Determination of monopile offshore structure response to stochastic wave loads via analog filter approximation and GV-GDEE procedure

Abstract

Efficient and accurate stochastic response analysis of offshore structures subjected to ocean wave loads has been a challenging problem for several decades. This is especially true for multi-degree-of-freedom nonlinear structures when information about the probability density is desired. How to account for the random field of the wave loads, and how to deal with the coupling of high-dimensional partial differential equation governing the joint probability density functions are among the major challenges. To this end, in the present paper an approach is proposed by incorporating the filter approximation of random fields of sea waves with the recently developed Globally-evolving based generalized density evolution equation (GV-GDEE). To deal with the first issue regarding the random wave filed, the analog filter technique is adopted. In particular, a filter approximation of the wave kinematics field distributed over a vertical line along the ocean domain is proposed. It comprises a linear differential equation set with white noise input. An augmented system is thereby constructed by incorporating the additional differential equation set yielding wave excitation simulated by an analog filter into the equation of motion of a monopile offshore structure. To circumvent the issue of coupling of high-dimensional equations for this augmented system with even higher dimension, the GV-GDEE approach is employed. Specifically, by constructing the effective drift coefficients based on the high-dimensional drift coefficients in the associated Fokker-Planck-Kolmogorov (FPK) equation, a two-dimensional GV-GDEE in terms of the response quantity of interest is derived. Further, this GV-GDEE is solved by the path integral method. Furthermore, two numerical examples are included. In particular, the nonstationary stochastic responses of a 5 megawatt (MW) fixed monopile offshore wind turbine structure under two operating conditions are studied. Comparisons with pertinent Monte Carlo simulations (MCS) demonstrate the accuracy and efficiency of the proposed approach.