线性化非定常气动力辨识的两种降阶模型比较
Comparisons of Two Reduced-Order Models for Linearized Unsteady Aerodynamic Identification
摘要：
本文比较了线性Volterra级数和带有外生输入的自回归（ARX）模型两种非定常气动力降阶模型（ROM）在动态线性气动力特性建模方面的性能。这两种方法的区别在于后一种模型有自回归项，而前一种模型只有输入相关项。第一个系统是低雷诺数流动中的一个压入圆柱，其中流动是稳定的（Re < 47）。虽然两种方法都能很好地拟合训练数据，但线性Volterra方法需要比ARX模型更高的模型阶数才能获得相同的精度。频率响应的比较表明，ARX模型更接近的频率响应，而在高雷诺数的频率响应是过拟合Volterra级数。第二个气动力系统是NACA 0012翼型俯仰流动，包括亚音速和跨音速状态。在不同的马赫数和平均攻角下，详细研究了模型关于延迟阶数的收敛性。随着马赫数或平均攻角的增加，所需的延迟阶数也将增加。但是ARX模型仍然在相同的精度水平上用少量的项来建模这个系统。结果表明，ARX模型在大多数情况下，特别是在接近不稳定状态时，其性能优于线性Volterra级数。
英文摘要：
This paper compares the performance of two unsteady aerodynamic reduced-order models (ROMs), namely linear Volterra series and the autoregressive with exogenous input (ARX) model, on modeling dynamically linear aerodynamic behaviors. The difference between these two methods is that the latter model has an autoregressive term while the former model has only the input-related term. The first system is a plunging cylinder in a low-Reynolds number flow, where the flow stable (Re < 47). Although the training data can be fitted well with both methods, the linear Volterra method requires a higher model order than the ARX model for the same accuracy. Comparison of the frequency response indicates that the ARX model approximates the frequency response more closely, while the frequency response at high Reynolds number is over-fitted by Volterra series. The second aerodynamic system is a flow over a pitching NACA0012 airfoil, including subsonic and transonic states. The convergence of the model with respect to delay orders, at different Mach numbers and mean angles of attack, is studied in detail. As the Mach number or the mean angle of attack increases, the required delay order will increase. But the ARX model still models this system with a small number of terms at the same level of accuracy. All results indicate that the ARX model outperforms the linear Volterra series in most of cases, especially when the flow is close to the unstable state.
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