Research on accuracy assessment method of aerodynamic parameters identified from wind tunnel free-flight test data
-
摘要: 当高超声速风洞自由飞试验的测量数据被有色噪声污染时，传统的Cramér-Rao界作为参数估计准度的度量往往过于乐观。文本采用一种修正协方差方法来处理传统的最大似然估计的残差，以便计算出有色残差情况下精确的Cramér-Rao下界，对辨识参数结果进行不确定度评价。以10°半锥角尖锥模型为例，通过大量的Monte Carlo仿真试验和风洞试验验证了修正协方差方法的有效性。结果表明，在风洞试验测量存在有色噪声情况下，修正协方差方法给出的标准差均值约为传统的Cramér-Rao界方法给出的标准差的3~5倍，与参数估计的统计标准差一致，客观反映了参数辨识结果的精准度。Abstract: The conventional Cramér-Rao lower bounds method is too optimistic to be a good quantitative assessment of the accuracy of aerodynamic parameters identified from the wind tunnel free-flight test data, considering the colored noise in the measurement data. This paper introduces a technique, that modified covariance matrix method, to process the residuals from a conventional maximum likelihood estimation to compute the accurate Cramér-Rao lower bounds for colored residuals. The modified accuracy assessment method is validated by Monte Carlo simulation and wind tunnel tests of pointed cone models with the semi-cone angle being 10°. The identified results indicate that the Cramér-Rao lower bounds calculated by the modified covariance matrix method are 3~5 times the quantity of the conventional. The modified results can be used as an accurate and impersonal assessment of the aerodynamic parameters estimated, which are consistent with the sample standard errors for the estimated parameters for colored residuals.
-
图 2 有色噪声时间历程和频谱图(θ，RUN=300)
Figure 2. Time history curve and power spectrum of example simulated colored noise (θ，RUN=300)
图 3 Monte Carlo仿真试验的参数估计值分布图
Figure 3. Aerodynamic parameter estimation results from Monte Carlo simulation
图 4 5次风洞试验主要气动参数辨识结果
Figure 4. Aerodynamic parameter estimation results from 5 wind tunnel free-flight tests
表 1 白噪声对气动参数辨识结果的影响
Table 1. Influence of white noise on aerodynamic parameter estimation results
气动
参数真值 估计值 传统 修正 $\overline{{\hat{\theta }}}$ s σ s/σ σc s/σc CD0 0.13500 0.13500 0.00022 0.00021 1.06 0.00013 1.69 CDα2 2.57020 2.56932 0.02244 0.02126 1.06 0.01385 1.62 CLα 2.15624 2.15877 0.06208 0.06107 1.02 0.04049 1.53 Czβ -2.15624 -2.15587 0.04092 0.04191 0.98 0.03054 1.34 mxβ -0.01000 -0.01000 0.00002 0.00001 1.07 0.00001 1.69 myβ -0.16616 -0.16616 0.00002 0.00002 1.00 0.00001 1.91 myωy -0.50000 -0.49994 0.00150 0.00141 1.06 0.00088 1.70 mzα -0.16616 -0.16616 0.00003 0.00003 1.00 0.00002 1.77 mzωz -0.50000 -0.49999 0.00246 0.00238 1.04 0.00144 1.71 
下载: 导出CSV
表 2 有色噪声对气动参数辨识结果的影响
Table 2. Influence of colored noise on aerodynamic parameter estimation results
气动
