A combined approach of linear convolution and higher-order Volterra series (VS) to reduced-order modeling of unsteady transonic aerodynamic loads is presented. Our framework offers a simple method to determine the memory depth of the system, clearly separates the linear and the nonlinear (NL) contributions, and significantly reduces the effort required to generate a model for a wide range of reduced frequencies. The generated models use step-response data in the linear and the NL ranges, thus separating the model generation from any specific input signal or a particular reduced frequency. The models were compared against and validated using the computational fluid dynamics results of an oscillating two-dimensional NACA 0012 airfoil.

提出了一种线性卷积和高阶 Volterra 级数 (VS) 的组合方法来对非定常跨音速气动载荷进行降阶建模。我们的框架提供了一种简单的方法来确定系统的内存深度，清楚地分离线性和非线性 (NL) 贡献，并显着减少了为各种降低的频率生成模型所需的工作量。生成的模型使用线性和 NL 范围内的阶跃响应数据，从而将模型生成与任何特定输入信号或特定降低频率分开。这些模型与振荡二维 NACA 0012 翼型的计算流体动力学结果进行了比较和验证。