空气动力二阶核函数辨识方法
收稿日期: 2014-02-17
修回日期: 2014-05-05
网络出版日期: 2014-05-12
基金资助
国家自然科学基金(11102085); 江苏高校优势学科建设工程资助项目
Identification Method of Second-order Kernels in Aerodynamics
Received date: 2014-02-17
Revised date: 2014-05-05
Online published: 2014-05-12
Supported by
National Natural Science Foundation of China (11102085); Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
采用截断三阶Volterra级数模型来研究空气动力二阶核函数的辨识问题,选取一簇正交化的切比雪夫多项式对二阶核函数进行参数化处理,并将非参数辨识问题转化成参数辨识问题.相比于其他方法,本文模型能有效降低对激励信号幅值的敏感程度,保证辨识出的核函数具有较好的保真度;只针对三阶Volterra降阶模型中的一阶、二阶核函数进行辨识,即可提升原系统一阶、二阶核函数的辨识精度,却不会显著增加辨识过程的工作量;参数化辨识方法属于整体性辨识,根据已有的部分数据对(输入、输出数据)就能完成系统辨识,且能达到较好的辨识精度,从而有效地减少了执行计算流体力学(CFD)代码程序的总次数,节约了大量的时间成本.算例表明,与目前流行的非参数化方法相比,本文提出的切比雪夫函数辨识方法,精度上达到预期要求,辨识过程消耗的CFD总时间量至少可降低一个数量级.
关键词： 系统辨识; Volterra 级数; 降阶模型; 切比雪夫展式方法; 参数化方法
王云海 , 韩景龙 , 张兵 , 员海玮 . 空气动力二阶核函数辨识方法[J]. 航空学报, 2014 , 35(11) : 2949 -2957 . DOI: 10.7527/S1000-6893.2014.0086
Based on the truncated third-order Volterra series model, this paper investigates the identification of second-order Volterra kernels in aerodynamics. In this model, the second-order Volterra kernels can be parameter treated by employing a cluster of Chebyshev orthogonal polynomials. And then the problem of non-parameter is converted to the problem of parameter. In comparison with other treatments, it has several advantages. First, it ensures that the second-order Volterra kernels can be identified with better fidelity due to the reduced signal amplitude sensitivity. Then, in this model, the accuracy of first- and second-order Volterra kernels can be improved and the third-order Volterra kernels do not need to be identified. That means the cost for identification is reasonable. Last, the proposed parametric methods treat the identification as a whole and the partial data is available to be used for identification. That means the total number of executing computational fluid dynamics (CFD) code can be reduced and the identification cost is highly time-saving. The numerical results show the efficiency and high accuracy compared to those non-parameter methods and the total amount of CFD time can be reduced by at least one order of magnitude.
[1] Silva W A. Discrete-time linear and nonlinear aerodynamic impulse responses for efficient CFD analyses[D]. Williamsburg: College of William & Mary, 1997.
[2] Raveh D E, Mavris D N. Reduced-order models based on CFD impulse and step responses, AIAA-2001-1527[R]. Reston: AIAA, 2001.
[3] Silva W A. Simultaneous excitation of multiple-input/ multiple-output CFD-based unsteady aerodynamic systems[J]. Journal of Aircraft, 2008, 45(4): 1267-1274.
[4] Dietmar F, Christian B. Efficient computation of unsteady aerodynamic loads using computational-fluid-dynamics linearized methods[J]. Journal of Aircraft, 2013, 50(2): 425-440.
[5] Li P B. System identification[M]. Beijing: China Water Conservancy and Electricity Press, 2010. (in Chinese) 李鹏波. 系统辨识[M]. 北京:中国水利水电出版社, 2010.
[6] Chen G, Xu M, Chen S L. Volterra-series-based reduced-order model for unsteady aerodynamics[J]. Journal of Astronautics, 2004, 25(5): 492-495. (in Chinese) 陈刚, 徐敏, 陈士橹. 基于Volterra级数的非线性非定常气动力低阶模型[J]. 宇航学报, 2004, 25(5): 492-495.
[7] Lind R, Prazenica R J, Brenner M J, et al. Identifying parameter-dependent Volterra kernels to predict aeroelastic instabilities[J]. AIAA Journal, 2005, 43(12): 2496-2502.
[8] Wu Z G, Yang C. Volterra series based transonic unsteady aerodynamics modeling[J]. Journal of Beijing University of Aeronautics and Astronautics, 2006, 32(4):373-376.(in Chinese) 吴志刚, 杨超. 基于Volterra级数的跨音速非定常气动力建模[J].北京航空航天大学学报, 2006, 32(4): 373-376.
[9] Wang Y H, Han J L, Zhang T. Computation of Volterra kernels identification to Riccati nonlinear equation[C]//International Conference on Computer Science and Information Technology, 2010: 6-8
[10] Wang Y H, Han J L, Zhou W. Third-order Volterra kernel identification technique in aerodynamics[J]. Applied Mechanics and Materials, 2011, 52-54: 618-623.
[11] Thomas J P, Dowell E H, Hall K C. Harmonic balance approach for modeling three-dimensional nonlinear unsteady aerodynamics and aeroelasticity[C]//International Mechanical Engineering Congress & Exposition, 2002.
[12] Antonios K A, Achilleas D Z. Wavelet neural networks: a practical guide[J]. Neural Networks, 2013, 42: 1-27.
[13] Liu X Y, Yang C, Wu Z G. Wavelet-based reduced-order method for unsteady aerodynamics applicable to aeroelasticity[J]. Acta Aeronautica et Astronautica Sinica, 2010, 31(6): 1149-1155. (in Chinese) 刘晓燕, 杨超, 吴志刚. 适用于气动弹性的小波非定常气动力降阶方法[J]. 航空学报, 2010, 31(6): 1149-1155.
[14] Wang Y H, Han J L. Approach to identification of a second-order Volterra kernel of nonlinear systems by Chebyshev polynomials method[J]. Research Journal of Applied Sciences, Engineering and Technology, 2013, 5(20): 4950-4955.
[15] Zhang B, Han J L. Spring-TFI hybrid dynamic mesh method with rotation correction[J]. Acta Aeronoutica et Astronautica Sinica, 2011, 32(10): 1815-1823. (in Chinese) 张兵, 韩景龙. 带旋转修正的弹簧-TFI混合动网格方法[J]. 航空学报, 2011, 32(10): 1815-1823.
[16] Rivera J A, Dansberry B E, Bennett R M, et al. RNACA0012 benchmark model experimental flutter results with unsteady pressure distributions, AIAA-1992-2396-CP[R]. Reston: AIAA, 1992.
/
| 〈 |
|
〉 |
CJA