A load-coupled DMDc method for long-term aerodynamic load prediction in controlled fluid–structure interaction systems

Abstract In controlled fluid–structure interaction (FSI) systems, nonlinear coupling between fluid loads and structural motion complicates reduced-order modeling and limits aerodynamic load prediction accuracy under different control inputs. To address the limited ability of dynamic mode decomposition with control (DMDc) to capture nonlinear dynamics, this study proposes a loadcoupled DMDc (LC-DMDc) method that incorporates nonlinear load effects into state evolution. The method combines proper orthogonal decomposition of the flow, structural motion, and interface loads with a radial basis function mapping, so that the predicted load coefficients provide nonlinear corrections to DMDc state evolution. The resulting model preserves displacement– velocity kinematic relations and is jointly optimized using multistep state and aerodynamic load prediction errors to improve long-term prediction accuracy. For a piezoelectrically actuated flatplate airfoil, models are trained on frequency-sweep data from high-fidelity FSI simulations and evaluated against standard DMDc and three representative methods under frequency-sweep, sinusoidal inputs with piecewise-constant frequencies, multisine, and step excitations. Over continuous predictions spanning 140 s, aerodynamic force and moment errors relative to highfidelity simulations do not exceed 7.33%, and wingtip displacement errors remain within 1.25% across all four cases. Compared with the best-performing baseline for each case and response component, LC-DMDc achieves error reductions of up to 75.1%. The method improves the accuracy of long-term aerodynamic load predictions and supports rapid response prediction and control-oriented modeling for controlled FSI systems.