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.

本文应用统计二次方化的方法来研究浮动式海上风力涡轮机平台在悬链系泊系统力和波流耦合相互作用下的一阶和二阶响应。流体动力学基于广义 Morison 方程，而悬链系泊系统基于准静态方法。统计二次方化的方法通过最小化非线性模型和均方意义上的近似模型之间的差异，使用等效线性项和二次项来代替非线性。在这方面，应用了迭代方案，其中基于通过 Gram-Charlier 展开生成的非高斯分布计算等效多项式系数。使用沃尔泰拉理论求解动力学，并用传递函数来描述，它可以直接集成到分布的中心矩中。结果表明，在频谱响应和概率分布方面与非线性时域模拟非常吻合。执行灵敏度研究以显示二阶运动对几种环境条件的贡献。尽管具有出色的精度，但统计二次化的主要优点是计算成本低，比非线性时域模拟快大约两个数量级。结果表明，在频谱响应和概率分布方面与非线性时域模拟非常吻合。执行灵敏度研究以显示二阶运动对几种环境条件的贡献。尽管具有出色的精度，但统计二次化的主要优点是计算成本低，比非线性时域模拟快大约两个数量级。结果表明，在频谱响应和概率分布方面与非线性时域模拟非常吻合。执行灵敏度研究以显示二阶运动对几种环境条件的贡献。尽管具有出色的精度，但统计二次化的主要优点是计算成本低，比非线性时域模拟快大约两个数量级。