﻿ 反演航天器在轨瞬态外热流的导热反问题
 文章快速检索 高级检索

Inverse heat conduction problem for transient external heat flux inversion of spacecraft on orbit
SONG Xin, ZHANG Youwei, LIU Zijun
Beijing Institute of Spacecraft System Engineering, Beijing 100094, China
Abstract: Spacecraft external heat flux is very important for researching deterioration law of thermal control coating on orbit, influence of various spatial factors on thermal control products, as well as plume thermal effect of spacecraft attitude and orbit control engine. However, there are many difficulties in direct heat flux measurement. Thus, the inverse heat conduction problem can be used to get results which can satisfy certain precision. Firstly, in order to deduce transient external heat flux of spacecraft on orbit from telemetry temperature of spacecraft equipment on orbit, inverse heat conduction problem mathematical model was set up and solved by the conjugate gradient method. Iterative process of conjugate gradient method was improved according to physics concept in order to increase its anti instabilit. Then, two numerical tests were used for the purpose of checking mathematical model effect. The numerical tests could represent external heat flux change of most both earth-orbiting spacecraft and deep space exploration spacecraft. The maximum relative deviation between inversion value and true value is 2.9% except step change data. Inversion results of the mathematical model is very good. Furthermore, satisfied results can be obtained by processing data analysis for absorbed external heat flux at step change location.
Key words: spacecraft     heat flux     radiation     inverse heat conduction problem     conjugate gradient method

1 数学模型

γ由式(8)计算:

1) 由式(12)可以看到,灵敏度系数$\frac{{\partial {T_i}}}{{\partial {q_n}}}$是温度T(x,τ)的函数,因此在每轮迭代得到新的T(x,τ)后,重新计算灵敏度系数$\frac{{\partial {T_i}}}{{\partial {q_n}}}$;

2) 从物理概念出发,航天器在轨吸收外热流不小于0,因此式(6)整理为

1) 求解导热方程(1)得到温度计算值Tcal,n.

2) 求解灵敏度方程(10)得到灵敏度系数$\frac{{\partial {T_i}}}{{\partial {q_n}}}$.

3) 根据温度计算值和在轨遥测值,检查收敛目标式(16)是否达到;如果达到收敛目标,则停止迭代,否则,转入第4)步.

4) 计算$\frac{{\partial J}}{{\partial {q_n}}}$、γ、βd.

5) 由式(17)计算得到下一轮迭代qnb+1,转入第1)步.

2 计算结果

1) 给出一组随时间变化的吸收外热流值qmea.

2) 以qmea为边界条件求解导热方程(1),得到的结果作为温度测量值Tmea.

3) Tmea作为导热反问题的输入条件,采用共轭梯度法反演吸收外热流值qcgm.

4) 比较qmeaqcgm,检验反演算法的效果.

2.1 数值试验1

 图 1 数值试验1的吸收外热流曲线 Fig. 1 Absorbed external heat flux curve of numerical experiment 1

 图 2 数值试验1的温度反演值与测量值比较 Fig. 2 Compare between inversion temperature and measuring data of numerical experiment 1

 图 3 数值试验1的吸收外热流反演值与真实值比较 Fig. 3 Compare between inversion absorbed external heat flux and real value of numerical experiment 1

 时间/s qmea/(W·m-2) qcgm/(W·m-2) 相对误差/% 时间/s qmea/(W·m-2) qcgm/(W·m-2) 相对误差/% 0 200 204 2.0 440 200 197 -1.5 20 400 390 -2.5 460 400 398 -0.5 40 600 598 -0.3 480 600 594 -1.0 60 800 806 0.8 500 800 800 0.0 80 1 000 1 019 1.9 520 1 000 1 016 1.6 100 1 200 1 177 -1.9 540 1 200 1 179 -1.8 120 1 000 1 012 1.2 560 1 000 1 015 1.5 140 800 796 -0.5 580 800 798 -0.3 160 600 593 -1.2 600 600 596 -0.7 180 400 398 -0.5 620 400 403 0.8 200 200 199 -0.5 640 200 196 -2.0 220 0 8 660 0 7 240 0 0 0.0 680 0 0 0.0 260 0 0 0.0 700 0 0 0.0 280 0 0 0.0 720 0 0 0.0 300 0 0 0.0 740 0 0 0.0 320 0 0 0.0 760 0 0 0.0 340 0 0 0.0 780 0 0 0.0 360 0 0 0.0 800 0 0 0.0 380 0 0 0.0 820 0 0 0.0 400 0 0 0.0 840 0 0 0.0 420 0 5 880 0 0 0.0

