Aeroelastic Uncertainty Quantification of Flexible Wing Nonlinear Dynamics Using Reduced Order Models

Uncertainty quantification of aeroelastic wing limit cycle oscillations (LCOs) is enabled using dynamically nonlinear reduced order models (ROMs). The ROM forms are generated by source–transformation automatic differentiation of the full order model (FOM) source code, and are data–free, not requiring the costly FOM dynamic response. The 288 degree of freedom (DOF) FOM, consisting of a geometrically exact nonlinear beam and 2D strip theory unsteady aerodynamics, is reduced to a 13 DOF nonlinear ROM form. The 13 DOF ROM accurately predicts LCO dynamics in wing root bending moment, and wing root torsion, with computational cost being over 700 times faster than the FOM. A ROM generation cost is incurred, which is on the order of magnitude of one representative FOM dynamic response, however this cost is incurred just once, in the offline phase. The resultant generated ROM code is valid for any wing geometry and flight condition input without requiring regeneration. The ROM form is used for the rapid training of surrogate models to predict LCO amplitudes over an envelope of supercritical flight speed and a varying intrinsic wing structural parameter. A statistical analysis is performed via Monte Carlo uncertainty propagation in order to quantify the variability of the root bending and torsional moments with respect to uncertainties of the moment of inertia during LCOs. This probabilistic approach reveals an increasing loads uncertainty as the flight speed moves farther away from the flutter point and highlights the challenges of matching the design loads with their most probable value when the wing is undergoing supercritical LCOs.