随机空间柔性多体系统动力学分析

郭祥; 靳艳飞; 田强

doi:10.6052/0459-1879-20-273

随机空间柔性多体系统动力学分析

doi: 10.6052/0459-1879-20-273

郭祥,
靳艳飞^2), ,,
田强^3), ,

北京理工大学宇航学院, 北京 100081

基金项目: 1) 国家自然科学基金资助项目(11772048);国家自然科学基金资助项目(11832005)

详细信息

作者简介:
3) 田强, 教授, 主要研究方向: 多体系统动力学建模与分析、动力学数值计算方法. E-mail: tianq@bit.edu.cn
2) 靳艳飞, 副教授, 主要研究方向: 随机动力学; 非线性动力学与控制. E-mail: jinyf@bit.edu.cn;

通讯作者:
靳艳飞,田强

靳艳飞,田强

中图分类号: O313.7
计量
- 文章访问数: 801
- HTML全文浏览量: 126
- PDF下载量: 169
- 被引次数: 0
出版历程
- 收稿日期: 2020-08-06
- 刊出日期: 2020-12-10

DYNAMICS ANALYSIS OF STOCHASTIC SPATIAL FLEXIBLE MULTIBODY SYSTEM

Guo Xiang,
Jin Yanfei^{2)
, ,},
Tian Qiang^{3)
, ,}

School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China

摘要

摘要: 轻质、高精度的柔性多体系统被广泛应用于实际工程领域中.由于实际设计公差、制造误差及环境温度等多种不确定因素的存在,使得柔性多体系统的结构参数(物理参数和几何参数)表现出随机性.具有随机结构参数的动力学模型能够客观地反映出真实系统的动力学行为,且结构参数的不确定性对空间柔性多体系统动力学响应的影响是不容忽视的.针对具有多个随机参数的空间柔性多体系统,提出了一种基于广义alpha算法的非侵入式随机柔性多体系统动力学计算方法.采用绝对节点坐标公式(absolute node coordinate formulation, ANCF)来描述柔性体, 推导建立多体系统动力学模型.利用混沌多项式展开(polynomial chaos expansion, PCE)法构建系统随机动力学方程的代理模型,然后将随机响应面法(stochastic response surface method, SRSM)嵌入广义-alpha方法中,分别采用改进抽样的回归方法(regression method of improved sampling, RMIS)和单项求容积法则(Monte Carlo simulation, MCR)来确定样本点.将数值计算结果与蒙特卡洛模拟(Monte Carlo simulation, MCS)结果进行对比, 验证了所提算法的有效性.在相同的定积分精度的条件下,根据单项求容积法则确定的样本点的计算结果稳定性更强, 且其计算效率更高.
- 柔性多体系统 /
- 绝对节点坐标法 /
- 混沌多项式 /
- 单项式容积法 /
- 随机响应面法
Abstract: Flexible multibody systems with light weight and high precision are widely used in practical engineering. The structural parameters (physical parameters and geometric parameters) of the flexible multibody system show randomness due to the existence of many uncertain factors such as actual design tolerance, manufacturing error and environmental temperature. The dynamic model with random structural parameters can objectively reflect the dynamic behavior of the real system, and the influence of the uncertainty of structural parameters on the dynamic response of the spatial flexible multibody system cannot be ignored. A non-intrusive calculation method is proposed based on the generalized-alpha algorithm to study the dynamic response of stochastic spatial flexible multibody system with multiple random parameters. The absolute node coordinate formulation (ANCF) is used to describe the flexible body, and the dynamic model of multibody system is established. The polynomial chaos expansion (PCE) method is used to construct the surrogate model of the stochastic dynamics equation of the system. Then, the stochastic response surface method (SRSM) is embedded into the generalized-alpha method. The regression method of improved sampling (RMIS) and the monomial cubature rules (MCR) are used to determine the sample points respectively. The numerical results are compared with those of Monte Carlo simulation (MCS), and the validity of the proposed algorithm is verified. Under the condition of the same definite integral precision, the calculation results of sample points determined by the monomial cubature rules are more stable and the calculation efficiency is higher.
- flexible multibody system /
- absolute node coordinate formulation /
- polynomial chaos expansion method /
- monomial cubature rules /
- stochastic response surface method

HTML全文

参考文献(1)

