基于极大似然估计的多参考点模态参数识别方法
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摘要
在考虑随机噪声的情况下,实现了一种基于极大似然估计的多参考点频域模态参数识别方法。该方法采用频响函数的右矩阵分式模型,通过噪声的协方差矩阵对误差向量加权,使用离散时间域中基函数改善数值求解性态。模态参数的估计过程分为两步:首先由基于最小二乘估计的polyLSCF算法获取迭代初值,然后通过Gauss-Newton方法对极大似然函数进行迭代优化,得到精度更高的模态参数识别结果。采用GARTEUR仿真算例对所给出的方法进行了验证,结果表明:在高噪声情况下,利用噪声信息的极大似然估计方法能够显著提高模态参数的识别精度,特别是阻尼的识别精度。
A frequency-domain modal parameters identification method based on maximum likelihood estimation is investigated considering stochastic noise.This method uses right matrix fraction description model of frequency response function.The noise covariance matrix is adopted as weighting function.The basis function in discrete time domain is utilized for improving numerical condition.First,the least square estimation is implemented to get the initial value of modal parameters.Then,the iterative optimization of Gauss-Newton method is carried out to get more precise identification result.A simulation case of GARTEUR model is employed to validate the method.Results show that the accuracy of modal parameters is improved obviously from maximum likelihood estimation method under high noise,especially for the damping ratio accuracy.
A frequency-domain modal parameters identification method based on maximum likelihood estimation is investigated considering stochastic noise.This method uses right matrix fraction description model of frequency response function.The noise covariance matrix is adopted as weighting function.The basis function in discrete time domain is utilized for improving numerical condition.First,the least square estimation is implemented to get the initial value of modal parameters.Then,the iterative optimization of Gauss-Newton method is carried out to get more precise identification result.A simulation case of GARTEUR model is employed to validate the method.Results show that the accuracy of modal parameters is improved obviously from maximum likelihood estimation method under high noise,especially for the damping ratio accuracy.
引文
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[2]Verboven P,Guillaume P,Cauberghe B,et al.Frequency-domain generalized total least-squares identification formodal analysis[J].Journal of Sound and Vibration,2004,278(22):21―38.
[3]Cauberghe B.Applied frequency-domain systemidentification in the field of experimental and operationalmodal analysis[D].Belgium:Vrije Universiteit Brussel,2004
[4]陈光,王永.密集模态挠性结构模型多变量频域辨识和控制[J].实验力学,2008(2):141―148.Chen Guang,Wang Yong.Multivariable Frequencydomain maximum likelihood identification and control offlexible structures with close modes[J].Journal ofExperimental Mechanics,2008(2):141―148.(inChinese)
[5]Schoukens J,Pintelon R,Renneboog J.A maximumlikelihood estimator for linear and nonlinear systems-apractical application of estimation techniques inmeasurement problem[J].IEEE Transactions onInstrument and Measures,1988,37(1):10―17.
[6]Guillaume P,Verboven P,Vanlanduit S.Frequency-domain maximum likelihood identification ofmodal parameters with confidence intervals[C]//Proceeding of ISMA 23,1998.
[7]Verboven P,Guillaume P,Cauberghe B,et al.Modalparameter estimation from input–output Fourier datausing frequency-domain maximum likelihoodidentification[J].Journal of Sound and Vibration,2004,276(22):957―979.
[8]Parloo E,Guillaume P,Cauberghe B.Maximumlikelihood identification of non-stationary operationaldata[J].Journal of Sound and Vibration,2003,268:971―991.
[9]Pintelon R,Schoukens J.Frequency domain maximumlikelihood estimation of linear dynamicerrors-in-variables models[J].Automatica,2007,43(4):621―630.
[10]Guillaume P,Verboven P,Vanlanduit S,et al.Apoly-reference implementation of the least-squarescomplex frequency domain estimator[C]//Proceeding ofthe 21th IMAC.Kissimmee,USA,February 2003:
[11]孙鑫晖.频域模态参数识别研究及其软件实现[D].南京:南京航空航天大学,2010.Sun Xinhui.Frequency domain modal parameteridentification and software implementation[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2010.(in Chinese)