参数真值 估计值 传统 修正 $\overline{{\hat{\theta }}}$ s σ s/σ σc s/σc CD0 0.13500 0.13485 0.00185 0.00034 5.52 0.00102 1.83 CDα2 2.57020 2.58595 0.17831 0.03430 5.20 0.10691 1.67 CLα 2.15624 2.13110 0.51014 0.10124 5.04 0.35518 1.44 Czβ -2.15624 -2.11901 0.37293 0.07006 5.32 0.24308 1.53 mxβ -0.01000 -0.01001 0.00012 0.00002 4.94 0.00008 1.53 myβ -0.16616 -0.16616 0.00014 0.00003 5.34 0.00006 2.32 myωy -0.50000 -0.50028 0.01210 0.00230 5.26 0.00666 1.82 mzα -0.16616 -0.16616 0.00024 0.00005 4.75 0.00012 2.03 mzωz -0.50000 -0.49938 0.01999 0.00390 5.13 0.01140 1.75
下载: 导出CSV
表 3 各尖锥模型及试验工况的基本参数
Table 3. Basic parameters of pointed cone models and operating conditions
参数 1 2 3 4 5 m/kg 0.2215 0.2217 0.2222 0.2215 0.2210 l/m 0.16918 0.16896 0.16932 0.16908 0.16922 D/m 0.06 0.06 0.06 0.06 0.06 质心位置 0.597 0.596 0.596 0.600 0.600 Jx/(10-5kg·m2) 2.696 2.777 2.547 2.561 2.622 Jy/(10-5kg·m2) 6.685 6.489 6.889 6.476 6.513 Jz/(10-5kg·m2) 6.685 6.489 6.889 6.476 6.513 Jxy/(10-5kg·m2) 0.0 0.0 0.0 0.0 0.0 p0/Pa 518010 514520 510070 511870 521640 T0/K 410 410 400 400 400
下载: 导出CSV
表 4 5 次风洞试验气动参数辨识统计结果
Table 4. Statistics of aerodynamic parameter estimation results from 5 wind tunnel free-flight tests
气动
参数估计值 传统 修正 $\overline{{\hat{\theta }}}$ s σ s/σ σc s/σc CD0 0.16390 0.03828 0.00587 6.52 0.01968 1.95 CDα2 1.00599 4.92853 0.89312 5.52 3.36375 1.47 CLα 2.76598 2.28743 0.15281 14.97 0.87767 2.61 Czβ 1.70980 2.54756 0.11755 21.67 0.60956 4.18 mxβ 0.00645 0.01744 0.00360 4.84 0.01135 1.54 myβ -0.19268 0.00972 0.00101 9.62 0.00269 3.61 myωy -0.71302 0.31171 0.06064 5.14 0.17015 1.83 mzα -0.18509 0.01369 0.00049 28.07 0.00170 8.06 mzωz -0.26206 0.36579 0.03127 11.70 0.11581 3.16
下载: 导出CSV
-
[1] 张守言. 模型自由飞试验[M]. 北京: 国防工业出版社, 2002. [2] Prislin R H. High amplitude dynamic stability characteristics of a blunt 10-degree cones[R]. AIAA-66-465, 1966. [3] Klein V. Determination of stability and control parameters of a light airplane from flight data two estimation methods[R]. NASA TP-1306, 1979. [4] Maine R E, Iliff K W. The theory and practice of estimating the accuracy of dynamic flight-determined coefficients[R]. NASA RP-1077, 1981. [5] Morelli E A, Klein V. Determining the accuracy of maximum likelihood parameter estimates with colored residuals[R]. NASA CR-194893, 1994. [6] Morelli E A, Klein V. Accuracy of aerodynamic model parameters estimated from flight test data[J]. Journal of Guidance, Control and Dynamics, 1997, 20 (1): 74-80. doi: 10.2514/2.3997 [7] 蔡金狮. 飞行器系统辨识学[M]. 北京: 国防工业出版社, 2003. [8] 汪清, 钱炜祺, 何开锋. 导弹气动参数辨识与优化输入设计[J]. 