Nonlinear Reduced-Order Modeling for Multiple-Input/Multiple-Output Aerodynamic Systems

Abstract

The paper presents a novel nonlinear reduced-order modeling approach for multi-input/multi-output aerodynamic systems. The nonlinear reduced-order model for an aerodynamic system includes a finite sum of Wiener-type cascade models. The nonlinear reduced-order model approach starts with fitting a Wiener-type cascade path between the inputs and outputs of the aerodynamic system first. Then, the approach computes the outputs of the path and subtracts them from the measured outputs. The second path is then fitted between the inputs and the output residuals. This process is repeated until the residuals contain only noise. To obtain an optimal path at each stage, a novel nonlinear model, a linear dynamic state-space element followed by a single-layer neural network model, is selected as the Wiener-type cascade model. The Wiener-type cascade model can be optimized by using the Levenberg–Marquadt algorithm. To demonstrate the performance of the proposed nonlinear reduced-order model in modeling the statically nonlinear and dynamically linearized behavior of a nonlinear aerodynamic system, the unsteady transonic compressible flow over a two-degree-of-freedom wing section with the NACA 64A010 airfoil is presented. The numerical results indicate that the proposed nonlinear reduced-order model can accurately identify the outputs of aerodynamic systems subject to a weak excitation. Then, the nonlinear reduced-order model is applied to the transonic flutter analysis of the Isogai wing model. Compared with the direct computational fluid dynamics and linear reduced-order model, the proposed nonlinear reduced-order model is accurate and efficient for transonic flutter prediction of nonlinear aeroelastic systems.