Uncertain reduced-order modeling for unsteady aerodynamics with interval parameters and its application on robust flutter boundary prediction

Computational fluid dynamics based unsteady aerodynamic reduced-order models can significantly improve the efficiency of transonic aeroelastic analysis. In this paper, the concept of the conventional model reduction method based on the system identification theory is extended to aerodynamic subsystems with the consideration of computational fluid dynamics-induced interval uncertainties in simulation to get the aerodynamic reduced-order model as uncertain as the original aerodynamic subsystem. The interval estimation of identified coefficients involved in the uncertain reduced-order model is obtained by utilizing the first-order interval perturbation method. The stability problem of the interval aeroelastic state-space model formulated based on the constructed uncertain aerodynamic reduced-order model is equivalently transformed into a standard interval eigenvalue problem associated with a real non-symmetric interval matrix in which the interval bounds of eigenvalues are evaluated by virtue of the first-order interval matrix perturbation algorithm. A new stability criterion for the interval aeroelastic state matrix is defined to predict the robust flutter boundary of the concerned uncertain aeroelastic system. Two numerical examples with respect to the uncertain aerodynamic ROM constructions and robust flutter boundary predictions of the two-dimensional Isogai wing and the three-dimensional AGARD 445.6 wing in transonic regime are implemented to assess the validity and accuracy of the presented approach. The obtained results are also compared with Monte Carlo simulation solutions as well as numerical and experimental results in the literatures indicating that the proposed method can provide a more robust and conservative prediction on the flutter boundary of an aeroelastic system compared with conventional deterministic aeroelastic analysis approaches.