC is exposed to frequent inlet uncovering during the crossing of large wave troughs, and thus to a discontinuous wave excitation. In general, standard approximate models do not account for this phenomenon, and therefore they exhibit in many cases a relatively low accuracy degree. In this paper, a novel statistical linearization scheme is developed for determining approximately the response statistics of a U-OWC exposed to severe sea states. A significant novelty of the proposed scheme relates to the fact that the determined parameters of the equivalent linear system include not only the standard mass, damping and stiffness coefficients, but also an equivalent excitation coefficient that accounts for the intermittent nature of the wave excitation. The reliability of the scheme is demonstrated by comparisons with relevant Monte Carlo simulation data.