协方差驱动随机子空间的Toeplitz矩阵行数选择方法

发布时间：2018-01-22 02:46

本文关键词： 随机子空间方法阻尼识别 Toeplitz矩阵条件数　出处：《振动与冲击》2015年07期 　论文类型：期刊论文

【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。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。
[Abstract]:Stochastic subspace recognition algorithm is a modal parameter identification method based on environment excitation, which can identify modal parameters only by response time history. The selection of rows of Toeplitz matrix in covariance-driven stochastic subspace method directly affects the recognition accuracy. The influence of row number I of Toeplitz matrix on the denoising ability of singular value decomposition in covariance-driven stochastic subspace method is studied. The condition number of Toeplitz matrix is introduced. According to the relation between I and the condition number of Toeplitz matrix, the influence of I on the recognition accuracy is proved again. The selection method of line number I of Toeplitz matrix is studied. The two-degree-of-freedom spring oscillator system is used. Two simulation examples of cutting tip delta wing model are used to study the selection method of Toeplitz matrix row number I. The results show that:. On the premise of determining the appropriate order of the system. The smaller the condition number of Toeplitz matrix is, the higher the recognition accuracy is.
【作者单位】：江苏省工程力学分析重点实验室;东南大学土木工程学院;
【基金】：国家自然科学基金(10902024) 教育部新世纪优秀人才支持计划(NCET-11-0086) 江苏省自然科学基金(BK2010397) 航空科学基金(20090869009) 江苏高校优势学科建设工程资助项目(1105007001)
【分类号】：TU311.3
【正文快照】： 随机子空间方法可以在激励未知、仅有响应数据的情况下识别系统的模态参数。根据识别过程中具体算法的不同,随机子空间可以分为数据驱动随机子空间和协方差驱动随机子空间[1-2]。协方差驱动随机子空间通过分解结构振动响应输出数据协方差矩阵(Toeplitz矩阵)的奇异值得到系统矩

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