宇航学报, 2008, 29 (3): 789-793. http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB200803009.htmWang Q, Qian W Q, He K F. Aerodynamic parameter identification and optimal input design for missile[J]. Journal of Astrinautics, 2008, 29 (3): 789-793. http://www.cnki.com.cn/Article/CJFDTOTAL-YHXB200803009.htm [9] Murphy P C. A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems[R]. NASA RP-1077, 1981. [10] Murphy P C, Klein V. Maximum likelihood algorithm using an efficient scheme for computing sensitivities and parameter confidence intervals[R]. AIAA-84-2084, 1984. [11] Murphy P C. Efficient computation of confidence intervals of parameters[R]. AIAA-87-2624, 1987. [12] Iliff K W, Maine R E. Further observations on maximum likelihood estimates of stability and control characteristics obtained from flight data[R]. AIAA-77-1133, 1977. [13] Maine R E, Iliff K W. Use of Cramér-Rao bounds on flight data with colored residuals[J]. Journal of Guidance, Control and Dynamics, 1981, 4 (2): 207-213. doi: 10.2514/3.56073 [14] Balakrishnan A V, Maine R E. Improvements in aircraft extraction programs[R]. NASA CR-145090, 1975. [15] Morelli E A, Klein V. Determing the accuracy of aerodynamic model parameters estimated from flight test data[R]. NASA CR-203351, 1995. [16] Bendat J S, Piersol A G. Random data analysis and measurement procedures[M]. 2nd ed. New York: Wiley, 1986. [17] 方振平, 陈万春, 张曙光. 航空飞行器飞行动力学[M]. 北京: 北京航空航天大学出版社, 2005. [18] 张天姣, 钱炜祺, 何开锋, 等. 基于最大似然法的风洞自由飞试验气动力参数辨识技术研究[J]. 实验流体力学, 2015, 29 (5): 8-14. http://www.syltlx.com/CN/abstract/abstract10868.shtmlZhang T J, Qian W Q, He K F, et al. Research on aerodynamic parameter identification technology in wind tunnel free-flight test based on Maximum Likelihood Estimation[J]. Journal of Experiments in Fluid Mechanics, 2015, 29 (5): 8-14. http://www.syltlx.com/CN/abstract/abstract10868.shtml [19] 顾均晓. 飞行稳定性和自动控制[M]. 北京: 国防工业出版社, 2008. [20] 贾区耀, 杨益农, 陈农. 风洞自由飞实验测量M=5, 10°半锥角尖锥、钝锥气动动稳特性[J]. 空气动力学学报, 2007, 25 (2): 24-28.Jia Q Y, Yang Y N, Chen N. Measurement of aerodynamic dynamic stability characters of M=5 pointed and blunted cones with semi-cone angles equal 10° in wind tunnel free flight experiment[J]. Acta Aerodynamica Sinica, 2007, 25 (2): 24-28. [21] 贾区耀, 杨益农. 锥动失稳与无控飞行器弹着点精度[J]. 气动物理—理论与应用, 2007, 2 (2): 183-186.Jia Q Y, Yang Y N. Conical lose of stability and unguided aircraft impact accuracy[J]. Physics of Gases: Theory and Applications, 2007, 2 (2): 183-186. [22] 陈农, 杨益农, 贾区耀. 小迎角下钝锥气动动态稳定性[C]//全国第九届分离流, 旋涡和流动控制会议论文集, 2002: 74-83. [23] 马家驩, 潘文欣, 翟曼玲, 等. 10°尖锥标模高超声速动导数的实验测量[J]. 空气动力学学报, 1997, 15 (4): 452-457. http://www.cnki.com.cn/Article/CJFDTOTAL-KQDX199704004.htmMa J H, Pan W X, Zhai M L, et al. 10° Cone model free flight experiment in hypersonic impulse type wind tunnel for dynamic stability measurement[J]. Acta Aerodynamica Sinica, 1997, 15 (4): 452-457. http://www.cnki.com.cn/Article/CJFDTOTAL-KQDX199704004.htm -
点击查看大图
计量
- 文章访问数: 241
- HTML全文浏览量: 101
- PDF下载量: 11
- 被引次数: 0
