桥梁时变系统的张量子空间识别方法研究及试验验证

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摘要针对二维矩阵子空间系统识别方法在系统识别计算效率、抗噪性与识别能力不强的问题，基于张量平行因子分解理论，引入时间维度，提出一种新的张量子空间系统识别方法以追踪非线性桥梁系统的模态参数时变规律。将时间维度引入至二维Hankel矩阵，构建Hankel时变三维张量；基于结构振动的状态空间模型，推导建立张量子空间系统识别数学模型；运用张量因子分解理论，结合稳定图方法，平行求解系统矩阵，剔除虚假模态信息。基于两座斜拉模型桥试验，通过与滑窗子空间系统识别方法对比，验证了方法在计算效率与结果精确性上的提升，其结果表明所提方法可用于求解确定和随机非线性时变桥梁系统识别问题。

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	张二华1
	吴涤1
	刘昊1
	单德山2

关键词 ：桥梁工程, 子空间系统识别, 张量分解, 时变系统

Abstract：In order to solve the problem of the weak computing efficiency, noise resistance and system identification ability of two-dimensional matrix subspace identification method, based on the theory of tensor parallel factor decomposition and introducing the time dimension, a new tensor subspace system identification method is proposed to track the time-varying law of modal parameters of nonlinear bridge systems. The time dimension is introduced into the two-dimensional Hankel matrix to construct the Hankel time-varying three-dimensional tensor. Based on the state space model of structural vibration, a mathematical model for the tensor subspace system identification is derived. By using the tensor factor decomposition theory and the stability graph method, the system matrix is solved in parallel and the false modal information is eliminated. Based on two cable-stayed model bridge tests, through the comparison with sliding window based subspace system identification methods, the improvement of calculation efficiency and result accuracy is verified. The results show that the proposed method can be used to solve the deterministic and stochastic nonlinear time-varying bridge system identification problems.

Key words： bridge engineering subspace system identification, tensor decomposition, time-varying system

收稿日期: 2020-08-27 出版日期: 2021-12-15

引用本文:

张二华1，吴涤1，刘昊1，单德山2. 桥梁时变系统的张量子空间识别方法研究及试验验证[J]. 振动与冲击, 2021, 40(23): 66-73.
ZHANG Erhua1, WU Di1, LIU Hao1, SHAN Deshan2. Tensor subspace identification method for bridge time-varying system and its test verification. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(23): 66-73.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2021/V40/I23/66

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