Reduced-Order Modeling of Flutter and Limit-Cycle Oscillations Using the Sparse Volterra Series

For the past two decades, the Volterra series reduced-order modeling approach has been successfully used for the purpose of flutter prediction, aeroelastic control design, and aeroelastic design optimization. The approach has been less successful, however, when applied to other important aeroelastic phenomena, such as aerodynamically induced limit-cycle oscillations. Similar to the Taylor series, the Volterra series is a polynomial-based approach capable of progressively approximating nonlinear behavior using quadratic, cubic, and higher-order functional expansions. Unlike the Taylor series, however, kernels of the Volterra series are multidimensional convolution integrals that are computationally expensive to identify. Thus, even though it is well known that aerodynamic nonlinearities are poorly approximated by quadratic Volterra series models, cubic and higher-order Volterra series truncations cannot be identified because their identification costs are too high. In this paper, a novel, sparse representation of the Volterra series is explored for which the identification costs are significantly lower than the identification costs of the full Volterra series. It is demonstrated that sparse Volterra reduced-order models are capable of efficiently modeling aerodynamically induced limit-cycle oscillations of the prototypical NACA 0012 benchmark model. These results demonstrate for the first time that Volterra series models are capable of modeling aerodynamically induced limit-cycle oscillations.