协方差驱动随机子空间的Toeplitz矩阵行数选择方法

Selection method of Toeplitz matrix row number based on covariance driven stochastic subspace identification

随机子空间识别算法是一种基于环境激励的模态参数识别方法,仅需要响应时程便可识别模态参数。其中,协方差驱动随机子空间方法中Toeplitz矩阵行数的选取直接影响识别精度。通过构造相关矩阵,研究了Toeplitz矩阵行数i对协方差驱动随机子空间方法中奇异值分解去噪能力的影响。引入Toeplitz矩阵条件数,根据i与Toeplitz矩阵条件数的关系再次证明了i对识别精度的影响。研究了Toeplitz矩阵行数i的选择方法。采用两自由度弹簧振子系统和切尖三角翼模型两个仿真算例研究了Toeplitz矩阵行数i的选择方法。结果表明:在确定合适的系统阶数的前提下,Toeplitz矩阵的条件数越小识别精度越高。

Stochastic Subspace Identification is a parameter identification method, which can effectively obtain modal parameters from the structural signal under ambient excitation. The choice of Toeplitz matrix row number directly influences the accuracy of identification. By constructing a correlation matrix, the influence of the dimension of Toeplitz matrix i on the denoising ability via SVD was derived. The concept of condition number was introduced in solving the system matrix. According to the relationship between i and condition number of Toeplitz matrix, it is proved once again that i has influence on identification accuracy. Then the selection method of Toeplitz matrix row number i was studied. Two examplic simulations in regard to a two-degree spring mass vibration system and a cropped delta wing model were presented to show the method in the selection of i. The results show that on the premise of determining a suitable system order, the smaller the Toeplitz matrix condition number is, the higher the identification accuracy is.