状态空间下基于小波变换的时变系统参数识别  

Parameter identification of time-varying system based on state space and wavelet transform method

作　　者：许鑫[1,2] 史治宇[1,2] 

机构地区：[1]南京航空航天大学飞行器结构力学与控制教育部重点实验室,江苏南京210016 [2]南京航空航天大学结构与强度研究所,江苏南京210016

出　　处：《振动工程学报》2010年第4期415-419,共5页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(10772076);江苏省研究生培养创新项目(CX10B-088Z)

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 parame- ters 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 fourstorey 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.

关 键 词：参数识别 时变系统 状态空间 小波变换 

分 类 号：TB123[理学—工程力学] O329[理学—力学]