基于多元正交函数的非线性快速气动建模

高鑫; 连峰; 孔轶男; 陈功; 张光华; 王文正

doi:10.7638/kqdlxxb-2022.0109

欢迎来到能源电力期刊网！

English Version 期刊登录

您当前的位置：

首页 >

文章列表页 >

基于多元正交函数的非线性快速气动建模

研究论文 | 更新时间：2026-05-28

- 基于多元正交函数的非线性快速气动建模
- Nonlinear rapid aerodynamic modeling based on multivariate orthogonal functions
- 空气动力学学报 2023年41卷第6期页码：81-88
- 作者机构：
  
  1. 西安交通大学,西安,710049
  2. 中国空气动力研究与发展中心,绵阳,621000
  3. 电子科技大学航空航天学院,成都,611731
- 作者简介：
  
  高鑫（1996-），男，山西朔州人，硕士研究生，研究方向：气动力数据融合与在线辨识研究. E-mail：gx19960413@163.com
  王文正*（1968-），男，四川简阳人，博士，研究方向：气动力建模、辨识和融合以及飞行控制. E-mail：wangwz@eustc.edu.cn
- 基金信息：
- DOI：10.7638/kqdlxxb-2022.0109
  中图分类号： V211.3;O241
- 纸质出版：2023
- 稿件说明：
移动端阅览
高鑫, 连峰, 孔轶男, 等. 基于多元正交函数的非线性快速气动建模[J]. 空气动力学学报, 2023, 41(6): 81−88.

GAO Xin, LIAN Feng, KONG Yinan, et al. Nonlinear rapid aerodynamic modeling based on multivariate orthogonal functions[J]. 2023, 41(6): 81-88.
高鑫, 连峰, 孔轶男, 等. 基于多元正交函数的非线性快速气动建模[J]. 空气动力学学报, 2023, 41(6): 81−88. DOI： 10.7638/kqdlxxb-2022.0109

GAO Xin, LIAN Feng, KONG Yinan, et al. Nonlinear rapid aerodynamic modeling based on multivariate orthogonal functions[J]. 2023, 41(6): 81-88. DOI： 10.7638/kqdlxxb-2022.0109.

摘要

多项式响应面模型是气动系数建模中常用的一种模型。实时采集的气动数据有较强的线性相关性，使用常规最小二乘回归方法估计模型参数时，由于回归矩阵的病态性导致估计误差较大。提出一种基于多元正交函数的多项式响应面建模方法，将回归矩阵进行QR分解后迭代实时数据，可以有效避免回归矩阵病态问题，提高多项式响应面模型的精确度；引入模型预测方差（PSE）与决定系数

，简化模型结构，避免了模型的过度拟合。基于F-16风洞试验部分气动数据，利用仿真程序对风洞数据进行样条函数插值，得到完整的实验数据集，用以验证实验算法。采用多元正交函数建模方法分别建立目标飞行器的6个无量纲气动力系数模型，并对建模过程中的实时性进行分析。建模结果表明，基于多元正交函数建立的多项式响应面模型对实时数据有较好的预测效果；同时，建模过程中各环节的时间消耗均是毫秒级的，满足实时建模的要求，说明该方法可以实时地建立目标飞行器的非线性气动力系数模型。

Abstract

The polynomial response surface model (RSM) is a standard model in aerodynamic coefficient modeling. Real-time collected aerodynamic data are strongly correlated. Estimating the parameters of RSM by conventional least-square regression methods will yield significant errors since the regression matrix is ill-posed. A polynomial RSM based on multivariate orthogonal functions proposed here can overcome such a shortcoming and improve RSM's accuracy by iterating real-time data on the R matrix of the QR decomposed regression matrix. Moreover

RSM is further simplified by introducing Predicted Squa

red Error (PSE) and the

coefficient to eliminate negligible items so that the over-fitting of the model is avoided. Part of the aerodynamic data of an F-16 wind tunnel test is interpolated with the spline function to obtain complete experimental data. The real-time data acquisition process is simulated by inputting data one by one to verify the effectiveness and real-time performance of the experimental algorithm. The multivariate orthogonal function modeling method is used to establish six models of dimensionless aerodynamic coefficients of the target aircraft

and the real-time performance of the modeling process is analyzed. Results show that the polynomial RSM based on multivariate orthogonal functions has a good predictive capability for real-time data. Meanwhile

the time consumption of each step in the modeling process is milliseconds

indicating that the method can establish the real-time modeling of the nonlinear aerodynamic coefficients of target aircraft.

关键词

Keywords

references

ZHANG Q, YE Z Y. Longitudinal stability analysis for X-37B like trans-atmospheric orbital test vehicle based on aerodynamic derivatives[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(1): 77-85(in Chinese).

ABZUG M J, LARRABEE E E. Airplane stability and control[M]. Cambrige: Cambridge University Press, 1997: 165.

