改进的子空间方法及其在时变结构参数辨识中的应用

AN IMPROVED SUBSPACE METHOD AND ITS APPLICATION TO PARAMETER IDENTIFICATION OF TIME-VARYING STRUCTURES

本文给出了一种可用于时变结构参数辨识的子空间跟踪方法。子空间方法运用特征分析理论,通过矩阵分解来得到信号子空间。首先将要跟踪的矩阵变换为一种适合在线跟踪的格式,将新的数据信息组合成一个维数不变的矩阵,通过对该矩阵的奇异值分解来更新上一步的信号子空间。这样就避免了对一个不断增长的Hankle阵做奇异值分解,有效的缩减了计算量。将该方法用于机械臂系统,通过施加一个随时间变化的力来改变机械臂的固有频率。选择合适的遗忘因子以协调跟踪能力和辨识仿真结果证实了算法跟踪时变参数的能力。

This paper develops a subspace tracking algorithm for parameter identification of time-varying structures. In subspace method, eigen-analysis is conducted and signal subspace is obtained through matrix decomposition. Firstly, the matrix to be tracked is transformed into a form suitable for on-line tracking. The new data information is put into a matrix with fixed dimension. The signal subspace is updated by singular value decomposition (SVD) of the matrix. Consequently, the SVD of an increasing Hankel matrix is avoided in the algorithm and therefore the computational effort is reduced. The algorithm is applied to a manipulator. The natural frequencies of the manipulator is controlled by a time-varying force. The tracking ability is reconciled with accuracy by introducing a forgetting factor. On-line identification simulation results demonstrate the ability of the algorithm to track time-varying parameters.