用机器学习建模跨音速非线性气动响应，提升设计精度。
Parametric Nonlinear Volterra Series via Machine Learning: Transonic Aerodynamics
- 基于伏尔泰拉级数与机器学习，构建参数化非线性气动模型。
- 包含二阶核的模型显著提升跨音速强非线性问题的预测精度。
- 适合概念设计阶段快速评估不同马赫数与迎角下的气动性能。
本研究提出一种在参数空间内建模非定常跨音速气动响应的方法，采用伏尔泰拉级数捕捉气动响应，并利用机器学习实现系数插值。一阶和二阶伏尔泰拉核由计算流体力学得到的脉冲响应推导，其中二阶核作为主导线性响应的修正项。采用人工神经网络与高斯过程回归算法，在马赫数与迎角定义的参数空间中对核系数进行插值。该方法应用于二维与三维跨音速算例。结果表明，引入二阶核可有效处理强非线性问题，且神经网络表现优异。该方法达到的概念设计可用精度水平。
原文摘要 · Abstract (English)
This study introduces an approach for modeling unsteady transonic aerodynamics within a parametric space, using Volterra series to capture aerodynamic responses and machine learning to enable interpolation. The first- and second-order Volterra kernels are derived from indicial aerodynamic responses obtained through computational fluid dynamics, with the second-order kernel calculated as a correction to the dominant linear response. Machine learning algorithms, specifically artificial neural network and Gaussian process regression, are used to interpolate kernel coefficients within a parameter space defined by Mach number and angle of attack. The methodology is applied to two and three dimensional test cases in the transonic regime. Results underscore the benefit of including the second-order kernel to address strong nonlinearity and demonstrate the effectiveness of neural networks. The approach achieves a level of accuracy that appears sufficient for use in conceptual design.
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