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 引用本文: 张家铭, 杨执钧, 黄锐. 基于非线性状态空间辨识的气动弹性模型降阶[J]. 力学学报, 2020, 52(1): 150-161.
Zhang Jiaming, Yang Zhijun, Huang Rui. REDUCED-ORDER MODELING FOR AEROELASTIC SYSTEMS VIA NONLINEAR STATE-SPACE IDENTIFICATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 150-161.
 Citation: Zhang Jiaming, Yang Zhijun, Huang Rui. REDUCED-ORDER MODELING FOR AEROELASTIC SYSTEMS VIA NONLINEAR STATE-SPACE IDENTIFICATION[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(1): 150-161.

## REDUCED-ORDER MODELING FOR AEROELASTIC SYSTEMS VIA NONLINEAR STATE-SPACE IDENTIFICATION

• 摘要: 高维、非线性气动弹性系统的模型降阶是当前气动弹性力学与控制领域的研究热点之一.然而国内外现有的非线性模型降阶方法仍存在辨识算法复杂、精度有待提高等问题.本研究提出了一种基于非线性状态空间辨识的跨音速气动弹性模型降阶方法. 首先,该方法基于非定常空气动力的单位脉冲响应数据,采用特征系统实现算法对非线性状态空间模型的线性动力学部分进行系统辨识. 其次,引入状态和控制输入的非线性函数, 采用优化算法对非线性函数的系数矩阵进行优化,进而得到考虑非线性效应的空气动力降阶模型.为了验证该降阶模型在预测跨音速气动弹性力学行为的精确性,本文以三维机翼为研究对象,分别从基于非线性降阶模型的气动力辨识、跨声速颤振边界计算和极限环振荡预测三方面进行了算例验证,并与现有的模型降阶方法进行了对比, 进一步说明本文所提出方法的有效性.研究结果表明, 该降阶模型对上述三类问题的计算精度与直接流-固耦合方法相吻合,可用于高效预测飞行器跨声速气动弹性力学行为.

Abstract: Reduced-order modeling for high dimensional nonlinear aeroelastic systems is one of the hot issues in the field of aeroelasticity and control. Some linear/nonlinear reduced-order modeling methodologies, such as autoregressive exogenous, auto regressive-moving-average model, Volterra series, artificial neural networks, Wiener model, and Kriging technique, were proposed for reconstructing low-dimensional aerodynamic models. However, the previous nonlinear reduced-order models, such as the nonlinear Wiener model and neural network model, still have some problems need to be addressed. For example, the identification algorithm is too complexity and the accuracy in reconstructing the dynamic behaviors needs to be improved further. In this paper, a nonlinear state-space identification-based reduced-order modeling methodology for transonic aeroelastic systems is proposed. Firstly, the unit impulse response of the transonic aerodynamic system was computed via computational fluid dynamic method. By using the snapshots of the unit impulse response, the linear dynamics part of the nonlinear state-space model is identified by using the eigensystem realization algorithm. Then, the nonlinear functions of the state variables and control input are introduced and the coefficient matrices of these nonlinear functions are optimized via the optimization algorithm. As a result, a nonlinear reduced-order aerodynamic model can be obtained. To verify the accuracy of the reduced-order modeling in predicting the transonic aeroelastic behaviors, a three-dimensional wing is selected as the testbed and the aerodynamic forces, transonic flutter computation, and limit-cycle oscillation prediction are implemented as the numerical examples. Moreover, to demonstrate the accuracy of the present reduced-order modeling method in predicting unsteady aerodynamic forces, the numerical results are also compared with other reduced-order modeling method. The numerical results show that the above three dynamic behaviors predicted via the present reduced-order model have a good agreement with the direct fluid-structure interaction method. The comparison proves that the present reduced-order aerodynamic model can be used to predict the transonic aeroelastic behaviors of aircraft with high efficiency.

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