基于噪声特性估计的气动系数辨识方法

doi:10.7527/S1000-6893.2024.30920

Abstract

Abstract:

Using flight data to verify and update the wind-tunnel aerodynamic database is an important part of flight vehicle design and evaluation program. In response to the lack of angular acceleration measurement in flight tests， a novel aerodynamic coefficient identification method has been developed in this paper. Firstly， a mathematical model of aerodynamic coefficient identification was constructed by modeling the derivatives of aerodynamic coefficient respect to time as first-order Gauss-Markov process. Then， analytical expressions for the unknown statistics， such as the covariances of process and measurement noise， were derived theoretically by maximizing the likelihood function. The state estimation was conducted by using the Square Root Unscented Kalman Filter （SRUKF） associated with the Unscented Rauch-Tung-Striebel Smoother （URTSS）. The unknown statistics were computed explicitly and updated iteratively， based on the state estimation results. Thereby， the time histories of aerodynamic coefficients， as the augmented state variables， were obtained. The effectiveness of the developed method was demonstrated by two examples of aircraft aerodynamic coefficient identification. The results showed that the unknown statistics and aerodynamic coefficients were estimated accurately. In addition， the method is of robust convergence with respect to the initial estimates of unknown statistics.

Key words: aerodynamic coefficient identification, noise covariance, square root unscented Kalman filter, unscented Rauch-Tung-Striebel smoother, likelihood function, flight test, aerodynamic parameter estimation

CLC Number:

V212

Qing WANG, Fengqi ZHENG, Di DING, Xi YUE. Aerodynamic coefficient identification method based on noise statistics estimation[J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(7): 130920.

Figures/Tables 17

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Table 1

Fig.8

Table 2

Fig.9

Fig.10

Table 3

Constant parameters in HFB-320 dynamic model

参数	取值
质量m/kg	7 472.0
转动惯量I_y /（kg∙m²）	22 847
参考面积S/m²	30.097
平均空气动力弦长 $c ¯$ /m	0.607 5
推力线倾斜角σ_T/rad	0.052 4
推力力臂（l_tx sinσ_T+l_tz cosσ_T）/m	-0.160 3
重力加速度g（m·s^-2）	9.806 65
空气密度ρ/（kg·m^-3）	0.792 0
参考速度V_ref/（m·s^-1）	104.67

