应用加速度响应Chirplet积分的线性时变系统参数识别

张杰; 史治宇

doi:10.13433/j.cnki.1003-8728.20200039

应用加速度响应Chirplet积分的线性时变系统参数识别

doi: 10.13433/j.cnki.1003-8728.20200039

张杰,
史治宇^,

南京航空航天大学航空学院机械结构力学及控制国家重点实验室，南京　210016

基金项目: 国家自然科学基金项目（11172131，11232007）与江苏高校优势学科建设工程项目

详细信息

作者简介:
张杰（1988−），博士研究生，研究方向为动态信号处理与动力学参数识别，jzhang1988@nuaa.edu.cn

通讯作者:
史治宇，教授，博士生导师，zyshi@nuaa.edu.cn

中图分类号: O321; TB123
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- 文章访问数: 143
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- 被引次数: 0
出版历程
- 收稿日期: 2019-07-22
- 刊出日期: 2021-02-02

Estimating Parameters of Linear Time Varying System using Chirplet Integration of Acceleration Response

ZHANG Jie,
SHI Zhiyu^,

State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aeronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

摘要

摘要: 提出了线调频小波积分运算方法，在仅获得加速度响应的情况下对结构速度和位移响应进行重构，将时变微分方程转化成区间线性方程组，进而构造最小二乘算法识别结构的时变物理参数。Chirplet基适用于处理时变信号，能在短区间拟合时变系统各阶响应，相比传统小波能更好地追踪信号频率变化特征，通过与微分方程结合提高了时变系统参数识别的效率。方法的有效性和适用性通过一个3自由度时变结构模型进行了验证。
- 线性时变系统 /
- Chirplet积分 /
- 加速度响应 /
- 物理参数识别
Abstract: This paperuses the Chirplet integration method totransform the time-varying differential equations into interval linear equations by reconstructing the structural velocity and displacement response when the acceleration response is measured. Then the physical parameters of the time-varyingsystem are identified based on the least squares algorithm. The Chirplet basis function is suitable for processing time-varying signals since it fits the time-varying system′s response in a short interval. Compared with the traditional wavelet, it tracks better the frequency variation of signals. It also improves the time-varying parameter identification efficiency by combining differential equations. The validity and applicability of the method is verified with a 3-DOF time-varying structure model.
- linear time varying system /
- Chirplet integration /
- acceleration response /
- physical parameter estimation

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图 1 3自由度系统示意图

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图 2 加速度响应

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图 3 刚度阻尼时变时，刚度识别结果

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图 4 刚度阻尼时变时，阻尼识别结果

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图 5 质量刚度时变时，质量识别结果

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图 6 质量刚度时变时，刚度识别结果

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图 7 刚度突变识别结果

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表 1 识别结果的误差分析 %

参数	SNR
参数	无噪声	100	50	20
${m_1}$	3.380	3.381	3.727	4.427
${m_2}$	4.155	4.153	4.804	6.133
${m_3}$	3.172	3.172	3.390	4.025
${k_1}$	6.331	6.331	7.431	9.301
${k_2}$	6.026	6.026	7.069	8.032
${k_3}$	6.753	6.750	8.053	9.774

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参考文献(14)

