A multi-scale reduced-order framework for robust aerodynamic shape optimisation of transonic wings

High-fidelity aerodynamic shape optimisation for transonic wings often suffers from the “curse of dimensionality,” where the strong coupling between planform and airfoil design variables leads to high gradient noise and prohibitive computational costs. This paper proposes a multiscale reduced-order optimisation framework that integrates Class Shape Transformation (CST) parameterisation with Proper Orthogonal Decomposition (POD) to achieve efficient dimension reduction and staged optimisation. The proposed framework first distills the high-dimensional design space into dominant modal variables and subsequently employs a multiscale strategy to decouple global planform updates from local airfoil refinements. The framework is validated using the NASA Common Research Model (CRM) wing. Results demonstrate that by reducing the design space from 37 physical variables to 16 dominant POD modes, the framework achieves a near-optimal drag level while reducing the number of high-fidelity CFD evaluations by approximately 28% compared to full-order optimisation. An additional 23% reduction in computational cost is achieved by optimizing the dominant POD modes in a multi-staged manner, while maintaining a comparable level of drag reduction. Furthermore, random-start optimisation cases reveal that the reduced-order strategy exhibits superior robustness against poor initialisations, consistently converging to feasible low-drag solutions where conventional full-space methods remain less efficient. The study indicates that the staged decoupling of design variables effectively suppresses detrimental parameter coupling, offering a promising approach for large-scale, high-fidelity aerodynamic design.