基于控制响应的时变系统模态参数辨识的改进子空间方法

An improved subspace method with time-varying system modal parameter identification based on control response data

提出了一种基于系统控制信号激发的响应数据来辨识时变系统模态参数的改进子空间方法。该方法以系统控制响应信号建立系统的状态空间输出方程并构造了一个广义Hankel矩阵,通过对该矩阵做奇异值分解(SVD),用广义能观阵的估计代替输出矩阵,然后利用奇异值矩阵的正交性,有效地降低了噪声敏感性和计算量,从而容易地辨识出等效状态下的系统矩阵,最后采用转换矩阵辨识出时变系统的模态参数。通过理论分析、仿真和实验,讨论了不同信噪比对辨识结果的影响,验证了该方法的有效性。

A data-processing method concerning subspace identification is presented to improve the identification of time-varying system modal parameters from measured system control response data. Using system control response data, the identification procedure of this method includes the following steps. A state space output equation was first founded, and then a generalized Hankel matrix was constructed. After that, the state space system matrix of structure was identified by singular value decomposition （SVD） of the Hankel matrix. By replacing the output matrix with the estimation of generalized observ-ability matrix and utilizing the orthogonality of the singular value matrix, the sensitivity to noise and computational complexity were abated effectively, making it easier to distinguish the equivalent system matrix. Finally, the time-varying system modal parameters were identified by conversion matrix. The practicability of the proposed method has been verified by theoretical analysis, simulation and experi-mental data.