基函数宽度对RBF神经网络气动力模型精度的影响研究

将带输出反馈的RBF（recursive radial basis function, RRBF）神经网络用于构建非定常气动力模型，能够得到一种动态非线性气动力降阶模型（reduced order model, ROM）。隐含层神经元的基函数宽度是该气动力模型的一个重要参数。为了研究基函数宽度对RRBF神经网络的影响,首先通过数学分析和计算仿真研究了训练过程中宽度与神经网络结构之间的关系,而后用NACA0012翼型俯仰运动作为算例,研究模型在不同训练信号、延迟阶数和流动状态的情况进行测试。测试结果表明,基函数宽度对此类非定常气动力模型的稳定性及泛化能力都有较大影响；最优宽度的选择随训练及预测信号的变化有所不同；较多样本时,通常选择55~75的宽度能够保证非定常气动力模型具有较高的预测精度。通过对随机俯仰运动样本的预测结果,验证了宽度的最优选择范围。

Research on the Effects of Basis Function Widths of Aerodynamic Modeling Based on RBF Neural Network

A recursive radial basis function (RRBF) neural network is applied to construct unsteady aerodynamic model, which leads to a dynamic nonlinear reduced order model (ROM). The widths of basis function in hidden layer is one of important parameters to this aerodynamic model.To investigate the effects of widths for RRBF neural network, mathematical analysis and simulations are executed at first, which shows the relationship between widths and framework of the model during training process. Then cases of NACA 0012 aerofoil with pitching maneuvers are simulated, to test the model under different training maneuvers, previous time steps and flow states. Results show that the widths of basis function have much impact on the stability and generalization ability of this type of aerodynamic model. The best width varies with different training and testing maneuvers. With more samples, higher predicting accuracy of aerodynamic model is guaranteed with widths between 55~75. Predicting results of random pitching maneuver verify the conclusion of best widths scale in the paper.