Prediction and validation of aeroelastic limit cycle oscillations using harmonic balance methods and Koopman operator

Abstract Nonlinearities in aerospace systems often induce self-sustaining oscillations known as Limit Cycle Oscillations (LCO), requiring costly analyses for identification. A major challenge is the computational expense of generating bifurcation diagrams, which limits the feasibility of nonlinear analysis in early design phases. This restriction not only constrains design possibilities but also impedes data-driven methods for nonlinear aeroelastic analysis, which rely on efficient data collection-a growing focus in the aerospace sector. This work proposes a computationally efficient numerical framework to predict LCO amplitudes and assess stability in nonlinear aeroelastic systems. The approach integrates the Harmonic Balance Method with the Hill method for stability analysis. To address the sorting problem, a Koopman operator-based data-driven method is employed. The framework is validated using numerical test cases with both smooth and nonsmooth nonlinearities, benchmarked against results from MATCONT, COCO and time-domain simulations. Finally, experimental validation is performed by comparing the framework’s predictions with LCO experimental data obtained through control-based continuation experiments.