Unsteady aerodynamics modeling method using Volterra series based on multiwavelet

Unsteady aerodynamics modeling must accurately describe the nonlinear aerodynamic characteristics in addition to unsteady aerodynamic characteristics. The Volterra series has got more and more attention as a powerful tool for nonlinear system modeling. The first order Volterra kernel can only describe the linear characteristics of the system. It is thus essential to incorporate the influence of the second order kernel or higher order kernels to build a nonlinear unsteady aerodynamics model. The main difficulty of higher order kernels identification is the number of parameters needed to be identified increases exponentially with the order of the kernel. This results in a dramatic increase of computational difficulty, and the so-called dimensional disaster arises. This paper expands the Volterra kernels using the piecewise-quadratic multiwavelet as the basis function. In the process of solving high dimensional and ill-posed equations, the paper utilizes the decomposition of multiwavelet multiresolution analysis in time and frequency to reduce the dimension of equations, and finally turns the problem into solving low dimensional equations and gets a stable solution. By identifying the second order kernel and the third order kernel of the lift coefficient, drag coefficient and pitching moment coefficient of the NACA0012 airfoil in plunging motion at Mach number 0.8, a nonlinear unsteady aerodynamics model is constructed. The aerodynamics in different reduced frequency is computed, and is compared with the CFD results to verify the ability of the Volterra series to describe nonlinear and unsteady aerodynamics and the effectiveness of the multiwavelet processing method.