月球探测器着陆动响应区间不确定性分析
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摘要
月球探测器软着陆动力学分析对探测器设计十分重要。目前软着陆动力学分析一般考虑确定的是着陆姿态和着陆速度,未考虑着陆参数的不确定性带来的动力学响应变化。基于Che-byshev多项式区间参数分析方法,针对探测器着陆过程动态特性,提出基于非线性有限元建模的探测器着陆动响应区间分析流程,计算得到了探测器着陆动响应上界和下界,并与蒙特卡洛仿真方法得到的响应上界和下界进行了对比,结果显示Chebyshev多项式区间方法分析结果可以完全包裹蒙特卡洛方法分析结果,并且结果区间没有被过度放大;对比分析截断阶数对区间分析误差的影响,结果表明截断阶数对分析误差影响较小。Chebyshev多项式区间参数分析方法具有包裹性强、分析效率高的优势。
Dynamic analysis of soft-landing is very important for the design of lunar lander. At present,the determined landing attitude and speed are considered while not considering the uncertainty of these parameters in the analysis of soft-landing dynamics. Based on Chebyshev interval analysis method,an analysis process of landing dynamic interval based on nonlinear finite-element model is proposed for the dynamic characteristics of landing process. The upper and lower bounds of dynamic response are calculated using Chebyshev method and compared with the simulated results of Monte Carlo method. Comparative result shows that the analyzed results of Chebyshev interval analysis method can fully cover those of Monte Carlo method,and the dynamic interval is not enlarged. The influence of truncation order on the analytic error of dynamic interval was analyzed. The analyzed result shows that the truncation order has little influence on analysis error. Chebyshev method has the advantage of high accuracy and efficiency.
Dynamic analysis of soft-landing is very important for the design of lunar lander. At present,the determined landing attitude and speed are considered while not considering the uncertainty of these parameters in the analysis of soft-landing dynamics. Based on Chebyshev interval analysis method,an analysis process of landing dynamic interval based on nonlinear finite-element model is proposed for the dynamic characteristics of landing process. The upper and lower bounds of dynamic response are calculated using Chebyshev method and compared with the simulated results of Monte Carlo method. Comparative result shows that the analyzed results of Chebyshev interval analysis method can fully cover those of Monte Carlo method,and the dynamic interval is not enlarged. The influence of truncation order on the analytic error of dynamic interval was analyzed. The analyzed result shows that the truncation order has little influence on analysis error. Chebyshev method has the advantage of high accuracy and efficiency.
引文
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[16] WU J L,ZHANG Y Q,CHEN L P,et al. A Chebyshev intervalmethod for nonlinear dynamic systems under uncertainty[J]. Ap-plied Mathematical Modelling,2013,37(6):4578-4591.
[17] WU J L,LUO Z,ZHANG Y P,et al. An interval uncertain opti-mization method for vehicle suspensions using chebyshev meta-models[J]. Applied Mathematical Modelling, 2014,38(15/16):3706-3723.
[18] WU J L,LUO Z,ZHENG J,P et al. Incremental modeling of anew high-order polynomial surrogate model[J]. Applied Mathe-matical Modelling,2016,40(7/8):4681-4699.
[19]吴景铼.基于Chebyshev多项式的动力学不确定性区间算法研究[D].武汉:华中科技大学,2013.WU J L. Dynamics uncertainty research based on interval arith-metic using Chebyshev polynomials[D]. Wuhan:Huazhong Uni-versity of Science and Technology,2013.(in Chinese)
[20] XIA B Z,QIN Y,YU D J,et al. Dynamic response analysis ofstructure under time-variant interval process model[J]. Journalof Sound and Vibration,2016,381:121-138.
[21] LI C,CHEN B S,PENG H J,et al. Sparse regression Cheby-shev polynomial interval method for nonlinear dynamic systemsunder uncertainty[J]. Applied Mathematical Modelling,2017,51(1):505-525.
[22]刘坚,雷济荣,夏百战.基于Chebyshev展开的区间穿孔板超材料分析[J].力学学报,2017,49(1):137-148.LIU J,LEI J R,XIA B Z. The interval analysis of multilayer-metamaterials with perforated apertures based on Chebyshev ex-pansion[J]. Chinese Journal of Theoretical and Applied Mecha-nics,2017,49(1):137-148.(in Chinese)
[23]陈剑,李士爱,刘策,等.基于Chebyshev区间方法的动力总成悬置系统稳健性优化[J].中国机械工程,2018,29(3):314-319.CHEN J,LI S A,LIU C,et al. Robustness optimization ofpowertrain mounting systems based on Chebyshev interval method[J]. China Mechanical Engineering,2018,29(3):314-319.(in Chinese)
[24] LAURENSON R,MELLIERE R,MOORE R,et al. Analysesand limited evaluation of payload and legged landing system struc-tures for the survivable soft landing of instrument payloads:NASA-CR-111919[R]. Washington,DC,US:NASA,1971.
