基于振型相关性的结构模态参数频域自动识别*
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（1 北京工业大学空间结构研究中心，北京 100124； 2 北京工业大学城市与工程安全减灾省部共建教育部重点实验室，北京 100124）［摘要］环境激励下，频域分解法(FDD)具有良好的结构模态频率和振型识别能力，但识别过程中需要基于频率准则人为判断奇异值曲线的峰值，无法准确识别出现近频交叠或重频情况的结构模态参数，而且不能自动进行模态参数的识别。对此，提出了基于振型相关性的MAC-FDD模态参数识别方法，该方法能自动搜索目标模态所对应的频率范围，并利用反映实测振型与理论振型良好相关性的最大模态置信准则（MAC) 值判断和识别结构真实振型。给出了该方法的具体实现过程，对平面桁架和空间网架算例进行了模态参数识别。结果表明，该方法能够准确识别出各阶模态频率和振型，可以有效避免模态遗漏，且具有很强的抗噪能力。该方法弥补了常规FDD的不足，适用于对频率密集或具有重频现象的空间网格结构的模态参数识别，且其过程便于编程实现。［关键词］模态参数; 频域分解法; 振型相关性; 自动识别; 网格结构中图分类号：TU393.3 文献标识码：A 文章编号：1002-848X(2015)05-0039-05An automated frequency domain modal identification method based on modal assurance criterionXu Qize1, Wu Jinzhi1,2, Zhang Yigang1,2（1 Space Structures Research Center, Beijing University of Technology, Beijing 100124, China; 2 Key Lab of Urban Security and Disaster Engineering, MOE, Beijing University of Technology， Beijing 100124, China）Abstract: Frequency domain decomposition (FDD) is known as one of the most powerful techniques for mode shape and frequency identification of structures subject to ambient excitation. However, the classical implementation of the technique requires user interaction by picking peaks as frequencies in singular vectors, thus it can not differentiate closely spaced or repeated modal parameter and carry out modal parameter identification automatically. An automated modal parameter identification procedure was proposed, namely MAC-FDD, which could be carried out automatically to search the target frequency range without any user interaction. And with the maximum modal assurance criterion (MAC) which could reflect the good correlation between measured and theoretic vibration modes, the real structure vibration modes were judged and identified. The implementation of the procedure and its application to two numerical examples, a planar truss and a spatial grid, were presented. The results indicate that MAC-FDD is capable to extract accurate mode shapes and frequencies without mode absence, showing great anti-noise capability. This friendly MAC-FDD method can be applied to modal parameter identification of spatial grid structures with closely spaced or repeated frequencies and can be easily implemented in programming to cover the shortage of the classical FDD.Keywords: modal parameter; frequency domain decomposition (FDD); modal correlation; automated identification; grid structure*国家自然科学基金项目(51278009)。通讯作者：吴金志，博士，副教授，Email：kongjian@bjut.edu.cn。参考文献［1］傅志方，华宏星. 模态分析理论与应用［M］. 上海：上海交通大学出版社，2000.［2］ZHANG L M, BRINCKER R, ANDERSEN P. An overview of operational modal analysis: major development and issues［C］//Proceedings 1st IOMAC. Copenhagen, Denmark, 2005.［3］续秀忠，华宏星，陈兆能. 基于环境激励的模态数辨识方法综述［J］. 振动与冲击，2002，21(3)：1-5.［4］沈方伟，杜成斌. 环境激励下结构模态参数识别方法综述［J］. 电子测试，2013 (5)：178-181.［5］BRINCKER R, ZHANG L M, ANDERSEN P. Modal identification from ambient response using frequency domain decomposition［C］//Proceedings of the 18th IMAC. San Antonio, Texas, USA, 2000:625-630.［6］BRINCKER R, ZHANG L M, ANDERSEN P. Modal identification of output only systems using frequency domain decomposition［J］. Smart Materials and Structures, 2001, 10 (3)： 441-445.［7］TARINEJAD R, DAMADIPOUR M. Modal identification of structures by a novel approach based on FDD-wavelet method［J］. Journal of Sound and Vibration, 2014,333（3）：1024-1045.［8］ZHANG L M, WANG T, YUKIO TAMURA. A frequency-spatial domain decomposition (FSDD) method for operational modal analysis［J］. Mechanical Systems and Signal Processing, 2010, 24(5)：1227-1239.［9］高维成，于岩磊，刘伟. 在役钢结构游泳馆的结构安全性检测研究［J］. 建筑结构学报，2009，30(4)：38-46.［10］王卓，闫维明，叶列平. 网壳结构运行模态分析的模型试验［J］. 清华大学学报:自然科学版，2011，51(6)：755-759.［11］BRINCKER R, ANDERSEN P, JACOBSEN N J. Automated frequency domain decomposition for operational modal analysis［C］//Proceedings of the 25th IMAC. Orlando, Florida, USA, 2007.［12］ALLEMANG R J. The modal assurance criterion-twenty years of use and abuse［J］. Sound and Vibration, 2003, 37(8): 14-23.［13］KAMMER D C. Sensor placement for on-orbit modal identification and correlation of large space structures［J］. Journal of Guidance, Control, and Dynamics, 1991,14 (2): 251-259.
