Nonlinear Aerodynamic Force Identification and Nonlinear Flutter Analysis Based on Autoencoder
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摘要:
为实现非线性动力系统的非线性气动力辨识和非线性颤振计算，提出一种基于神经网络方法和运动方程数值求解方法的自编码器模型. 以5∶1矩形断面为研究对象，通过节段模型自由振动风洞试验，详细测试系统非线性阻尼的振幅依存性和非线性颤振稳态振幅响应，明确该断面在不同折算风速下稳态振幅的唯一性；基于试验数据对所提出的自编码器模型进行训练，获取精准描述与位移和速度相关的非线性气动力编码器模型，实现不同动力参数下5∶1矩形断面非线性颤振运动时程分析. 研究结果表明：所提出的自编码器模型能够仅依赖自由振动风洞试验而无需测力或测压试验，即可精确辨识包含奇数次高次谐波分量的非线性气动力时程；能够精确复现不同初始条件下断面非线性颤振运动时程和不同折算风速下的稳态振幅响应，扭转稳态振幅最大误差不超过5%，平均误差为1.15%；具有较高的拓展性，可为后续相关研究提供参考.
Abstract:In order to identify the nonlinear aerodynamic forces and calculate nonlinear flutters of a nonlinear dynamic system, an autoencoder model based on the neural network method and numerical solution of motion equation was proposed. The 5∶1 rectangular cross-section was taken as the research object. Through free vibration wind tunnel tests of the sectional model, the amplitude dependence of the nonlinear damping and the steady-state amplitude responses of the nonlinear flutter of the system were tested, and it was clarified that the tested cross-section had the only steady-state flutter response at different reduced wind speeds. Based on the experimental data, the proposed autoencoder model was trained. The nonlinear aerodynamic force encoder model that accurately described displacement and speed was obtained to realize motion time-history analysis of the nonlinear flutter of the 5∶1 rectangular cross-section under different dynamic parameters. Research results show that the proposed autoencoder model can accurately identify the nonlinear aerodynamic force time-history containing high-order harmonic components only by relying on a free vibration wind tunnel test without the need to carry out force or pressure tests; the proposed model can accurately reproduce the motion time-history of nonlinear flutter under different initial conditions and the steady-state amplitude responses at different reduced wind speeds. The maximum error of torsional steady-state amplitude is less than 5%, and the average error is 1.15%. It has high extensibility and can provide a reference for subsequent related research.
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Key words:
- nonlinear flutter /
- wind tunnel test /
- neural network /
- encoder /
- decoder
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图 4 不同初始激励下的运动响应时程
Figure 4. Motion response time-history under different initial excitations
图 5 稳态扭转响应振幅随折算风速的变化
Figure 5. Variation of steady-state torsional response amplitude with reduced wind speed
图 7 非线性结构阻尼随扭转振幅的变化
Figure 7. Variation of nonlinear structural damping with torsional amplitude
图 9 训练预测值和试验值对比 （$ V=8.24 $）
Figure 9. Comparison of prediction results in training and testing results ($ V=8.24 $)
图 10 气动力训练预测值和试验值对比（$ V=8.24 $）
Figure 10. Comparison of prediction results in aerodynamic force training and testing results ($ V=8.24 $)
图 11 不同折算风速下非线性颤振响应 （D1）
Figure 11. Nonlinear flutter responses at different reduced wind speeds (D1)
图 12 非线性颤振运动时程验证预测值和试验值对比（$ V=8.24 $）
Figure 12. Comparison of prediction results and testing results for motion time-history of nonlinear flutter ($ V=8.24 $)
图 13 气动力验证预测值和试验值对比（$ V=8.24 $）
Figure 13. Comparison of prediction results and testing results of aerodynamic force ($ V=8.24 $)
图 14 不同折算风速下非线性颤振响应 （D2）
Figure 14. Nonlinear flutter responses at different reduced wind speeds (D2)
表 1 节段模型试验动力参数
Table 1. Dynamic parameters of sectional model test
动力参数
类型m/kg I/（kg•m2•m−1） fh/Hz ft/Hz D1 18.56 0.4928 1.768 3.038 D2 15.36 0.2152 1.875 4.435 
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