2.2 数值试验2

 图 4 数值试验2的吸收外热流曲线 Fig. 4 Absorbed external heat flux curve of numerical experiment 2

 图 5 数值试验2的温度反演值与测量值比较 Fig. 5 Compare between inversion temperature and measuring data of numerical experiment 2

 图 6 数值试验2的吸收外热流反演值与真实值比较 Fig. 6 Compare between inversion absorbed externalheat flux and real value of numerical experiment 2

 时间/s qmea/(W·m-2) qcgm/(W·m-2) 相对 误差/% 时间/s qmea/(W·m-2) qcgm/ (W·m-2) 相对误差/% 0 1 000 986 -1.4 440 1 000 707 -29.3 20 1 000 992 -0.8 460 1 000 1 002 0.2 40 1 000 1 001 0.1 480 1 000 1 023 2.3 60 1 000 1 010 1.0 500 1 000 1 019 1.9 80 1 000 1 013 1.3 520 1 000 1 024 2.4 100 1 000 1 008 0.8 540 1 000 1 026 2.6 120 1 000 997 -0.3 560 1 000 1 016 1.6 140 1 000 991 -0.9 580 1 000 1 004 0.4 160 1 000 1 000 0.0 600 1 000 1 008 0.8 180 1 000 982 -1.8 620 1 000 990 -1.0 200 1 000 695 -30.5 640 1 000 684 -31.6 220 0 0 0.0 660 0 0 0.0 240 0 0 0.0 680 0 0 0.0 260 0 0 0.0 700 0 0 0.0 280 0 0 0.0 720 0 0 0.0 300 0 0 0.0 740 0 0 0.0 320 0 0 0.0 760 0 0 0.0 340 0 0 0.0 780 0 0 0.0 360 0 0 0.0 800 0 0 0.0 380 0 0 0.0 820 0 0 0.0 400 0 0 0.0 840 0 0 0.0 420 0 0 0.0 880 0 0 0.0

