非线性动力学系统的辨识:时频滤波与骨架曲线

基金项目: 国家自然科学基金资助项目(19632001);西安交通大学在职博士基金;中国博士后基金

Identification of Nonlinear Dynamic Systems:Time-Frequency Filtering and Skeleton Curves

1.
School of Civil Engineering and Mechanics, Xi'an Jiaotong University, Xi'an 710049, P. R. China;
2.
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100080, P. R. China

摘要: 利用非平稳信号的时频分析方法研究了一类非线性系统的频率特性和阻尼特性随运动形态的变化规律,得到了能简洁、直观地反映系统基本非线性动力学特性的广义骨架线性系统(简称GSLS)和骨架曲线.在此基础上,利用时频滤波方法根据系统非平稳响应信号对非线性系统进行辨识.该项工作为非线性系统反问题的研究提供了一条新的途径.
- 系统识别 /
- 非线性动力学系统 /
- 非平稳信号 /
- 时频分析 /
- 希尔伯特变换
Abstract: The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator on definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system(GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.
- system identification /
- nonlinear dynamic system /
- non-stationary signal /
- time-frequency analysis /
- Hilbert transform

[1]	Imregun M.A survey of nonlinear analysis tools for structural systems[J].The Shock and Vibration Digest,1998,30(5):363-369.
[2]	Michael Feldman.Non-linear system vibration analysis using Hilbert transform Ⅰ.Free vibration analysis method ‘freevib'[J].Mechanical Systems and Signal Processing,1994,8(2):119-127.
[3]	Michael Feldman.Non-linear system vibration analysis using Hilbert transform Ⅱ.Forced vibration analysis method ‘forcevib'[J].Mechanical Systems and Signal Processing,1994,8(3):309-318.
[4]	WANG Li-li,ZHANG Jing-hui,HU Shi-yue.The accompanied slowly-variant-system of nonlinear dynamic systems[J].Acta Mechanica Sinica(English Series),1999,15(1):73-81.
[5]	刘贵忠,刘志梅.一种新的二次时频分布和几种主要二次时频分布的比较研究[J].电子科学学刊,1996,18(5):455-461.
[6]	王丽丽.动力学系统的时频分析及其在非线性建模中的应用[D].博士学位论文.西安:西安交通大学,1999.
[7]	WANG Li-li,ZHANG Jing-hui,HU Shi-yue.Study of non-linearity through the quadratic time-frequency distribution[A].In:Zhang J H,Zhang X N Eds.International Conference on Advanced Problems in Vibration Theory and Applications[C].Xi'an,Beijing:Science Press,2000,552-554.
[8]	科恩L.时-频分析:理论与应用[M].白居宪译.西安:西安交通大学出版社,1998.