用于时变系统辨识的自由响应递推子空间方法

Time-varying system identification using recursive subspace method based on free response data

通过对自由响应数据组成的广义Hankel矩阵做满秩分解得到系统的广义能观阵,利用广义能观阵的性质估计系统矩阵,得到与特征系统实现算法(ERA)等同的子空间方法,然后使用投影估计子空间跟踪算法(PAST)替代奇异值分解,跟踪广义Hankel矩阵的左奇异向量矩阵的变化,从而跟踪系统参数的变化,得到了利用自由响应数据(或脉冲响应数据)的递推子空间方法。通过移动质量块-简支梁模型的仿真试验检验,该方法可以有效地辨识时变系统的参数变化,而且计算量小,跟踪精度高,对噪声不敏感。

A novel recursive subspace method is presented in this paper. The generalized observability matrix is obtained by full rank decomposition of the generalized Hankel matrix consisting of free response data at first. Then the system matrix is calculated according to the shift invariant property of the generalized observability matrix. This method is equal to the Eigen-system Realization Algorithm (ERA). The novel method is obtained using Projection Approximation Subspace Tracking (PAST) method instead of the Eigen Value Decomposition (EVD). The variant of the left singular value vector matrix is tracked while the new data is added. The variant of the system parameter is also tracked according to this. At last a moving mass and simply-supported beam model is presented and the novel method is verified. The novel method is proved to be less computational complexity, more accurate in tracking and more noise-insensitivity.