[25]董威利,刘莉,周思达.含局部非线性的月球探测器软着陆动力学模型降阶分析[J].航空学报,2014,35(5):1319-1328.DONG W L,LIU L,ZHOU S D. Model reduction analysis of softlanding dynamics for lunar lander with local nonlinearities[J].Acta Aeronautica et Astronautica Sinica,2014,35(5):1319-1328.(in Chinese)
[26]陈树霖,刘莉,董威利.月球探测器着陆腿动力学建模与仿真[J].南京航空航天大学学报,2014,46(3):469-474.CHEN S L,LIU L,DONG W L. Dynamics modeling and simu-lation for landing legs of lunar lander[J]. Journal of Nanjing U-niversity of Aeronautics&Astronautics,2014,46(3):469-474.(in Chinese)
[27]董威利.月球探测器软着陆动力学分析及动态子结构技术研究[D].北京:北京理工大学,2015.DONG W L. Dynamic analysis of lunar detector soft landing andresearch on dynamic substructure technology[D]. Beijing:Bei-jing Institute of Technology,2015.(in Chinese)
[28]梁东平,柴洪友.着陆冲击仿真月壤本构模型及有限元建模[J].航天器工程,2012,21(1):18-24.LIANG D P,CHAI H Y. Lunar soil constitutive model and finiteelement modeling for landing impact simulation[J]. SpacecraftEngineering,2012,21(1):18-24.(in Chinese)
[2]王少纯,邓宗全,杨涤,等.月球着陆器新结构的ADAMS仿真研究[J].哈尔滨工业大学学报,2007,39(9):1392-1394.WANG S C,DENG Z Q,YANG D,et al. Simulation research onnovel structure of lunar lander based on ADAMS[J]. Journal ofHarbin Institute of Technology,2007,39(9):1392-1394.(inChinese)
[3]董威利,刘莉,周思达,等.月球探测器软着陆动力学及影响因素分析[J].宇航学报,2014,35(4):388-396.DONG W L,LIU L,ZHOU S D,et al. Analysis on soft-landingdynamics and influence factors of lunar lander[J]. Journal of As-tronautics,2014,35(4):388-396.(in Chinese)
[4]蒋万松,黄伟,沈祖炜,等.月球探测器软着陆动力学仿真[J].宇航学报,2011,32(3):462-469.JIANG W S,HUANG W,SHEN Z W,et al. Softlanding dynam-ics simulation for lunar explorer[J]. Journal of Astronautics,2011,32(3):462-469.(in Chinese)
[5]万峻麟,聂宏,李立春,等.基于瞬态动力学方法的月球探测器软着陆腿着陆冲击性能分析[J].兵工学报,2010,31(5):567-573.WAN J L,NIE H,LI L C,et al. Analysis of the landing impactperformance for lunar landing leg with transient dynamic method[J]. Acta Armamentarii,2010,31(5):567-573.(in Chinese)
[6]万峻麟,聂宏,陈金宝,等.月球着陆器有效载荷着陆冲击响应分析[J].宇航学报,2010,31(11):2456-2464.WAN J L,NIE H,CHEN J B,et al. Impact response analysis ofpayloads of lunar lander for lunar landing[J]. Journal of Astronau-tics,2010,31(11):2456-2464.(in Chinese)
[7] MERCHANT D,SAWDY D. Monte Carlo dynamic analysis for lu-nar module landing loads[J]. Journal of Spacecraft and Rockets,1971,8(1):48-55.
[8]陈金宝,万峻麟,李立春,等.月球探测器着陆性能若干影响因素分析[J].宇航学报,2010,31(3):669-673.CHEN J B,WAN J L,LI L C,et al. Analysis on the influencingfactors of performance in lunar lander[J]. Journal of Astronautics,2010,31(3):669-673.(in Chinese)
[9] QIU Z P,CHEN S H,SONG D T. The displacement bound esti-mation for structures with an interval description of uncertain pa-rameters[J]. Communications in Numerical Methods in Engineer-ing,1996,12(1):1-11.
[10] ALEFELD G,MYLER G. Interval analysis:theory and applica-tions[J]. Journal of Computational and Applied Mathematics,2000,121(1):421-464.
[11] QIU Z P,WANG X J. Comparison of dynamic response of struc-tures with uncertain-but-bounded parameters using non-probabi-listic interval analysis method and probabilistic approach[J]. In-ternational Journal of Solids and Structures,2003,40(20):5423-5439.
