多工况功率谱密度传递率矩阵运行模态分析方法

doi:10.3901/JME.2025.09.350

机械工程学报 ›› 2025, Vol. 61 ›› Issue (9): 350-357.doi: 10.3901/JME.2025.09.350

• 机械动力学 • 上一篇

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多工况功率谱密度传递率矩阵运行模态分析方法

褚志刚, 赵世浩, 潘锋

重庆大学机械与运载工程学院重庆 400044

收稿日期:2024-05-06 修回日期:2024-11-05 发布日期:2025-06-12
通讯作者: 褚志刚,男,1978年出生,博士,教授。主要研究方向为振动噪声测量分析技术,声源识别技术理论及其应用。E-mail:zgchu@cqu.edu.cn E-mail:zgchu@cqu.edu.cn
基金资助:
国家重点研发计划资助项目(2023YFF0716700)。

Operational Modal Analysis Method Based on Power Spectral Density Transmissibility Matrix under Multiple Load Cases

CHU Zhigang, ZHAO Shihao, PAN Feng

College of Mechanical and Vehicle Engineering, Chongqing University, Chongqing 400044

Received:2024-05-06 Revised:2024-11-05 Published:2025-06-12

摘要/Abstract

摘要： 功率谱密度传递率运行模态分析方法抗噪声干扰能力强，但其模态参数识别结果易受谐波激励的干扰。鉴于此，建立了基于多工况功率谱密度传递率矩阵法的运行模态参数识别方法。该方法首先构造多工况下测量信号的功率谱密度传递率矩阵，其次对该矩阵的摩尔-彭若斯逆矩阵内所有元素进行平均并对其拟合以提取模态频率和阻尼比，基于该矩阵的左奇异矩阵获取模态振型，最后根据多工况测量信号的功率谱密度传递率矩阵在模态和谐波所对应频率处秩不同的性质在所求的模态参数中识别并剔除谐波模态，继而获得最终的模态参数。5自由度质量-弹簧-阻尼系统仿真结果及钢质梁的运行模态试验结果均验证该方法的有效性。

关键词: 运行模态分析, 功率谱密度传递率, 谐波剔除, 模态参数识别

Abstract: The operational modal analysis method based on power spectral density transmissibility is highly resistant to noise interference, but its modal parameter identification results are susceptible to interference from harmonic excitation. In view of this, an operational modal parameter identification method based on the power spectral density transmissibility matrix under multiple load cases is established. The method firstly constructs the power spectral density transmissibility matrix (PSDTM) from the measured signals under multiple load cases, then averages and fits all the elements within the Moore-Penrose inverse matrix of the PSDTM to extract the modal frequencies and damping ratios, and obtains the modal vibration shapes based on the left singularity matrix of the PSDTM. Finally, based on the property that PSDTM of the measurement signals under multiple load cases has different ranks at the frequencies corresponding to modes and harmonics, the harmonic modes are eliminated from the identified modal parameters, and then the final modal parameters are obtained. The simulation results of the 5-degree-of-freedom mass-spring-damping system and the operational modal test results of the steel beam verify the validity of the method.

Key words: operational modal analysis, power spectrum density transmissibility, harmonic elimination, modal parameter identification

中图分类号:

TB123

褚志刚, 赵世浩, 潘锋. 多工况功率谱密度传递率矩阵运行模态分析方法[J]. 机械工程学报, 2025, 61(9): 350-357.

CHU Zhigang, ZHAO Shihao, PAN Feng. Operational Modal Analysis Method Based on Power Spectral Density Transmissibility Matrix under Multiple Load Cases[J]. Journal of Mechanical Engineering, 2025, 61(9): 350-357.

