DU Xiu-li, WANG Feng-quan. A New Modal Identification Method Under the Non-Stationary Gaussian Ambient Excitation[J]. Applied Mathematics and Mechanics, 2009, 30(10): 1213-1222. doi: 10.3879/j.issn.1000-0887.2009.10.009
 Citation: DU Xiu-li, WANG Feng-quan. A New Modal Identification Method Under the Non-Stationary Gaussian Ambient Excitation[J]. Applied Mathematics and Mechanics, 2009, 30(10): 1213-1222.

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

##### doi: 10.3879/j.issn.1000-0887.2009.10.009
• Rev Recd Date: 2009-07-10
• Publish Date: 2009-10-15
• 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.
•  [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. [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. [3] Bonato P,Ceravolo R,De Stefano A,et al. Use of cross time-frequency estimators for structural identification in non-stationary conditions and under unknown excitation[J].Journal of Sound and Vibration,2000,237(5):775-791. [4] Lardies J,Ta M N,Berthillier M. Modal parameter estimation based on the wavelet transform of output data[J].Archive of Applied Mechanics,2004,73(9/10):718-733. [5] Yang J N,Lei Y,Pan S W,et al. System identification of linear structures based on Hilbert-Huang spectral analysis.part 1: normal modes[J].Earthquake Engineering and Structural Dynamics,2003,32(9):1443-1467. doi: 10.1002/eqe.287 [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. [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. [8] Peng Z K,Tse P W,Chu F L.An improved Hilbert-Huang transform and its application in vibration signal analysis[J].Journal of Sound and Vibration,2005,286(1/2):187-205. [9] 李杰，陈隽.未知输入条件下的结构物理参数识别研究[J].计算力学学报,1999,16(1):32-40. [10] 陈健云，王建有，林皋.未知输入下的复合反演研究[J].工程力学,2006,23(1):6-10. [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 [13] Brockwell P,Davis R A,Yu Y.Continuous-time Gaussian autoregression[J].Statistica Sinica,2007,17(1): 63-80 [14] Karatzas L,Shreve S E.Brownian Motion and Stochastic Calculus[M].New York:Springer Press,2000. [15] Harris C M,Crede C E.Shock and Vibration Handbook[M].New York: McGraw-Hill Book Company,1976.

### Catalog

###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142