Table 3

Fig.11

Fig.12

Fig.13

Table 4

References 38

1	HAMEL P G， JATEGAONKAR R V. Evolution of flight vehicle system identification‍［J］. Journal of Aircraft， 1996， 33（1）： 9-28.
2	GREENBERG H. A survey of methods for determining stability parameters of an airplane from dynamic flight measurements： NACA TN-2340‍［R］. Washington， D.C.： NASA， 1951.
3	MAINE R E， ILIFF K W. Application of parameter estimation to aircraft stability and control， the output error approach： NASA RP-1168‍［R］. Washington， D.C.： NASA， 1986.
4	MAINE R E， ILIFF K W. Formulation and implementation of a practical algorithm for parameter estimation with process and measurement noise‍［C］‍∥6th Atmospheric Flight Mechanics Conference. Reston： AIAA， 1980.
5	JATEGAONKAR R V， PLAETSCHKE E. Identification of moderately nonlinear flight mechanics systems with additive process and measurement noise［J］. Journal of Guidance， Control， and Dynamics， 1990， 13（2）： 277-285.
6	GRAUER J A， MORELLI E A. A new formulation of the filter-error method for aerodynamic parameter estimation in turbulence‍［C］‍∥Proceedings of the AIAA Atmospheric Flight Mechanics Conference. Reston： AIAA， 2015.
7	WANG Q， ZHENG F Q， QIAN W Q， et al. A practical filter error method for aerodynamic parameter estimation of aircraft in turbulence［J］. Chinese Journal of Aeronautics， 2023， 36（2）： 17-28.
8	MORELLI E. Practical aspects of the equation-error method for aircraft parameter estimation［C］‍∥AIAA Atmospheric Flight Mechanics Conference and Exhibit. Reston： AIAA， 2006.
9	DE VISSER C C， POOL D M. Stalls and splines： Current trends in flight testing and aerodynamic model identification‍［J］. Journal of Aircraft， 2023， 60（5）： 1480-1502.
10	MOKHTARI M A， SABZEHPARVAR M. Identification of spin maneuver aerodynamic nonlinear model by applying ensemble empirical mode decomposition and extended multipoint modeling［J］. Proceedings of the Institution of Mechanical Engineers， Part G： Journal of Aerospace Engineering， 2019， 233（5）： 1865-1878.
11	OVCHARENKO V N， POPLAVSKY B K. Identification of nonstationary aerodynamic characteristics of an aircraft based on flight data‍［J］. Journal of Computer and Systems Sciences International， 2021， 60（6）： 864-874.
12	LI J S， ZHUANG L， SONG J H， et al. An aerodynamic model identification method suitable for low-quality flight data［C］∥2020 3rd International Conference on Unmanned Systems （ICUS）. Piscataway： IEEE， 2020： 381-388.
13	颜楚雄，童轶男，宋加洪，等. 基于贝叶斯估计理论的再入飞行器气动辨识方法［J］. 中国科学：物理学力学天文学， 2021， 51（10）： 104705.
	Yan C X， TONG Y N， SONG J H， et al. Aerodynamic identification method of maneuverable vehicles based on the Bayes estimation theorem‍［J］. Scientia Sinica Physica， Mechanica & Astronomica， 2021， 51（10）： 104705 （in Chinese）.
14	STALFORD H L. High-alpha aerodynamic model identification of T-2C aircraft using the EBM method［J］. Journal of Aircraft， 1981， 18（10）： 801-809.
15	王启，简政，张培田，等. 利用大迎角试飞数据辨识飞机气动导数［J］. 飞行力学， 2005， 23（1）： 68-72.
	WANG Q， JIAN Z， ZHANG P T， et al. Aircraft aer-odynamic parameter identification by using HAOA flight test data［J］. Flight Dynamics， 2005， 23（1）： 68-72 （in Chinese）.
16	臧剑文，毕晓烨，金钊，等. 基于迎角分区的全局飞行器气动参数辨识方法［J］. 系统工程与电子技术， 2022， 45（11）： 3588-3596.
	ZANG J W， BI X Y， JIN Z， et al. Global aircraft aerodynamic parameter identification method based on angle of attack partitioning‍［J］. Systems Engineering and Electronic， 2022， 45（11）： 3588-3596 （in Chinese）.
17	DAS S， KUTTIERI R A， SINHA M， et al. Neural partial differential method for extracting aerodynamic derivatives from flight data‍［J］. Journal of Guidance， Control， and Dynamics， 2010， 33（2）： 376-384.
18	WANG Q， WU K Y， ZHANG T J， et al. Aerodynamic modeling and parameter estimation from QAR data of an airplane approaching a high-altitude airport［J］. Chinese Journal of Aeronautics， 2012， 25（3）： 361-371.
19	SINGH S， GHOSH A. Parameter estimation from flight data of a missile using maximum likelihood and neural network method‍［C］‍∥AIAA Atmospheric Flight Mechanics Conference and Exhibit. Reston： AIAA， 2006.
20	TONDJI Y， GHAZI G， BOTEZ R M. CRJ 700 longitudinal aerodynamic coefficients identification using support vector machine‍［C］‍∥AIAA Aviation 2023 Forum. Reston： AIAA， 2023.
21	蔡金狮，汪清，王文正，等. 飞行器系统辨识学［M］. 北京：国防工业出版社， 2003： 293-296.
	CAI J S， WANG Q， WANG W Z， et al. System identification of aircraft［M］. Beijing： National Defense Industry Press， 2003： 293-296 （in Chinese）.
22	KLEIN V， MORELLI E A. Aircraft system identification-Theory and practice［M］. Reston： AIAA， 2006： 367-369.
23	MORELLI E A. Estimating noise characteristics from flight test data using optimal Fourier smoothing［J］. Journal of Aircraft， 1995， 32（4）： 689-695.
24	HOFF J C. Fortran programs for aircraft parameter identification using the estimation-before-modelling technique： College of Aeronautics Report No. 9709［R］. Cranfield， Bedford： Cranfield University， 1997.
25	SARKAR A， PANNEERSELVAM S， SUNDARRAJAN R. Aerodynamic coefficients estimation of different flight vehicles under limited measurements［C］‍∥24th Atmospheric Flight Mechanics Conference. Reston： AIAA， 1999.
26	VAN DER MERWE R， WAN E A. The square-root unscented Kalman filter for state and parameter-estimation［C］∥2001 IEEE International Conference on Acoustics， Speech， and Signal Processing. Proceedings （Cat. No.01CH37221）. Piscataway： IEEE， 2001： 3461-3464.
27	BRUNKE S， CAMPBELL M E. Square root sigma point filtering for real-time， nonlinear estimation‍［J］. Journal of Guidance， Control， and Dynamics， 2004， 27（2）： 314-317.
28	GEERAERT J L， MCMAHON J W. Square-root unscented Schmidt-Kalman filter［J］. Journal of Guidance， Control， and Dynamics， 2017， 41（1）： 280-287.
29	SÄRKKÄ S. Unscented Rauch-Tung-Striebel smoother［J］. IEEE Transactions on Automatic Control， 2008， 53（3）： 845-849.
30	GARCIA-VELO J， WALKER B K. Aerodynamic parameter estimation for high-performance aircraft using extended Kalman filtering［J］. Journal of Guidance， Control， and Dynamics， 1997， 20（6）： 1257-1260.
31	CHOWDHARY G， JATEGAONKAR R. Aerodynamic parameter estimation from flight data applying extended and unscented Kalman filter‍［C］‍∥AIAA Atmospheric Flight Mechanics Conference and Exhibit. Reston： AIAA， 2006.
32	JULIER S， UHLMANN J， DURRANT-WHYTE H F. A new method for the nonlinear transformation of means and covariances in filters and estimators［J］. IEEE Transactions on Automatic Control， 2000， 45（3）： 477-482.
33	JULIER S J， UHLMANN J K. Unscented filtering and nonlinear estimation［J］. Proceedings of the IEEE， 2004， 92（3）： 401-422.
34	MORELLI E A. Flight test maneuvers for efficient aerodynamic modeling［J］. Journal of Aircraft， 2012， 49（6）： 1857-1867.
35	GRESHAM J L， SIMMONS B M， FAHMI J M W， et al. Remote uncorrelated pilot input excitation assessment for unmanned aircraft aerodynamic modeling［J］. Journal of Aircraft， 2023， 60（3）： 955-967.
36	JATEGAONKAR R V. Flight vehicle system identification： A time domain methodology［M］. Reston： AIAA， 2006： 167-171， 207-215， 257-259.
37	YOKOYAMA N. Parameter estimation of aircraft dynamics via unscented smoother with expectation-maximization algorithm‍［J］. Journal of Guidance， Control， and Dynamics， 2011， 34（2）： 426-436.
38	LIU Y Y， WANG H W， ZHANG W. Robust parameter estimation with outlier-contaminated correlated measurements and applications to aerodynamic coefficient identification‍［J］. Aerospace Science and Technology， 2021， 118： 106995.

