Transonic aeroelastic analysis can be carried out accurately and efficiently by using the aerodynamic Reduced-Order Modeling (ROM) approach. However, the efficiency and generalization capability of traditional time-dependent ROM should be further enhanced, especially when dealing with the case for varying flight parameters. For such a purpose, a set of flight samples for different Mach numbers and mean angles of attack in transonic regime are selected to cover the concerned parameter space. Subsequently, a typical filtered white Gaussian noise is used as the input signal to excite the dynamical behavior of the aerodynamic system via the direct Computational Fluid Dynamic (CFD) technique, and the corresponding input and output data at all the flight samples are used as the training data set. Afterwards, based on the CFD training data set, the dynamical relationship between aerodynamic output and displacement input for varying Mach number and mean angle of attack can be approximately fitted by using the Long Short Term Memory (LSTM) network, which is a time-series prediction approach of deep learning method. Finally, the transonic flutter boundaries of a NACA 64A010 airfoil are investigated to assess the validity of the proposed approach. The comparison with CFD results shows that, the ROM can predict the unsteady aerodynamic response and aeroelastic characteristics well with low computation cost. In particular, the flutter boundaries of the concerned airfoil at different Mach numbers and mean angles of attack are obtained, due to the absence of time-delay term in surrogate model, the generalization capacity and modeling efficiency of the ROM are improved.

通过使用气动降阶建模（ROM）方法，可以准确而有效地进行跨音速气动弹性分析。但是，传统时变ROM的效率和泛化能力应进一步提高，尤其是在处理飞行参数变化的情况下。为此，选择跨音速状态下不同马赫数和平均攻角的一组飞行样本，以覆盖相关的参数空间。随后，将典型的滤波后的高斯白噪声用作输入信号，以通过直接计算流体动力学（CFD）技术激发空气动力学系统的动力学行为，并将所有飞行样本的相应输入和输出数据用作输入信号。训练数据集。之后，根据CFD培训数据集，通过使用长期学习记忆（LSTM）网络，可以近似拟合变化的马赫数和平均攻角下的气动输出与位移输入之间的动力学关系，这是深度学习方法的时间序列预测方法。最后，研究了NACA 64A010机翼的跨音速颤振边界，以评估所提出方法的有效性。与CFD结果的比较表明，ROM可以很好地预测不稳定的空气动力响应和气动弹性特征，而计算成本却很低。特别地，由于代理模型中没有时间延迟项，因此获得了在不同马赫数和平均攻角下有关机翼的扑动边界，从而提高了ROM的泛化能力和建模效率。