基于随机激励响应的时变系统物理参数子空间识别方法研究

SUBSPACE-BASED PHYSICAL PARAMETER IDENTIFICATION OF TIME-VARYING SYSTEM USING RANDOM EXCITATION RESPONSE

该文提出了一种基于任意组合的DVA(displacement,velocity and acceleration)及输入激励识别时变系统物理参数的子空间方法。该方法以任意组合的位移、速度、加速度(DVA)随机响应信号为测量信息,仅利用一组输入、输出信号组成Hankel矩阵,通过奇异值分解的方法识别出等效状态的系统矩阵,然后运用推导出来的通用时变系统的转换矩阵,将等效状态系统矩阵转换成为实际物理状态下的系统矩阵,从而识别出实际系统的质量矩阵、刚度矩阵、阻尼矩阵。以二自由度弹簧-质量-阻尼模型为算例,研究了突变、线性变化和周期变化三种变化形式下物理参数的识别,并讨论了不同噪信比下噪声对识别结果的影响,仿真算例验证了该方法的正确性和有效性。

A physical parameter identification method is presented. For an arbitrarily time-varying system, a series of Hankel matrices are established directly from the combined measurements of displacements, velocities and accelerations （DVA） together with random excitations, which have been obtained through only one experiment of the system. The varying equivalent state space system matrices of structures at each moment are then identified by singular value decomposition （SVD） using random response data. A varying transformation matrix to transform the identified equivalent system matrices into the physical system matrices is developed to determine the mass, stiffness and damping matrices. Finally, a 2DOF spring-mass-damping model with three kinds of time-varying cases is investigated. The results demonstrate the accuracy and effectiveness of the proposed method in identifying the time-varying physical parameters.