过程噪声标准差	真值	估计值	测量噪声标准差	真值	估计值
q₁/（m·s^-1）	0.005	0.004 93	r₁/（m·s^-1）	0.005	0.003 68
q₂/（m·s^-1）	0.100	0.094 84	r₂/rad	0.001	0.000 75
q₃/（m·s^-1）	0.100	0.094 46	r₃/rad	0.001	0.000 75
q₄/（rad·s^-1）	0.001	0.000 94	r₄/（rad·s^-1）	0.001	0.000 65
q₅/（rad·s^-1）	0.001	0.000 96	r₅/（rad·s^-1）	0.001	0.000 66
q₆/（rad·s^-1）	0.001	0.000 93	r₆/（rad·s^-1）	0.001	0.000 65
q₇/rad	0.001	0.000 77	r₇/（m·s^-2）	0.020	0.017 39
q₈/rad	0.001	0.000 74	r₈/（m·s^-2）	0.020	0.017 55
			r₉/（m·s^-2）	0.020	0.017 54
			r₁₀/rad	0.001	0.000 77
			r₁₁/rad	0.001	0.000 74

参数	真值	估计值	参数	真值	估计值
C_A₀	0.081 0	0.081 0	C_Yβ	-1.126 9	-1.126 3
C_Aα₂	-4.107 4	-4.113 7	C_Yδ_r	0.107 2	0.106 5
C_Aδ_e	0.104 0	0.103 6	C_lβ	-0.113 0	-0.112 9
C_N₀	0.166 2	0.165 8	C_lδ_r	0.036 3	0.036 3
C_Nα	5.216 8	5.208 9	C_lδ_a	-0.192 0	-0.191 7
C_Nδ_e	0.737 2	0.746 0	C_lp	-0.759 6	-0.757 6
C_Nq	29.646 0	29.798 0	C_nβ	0.241 8	0.242 5
C_m₀	0.110 7	0.110 5	C_nδ_r	-0.165 4	-0.165 8
C_mα	-1.137 4	-1.137 6	C_nδ_a	-0.025 7	-0.027 4
C_mδ_e	-1.656 9	-1.652 8	C_nr	-0.535 1	-0.536 0
C_mq	-‍20.184 4	-‍20.119 7

