协方差驱动随机子空间的Toeplitz矩阵行数选择方法

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振动与冲击 ›› 2015, Vol. 34 ›› Issue (7) : 71-75.

论文

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。本文通过构造相关矩阵，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本文中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。

作者信息 +

The Selection Method of Toeplitz Matrix Row Number Based on Covariance Driven Stochastic Subspace Identification

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, this paper derives the dimension of Toeplitz matrix influence the denoising ability ver SVD. The concept of condition number is introduced in solving the system matrix. according to the relationship between i and condition number of Toeplitz matrix, proving once again that i has influence on identification accuracy. Then researching the selection method of Toeplitz matrix row number i. Two simulations with two-degree spring vibration and a cropped delta wing model are used to research the method. The results show that after the determination of the suitable system order the smaller the Toeplitz matrix condition number is, the higher identification accuracy is.

Author information +

文章历史 +

摘要

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。本文通过构造相关矩阵，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本文中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。

Abstract

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, this paper derives the dimension of Toeplitz matrix influence the denoising ability ver SVD. The concept of condition number is introduced in solving the system matrix. according to the relationship between i and condition number of Toeplitz matrix, proving once again that i has influence on identification accuracy. Then researching the selection method of Toeplitz matrix row number i. Two simulations with two-degree spring vibration and a cropped delta wing model are used to research the method. The results show that after the determination of the suitable system order the smaller the Toeplitz matrix condition number is, the higher identification accuracy is.

导出引用

王燕1,2，杭晓晨1,2，姜东1,2，韩晓林1,2，费庆国1,2. 协方差驱动随机子空间的Toeplitz矩阵行数选择方法[J]. 振动与冲击, 2015, 34(7): 71-75

Wang Yan1, 2, Hang Xiaochen1, 2, Jiang Dong1, 2, Han Xiaolin1, 2, Fei Qingguo1, 2. The Selection Method of Toeplitz Matrix Row Number Based on Covariance Driven Stochastic Subspace Identification[J]. Journal of Vibration and Shock, 2015, 34(7): 71-75

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