Closure Schemes for Nonlinear Bistable Systems Subjected to Correlated Noise: Applications to Energy Harvesting from Water Waves

Abstract

The moment equation closure minimization (MECM) method has been developed for the inexpensive approximation of the steady-state statistical structure of bistable systems, which have bimodal potential shapes and which are subjected to correlated excitation. Our approach relies on the derivation of moment equations that describe the dynamics governing the two-time statistics. These are then combined with a closure scheme that arises from a non-Gaussian probability density function (PDF) representation for the joint response-excitation statistics. We demonstrate its effectiveness through the application on a bistable nonlinear single-degree-of-freedom (SDOF) ocean wave energy harvester with linear damping, and the results compare favorably with direct Monte Carlo simulations.