[12] MAKINO K,BERZ M. Taylor models and other validated func-tional inclusion methods[J]. International Journal of Pure andApplied Mathematics,2003,4(4):379-456.
[13] NEDIALKOV N S. Computing rigorous bounds on the solution ofan initial value problem for an ordinary differential equation[D]:Toronto,Canada:University of Toronto,1999.
[14] QIU Z P,WANG X P. Parameter perturbation method for dyna-mic responses of structures with uncertain-but-bounded parame-ters based on interval analysis[J]. International Journal of Solidsand Structures,2005,42(18/19):4958-4970.
[15] QIU Z P,MA L H,WANG X J. Non-probabilistic intervalanalysis method for dynamic response analysis of nonlinearsystems with uncertainty[J]. Journal of Sound and Vibration,2009,319(1/2):531-540.
[16] WU J L,ZHANG Y Q,CHEN L P,et al. A Chebyshev intervalmethod for nonlinear dynamic systems under uncertainty[J]. Ap-plied Mathematical Modelling,2013,37(6):4578-4591.
[17] WU J L,LUO Z,ZHANG Y P,et al. An interval uncertain opti-mization method for vehicle suspensions using chebyshev meta-models[J]. Applied Mathematical Modelling, 2014,38(15/16):3706-3723.
[18] WU J L,LUO Z,ZHENG J,P et al. Incremental modeling of anew high-order polynomial surrogate model[J]. Applied Mathe-matical Modelling,2016,40(7/8):4681-4699.
[19]吴景铼.基于Chebyshev多项式的动力学不确定性区间算法研究[D].武汉:华中科技大学,2013.WU J L. Dynamics uncertainty research based on interval arith-metic using Chebyshev polynomials[D]. Wuhan:Huazhong Uni-versity of Science and Technology,2013.(in Chinese)
[20] XIA B Z,QIN Y,YU D J,et al. Dynamic response analysis ofstructure under time-variant interval process model[J]. Journalof Sound and Vibration,2016,381:121-138.
[21] LI C,CHEN B S,PENG H J,et al. Sparse regression Cheby-shev polynomial interval method for nonlinear dynamic systemsunder uncertainty[J]. Applied Mathematical Modelling,2017,51(1):505-525.
[22]刘坚,雷济荣,夏百战.基于Chebyshev展开的区间穿孔板超材料分析[J].力学学报,2017,49(1):137-148.LIU J,LEI J R,XIA B Z. The interval analysis of multilayer-metamaterials with perforated apertures based on Chebyshev ex-pansion[J]. Chinese Journal of Theoretical and Applied Mecha-nics,2017,49(1):137-148.(in Chinese)
[23]陈剑,李士爱,刘策,等.基于Chebyshev区间方法的动力总成悬置系统稳健性优化[J].中国机械工程,2018,29(3):314-319.CHEN J,LI S A,LIU C,et al. Robustness optimization ofpowertrain mounting systems based on Chebyshev interval method[J]. China Mechanical Engineering,2018,29(3):314-319.(in Chinese)
[24] LAURENSON R,MELLIERE R,MOORE R,et al. Analysesand limited evaluation of payload and legged landing system struc-tures for the survivable soft landing of instrument payloads:NASA-CR-111919[R]. Washington,DC,US:NASA,1971.
[25]董威利,刘莉,周思达.含局部非线性的月球探测器软着陆动力学模型降阶分析[J].航空学报,2014,35(5):1319-1328.DONG W L,LIU L,ZHOU S D. Model reduction analysis of softlanding dynamics for lunar lander with local nonlinearities[J].Acta Aeronautica et Astronautica Sinica,2014,35(5):1319-1328.(in Chinese)
[26]陈树霖,刘莉,董威利.月球探测器着陆腿动力学建模与仿真[J].南京航空航天大学学报,2014,46(3):469-474.CHEN S L,LIU L,DONG W L. Dynamics modeling and simu-lation for landing legs of lunar lander[J]. Journal of Nanjing U-niversity of Aeronautics&Astronautics,2014,46(3):469-474.(in Chinese)
[27]董威利.月球探测器软着陆动力学分析及动态子结构技术研究[D].北京:北京理工大学,2015.DONG W L. Dynamic analysis of lunar detector soft landing andresearch on dynamic substructure technology[D]. Beijing:Bei-jing Institute of Technology,2015.(in Chinese)
[28]梁东平,柴洪友.着陆冲击仿真月壤本构模型及有限元建模[J].航天器工程,2012,21(1):18-24.LIANG D P,CHAI H Y. Lunar soil constitutive model and finiteelement modeling for landing impact simulation[J]. SpacecraftEngineering,2012,21(1):18-24.(in Chinese)