状态空间下基于小波变换的时变系统参数识别
|
摘要
基于状态空间和小波理论提出了时变系统的参数识别方法。该方法将线性时变系统的二阶振动微分方程转化为状态空间里的一阶微分方程组,再对系统的自由响应数据进行小波变换,利用小波尺度函数的正交性,又将一阶微分方程组的求解转化为线性代数方程组的求解问题。识别出等效的系统转移矩阵,再利用特征值分解,可以得到系统的模态参数,然后将等效的系统转移矩阵与实际物理模型中的质量、刚度和阻尼矩阵对照,识别出系统的刚度和阻尼矩阵。以4层楼房剪切模型为例,对突变、线性变化和周期变化3种情形下的时变参数进行了识别,仿真算例验证了该方法的正确性和有效性。
A parameter identification method is presented in this paper based on state space and wavelet transform method.For an arbitrarily linear time-varying system,the second-order vibration equations can firstly be rewritten and reduced to first-order difference equations by using state-space method.Subsequently,free response signals are decomposed using the Daubechies wavelet scaling functions,and then the state-space equations of the time-varying dynamic system are transformed into simple linear equations based on the orthogonality of the scaling functions.The varying equivalent state-space system matrices of structures at each moment are then identified directly by solving the linear equations.The system modal parameters are extracted though eigenvalue decomposition of the state-space system matrices and the stiffness and damping matrices are determined by comparing the identified equivalent system matrices with the physical system matrices.Finally,a four-storey shear-beam building model with three kinds of time-varying cases is investigated.Numerical results show that the proposed method is accurate and effective to identify the time-varying physical parameters.
A parameter identification method is presented in this paper based on state space and wavelet transform method.For an arbitrarily linear time-varying system,the second-order vibration equations can firstly be rewritten and reduced to first-order difference equations by using state-space method.Subsequently,free response signals are decomposed using the Daubechies wavelet scaling functions,and then the state-space equations of the time-varying dynamic system are transformed into simple linear equations based on the orthogonality of the scaling functions.The varying equivalent state-space system matrices of structures at each moment are then identified directly by solving the linear equations.The system modal parameters are extracted though eigenvalue decomposition of the state-space system matrices and the stiffness and damping matrices are determined by comparing the identified equivalent system matrices with the physical system matrices.Finally,a four-storey shear-beam building model with three kinds of time-varying cases is investigated.Numerical results show that the proposed method is accurate and effective to identify the time-varying physical parameters.
引文
[1]Feldman M.Non-linear system vibration analysisusing Hilbert transform-I:free vibration analysismethod FREEV B[J].Mechanical Systems andSignal Processing,1994,8(2):119—127.
[2]Shi Z Y,Law S S,Xu X.Identification of linear time-varying mdof dynamical systems from forcedexcitation using Hilbert transform and EMD method[J].Journal of Sound and Vibration,2009,321:572—589.
[3]Liu K.Identification of linear time-varying systems[J].Journal of Sound and Vibration,1997,206(4):487—505.
[4]Ko W J,Huang C F.Extraction of structural systemmatrices from an identified state-space system usingcombined measurements of DVA[J].Journal ofSound and Vibration,2002,249(5):955—970.
[5]庞世伟,于开平,邹经湘.用于时变系统辨识自由响应递推子空间方法[J].振动工程学报,2005,18(2):233—237.
[6]Amaratunga K,Williams J R,Qian S.Wavelet-galerkin solutions for one dimensional partialdifferential equation[J].International Journal forNumerical Methods in Engineering,1994,37:2703—2 716.
[7]Ghanem R.Romeo F.A wavelet-based approach forthe identification of linear time-varying dynamicalsystems[J].Journal of Sound and Vibration,2000,234(4):555—576.
[8]邹经湘,于开平,杨炳渊.时变结构的参数识别方法[J].力学进展,2000,30(3):370—377.
[9]Juang J N,Pappa R S.An eigensystem realizationalgorithm for modal parameter identification andmodel reduction[J].Journal of Guidance,Controland Dynamics,1985,8(5):620—627.
[10]Liu K.Extension of modal analysis to linear time-varying systems[J].Journal of Sound and Vibration,1999,226(1):149—167.
[11]于开平,谢礼立,樊久铭,等.移动质量-简支梁系统的参数辨识[J].地震工程与工程振动,2002,22(5):14—17.
[12]李会娜,史治宇.基于自由响应数据的时变系统物理参数识别[J].振动工程学报,2007,20(4):348—352.
[13]Mitra M,Gopalakrishnan S.Spectrally formulatedwavelet finite element for wave propagation andimpact force identification in connected 1-Dwaveguides[J].International Journal of Solids andStructures,2005,42:4 695—4 721.
[14]史治宇,沈林.基于小波方法的时变动力系统参数识别[J].振动、测试与诊断,2008,28(2):108—112.
[15]Latto A,Resnikoff H L,Tenenbaum E.Theevolution connection coefficients of compactlysupported wavelets[A].Proceedings of the French-USA Workshop on Wavelets and Turbulence[C].NY:Springer-Verlag,1991.
[2]Shi Z Y,Law S S,Xu X.Identification of linear time-varying mdof dynamical systems from forcedexcitation using Hilbert transform and EMD method[J].Journal of Sound and Vibration,2009,321:572—589.
[3]Liu K.Identification of linear time-varying systems[J].Journal of Sound and Vibration,1997,206(4):487—505.
[4]Ko W J,Huang C F.Extraction of structural systemmatrices from an identified state-space system usingcombined measurements of DVA[J].Journal ofSound and Vibration,2002,249(5):955—970.
[5]庞世伟,于开平,邹经湘.用于时变系统辨识自由响应递推子空间方法[J].振动工程学报,2005,18(2):233—237.
[6]Amaratunga K,Williams J R,Qian S.Wavelet-galerkin solutions for one dimensional partialdifferential equation[J].International Journal forNumerical Methods in Engineering,1994,37:2703—2 716.
[7]Ghanem R.Romeo F.A wavelet-based approach forthe identification of linear time-varying dynamicalsystems[J].Journal of Sound and Vibration,2000,234(4):555—576.
[8]邹经湘,于开平,杨炳渊.时变结构的参数识别方法[J].力学进展,2000,30(3):370—377.
[9]Juang J N,Pappa R S.An eigensystem realizationalgorithm for modal parameter identification andmodel reduction[J].Journal of Guidance,Controland Dynamics,1985,8(5):620—627.
[10]Liu K.Extension of modal analysis to linear time-varying systems[J].Journal of Sound and Vibration,1999,226(1):149—167.
[11]于开平,谢礼立,樊久铭,等.移动质量-简支梁系统的参数辨识[J].地震工程与工程振动,2002,22(5):14—17.
[12]李会娜,史治宇.基于自由响应数据的时变系统物理参数识别[J].振动工程学报,2007,20(4):348—352.
[13]Mitra M,Gopalakrishnan S.Spectrally formulatedwavelet finite element for wave propagation andimpact force identification in connected 1-Dwaveguides[J].International Journal of Solids andStructures,2005,42:4 695—4 721.
[14]史治宇,沈林.基于小波方法的时变动力系统参数识别[J].振动、测试与诊断,2008,28(2):108—112.
[15]Latto A,Resnikoff H L,Tenenbaum E.Theevolution connection coefficients of compactlysupported wavelets[A].Proceedings of the French-USA Workshop on Wavelets and Turbulence[C].NY:Springer-Verlag,1991.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心