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基于信号分解和切比雪夫多项式的多体系统区间不确定性分析方法

蒋鑫 白争锋 宁志远 王思宇

蒋鑫, 白争锋, 宁志远, 王思宇. 基于信号分解和切比雪夫多项式的多体系统区间不确定性分析方法. 力学学报, 2022, 54(6): 1-12 doi: 10.6052/0459-1879-22-092
引用本文: 蒋鑫, 白争锋, 宁志远, 王思宇. 基于信号分解和切比雪夫多项式的多体系统区间不确定性分析方法. 力学学报, 2022, 54(6): 1-12 doi: 10.6052/0459-1879-22-092
Jiang Xin, Bai Zhengfeng, Ning Zhiyuan, Wang Siyu. Interval uncertainty analysis methods for multibody systems based on signal decomposition and chebyshev polynomials. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1-12 doi: 10.6052/0459-1879-22-092
Citation: Jiang Xin, Bai Zhengfeng, Ning Zhiyuan, Wang Siyu. Interval uncertainty analysis methods for multibody systems based on signal decomposition and chebyshev polynomials. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(6): 1-12 doi: 10.6052/0459-1879-22-092

基于信号分解和切比雪夫多项式的多体系统区间不确定性分析方法

doi: 10.6052/0459-1879-22-092
基金项目: 国家重点研发计划项目(2020 YFB1709800), 国家自然科学基金项目(51775128)资助.
详细信息
    作者简介:

    白争锋, 副教授, 主要研究方向: 多柔体系统动力学, 结构动力学, 软体机器人等. E-mail:zfbai@hit.edu.cn

  • 中图分类号: TH113

INTERVAL UNCERTAINTY ANALYSIS METHODS FOR MULTIBODY SYSTEMS BASED ON SIGNAL DECOMPOSITION AND CHEBYSHEV POLYNOMIALS

  • 摘要: 参数的不确定性会对多体系统动力学响应产生显著影响, 区间分析方法只需根据不确定性参数的边界信息, 便可实现在多体系统动力学分析中考虑参数的不确定性. 考虑区间参数不确定性, 采用切比雪夫区间方法(Chebyshev interval method CIM)在分析多体系统动力学响应时, 随着时间的增大, 响应边界精度会越来越低. 为解决CIM的这一问题, 本文将信号分解技术与切比雪夫多项式结合, 采用切比雪夫多项式分别对HHT变换(Hilbert-Huang transform, HHT)和局域均值分解(Local mean decomposition, LMD)得到的瞬时幅值和瞬时相位近似, 提出CIM-HHT方法和CIM-LMD方法, 以获得含区间参数的长周期动力学响应边界. HHT和LMD分解能够将多体系统的多分量响应分解为多个单分量和一个趋势分量(残余分量)之和, CIM-HHT和CIM-LMD对每个分量的瞬时幅值和瞬时相位、和趋势分量采用切比雪夫多项式近似, 进而建立系统响应的耦合模型, 可以得到系统的动力学响应边界. 最后, 考虑单摆和曲柄滑块机构中的参数不确定性, 验证了CIM-HHT和CIM-LMD方法的有效性. 结果表明, 相比CIM, 在长周期区间动力学响应分析中CIM-HHT和CIM-LMD能够获得较准确的结果. 此外, 相比CIM-HHT, CIM-LMD具有更弱的末端效应, 计算精度更高.

     

  • 图  1  CIM-HHT和CIM-LMD计算流程

    Figure  1.  Flowchart for CIM-HHT and CIM-LMD

    图  2  单摆

    Figure  2.  Simple pendulum

    图  3  末端位置和速度的HHT和LMD分解

    Figure  3.  HHT and LMD decomposition of position and velocity response of end-tip

    图  4  不同样本的末端位置响应分解

    Figure  4.  Decomposition of position response of end tip under different samples

    图  5  末端位置响应边界

    Figure  5.  Bounds for position responses of end-tip

    图  6  末端速度响应边界

    Figure  6.  Bounds for velocity responses of end-tip

    图  7  不同方法得到的位置响应边界

    Figure  7.  Bounds for position responses of end-tip obtained by different methods

    图  8  曲柄滑块机构示意图

    Figure  8.  schematic diagram for crank slider

    图  9  滑块位移和速度响应的HHT和LMD分解

    Figure  9.  HHT and LMD decomposition for position and velocity response of slider

    图  10  滑块位移响应边界

    Figure  10.  Bounds for position response of slider

    图  11  滑块速度上边界

    Figure  11.  Bounds for position responses of slider

    图  12  曲柄角度边界

    Figure  12.  Bounds for angle of crank

    图  13  曲柄角速度边界

    Figure  13.  Bounds for angular velocity of crank

    图  14  不同方法得到的滑块速度响应边界

    Figure  14.  Bounds for response of slider velocity using different methods

    图  15  不确定度为5%时CIM-LMD和RS-LMD得到的响应边界

    Figure  15.  Bounds of responses using CIM-LMD and RS-LMD under 5% uncertainty level

    表  1  曲柄机构参数

    Table  1.   Parameters for crank slider

    ParameterValue
    Length of crank/m0.15
    Mass of crank/kg0.37
    Length of connector/m0.56
    Mass of connector/kg0.77
    Mass of slider/kg0.45
    τ/(N·m)−0.5
    c/(N·m·s−1)1
    k/(N·m−1)5
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-03-03
  • 录用日期:  2022-04-22
  • 网络出版日期:  2022-04-19

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