[1]	周传荣, 赵淳生. 机械振动参数识别及其应用[M]. 北京: 科学出版社, 1989 ZHOU C R, ZHAO C S. Identification of vibration parameters for mechanical systems and its application[M]. Beijing: Science Press, 1989 (in Chinese)
[2]	于开平, 庞世伟, 赵婕. 时变线性/非线性结构参数识别及系统辨识方法研究进展[J]. 科学通报, 2009, 54(20): 3147-3156 doi: 10.1360/972008-2471 YU K P, PANG S W, ZHAO J. Advances in method of time-varying linear/nonlinear structural system identification and parameter estimate[J]. Chinese Science Bulletin, 2009, 54(20): 3147-3156 (in Chinese) doi: 10.1360/972008-2471
[3]	程军圣, 张亢, 杨宇, 等. 局部均值分解与经验模式分解的对比研究[J]. 振动与冲击, 2009, 28(5): 13-16 doi: 10.3969/j.issn.1000-3835.2009.05.004 CHENG J S, ZHANG K, YANG Y, et al. Comparison between the methods of local mean decomposition and empirical mode decomposition[J]. Journal of Vibration and Shock, 2009, 28(5): 13-16 (in Chinese) doi: 10.3969/j.issn.1000-3835.2009.05.004
[4]	徐晴晴, 史治宇. 基于改进EMD分解的时变结构密集模态的瞬时参数识别[J]. 机械科学与技术, 2015, 34(8): 1161-1165 XU Q Q, SHI Z Y. Identifying parameters of time varying structures with closely spaced modes based on improved EMD method[J]. Mechanical Science and Technology for Aerospace Engineering, 2015, 34(8): 1161-1165 (in Chinese)
[5]	LIU K. Identification of linear time-varying systems[J]. Journal of Sound and Vibration, 1997, 206(4): 487-505 doi: 10.1006/jsvi.1997.1105
[6]	庞世伟, 于开平, 邹经湘. 识别时变结构模态参数的改进子空间方法[J]. 应用力学学报, 2005, 22(2): 184-188 doi: 10.3969/j.issn.1000-4939.2005.02.007 PANG S W, YU K P, Zou J X. Improved subspace method with application in linear time-varying structural modal parameter identification[J]. Chinese Journal of Applied Mechanics, 2005, 22(2): 184-188 (in Chinese) doi: 10.3969/j.issn.1000-4939.2005.02.007
[7]	TASKER F, BOSSE A, FISHER S. Real-time modal parameter estimation using subspace methods: theory[J]. Mechanical Systems and Signal Processing, 1998, 12(6): 797-808 doi: 10.1006/mssp.1998.0161
[8]	DZIEDZIECH K, STASZEWSKI W J, BASU B, et al. Wavelet-based detection of abrupt changes in natural frequencies of time-variant systems[J]. Mechanical Systems and Signal Processing, 2015, 64-65: 347-359 doi: 10.1016/j.ymssp.2015.03.012
[9]	HERA A, SHINDE A, HOU Z K. Issues in tracking instantaneous modal parameters for structural health monitoring using wavelet approach[C]//Proceedings of the 23rd International Modal Analysis Conference. Orlando, Florida, USA, 2005: 338-347
[10]	许鑫, 史治宇, 龙双丽. 基于小波状态空间法的时变结构瞬时频率识别[J]. 中国机械工程, 2011, 22(8): 901-904, 925 XU X, SHI Z Y, LONG S L. Instantaneous frequency identification of a time-varying structure using wavelet-based state space method[J]. China Mechanical Engineering, 2011, 22(8): 901-904, 925 (in Chinese)
[11]	ZHOU S D, MA Y C, LIU L, et al. Output-only modal parameter estimator of linear time-varying structural systems based on vector TAR model and least squares support vector machine[J]. Mechanical Systems and Signal Processing, 2018, 98: 722-755 doi: 10.1016/j.ymssp.2017.05.026
[12]	DENG Y, CHENG C M, YANG Y, et al. Parametric identification of nonlinear vibration systems via polynomial chirplet transform[J]. Journal of Vibration and Acoustics, 2016, 138(5): 051014 doi: 10.1115/1.4033717
[13]	王宏禹, 邱天爽. 非平稳确定性信号与非平稳随机信号统一分类法的探讨[J]. 通信学报, 2015, 36(2): 1-10 doi: 10.11959/j.issn.1000-436x.2015028 WANG H Y, QIU T S. Unified classification methods for determinate nonstationary signals and random nonstationary signals[J]. Journal on Communications, 2015, 36(2): 1-10 (in Chinese) doi: 10.11959/j.issn.1000-436x.2015028
[14]	彭富强, 于德介, 刘坚. 一种基于多尺度线调频基的稀疏信号分解方法[J]. 振动工程学报, 2010, 23(3): 333-338 doi: 10.3969/j.issn.1004-4523.2010.03.015 PENG F Q, YU D J, LIU J. Sparse signal decomposition method based on multi-scale chirplet[J]. Journal of Vibration Engineering, 2010, 23(3): 333-338 (in Chinese) doi: 10.3969/j.issn.1004-4523.2010.03.015