参数	FEM^［36］		EM^［37］	MEM+MRS^［38］	本文方法
参数	估计值	σ/%	EM^［37］	MEM+MRS^［38］	估计值	σ/%
C_D₀	0.123	2.45	0.123	0.126	0.122 5	1.30
C_Dα	0.320	2.26	0.321	0.315	0.324 9	1.17
C_DV	-0.064 5	3.95	-0.065 1	-0.066 7	-0.064 8	2.08
C_L₀	-0.092 9	21.1	-0.091 1	-0.108 7	-0.068 5	29.51
C_Lα	4.328	1.08	4.308	4.338	4.257 3	1.13
C_LV	0.149	11.1	0.149	0.160	0.132 4	12.94
C_m₀	0.112	3.27	0.107	0.233	0.097 7	4.18
C_mα	-0.968	1.12	-1.000	-1.809	-0.965 6	1.36
C_mδ_e	-1.529	1.27	-1.616	-1.874	-1.549 7	1.62
C_mq	-34.710	2.27	-38.634	-52.972	-37.335 1	2.48
C_mV	0.003 9	82.1	0.011 6	-0.028 6	0.017 4	21.44

[1]	Zhiqiang WAN, Shanshan ZHANG, Xiaozhe WANG, Liang MA, Ao XU, Zhigang WU, Chao YANG. Maneuver load analysis and alleviation technology of flexible aircraft: Review [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(3): 30279-030279.
[2]	Zibo LIU, Ran ZHANG, Wenchao XUE, Huifeng LI. Active disturbance rejection control for load relief of launch vehicles considering elastic effects [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(1): 330319-330319.
[3]	Weiguo ZHANG, Min TANG, Jie WU, Xianmin PENG, Guichuan ZHANG, Bowen NIE, Liangquan WANG, Chaoqun LI. Overview of wind tunnel test research on tiltrotor aircraft [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 530114-530114.
[4]	Bowen NIE, Liangquan WANG, Zhiyin HUANG, Long HE, Shipeng YANG, Hongtao YAN, Guichuan ZHANG. Flight dynamics modeling and control scheme design of compound high-speed unmanned helicopters [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(9): 529848-529848.
[5]	Yanxiang HOU, Lihao FENG. Wind tunnel virtual flight test of flying wing configuration with active flow control [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(24): 630636-630636.
[6]	Guochi GAO, Bo ZHANG, Jingze QUAN, Chong YIN, Li DING, Yubiao JIANG. Airworthiness certification technology of normal aircraft natural icing flight test [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(1): 128531-128531.
[7]	Wenlong LI, Bo WU, Shuai XIE. Technology of wing load measurement for wing-body integrated structure with landing gear layout [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(1): 229525-229525.
[8]	Guanmian LIU, Fan ZHANG, Zhihang CHENG, Kangzhi YANG, Hejun QIN. Installation location of cloud combination probe for multi⁃engine propeller aircraft [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S2): 729295-729295.
[9]	Jing NI, Bo MA, Zhaoxu YANG, Chenggang TAO, Yan ZHOU, Yiwen HU. Design and test of visual-inertial integrated method for landing guidance [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S1): 727636-727636.
[10]	Xin DU, Zhe ZHU, Fangfang HU, Jiangtao HUANG, Gang LIU, Sheng ZHANG, Enguang SHAN, Jigang TANG. Guidance, navigation and control for airborne docking of autonomous aerial refueling [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(20): 628827-628827.
[11]	Yahui SONG, Gaoyu FAN, Lixia QU, Yuelin ZHANG, Yue XU, Shuo HAN. Progress of aircraft sonic boom flight test measurement technology: Review [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(2): 626186-626186.
[12]	Liu ZHANG, Yong HUANG, Fuzheng CHEN, Zhenglong ZHU, Tianhao GUO, Yubiao JIANG, Zhu ZHOU. Rudderless attitude control flight test based on circulation control of tailless flying wing in pitch and roll axes [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(18): 128224-128224.
[13]	Junliang DING, Lili ZHAO, Tao YANG, Haini ZHANG, Xiaoxia SHEN. Flight test technology of natural icing [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(17): 28270-028270.
[14]	Sheng ZHANG, Pan ZHOU, Yang HE, Jiangtao HUANG, Gang LIU, Jigang TANG, Huaizhi JIA, Xin DU. Air combat maneuver decision-making test based on deep reinforcement learning [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(10): 128094-128094.
[15]	Shuai SHAO, Zheng GUO, Gaowei JIA, Qingyang CHEN, Zhongxi HOU, Laiping ZHANG. Roll control of medium-aspect-ratio flying-wing UCAV based on trailing-edge jet [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(10): 127437-127437.

Aerodynamic coefficient identification method based on noise statistics estimation

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 17

References 38

Related Articles 15

Recommended Articles

Metrics

Comments