ACTA AERONAUTICAET ASTRONAUTICA SINICA >
A robust shape control method for space-borne antenna reflectors based on P-CS uncertainty quantification model and digital twin
Received date: 2022-12-01
Revised date: 2023-02-01
Accepted date: 2023-03-07
Online published: 2023-03-21
Supported by
National Natural Science Foundation of China(11972104);Shenzhen Stability Support Key Program in Colleges and Universities of China(GXWD20220817133329001)
The surface precision of the space-borne antenna reflector is the main influence factor of its electromagnetic performance. The active shape control methodology is an effective way to guarantee the surface precision of space-borne antenna reflectors in orbit. Considering the uncertain material properties of the space-borne antenna reflectors in orbit， a robust shape control method is proposed based on Probability-Convex Set （P-CS） model and digital twin in this paper. The uncertain material properties are quantified in a uniform model （P-CS model）. The P-CS model can be updated based on the Bayesian theory and driven by displacement monitoring data. According to the P-CS model， a voltage layout optimization model is proposed to achieve the optimal robustness of the surface precision under uncertainties. To solve such voltage layout optimization problem with multiple local optimal solutions and large scale of discrete variables， the voltage layout is described by a bounded field with space correlation based on the continuous representation and dimensionality reduction method， and then the design space is discretized and sequential sub-optimization problems are formed. The optimal solution can be achieved by solving sub-optimization problems one by one. The proposed method is used to solve an active shape control problem for a regular hexagon space-borne antenna reflector. Two cases with the constraints of applying one kind of voltage and four kinds of voltage are analyzed to demonstrate the validity and applicability of the proposed method.
Jiaqi HE , Weida WU , Yangjun LUO . A robust shape control method for space-borne antenna reflectors based on P-CS uncertainty quantification model and digital twin[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023 , 44(19) : 328343 -328343 . DOI: 10.7527/S1000-6893.2023.28343
| 1 | 宋祥帅， 谭述君， 高飞雄， 等. 星载天线反射器形面主动控制研究现状与展望［J］. 空间电子技术， 2022， 19（1）： 1-12. |
| SONG X S， TAN S J， GAO F X， et al. Research progresses and prospect of active shape control for space-borne antenna reflectors［J］. Space Electronic Technology， 2022， 19（1）： 1-12 （in Chinese）. | |
| 2 | TANAKA H. Surface error estimation and correction of a space antenna based on antenna gainanalyses［J］. Acta Astronautica， 2011， 68（7-8）： 1062-1069. |
| 3 | SONG X S， TAN S J， WANG E M， et al. Active shape control of an antenna reflector using piezoelectric actuators［J］. Journal of Intelligent Material Systems and Structures， 2019， 30（18-19）： 2733-2747. |
| 4 | HAFTKA R T， ADELMAN H M. An analytical investigation of shape control of large space structures by applied temperatures［J］. AIAA Journal， 1985， 23（3）： 450-457. |
| 5 | SONG X S， CHU W M， TAN S J， et al. Adaptive shape control for antenna reflectors based on feedback error learning algorithm［J］. AIAA Journal， 2020， 58（7）： 3229-3240. |
| 6 | LU Y F， YUE H H， DENG Z Q， et al. Adaptive shape control for thermal deformation of membrane mirror with in-plane PVDF actuators［J］. Chinese Journal of Mechanical Engineering， 2018， 31（1）： 1-11. |
| 7 | XU X， LUO Y Z. Multi-objective shape control of prestressed structures with genetic algorithms［J］. Proceedings of the Institution of Mechanical Engineers， Part G： Journal of Aerospace Engineering， 2008， 222（8）： 1139-1147. |
| 8 | SHAO S B， SONG S Y， XU M L， et al. Mechanically reconfigurable reflector for future smart space antenna application［J］. Smart Materials and Structures， 2018， 27（9）： 095014. |
| 9 | HILL J， WANG K W， FANG H. Advances of surface control methodologies for flexible space reflectors［J］. Journal of Spacecraft and Rockets， 2013， 50（4）： 816-828. |
| 10 | WANG Z W， LI T J， CAO Y Y. Active shape adjustment of cable net structures with PZT actuators［J］. Aerospace Science and Technology， 2013， 26（1）： 160-168. |
| 11 | ZHANG S X， DU J L， DUAN B Y， et al. Integrated structural-electromagnetic shape control of cable mesh reflector antennas［J］. AIAA Journal， 2014， 53（5）： 1395-1399. |
