基于统计信息的多体系统区间不确定性分析

PDF(1456 KB)

振动与冲击 ›› 2019, Vol. 38 ›› Issue (8) : 117-125.

论文

基于统计信息的多体系统区间不确定性分析

陈光宋，钱林方，王明明，林通

作者信息 +

An interval analysis method based on statistical information for a multibody system with uncertainty

CHEN Guangsong，QIAN Linfang，WANG Mingming，LIN Tong

Author information +

文章历史 +

摘要

本文构造了一种区间方法分析机械系统多体动力学动态不确定性问题，该方法首先将系统中的输入不确定性参数用参数上界和下界构造的区间描述，无需概率分布信息。为有效抑制在动态分析过程中由于“包裹效应”导致的输出参数区间逐渐放大问题，采用极大极小距离拉丁超立方采样(Latin hypercube sampling, LHS)方法对输入参数进行采样，通过Bootstrap方法统计获得输出参数的前四阶统计矩，并采用极大熵方法获得输出参数的分布函数，进而根据分布函数通过泰勒展开估计出输出参数的区间。算例1表明本文能够在较少样本的情况下获得有效的输出参数区间，并通过两个典型的机械系统动态不确定性问题验证了本文方法的有效性，最后将本文方法应用于一个具体的工程算例。

Abstract

In this paper, an interval method was proposed to analyze the multibody dynamic of a mechanical system with uncertainty.The input uncertain parameters of the system were described by interval.Only the upper and lower bounds of the input parameters were required, and the probability distribution was not needed.In order to effectively suppress the overestimation of the output parameters due to the inherent “wrapping effect” of the interval method in the dynamic analysis process, the maximal minimum distance Latin hypercube sampling (LHS) was used to get the sample.The first four order statistical moments of the output parameters were estimated by the bootstrap method.The distribution function of the output parameters was obtained by the maximal entropy method.Finally, the output parameters were evaluated by the Taylor expansion based on the distribution function.An example shows that the presented method can obtain the tightest interval of output parameter in the case of fewer samples.The validity of the method was verified by two typical dynamic uncertainties of the mechanical system, and the method was applied to an engineering problem in another example.

导出引用

陈光宋，钱林方，王明明，林通. 基于统计信息的多体系统区间不确定性分析[J]. 振动与冲击, 2019, 38(8): 117-125

CHEN Guangsong，QIAN Linfang，WANG Mingming，LIN Tong. An interval analysis method based on statistical information for a multibody system with uncertainty[J]. Journal of Vibration and Shock, 2019, 38(8): 117-125

参考文献

[1] Lee B W, Lim O K. Application of the First-order Perturbation Method to Optimal Structural Design[J]. Sturctural Engineering and Mechanics, 1996, 4(4): 425-436.
[2] Katafygiotis L S, Papadimitriou C. Dynamic Variability of Structures with Uncertain Properties[J]. Earthquake Engineering and Structural Dynamics, 1996, 25(8): 775-793.
[3] Xiu D, Karniadakis G E. Modeling Uncertainty in Flow Simulations via Generalized Polynomial Chaos[M]. Academic Press Professional, Inc. 2003.
[4] Wan X, Kanmiadakis G E. An Adaptive Multi-element Generalized Polynomial Chaos Mehtod for Stochastic Equations[J]. Journal of Computational Physics, 2005, 209(2): 617-642.
[5] Qian Y, Tessier P J C, Dumont G A. Application of Fuzzy Relational Modeling to Industrial Product Quality Control[M]. Reliability and Safety Analyses under Fuzziness, Physica, Heidelberg, 1995: 203-216.
[6] Hanss M. The Transformation Method for the Simulation and Analysis of Systems with Uncertain Parameters[J]. Fuzzy and System, 2002, 130(3): 277-289.
[7] Nieto J J, Khastan A, Ivaz K. Numerical solution of fuzzy differential Equations under Generalized Differentiability[J]. Nonlinear Analysis: Hybrid Systems, 2009, 3(4): 700-707.
[8] Moore R E. Interval Analysis[M]. Englewood Cliffs: Prentice-Hall, 1986.
[9] Qiu Z. Comparison of Static Response of Structures using Convex Models and Interval Analysis Method[J]. International Journal of Numerical Method in Engineering, 2003, 56(12): 1735-1753.
[10] Jiang C, Han X, Liu G R, et al. A Nonlinear Interval Number Programming Method for Uncertain Optimization Problems[J]. European Journal of Operational Research, 2008, 188(1): 1-13.
[11] Moore R E. Methods and Applications of Interval Analysis[M]. Society for Industrial and Applied Mathematics, 1979.
[12] Jackson K R, Nedialkov N S. Some Recent Advances in Validated Methods for IVPs for ODEs[J]. Applied Mathematics and Computation, 2002, 42(1-3): 269–284.
[13] Berz M, Makino K. Efficient Control of the Dependency Problem based on Taylor Model Methods[J]. Reliable Computing, 1999, 5(1):3–12.
[14] Wu J L, Zhang Y Q, Chen L P, Luo Z. An Interval Method with Chebyshev series for Dynamic Response of Nonlinear Systems under Uncertainty[J]. Applied Mathematical Modelling, 2013, 37(6):4578–4591.
[15] Wu J L, Luo Z, Zhang N, Chen L P. Interval Uncertain Method for Multibody Mechanical System using Chebyshev Inclusion Functions[J]. International Journal for Numerical Methods in Engineering, 2013, 95(7): 608-630.
[16] Wu J L, Luo Z, Zhang N, Zhang Y Q. A new uncertain analysis method and its application in vehicle dynamics[J]. Mechanical System and Signal Processing, 2015, 50-51(1-2): 659-675.
[17] Li C, Chen B, Peng H, Zhang S. Sparse regression Chebyshev polynomial interval method for nonlinear dynamic systems under uncertainty[J]. Applied Mathematical Modelling, 2017, 51(11): 505-525.
[18] Dan N, Jay L O, Khude N. A Discussion of Low-Order Numerical Integration Formulas for Rigid and Flexible Multibody Dynamics[J]. Journal of Computational and Nonlinear Dynamics, 2009, 4(2): 149-160.
[19] 洪嘉振. 计算多体系统动力学[M]. 高等教育出版社, 1999.
HONG Jia-zhen. Computational Dynamics of Multibody Systems[M]. Higher Education Press, 1999.
[20] Baumgarte J. Stabilization of constraints and integrals of motion in dynamical systems[J]. Computer Methods in Applied Mechanics & Engineering, 1972, 1(1):1-16.
[21] Deutsch J L, Deutsch C V. Latin Hypercube Sampling with Multidimensional Uniformity[J]. Journal of Statistical Planning and Inference, 2012, 142(3): 763-772.
[22] Jaynes E T. Information theory and statistical mechanics[J]. The Physical Review, 1957, 106(4): 620-630.