2.3 小 结

3 结 论

 [1] 张天宇,董长虹.基于自适应反演法的导弹直/气复合制导[J].北京航空航天大学学报, 2013, 39(7):902-906. Zhang T Y, Dong C H.Compound control system design based on adaptive backstepping theory[J].Journal of Beijing University of Aeronautics and Astronautics, 2013, 39(7):902-906(in Chinese). Cited By in Cnki [2] 杨尔辅,张振鹏,刘国球.一种推进系统故障诊断反问题模型与算法[J].北京航空航天大学学报, 1999, 25(6):684-687. Yang E F, Zhang Z P, Liu G Q.Model and algorithm of inverse-problems on fault diagnosis for propulsion systems[J].Journal of Beijing University of Aeronautics and Astronautics, 1999, 25(6):684-687(in Chinese). Cited By in Cnki (3) [3] 程文龙,刘娜,钟奇,等.卫星稳态热模型参数修正方法研究[J].宇航学报, 2010, 31(1):270-275. Cheng W L, Liu N, Zhong Q, et al.Study on parameters correction method of steady-state thermal model for spacecraft[J].Journal of Astronautics, 2010, 31(1):270-275(in Chinese). Cited By in Cnki (8) [4] 程文龙,刘娜,李志,等.卫星热模型蒙特卡罗混合算法的修正方法应用研究[J].科学通报, 2010, 55(20):2056-2061. Cheng W L, Liu N, Li Z, et al.Application study of a correction method for a spacecraft thermal model with a Monte-Carlo hybrid algorithm[J].Chinese Science Bulletin, 2010, 55(20):2056-2061(in Chinese). Cited By in Cnki (1) [5] 杨沪宁,钟奇.航天器热模型蒙特卡罗法修正论述[J].航天器工程, 2009, 18(3):53-58. Yang H N, Zhong Q.Monte-Carlo method for thermal model correction of spacecraft[J].Spacecraft Engineering, 2009, 18(3):53-58(in Chinese). Cited By in Cnki (7) [6] 张镜洋,常海萍,王立国.小卫星瞬态热分析模型修正方法[J].中国空间科学技术, 2013, 33(4):24-30. Zhang J Y, Chang H P, Wang L G.Correction method for transient thermal analysis model of small satellite[J].Chinese Space Science and Technology, 2013, 33(4):24-30(in Chinese). Cited By in Cnki (1) [7] 张中礼,李明海,胡绍全.外壁热流响应计算的导热反问题方法及其验证[J].强度与环境, 2009, 36(4):54-59. Zhang Z L, Li M H, Hu S Q.Nonlinear transient inverse heat conduction problems method of calculating the boundary heat response[J].Structure & Environment Engineering, 2009, 36(4):54-59(in Chinese). Cited By in Cnki [8] Lin D T, Yan W M, Li H Y.Inverse problem of unsteady conjugated forced convection in parallel plate channels[J].International Journal of Heat and Mass Transfer, 2008, 51(5-6):993-1002. Click to display the text [9] Chen U C, Cheng W J, Hsu J C.Two-dimensional inverse problem in estimating heat flux of pin fins[J].International Communication of Heat and Mass Transfer, 2001, 28(6):793-801. Click to display the text [10] Huang C H, Wang S P.A three-dimensional inverse heat conduction problem in estimated surface heat flux by conjugate gradient method[J].International Journal of Heat and Mass Transfer, 1999, 42(18):3387-3403. Click to display the text [11] Huang C H, Chen W C.A three-dimensional inverse forced convection problem in estimating surface heat flux by conjugate gradient method[J].International Journal of Heat and Mass Transfer, 2000, 43(17):3171-3181. Click to display the text [12] 薛齐文,杨海天,胡国俊.共轭梯度法求解瞬态传热组合边界条件多宗量反问题[J].应用基础与工程科学学报, 2004, 12(2):113-120. Xue Q W, Yang H T, Hu G J.Solving inverse heat conduction problems with multi-variables of boundary conditions in transient-state via conjugate gradient method[J].Journal of Basic Science and Engineering, 2004, 12(2):113-120(in Chinese). Cited By in Cnki (10) [13] Xue Q W, Yan H T.A conjugate gradient method for the hyperbolic inverse heat conduction problem with multi-variables[J].Chinese Journal of Computational Physics, 2005, 22(5):417-424. Click to display the text [14] 杨海天,胡国俊.共轭梯度法求解多宗量稳态传热反问题[J].应用基础与工程科学学报, 2002, 10(2):174-181. Yang H T, Hu G J.Solving inverse heat conduction problems with multi-variables in steady-state via conjugate gradient method[J].Journal of Basic Science and Engineering, 2002, 10(2):174-181(in Chinese). Cited By in Cnki (23) [15] 王登刚,刘迎曦,李守巨,等.非线性二维稳态导热反问题的一种数值解法[J].西安交通大学学报, 2000, 34(1):49-52. Wang D G, Liu Y X, Li S J, et a1.Two dimensional numerical solution for nonlinear inverse steady heat conduction[J].Journal of Xi'an Jiaotong University, 2000, 34(1):49-52(in Chinese Cited By in Cnki (34) [16] 范春利,孙丰瑞,杨立.基于红外侧温的试件内部缺陷的识别算法研究[J].工程热物理学报, 2007, 28(2):304-306. Fan C L, Sun F R, Yang L.An algorithm study on identification of subsurface defect based on thermographic temperature measurement[J].Journal of Engineering Thermophysics, 2007, 28(2):304-306(in Chinese). Cited By in Cnki (22)

#### 文章信息

SONG Xin, ZHANG Youwei, LIU Zijun

Inverse heat conduction problem for transient external heat flux inversion of spacecraft on orbit

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(11): 2061-2066.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0719