| 12 | 孟松鹤， 叶雨玫， 杨强， 等. 数字孪生及其在航空航天中的应用［J］. 航空学报， 2020， 41（9）： 023615. |
| MENG S H， YE Y M， YANG Q， et al. Digital twin and its aerospace applications［J］. Acta Aeronautica et Astronautica Sinica， 2020， 41（9）： 023615 （in Chinese）. | |
| 13 | Cearley D W， Burke B， Searle S， et al. Top 10 strategic technology trends for 2018 ［EB/OL］. （2017-10-03） ［2023-03-21］. . |
| 14 | 董雷霆， 周轩， 赵福斌， 等. 飞机结构数字孪生关键建模仿真技术［J］. 航空学报， 2021， 42（3）： 023981. |
| DONG L T， ZHOU X， ZHAO F B， et al. Key technologies for modeling and simulation of airframe digital twin［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（3）： 023981 （in Chinese）. | |
| 15 | YU J S， SONG Y， TANG D Y， et al. A digital twin approach based on nonparametric Bayesian network for complex system health monitoring［J］. Journal of Manufacturing Systems， 2021， 58： 293-304. |
| 16 | LI C Z， MAHADEVAN S， LING Y， et al. Dynamic Bayesian network for aircraft wing health monitoring digital twin［J］. AIAA Journal， 2017， 55（3）： 930-941. |
| 17 | ELISHAKOFF I. Essay on uncertainties in elastic and viscoelastic structures： From A. M. Freudenthal’s criticisms to modern convex modeling［J］. Computers & Structures， 1995， 56（6）： 871-895. |
| 18 | JIANG C， HAN X， LU G Y， et al. Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique［J］. Computer Methods in Applied Mechanics and Engineering， 2011， 200（33-36）： 2528-2546. |
| 19 | LIMBOURG P， DE ROCQUIGNY E. Uncertainty analysis using evidence theory - confronting level-1 and level-2 approaches with data availability and computational constraints［J］. Reliability Engineering & System Safety， 2010， 95（5）： 550-564. |
| 20 | FAES M G R， DAUB M， MARELLI S， et al. Engineering analysis with probability boxes： A review on computational methods［J］. Structural Safety， 2021， 93： 102092. |
| 21 | 董玉革， 陈心昭， 赵显德， 等. 基于模糊事件概率理论的模糊可靠性分析通用方法［J］. 计算力学学报， 2005， 22（3）： 281-286. |
| DONG Y G， CHEN X Z， ZHAO X D， et al. A general approach for fuzzy reliability analysis based on the fuzzy probability theory［J］. Chinese Journal of Computational Mechanics， 2005， 22（3）： 281-286 （in Chinese）. | |
| 22 | LI J W， JIANG C. A novel imprecise stochastic process model for time-variant or dynamic uncertainty quantification［J］. Chinese Journal of Aeronautics， 2022， 35（9）： 255-267. |
| 23 | PING M H， HAN X， JIANG C， et al. A time-variant uncertainty propagation analysis method based on a new technique for simulating non-Gaussian stochastic processes［J］. Mechanical Systems and Signal Processing， 2021， 150： 107299. |
| 24 | WANG L， WANG X J， CHEN X， et al. Time-variant reliability model and its measure index of structures based on a non-probabilistic interval process［J］. Acta Mechanica， 2015， 226（10）： 3221-3241. |
| 25 | MENG Z， GUO L B， HAO P， et al. On the use of probabilistic and non-probabilistic super parametric hybrid models for time-variant reliability analysis［J］. Computer Methods in Applied Mechanics and Engineering， 2021， 386： 114113. |
| 26 | BISSIRI P G， HOLMES C C， WALKER S G. A general framework for updating belief distributions［J］. Journal of the Royal Statistical Society Series B， Statistical Methodology， 2016， 78（5）： 1103-1130. |
| 27 | WANG R C. Analysis and improvement of combination rule in D-S theory［J］. Applied Mechanics and Materials， 2014， 556-562： 3930-3934. |
| 28 | PAN Y， ZHANG L M， LI Z W， et al. Improved fuzzy Bayesian network-based risk analysis with interval-valued fuzzy sets and D-S evidence theory［J］. IEEE Transactions on Fuzzy Systems， 2020， 28（9）： 2063-2077. |
| 29 | HE J Q， LUO Y J. A Bayesian updating method for non-probabilistic reliability assessment of structures with performance test data［J］. Computer Modeling in Engineering & Sciences， 2020， 125（2）： 777-800. |
| 30 | 何佳琦， 贾晓璇， 吴伟达， 等. P-CS不确定性量化模型与其性能数据驱动更新方法［J］. 力学学报， 2022， 54（10）： 2808-2824. |
| HE J Q， JIA X X， WU W D， et al. P-CS uncertainty quantification model and its performance data-driven updating method［J］. Chinese Journal of Theoretical and Applied Mechanics， 2022， 54（10）： 2808-2824 （in Chinese）. | |
| 31 | SILVA G A DA， CARDOSO E L， BECK A T. Comparison of robust， reliability-based and non-probabilistic topology optimization under uncertain loads and stress constraints［J］. Probabilistic Engineering Mechanics， 2020， 59： 103039. |
| 32 | KANNO Y. On three concepts in robust design optimization： absolute robustness， relative robustness， and less variance［J］. Structural and Multidisciplinary Optimization， 2020， 62（2）： 979-1000. |
