Unsteady aerodynamics modeling using Volterra series expansed by basis function

Unsteady aerodynamics modeling must accurately describe nonlinear aerodynamic characteristics in addition to unsteady aerodynamic characteristics. The Volterra series has attracted increasing attention as a powerful tool for nonlinear system modeling. It is essential to incorporate the influence of the second-order Volterra kernel or higher-order kernels to build a nonlinear unsteady aerodynamics model. The main difficulty in the identification of higher-order kernels is that the number of parameters to be identified increases exponentially with the order of a kernel. This paper expands the Volterra kernels with the four-order B-spline wavelet on the interval as the basis function, converts the problem into the solution of low-dimensional equations, and obtains a stable solution. A nonlinear unsteady aerodynamics model is built by identifying the second-order and third-order kernels of the lift, drag, and pitching moment coefficients of the NACA0012 airfoil. Then the model is verified at different reduced frequencies using CFD.