Enhanced nonlinear state–space identification for efficient transonic aeroelastic predictions

Transonic aerodynamic systems exhibit strong nonlinearities due to various factors such as flow separations and shock wave oscillations. Thus, transonic aerodynamic modeling methods based on system identifications have attracted increasing attention. However, the dimensions of the models constructed via the current system identification methods are so high that it is difficult to predict transonic flutters and limit cycle oscillations simultaneously. This paper proposes an enhanced nonlinear state–space modeling method to identify a two-dimensional aerodynamic system in the transonic region. At first, the parsimonious linear model with modified inputs is identified by using the eigensystem realization algorithm. The model order is reduced by substituting the generalized displacement of the first-order mode (dominated by plunge) with its generalized velocity in the inputs. The polynomial functions are then used to represent the nonlinearities in the transonic aerodynamic systems. The polynomial functions do not contribute to the system linearization around the equilibrium such that the linear and nonlinear modeling stages are independent. The coefficients of these nonlinear terms are determined via nonlinear optimization. Finally, a nonlinear aerodynamic model is established and applied to aeroelastic applications. To demonstrate the accuracy and efficiency of this method, a two-dimensional, transonic aeroelastic wing with an NACA0012 profile is investigated. The simulation results show that the nonlinear state–space model with modified inputs improves the efficiency and accuracy of transonic aerodynamic nonlinear modeling. Moreover, the aerodynamic model coupled with the structural model can accurately predict the transonic flutter boundary and limit cycle oscillations.