ZHU H T, BAI W. Static and dynamic pitch derivatives of transonic full aircraft configuration with unsteady CFD method[J]. Aeronautical Science Technology, 2017, 28(7): 19-24(in Chinese).

ZHUO LJ, LIAO HL, ZHOU Q, et al. Identification of Aerodynamic Derivatives of a Box-Girder Bridge Deck with Twin Active Flaps Using CFD Simulations[J]. Journal of Bridge Engineering , 2022, 27(3): 4022002.1-4022002.13. doi:10.1061/(ASCE)BE.1943-5592.0001830

GOMAN M, KHRABROV A. State-space representation of aerodynamic characteristics of an aircraft at high angles of attack[J]. Journal of Aircraft, 1994, 31(5): 1109-1115. DOI:10.2514/3.46618

WANG Y L, BU C, FENG S, et al. Modeling of lateral state-space of aerodynamic characteristics at high angle of attack[J]. Flight Dynamics, 2021, 39(4): 13-18(in Chinese).

MEJARI M, MAVKOV B, FORGIONE M, et al. Direct identification of continuous-time LPV state-space models via an integral architecture[J]. Automatica, 2022, 142: 110407. DOI:10.1016/j.automatica.2022.110407

TOBAK M, SCHIFF L. On the formulation of the aerodynamic characteristics in aircraft dynamics[R]. NASATRR-456, 1976.

ROKHSAZ K, STECK J E. Use of neural networks in control of high-alpha maneuvers[J]. Journal of Guidance, Control, and Dynamics, 1993, 16(5): 934-939. DOI:10.2514/3.21104

FU J Q, SHI Z W, CHEN K, et al. Applications of real-time recurrent neural network based on extended Kalman filter in unsteady aerodynamics modeling[J]. Acta Aerodynamica Sinica, 2018, 36(4): 658-663(in Chinese).

WANG C, WANG G D, BAI P. Machine learning method for aerodynamic modeling based on flight simulation data[J]. Acta Aerodynamica Sinica, 2019, 37(3): 488-497(in Chinese).

SHI Z W, WU G X. Fuzzy logic model of nonlinear unsteady aerodynamics with multiple variables[J]. Acta Aerodynamica Sinica, 2001, 19(1): 103-108(in Chinese).

BRANDON J M, MORELLI E A. Real-time onboard global nonlinear aerodynamic modeling from flight data[C]// AIAA Atmospheric Flight Mechanics Conference, Atlanta, GA. Reston, Virginia: AIAA, 2014: 2554. doi: 10.2514/6.2014-2554

MORELLI E A. Autonomous real-time global aerodynamic modeling in the frequency domain[C]// AIAA Scitech 2020 Forum, Orlando, FL. Reston, Virginia: AIAA, 2020: 0761. doi: 10.2514/6.2020-0761

MORELLI E A. Practical aspects of real-time modeling for the learn-to-fly concept[C]// 2018 Atmospheric Flight Mechanics Conference, Atlanta, Georgia. Reston, Virginia: AIAA, 2018: 3309. doi: 10.2514/6.2018-3309

MORELLI E A. Determining aircraft moments of inertia from flight test data[C]// AIAA Scitech 2021 Forum, VIRTUAL EVENT. Reston, Virginia: AIAA, 2021: 1642. doi: 10.2514/6.2021-1642

MORELLI E A. Flight test maneuvers for efficient aerodynamic modeling[J]. Journal of Aircraft, 2012, 49(6): 1857-1867. DOI:10.2514/1.C031699

KLEIN V, MORELLI E A. Aircraft system identification: theory and practice[M]. AIAA Education Series, AIAA Reston, VA, 2006, Chaps 9.

RUSSELL RS. Nonlinear f-16 simulations using Simulink and Matlab[R]. Technical report, University of Minnesota, 2003.

SONNEVELDT L. Nonlinear F-16 model description[D]. Netnerlands: Delft University of Technology, 2010.

NGUYEN L T, OGBURN M E, GILBERT W P, et al. Simulator study of stall/post-stall characteristics of a fighter airplane with relaxed longitudinal static stability[R]. Technical report, NASA Langley Research Center, 1979.

OMRAN A, NEWMAN B, LANDMAN D. Global aircraft aero-propulsive linear parameter-varying model using design of experiments[J]. Aerospace Science and Technology, 2012, 22(1): 31-44. DOI:10.1016/j.ast.2011.05.008

LU X J, ZHENG Z Q. Identification of continuous state-space model parameters for a class of MIMO systems: a frequency domain approach[J]. Acta Automatica Sinica, 2016, 42(1): 145-153. (in Chinese)

浏览量

下载量

CSCD

文章被引用时，请邮件提醒。

提交

工具集

关联资源

某型电动跑车尾翼气动设计的仿真与试验研究

风扇叶片颗粒侵蚀特性的多因素分析与模拟

交错型CPR方法的保正实现策略及其对比研究

个体间距对多扑翼气动噪声的影响特性

类HyTRV升力体阻尼/交叉动导数特性分析