数据驱动随机子空间法矩阵维数选择与噪声问题研究

数据驱动随机子空间法作为一种线性系统辩识方法，可以有效地从环境激励的结构振动响应中获取模态参数。其中，Hankel矩阵维数的选择直接影响到数据驱动随机子空间法消噪能力。本文理论上分析了噪声与数据驱动随机子空间法Hankel矩阵维数之间的关系，并基于归一化奇异值（SVD）、稳定图以及有限元模态识别结果（FE），提出了一种评估数据驱动随机子空间法矩阵维数选择优劣的方法，并通过数值算例和导管架平台振动台试验系统地验证了该方法的有效性，结果表明：非方阵的Hankel矩阵使数据驱动随机子空间法具备更强的消噪能力和更高的模态识别精度。

STUDY ON RELATION BETWEEN NOISE AND MATRIX DIMENSION OF DATA-DRIVEN STOCHASTIC SUBSPACE IDENTIFICATION METHTOD

As a linear system identification method, the data-driven stochastic subspace method can effectively obtain modal parameters from the signal associated with structure under ambient excitation. Noise reduction ability of data-driven stochastic subspace identification method is related with its Hankel matrix dimension. We introduce theoretically the relation between noise and Hankel matrix of data-driven subspace identification method. And we also propose a verification procedure to justify the noise can be eliminated properly by data-driven subspace identification method with selected Hankel matrix, the procedure includes SVD, stability diagram and finite element result(FE). Finally based on data associated with numerical study and jacket platform vibration test separately, we demonstrate systematically that data-driven stochastic subspace identification method with non-square Hankel matrix has better capacity of denoising and estimating the modal with higher accuracy.