Floating offshore wind turbines (FOWTs) exhibit strongly nonlinear dynamics due to slack-taut mooring behaviour and platform-tower coupling, which, under parametric uncertainty, can induce bifurcations, bistability, and quasi-periodic responses. This study develops a reduced-order nonlinear model of a barge-type FOWT equipped with a geometric nonlinear tuned mass damper (TMD). The deterministic response is analysed using the harmonic balance method with alternating frequency-time. Uncertainty quantification is performed using both intrusive and non-intrusive polynomial chaos expansion (PCE), validated against Monte Carlo simulation (MCS). Intrusive PCE is accurate for smooth polynomial nonlinearities, whereas the mean-state approximation required to project the tanh-regularised slack-taut mooring term leads to overestimated confidence bounds near the bifurcation. The non-intrusive formulation stays accurate across the resonance, bifurcation, and post-resonance regimes of the present model, matching MCS to within about 3% in the mean and standard deviation. Under mooring stiffness uncertainty, bimodal distributions, non-Gaussian behaviour, and a narrow quasi-periodic band with pronounced amplitude modulation are observed. For the present model and parameter settings, the optimised nonlinear TMD suppresses the resonant response and removes the fold bifurcation. Non-intrusive PCE thus provides a robust uncertainty quantification framework for the reduced-order FOWT model considered, with a promising basis for extension to higher-fidelity systems.
Baiyang Shi (Tue,) studied this question.