[1]	Shabana AA. Flexible multibody dynamics: Review of past and recent developments. Multibody System Dynamics, 1997,1(2):189-222
[2]	Gerstmayr J, Sugiyama H, Mikkola A. A review on the absolute nodal coordinate formulation for large deformation analysis of multibody systems. Journal of Computational and Nonlinear Dynamics, 2013,8(3):031016
[3]	Shabana AA. An absolute nodal coordinates formulation for the large rotation and deformation analysis of flexible bodies. Technical Report. No. MBS96-1-UIC, 1996
[4]	Tian Q, Chen LP, Zhang YQ. An efficient hybrid method for multibody dynamics simulation based on absolute nodal coordinate formulation. Journal of Computational and Nonlinear Dynamic, 2009,4(2):0210091-02100914
[5]	Lan P, Tian QL, Yu ZQ. A new absolute nodal coordinate formulation beam element with multilayer circular cross section. Acta Mechanica Sinica, 2020,36(1):82-96
[6]	Sun JL, Tian Q, Hu HY, et al. Axially variable-length solid element of absolute nodal coordinate formulation. Acta Mechanica Sinica, 2019,35(3):653-663
[7]	孙加亮, 田强, 胡海岩. 多柔体系统动力学建模与优化研究进展. 力学学报, 2019,51(6):1565-1586
[7]	( Sun Jialiang, Tian Qiang, Hu Haiyan. Advances in dynamic modeling and optimization of flexible multibody systems. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(6):1565-1586 (in Chinese))
[8]	王光远. 论不确定性结构力学的发展. 力学进展, 2005,35(3):338-344
[8]	( Wang Guangyuan. On the development of uncertain structural mechanics. Advances in Mechanics, 2005,35(3):338-344 (in Chinese))
[9]	Wu JL, Zhang YQ. The dynamic analysis of multibody systems with uncertain parameters using interval method. Applied Mechanics & Materials, 2012, 152-154:1555-1561
[10]	赵宽, 陈建军, 阎彬等. 含随机参数的多体系统动力学分析. 力学学报, 2012,44(4):802-806
[10]	( Zhao Kuan, Chen Jianjun, Yan Bin, et al. Dynamic analysis of multibody systems with probabilistic parameters. Chinese Journal of Theoretical and Applied Mechanics, 2012,44(4):802-806 (in Chinese))
[11]	Wang Z, Tian Q, Hu HY. Dynamics of spatial rigid-flexible multibody systems with uncertain interval parameters. Nonlinear Dynamics, 2016,84(2):527-548
[12]	Paez TL, Red-Horse J. Structural dynamics challenge problem: Summary. Computer Methods in Applied Mechanics and Engineering, 2008,197(29):2660-2665
[13]	Liu GP, Luo R, Liu S. A new interval multi-objective optimization method for uncertain problems with dependent interval variables. International Journal of Computational Methods, 2020: 2050007
[14]	Mo J, Wang L, Qiu ZP, et al. A nonprobabilistic structural damage identification approach based on orthogonal polynomial expansion and interval mathematics. Structural Control and Health Monitoring, 2019,26(8):1-22
[15]	Fu CM, Liu YX, Xiao Z. Interval differential evolution with dimension-reduction interval analysis method for uncertain optimization problems. Applied Mathematical Modelling, 2019,69:441-452
[16]	熊芬芬, 杨树兴, 刘宇等. 工程概率不确定分析方法. 北京: 科学出版社, 2015
[16]	( Xiong Fenfen, Yang Shuxing, Liu Yu, et al. Engineering Probabilistic Uncertainty Analysis Method. Beijing: Science Press, 2015 (in Chinese))
[17]	Adhikari S, Khodaparast HH. A spectral approach for fuzzy uncertainty propagation in finite element analysis. Fuzzy Sets and Systems, 2014,243:1-24
[18]	Sun L, Zheng ZW. Saturated adaptive hierarchical fuzzy attitude-tracking control of rigid spacecraft with modeling and measurement uncertainties. IEEE Transactions on Industrial Electronics, 2019,66(5):3742-3751
[19]	Zhang HY, Meng DY, Wang J, et al. Synchronisation of uncertain chaotic systems via fuzzy-regulated adaptive optimal control approach. International Journal of Systems Science, 2020,51(3):473-487
[20]	Huber PJ. Robust Statistical Procedures, 2nd ed. Philadelphia, PA: SIAM, 1996
[21]	George SF. Monte Carlo. New York: Springer, 1996
[22]	Luo YF, Bai HY, Hsu D, et al. Importance Sampling for Online Planning under Uncertainty. The International Journal of Robotics Research, 2018,38(2-3):162-181
[23]	王馨月, 景丽萍. 基于分层抽样的不均衡数据集成分类. 深圳大学学报(理工版), 2019,36(1):24-32
[23]	( Wang Xinyue, Jing Liping. Stratified sampling based ensemble classification for imbalanced data. Journal of Shenzhen University (Science and Engineering), 2019,36(1):24-32 (in Chinese))
[24]	Donovan D, Burrage K, Burrage P, et al. Estimates of the coverage of parameter space by Latin Hypercube and Orthogonal Array-based sampling. Applied Mathematical Modelling, 2017,57:553-564
[25]	Shi X, Yan H, Wang JX, et al. An efficient adaptive importance sampling method for SRAM and analog yield analysis. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2020: 1-1