| 33 | CHENG J， LIU Z Y， QIAN Y M， et al. Non-probabilistic robust equilibrium optimization of complex uncertain structures［J］. Journal of Mechanical Design， 2020， 142（2）： 021405. |
| 34 | RIBEIRO L H M S， POGGETTO V F DAL， ARRUDA J R F. Robust optimization of attenuation bands of three-dimensional periodic frame structures［J］. Acta Mechanica， 2022， 233（2）： 455-475. |
| 35 | ZHAN J J， LUO Y J. Robust topology optimization of hinge-free compliant mechanisms with material uncertainties based on a non-probabilistic field model［J］. Frontiers of Mechanical Engineering， 2019， 14（2）： 201-212. |
| 36 | KANG Z， WU C L， LUO Y J， et al. Robust topology optimization of multi-material structures considering uncertain graded interface［J］. Composite Structures， 2019， 208： 395-406. |
| 37 | ZHANG S X， DUAN B Y. Integrated structural-electromagnetic optimization of cable mesh reflectors considering pattern degradation for random structural errors［J］. Structural and Multidisciplinary Optimization， 2020， 61（4）： 1621-1635. |
| 38 | YUE X W， WEN Y C， HUNT J H， et al. Surrogate model-based control considering uncertainties for composite fuselage assembly［J］. Journal of Manufacturing Science and Engineering， 2018， 140（4）： 041017. |
| 39 | LUO Y Q， WANG Z D， WEI G L， et al. Fuzzy-logic-based control， filtering， and fault detection for networked systems： A survey［J］. Mathematical Problems in Engineering， 2015， 2015： 1-11. |
| 40 | FENG Z Y， SHE J H， XU L. A brief review and insights into matrix inequalities for H∞ static-output-feedback control and a local optimal solution［J］. International Journal of Systems Science， 2019， 50（12）： 2292-2305. |
| 41 | WANG L， XIONG C， WANG X J， et al. Hybrid time-variant reliability estimation for active control structures under aleatory and epistemic uncertainties［J］. Journal of Sound and Vibration， 2018， 419： 469-492. |
| 42 | ZHU L P， ELISHAKOFF I， STARNES J H. Derivation of multi-dimensional ellipsoidal convex model for experimental data［J］. Mathematical and Computer Modelling， 1996， 24（2）： 103-114. |
| 43 | LI Y L， WANG X J， WANG C， et al. Non-probabilistic Bayesian update method for model validation［J］. Applied Mathematical Modelling， 2018， 58： 388-403. |
| 44 | SUN Y， ZHOU Y， KE Z， et al. Stiffener layout optimization framework by isogeometric analysis-based stiffness spreading method［J］. Computer Methods in Applied Mechanics and Engineering， 2022， 390： 114348. |
| 45 | HAO P， LIU D C， ZHANG K P， et al. Intelligent layout design of curvilinearly stiffened panels via deep learning-based method［J］. Materials & Design， 2021， 197： 109180. |
| 46 | FERRARI F， SIGMUND O. Revisiting topology optimization with buckling constraints［J］. Structural and Multidisciplinary Optimization， 2019， 59（5）： 1401-1415. |
| 47 | LUO Y J， ZHAN J J. Linear buckling topology optimization of reinforced thin-walled structures considering uncertain geometrical imperfections［J］. Structural and Multidisciplinary Optimization， 2020， 62（6）： 3367-3382. |
| 48 | LUO Y J， BAO J W. A material-field series-expansion method for topology optimization of continuum structures［J］. Computers & Structures， 2019， 225： 106122. |
| 49 | LI C C， DER KIUREGHIAN A. Optimal discretization of random fields［J］. Journal of Engineering Mechanics， 1993， 119（6）： 1136-1154. |
| 50 | ROSENBLATT M. Remarks on a multivariate transformation［J］. The Annals of Mathematical Statistics， 1952， 23（3）： 470-472. |
| 51 | JONES D R， SCHONLAU M， WELCH W J. Efficient global optimization of expensive black-box functions［J］. Journal of Global Optimization， 1998， 13（4）： 455-492. |
| 52 | Joseph VR， Hung Y. Orthogonal-maximin Latin hypercube designs［J］. Statistica Sinica， 2008， 18（1）： 171-186. |
| 53 | SVANBERG K. The method of moving asymptotes—a new method for structural optimization［J］. International Journal for Numerical Methods in Engineering， 1987， 24（2）： 359-373. |
| 54 | STEEVES J， PELLEGRINO S. Ultra-thin highly deformable composite mirrors： AIAA-2013-1523［R］. Reston： AIAA， 2013. |
| 55 | LAN L， JIANG S D， ZHOU Y， et al. An experimental study on reflector wave-front error correction using PZT actuators［C］∥ SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring. San Francisco： SPIE， 2016： 86-100. |
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