Wavelet-based reduced-order method for unsteady aerodynamics applicable to aeroelasticity

The goal behind the development of reduced-order models for unsteady aerodynamics is to reduce computational cost and facilitate the use of computational fluid dynamics information in aeroservoelasticity and design optimization. In this article reduced-order aerodynamic models are derived by utilizing wavelet approximations of kernels appearing in Volterra series representations. During the process of model identification, input excitation is smooth and continuous and it is discretized by employing a zero-order hold with a sampling rate of 2 integer power. The approximated first-order kernel is expanded based on the Haar scaled function family. The first-order kernel can be truncated in a properly limited time length as a result of the Volterra kernel decay characteristic in system responses. In order to obtain the coefficients of the Volterra kernel, the overdetermined equation composed of the input/output data must be solved via singular value decomposition. Finally, an example of a two-dimensional NACA64a010 airfoil validates the wavelet-based modeling approach. The numerical results show that the proposed method is able to predict more accurately the unsteady aerodynamic responses due to structural small-amplitude motions and describe certain nonlinear phenomena.