Stochastic Response Analysis of a Spar-Type FOWT Subjected to Extreme Waves by a Novel Filter Wave Model and the DR-PDEE

Abstract

Extreme waves pose one of the major threats to marine structures. Furthermore, their non-stationary nature makes proper stochastic analysis of their responses a challenging problem. To address this issue, this paper proposes a method based on a novel linear filter wave model incorporated into the dimension-reduced probability density evolution equation (DR-PDEE). The linear filter system is capable of simulating random background waves conforming with the Joint North Sea Wave Project (JONSWAP) spectrum of any arbitrary sea state by adjusting the parameters of filters directly related to the parameters of the JONSWAP spectrum without reidentification. In particular, by conducting the digital filtering, wave kinematics at different depths below the sea surface can be reproduced conveniently, and therefore only one filter is adequate for the depthwise wave kinematics field. Extreme ocean waves are treated as the superposition of background waves and extreme crests according to the constrained quasi-determinism method, with randomness from both parts. Incorporating the filter into the equation of motion of the offshore structure of interest leads to an augmented high-dimensional stochastic system with multiple random variables. The DR-PDEE then is employed to reduce the dimensions of the equation governing the evolution of probability density of responses of the original complex system to two. Solving the DR-PDEE using the path integral method yields the probability function of the response at each time step. A numerical example involving the response of a National Renewable Energy Laboratory (NREL) 5-MW spar-type floating offshore wind turbine (FOWT) subjected to extreme waves was studied to assess the reliability of the proposed method. The method provides an effective tool for the determination of the stochastic extreme response of offshore structures, and provides a foundation for further dynamic analyses.