融合多工况功率谱密度函数的工作模态分析方法

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摘要频域分解(Frequency Domain Decomposition，FDD)方法是开展环境激励下结构工作模态分析(Operational Modal Analysis,OMA)的常用方法。但是，现有的FDD方法存在一些不足：(1)无法剔除非白激励及谐波激励引起的虚假模态；(2)无法区分结构密集模态与不相关非白激励产生的虚假模态。通过研究发现功率谱密度(Power Spectral Density，PSD)矩阵的秩是FDD方法性能的决定性因素。在此基础上，提出一种新的工作模态识别OMA方法，该方法结合了不同激励工况下的响应PSD函数矩阵，并分别对单个激励工况下的响应PSD矩阵与多工况下的增广响应PSD矩阵进行奇异值分解，通过对比单工况PSD矩阵与增广PSD矩阵在奇异值峰值处秩的变化，识别出包括密集模态在内的结构模态参数，并消除由非白激励产生的虚假模态。采用桁架结构仿真算例和广州塔的工程数据集验证所提方法的有效性。

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	曾舒洪
	康杰
	孙嘉宝
	罗杰

关键词 ：工作模态分析, 非白噪声激励, 密集模态, 功率谱密度

Abstract：The frequency domain decomposition (FDD) method is a common method for structural operational modal analysis ( OMA ) under ambient excitation. However, the existing FDD methods have some shortcomings : (1) spurious modes caused by non-white excitation and harmonic excitation cannot be eliminated ; (2) It is impossible to distinguish between structurally closely-spaced modes and spurious modes generated by uncorrelated non-white excitations. It is found that the rank of power spectral density ( PSD ) matrix is the decisive factor for the performance of FDD method. On this basis, a new OMA method is proposed. This method combines the response PSD function matrix under different excitation conditions, and performs singular value decomposition on the response PSD matrix under a single excitation condition and the augmented response PSD matrix under multiple excitation conditions. By comparing the rank changes of the single-case PSD matrix and the augmented PSD matrix at the peak of the singular value, the structural modal parameters including the closely-spaced mode are identified, and the spurious mode generated by the non-white excitation is eliminated. The effectiveness of the proposed method is verified by a truss structure simulation example and the engineering data set of Guangzhou Tower.

Key words： Operational modal analysis Non-white excitation Closely-spaced modes Power spectral density

收稿日期: 2023-03-01 出版日期: 2024-02-28

引用本文:

曾舒洪，康杰，孙嘉宝，罗杰. 融合多工况功率谱密度函数的工作模态分析方法[J]. 振动与冲击, 2024, 43(4): 179-189.
ZENG Shuhong,KANG Jie,SUN Jiabao,LUO Jie. An operational modal analysis method fusing multi-condition power spectral density function. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(4): 179-189.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2024/V43/I4/179

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