[26]	Kriegesmann B, Lüdeker JK. Robust compliance topology optimization using the first-order second-moment method. Structural and Multidiplinary Optimization, 2019,60(1):269-286
[27]	Zhao W, Chen YY, Liu JK. An effective first order reliability method based on Barzilai-Borwein step. Applied Mathematical Modelling, 2020,77(2):1545-1563
[28]	Armen DK, Taleen D. Multiple design points in first and second-order reliability. Structural Safety, 1998,20(1):37-49
[29]	Lee SH, Chen W. A comparative study of uncertainty propagation methods for Black-box type functions. Structural Multidisciplinary Optimization, 2008,37(3):39-253
[30]	Ping MH, Han X, Jiang C, et al. A frequency domain reliability analysis method for electromagnetic problems based on univariate dimension reduction method. Science China Technological Sciences, 2019,62(5):787-798
[31]	He WX, Zeng Y, Li G. A novel structural reliability analysis method via improved maximum entropy method based on nonlinear mapping and sparse grid numerical integration. Mechanical Systems and Signal Processing, 2019,133:106247
[32]	Wang K, Chen F, Yu JY, et al. Nested sparse-grid stochastic collocation method for uncertainty quantification of blade stagger angle. Energy, 2020,201:117583
[33]	Schneider F, Papaioannou I, Ehre M, et al. Polynomial chaos based rational approximation in linear structural dynamics with parameter uncertainties. Computers & Structure, 2020,233:106223
[34]	许灿, 朱平, 刘钊等. 平纹机织碳纤维复合材料的多尺度随机力学性能预测研究. 力学学报, 2020,52(3):763-773
[34]	( Xu Can, Zhu Ping, Liu Zhao, et al. Research on multiscale stochastic mechanical properties prediction of plain woven carbon fiber composites. Chinese Journal of Theoretical and Applied Mechanics, 2020,52(3):763-773 (in Chinese))
[35]	Son J, Du YC. Comparison of intrusive and nonintrusive polynomial chaos expansion-based approaches for high dimensional parametric uncertainty quantification and propagation. Computers & Chemical Engineering, 2020,134:106685
[36]	Benedict E, Bastian R, Felix G, et al. Non-intrusive uncertainty quantification in the simulation of turbulent spray combustion using polynomial chaos expansion: A case study. Combustion and Flame, 2020,213:26-38
[37]	Sandu A, Sandu C, Ahmadian M. Modeling multibody systems with uncertainties. Part I: Theoretical and computational aspects. Multibody System Dynamics, 2006,15(4):369-391
[38]	Sandu C, Sandu A, Ahmadian M. Modeling multibody systems with uncertainties. Part II: Numerical applications. Multibody System Dynamics, 2006,15(3):241-262
[39]	Acharjee S, Zabaras N. A non-intrusive stochastic Galerkin approach for modeling uncertainty propagation in deformation processes. Computers & Structures, 2007,85(5):244-254
[40]	黄斌, 贺志赟, 张衡. 随机桁架结构几何非线性问题的混合摄动-伽辽金法求解. 力学学报, 2019,51(5):1424-1436
[40]	( Huang Bin, He Zhiyun, Zhang Heng. Hybrid perturbation-Galerkin method for geometrical nonlinear analysis of truss structures with random parameters. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(5):1424-1436 (in Chinese))
[41]	Isukapalli SS. Uncertainty analysis of transport-transformation models. [PhD Thesis]. New Jersey: Rutgers, The State University of New Jersey, 1999
[42]	Atkinson KE. An Introduction to Numerical Analysis. New York: John Wiley & Sons, 1989
[43]	靳红玲. 不确定性结构的动力学分析. [博士论文]. 西安: 西安电子科技大学, 2014
[43]	( Jin Hongling. Dynamics Analysis for Uncertain Structures. [PhD Thesis]. Xi'an: Xidian University, 2014 (in Chinese))
[44]	皮霆, 张云清, 吴景铼. 基于多项式混沌方法的柔性多体系统不确定性分析. 中国机械工程, 2011,22(29):2341-2348
[44]	( Pi Ting, Zhang Yunqing, Wu Jinglai. Uncertainty analysis of flexible multibody systems using polynomial chaos methods. China Mechanical Engineering, 2011,22(29):2341-2348 (in Chinese))
[45]	Krylov VI, Stroud AH. Approximate calculation of multiple integrals. Dover: Dover Publications, 2006
[46]	刘铖. 基于绝对坐标描述的柔性空间结构展开动力学研究. [博士论文]. 北京: 北京理工大学, 2013
[46]	( Liu Cheng. Deployment dynamics of flexible space structures described by absolute-coordinate-based method. [PhD Thesis]. Beijing: Beijing Institute of Technology, 2013 (in Chinese))
[47]	Tatang MA. Direct incorporation of uncertainty in chemical and environmental engineering systems. [PhD Thesis]. Cambridge: Massachusetts Institute of Technology, 1995
[48]	Garcia-Vallejo D, Escalona JL, Mayo J, et al. Describing rigid-flexible multibody systems using absolute coordinates. Nonlinear Dynamics, 2003,34(1):75-94
[49]	Shabana AA, Yakoub RY. Three dimensional absolute nodal coordinate formulation for beam elements: Theory. Journal of Mechanical Design, 2001,123(4):606-613