飞行器气动参数估计不确定度评价方法研究
收稿日期: 2012-10-22
修回日期: 2012-12-13
网络出版日期: 2013-02-26
基金资助
国家自然科学基金(90816026)
Study on Uncertainty Evaluation Methods of Aerodynamic Parameter Estimation for Aircraft
Received date: 2012-10-22
Revised date: 2012-12-13
Online published: 2013-02-26
Supported by
National Natural Science Foundation of China (90816026)
为了有效地利用飞行器气动参数估计结果,必须同时给出估计结果的不确定度,因此研究了不确定度评价方法。当试验样本较多时,样本标准差具有明确的统计含义,比分散度能够更好地描述参数估计的不确定度。对于单个试验样本,基于不确定度椭球导出的C-R(Cramer-Rao)界是参数估计不确定度最好的理论预测,但利用飞行实测数据得到的C-R界普遍比样本标准差小。鉴于此,通过在低频有色噪声的基础上构造白噪声的方法,得到了一种C-R界修正方法,并通过仿真算例验证了修正方法的正确性。最后,将C-R界修正方法应用于飞行实测数据,得到的修正C-R界与利用多次飞行试验参数估计结果计算的样本标准差比较一致,表明该修正方法能够较好地给出参数估计的不确定度区间。
王贵东 , 陈则霖 , 刘子强 . 飞行器气动参数估计不确定度评价方法研究[J]. 航空学报, 2013 , 34(9) : 2057 -2063 . DOI: 10.7527/S1000-6893.2013.0317
In order to make effective use of aerodynamic parameter estimation results for an aircraft, it is necessary to provide at the same time an aerodynamic parameter uncertainty interval, for which the uncertainty evaluation methods are studied in this paper. If test runs are sufficient in number, the sample standard deviation has a clear statistical significance. Therefore it is a good criterion for uncertainty evaluation. The C-R (Cramer-Rao) bound based on the uncertainty ellipsoid is the best theoretical prediction of uncertainty for a single flight test, but C-R bound is different from the sample standard deviation due to colored residuals. A correction method by constructing the Gauss noises based on colored noises is proposed, and the accuracy of the corrected C-R bound is validated through comparing it the with sample standard deviation. Finally the correction method of C-R bound is applied to flight test data, and the corrected C-R bound is found to be close to the sample standard deviation, which demonstrates that the uncertainty evaluation method is valid.
[1] Cai J S, Wang Q. Aircraft system identification. Beijing: Defense Industry Press, 2003: 271-285.(in Chinese) 蔡金狮, 汪清. 飞行器系统辨识学. 北京: 国防工业出版社, 2003: 271-285.
[2] Abate G, Klomfass A. Affect upon aeroballistic parameter identification from flight data errors. AIAA-2005-439, 2005.
[3] Maine R E, Iliff K W. The theory and practice of estimating the accuracy of dynamic flight-determined coefficients. NASA RP-1077, 1981.
[4] Klevin V. Determination of stability and control parameters of a light airplane from flight data using two estimation methods. NASA TP-1306, 1979.
[5] Iliff K W, Maine R E. Practical aspect of using a maximum likelihood estimation method to extract stability and control derivatives from flight data. NASA TN D-8209, 1976.
[6] Maine R E, Iliff K W. Use of Cramer-Rao bounds on flight data with colored residuals. Journal of Guidance Control and Dynamics, 1981, 4(2): 207-213.
[7] Wells W R, Ramachandran S. Flight test design for efficient extraction of aircraft parameters. Proceedings, ALAA 3rd Atmospheric Flight Mechanics Conference, 1976: 101-107.
[8] Suit W T. Aerodynamic parameters of the navion airplane extracted from flight data. NASA TN D-6643, 1972.
[9] Morelli E A, Klein V. Determining the accuracy of aerodynamic model parameter estimation from flight test data. AIAA-1995-3499, 1995.
[10] Morelli E A, Klein V. Determining the accuracy of maximum likelihood parameter estimations with colored residuals. NASA CR-194893, 1994.
[11] Balakrishnan A V. Communication theory. London: Mc Graw-Hill Book Company, 1968: 301-347.
[12] Caines P E, Ljung L. Asymptotic normality and accuracy of prediction error estimators. Proceedings of the 1976 Joint Automatic Control Conference, 1976: 586-592.
[13] Taylor L W, Iliff K W, Powers B G. A Comparison of newton-raphson and other method for determining stability derivatives from flight data. AIAA-1969-315, 1969.
[14] Murphy P C. An algorithm for maximum likelihood estimation using an efficient method for approximating sensitivities. NASA TP-2311, 1984.
[15] Maine R E, Iliff K W. Estimation of the accuracy dynamic flight-determined coefficients. AIAA-1980-171, 1980.
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