参考文献

[1] DING G,LI M,GAO X,et al. Propeller's operational modal parameters identification based on Fiber Bragg Grating sensing[J]. Ocean Engineering,2022,266(2):112737.
[2] 张永祥,刘心,褚志刚,等. 基于随机子空间法的模态参数自动提取[J]. 机械工程学报,2018,54(9):187-194. ZHANG Yongxiang,LIU Xin,CHU Zhigang,et al. Autonomous modal parameter extraction based on stochastic subspace identification[J]. Journal of Mechanical Engineering,2018,54(9):187-194.
[3] CARA J. Computing the modal mass from the state space model in combined experimental-operational modal analysis[J]. Journal of Sound and Vibration,2016,370:94-110.
[4] MODAK S V. Influence of a harmonic in the response on randomdec signature[J]. Mechanical Systems and Signal Processing,2011,25(7):2673-2682.
[5] SADEQI A,MORADI S. A new SVD-based filtering technique for operational modal analysis in the presence of harmonic excitation and noise[J]. Journal of Sound and Vibration,2021,510:116252.
[6] BRINCKER R,ANDERSEN P,MOLLER N. An indicator for separation of structural and harmonic modes in output-only modal testing[C]//Proceedings of SPIE-The International Society for Optical Engineering,February 7-11,2000,San Antonio,TX,USA,4062:1649-1654.
[7] DEVRIENDT C,GUILLAUME P. The use of transmissibility measurements in output-only modal analysis[J]. Mechanical Systems and Signal Processing,2007,21(7):2689-2696.
[8] DEVRIENDT C,GUILLAUME P. Identification of modal parameters from transmissibility measurements[J]. Journal of Sound and Vibration,2008,314(1-2):343-356.
[9] DEVRIENDT C,WEIJTJENS W,DE SITTER G,et al. Combining multiple single-reference transmissibility functions in a unique matrix formulation for operational modal analysis[J]. Mechanical Systems and Signal Processing,2013,40(1):278-287.
[10] 陈涛,褚志刚,李沛然,等. 基于伪频响函数矩阵法的运行模态分析方法[J]. 机械工程学报,2021,57(20):266-276. CHEN Tao,CHU Zhigang,LI Peiran,et al. Operational modal analysis method based on the pseudo frequency response function matrix[J]. Journal of Mechanical Engineering,2021,57(20):266-276.
[11] YAN W,REN W. Operational modal parameter identification from power spectrum density transmissibility[J]. Computer-Aided Civil and Infrastructure Engineering,2012,27(3):202-217.
[12] SUN Q,YAN W,REN W,et al. Application of transmissibility measurements to operational modal analysis of railway,highway,and pedestrian cable-stayed bridges[J]. Measurement,2019,148:106880.
[13] KANG J,JU H,LIU L. Comparison of response transmissibility and power spectral density transmissibility on operational modal analysis[J]. Mechanical Systems and Signal Processing,2021,160:107912.
[14] ARAUJO I G,LAIER J E. Operational modal analysis using SVD of power spectral density transmissibility matrices[J]. Mechanical Systems and Signal Processing,2014,46(1):129-145.
[15] 李星占,岳晓斌,黄文,等. 振动响应传递率及其工作模态分析方法综述[J]. 振动与冲击,2019,38(18):24-34,45. LI Xingzhan,YUE Xiaobin,HUANG Wen,et al. Vibration response transmissibility and operational modal analysis methods:A review and comparative study[J]. Journal of Vibration and Shock,2019,38(18):24-34,45.
[16] ARAUJO I G,LAIER J E. Operational modal analysis approach based on multivariable transmissibility with different transferring outputs[J]. Journal of Sound and Vibration,2015,351:90-105.
[17] KANG J. Operational modal analysis method by combining power spectral density transmissibility functions under different load cases[J]. Mechanical Systems and Signal Processing,2022,180:109433.
[18] ZHAO X,YE B. Selection of effective singular values using difference spectrum and its application to fault diagnosis of headstock[J]. Mechanical Systems and Signal Processing,2011,25(5):1617-1631.

多工况功率谱密度传递率矩阵运行模态分析方法

Operational Modal Analysis Method Based on Power Spectral Density Transmissibility Matrix under Multiple Load Cases

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