Nonlinear dynamics of a floating offshore wind turbine platform via statistical quadratization — Mooring, wave and current interaction

Abstract This paper applies the method of statistical quadratization to investigate the first and second-order responses of a floating offshore wind turbine platform due to forces from a catenary mooring system, and wave–current coupled interaction. The hydrodynamics are based on the generalized Morison’s equation, while the catenary mooring system is based on a quasi-static approach. The method of statistical quadratization replaces the nonlinearities using equivalent linear and quadratic terms by minimizing the difference between the nonlinear model and the approximated model in a mean-square sense. In this regard, an iterative scheme is applied, in which the equivalent polynomial coefficients are calculated based on the non-Gaussian distribution generated by means of Gram–Charlier expansions. The dynamics are solved using the Volterra theory, and described in terms of transfer functions, which can be directly integrated into the central moments of the distribution. The results demonstrate an excellent agreement with nonlinear time-domain simulations in terms of spectral response and probability distribution. Sensitivity studies are performed to show the contribution of the second-order motion over several environmental conditions. Despite the excellent accuracy, the main advantage of the statistical quadratization is the low computational cost, which is approximately two orders of magnitude faster than nonlinear time-domain simulations.