非平稳Gauss环境激励下模态参数识别的新方法

杜秀丽; 汪凤泉

doi:10.3879/j.issn.1000-0887.2009.10.009

非平稳Gauss环境激励下模态参数识别的新方法

doi: 10.3879/j.issn.1000-0887.2009.10.009

杜秀丽¹,
汪凤泉²

1.
南京师范大学数学科学学院,南京 210046;2.东南大学土木工程学院,南京 210096

基金项目: 国家自然科学基金(重点)资助项目(50278017)

详细信息

作者简介:
杜秀丽(1974- ),女,山西人,讲师,博士(联系人.Tel:+86-25-85328301;E-mail:duxiuli@njnu.edu.cn).

中图分类号: O324,O211.63,TU311.3
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- 文章访问数: 1519
- HTML全文浏览量: 121
- PDF下载量: 879
- 被引次数: 0
出版历程
- 收稿日期: 2009-01-06
- 修回日期: 2009-07-10
- 刊出日期: 2009-10-15

A New Modal Identification Method Under the Non-Stationary Gaussian Ambient Excitation

DU Xiu-li¹,
WANG Feng-quan²

1.
College of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, P. R. China;

摘要

摘要: 结合多元连续时间自回归模型，针对受均匀调制Gauss随机激励的线性时不变系统，提出了一种时域模态识别的新方法．该方法仅从响应数据就能够识别系统的物理参数．首先把结构动力学方程转化为一个3阶的连续时间自回归模型；接着基于在非常短的时间段内均匀调制函数接近于一个常数矩阵以及随机微分方程强解的性质，得到均匀调制函数的估计, 并针对两种特殊情况进行讨论；然后利用Girsanov定理，对条件似然函数进行极大化，得到物理参数的精确极大似然估计．数值结果表明，该估计不仅具有极高的精度和稳健性，而且计算效率非常高．
- 模态识别 /
- 均匀调制函数 /
- 连续时间自回归模型 /
- Brown运动 /
- 精确极大似然估计
Abstract: Based on the multivariate continuous tmie autoregressive model, a new time-domain modal identification method of LTI system driven by the uniformly modulated Gaussian random excitation was presented. The method canidentify the physical parameters of the system from the response data. First, the structural dynamic equation is transformed into the continuous tmie autoregressive model of order 3. Second, based on the assumption that the uniformly modulated function is approx miately equal to a constant matrix in a very short time period and the property of the strong solution of the stochastic differential equation, the uniformly modulated function is identified piecewise, an d two special situations are discussed too. Finally, by virtue of the Girsanov theorem, a likelihood function was in troduced, which is just a conditional density function. Maxmiizing the likelihood function gives the exact maximum likelihood estmiators of model parameters. Numerical results show that the method has high precision and computing efficiency.
- modal identification /
- uniformly modulated function /
- continuous time autoregres-sive model /
- Brownian motion /
- exactmaximum likelihood estmiator

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参考文献(15)

[1]	Conforto S, D′Alessio T. Spectral analysis for non-stationary signals from mechanical measurements: a parametric approach[J].Mechanical Systems and Signal Processing, 1999,13(3):395-411. doi: 10.1006/mssp.1998.1220
[2]	Zhang Z Y,Hua H X, Xu X Z,et al.Modal parameter identification through Gabor expansion of response signals[J].Journal of Sound and Vibration,2003,266(5):943-955. doi: 10.1016/S0022-460X(02)01381-0
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[6]	Tse P,Yang W X,Tam H Y.Machine fault diagnosis through an effective exact wavelet analysis[J].Journal of Sound and Vibration,2004,277(4/5):1005-1024. doi: 10.1016/j.jsv.2003.09.031
[7]	Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis[J].Proceedings of the Royal Society of London,Series A,1998,454(1971):903-951. doi: 10.1098/rspa.1998.0193
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[11]	Poulimenos A G,Fassois S D. Non-stationary mechanical vibration modelling and analysis via functional series TARMA models[A].In:Van den Hof P M J,Wahlberg B,Weiland S Eds.Proceedings of the 13th IFAC Symposium on System Identification[C].Rotterdam,Netherlands,2003,965-970.
[12]	Poulimenos A G,Fassois S D.Parametric time-domain methods for non-stationary random vibration modelling and analysis: a critical survey and comparison[J].Mechanical Systems and Signal Processing,2006,20(4):763-816 doi: 10.1016/j.ymssp.2005.10.003
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非平稳Gauss环境激励下模态参数识别的新方法

doi: 10.3879/j.issn.1000-0887.2009.10.009

作者简介:
杜秀丽(1974- ),女,山西人,讲师,博士(联系人.Tel:+86-25-85328301;E-mail:duxiuli@njnu.edu.cn).

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A New Modal Identification Method Under the Non-Stationary Gaussian Ambient Excitation

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留言板

非平稳Gauss环境激励下模态参数识别的新方法

doi: 10.3879/j.issn.1000-0887.2009.10.009

作者简介: 杜秀丽(1974- ),女,山西人,讲师,博士(联系人.Tel:+86-25-85328301;E-mail:duxiuli@njnu.edu.cn).

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出版历程

A New Modal Identification Method Under the Non-Stationary Gaussian Ambient Excitation

计量

出版历程

目录

作者简介:
杜秀丽(1974- ),女,山西人,讲师,博士(联系人.Tel:+86-25-85328301;E-mail:duxiuli@njnu.edu.cn).