Stochastic response determination of U-OWC energy harvesters: a statistical linearization solution treatment accounting for intermittent wave excitation

A novel statistical linearization technique is developed for determining approximately the response statistics and the power output of U-Oscillating Water Column (U-OWC) energy harvesting systems. In this regard, first, the governing equations are derived by employing the unsteady Bernoulli equation. Note that the intermittent, i.e., non-stationary, nature of the wave excitation, occurring in severe sea states due to uncovering of the U-OWC inlet, is explicitly accounted for in the herein proposed model. This is done by multiplying the excitation process with a Heaviside function dependent on the instantaneous free surface displacement. Next, the resulting coupled system of nonlinear integro-differential stochastic equations is solved approximately by relying on a statistical linearization technique. Specifically, the original system of nonlinear equations is replaced by an equivalent linear one, whose parameters and response first- and second-order statistics are obtained by minimizing the mean square error between the two systems. A significant novel aspect of the technique relates to the fact that the Heaviside function is replaced in the equivalent linear system by an “equivalent excitation” coefficient to be determined as part of the statistical linearization solution scheme. Further, compared with other relevant solution schemes adopted in earlier research efforts in the literature, it is shown that the developed technique can be construed as a direct generalization that exhibits an enhanced accuracy degree. The U-OWC installed in the Civitavecchia harbor (Rome, Italy) is considered as an illustrative numerical example, where the reliability of the approximate technique is demonstrated by comparisons with pertinent Monte Carlo simulation data.