This work presents a design coupling analysis (DCA) framework to investigate the interactions among control and plant design variables in floating offshore wind turbine (FOWT) and to support the formulation of tractable control co-design (CCD) optimization strategies. DCA provides quantitative information that reveals the relationships and dependencies among design variables and to objective function, enabling improved design variable selection, identification of dominant variables that drive system interactions, and informed selection of optimization solution strategies. However, applying DCA to complex systems is challenging because the models used to describe their dynamics are computationally expensive, and constructing DCA information requires exhaustive model evaluations and optimizations. Here, a surrogate model of the FOWT system is employed to make the repeated model evaluations required for DCA computationally feasible. Using this framework, the bidirectional couplings between control and plant design variables, as well as the couplings among plant design variables, are estimated. The results reveal strong interactions among various design variables, and identify the most influential plant design variables affecting system performance. These insights guide the development of two DCA-based optimization strategies for large CCD problems: a sequential decomposition approach that preserves dominant design variable couplings while reducing problem size at each stage, and a reduced dimensional optimization approach that focuses on collectively the most influential variables. The results demonstrate that these strategies significantly reduce computational complexity while achieving solutions comparable to those obtained through full simultaneous optimization, demonstrating the value of DCA for understanding and solving complex design problems.

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