Uncertainty quantification in operational modal analysis of bridge structure
QIN Shi-qiang1, GOU Hong-ye2, JIA Hong-yu3, PU Qian-hui2
1. Hubei Key Laboratory of Roadway Bridge and Structure Engineering, Wuhan University of Technology, Wuhan 400370;
2. School of civil engineering, Southwest Jiaotong University, Chengdu, 610031,
3. Department of civil engineering, Southwest Jiaotong University, Emei, 614202
Abstract：In order to quantify the uncertainty for operational modal analysis (OMA), two methods were employed to estimate the uncertainty of natural frequencies and damping ratios by using Stochastic Subspace Identification (SSI) as an example. Firstly, mathematical expectation and standard deviation of modal parameters identified from different setups were used to measure its overall size and dispersion, and the overall confidence intervals of modal parameters were constructed. Secondly, a method to quantify the uncertainty of modal parameters obtained from a single setup through matrix sensitive analysis was introduced, and the stabilization diagram with confidence intervals is established. The ambient vibration test of the arch rib of Caiyuanba Yangtze River Bridge was taken as an example. The study shows that the overall confidence intervals is a supplement to the existing single mode to assessing modal parameters. The stabilization diagram with confidence intervals can help testers to distinguish the spurious modes from system modes. Two methods introduced can measure the uncertainty of the modal parameters from overall and local viewpoint, respectively, which provide a basis to assess the credibility of the estimated modal parameters from OMA.
[1] PEETERS．B，VENTRURA．C E．Comparative study of modal analysis techniques for bridge dynamic characteristics [J]．Mechanical System and Signal Processing，2003，17(5)：965-988．
[2] 单德山，徐敏．数据驱动随机子空间算法的桥梁运营模态分析[J]. 桥梁建设，2011，06:16-21.
ShAN De-shan, XU Min. Operational modal analysis of bridge structure based on data-driven stochastic subspace identification algorithm [J]. Bridge Construction, 2011, 06:16-21.
[3] CHEN．W，LU．Z，LIN．W，et al．Theoretical and experimental modal analysis of Guangzhou New TV Tower [J]．Engineering Structures，2011，33(12)：3628-3646．
[4] MAGALHAES．F，CUNHA．A．Explaining operational modal analysis with data from an arch bridge [J]． Mechanical Systems and Signal Processing，2011，25(5)：1431-1450．
[5] LARDIES．J，MINHNGI．T．Modal parameter identification of stay cables from output-only measurements [J]．Mechanical Systems and Signal Processing，2011，25(1)：133-150．
[6] REN．W，PENG．X，LIN．Y．Experimental and analytical studies on dynamic characteristics of a large span cable-stayed bridge [J]．Engineering Structures，2005，27 (4)：535–548．
[7] 续秀忠，华宏星，陈兆能．基于环境激励的模态参数辨识综述[J]．振动与冲击，2002，21(3)：1-5．
XU Xiu-zhong，HUA Hong-xing，CHEN Zhao-neng．Review of modal parameter identification method based on ambient excitation [J]．Journal of Vibration and Shock，2002，21(3)：1-5．
[8] 秦世强，蒲黔辉，施洲．环境激励下大型桥梁模态参数识别的一种方法[J]．振动与冲击，2012，31(2)：95-100．
QIN Shi-qiang，PU Qian-hui，SHI Zhou．A method of modal parameters identification using ambient vibration measurements for a large-scale bridge [J]．Journal of Vibration and Shock，2012，31(2)：95-100．
[9] 宗周红，BIJAYA．J，林友勤，等．西宁北川河钢管混凝土拱桥的理论和实验模态分析[J]．铁道学报，2003，25(4)：89-96．
ZONG Zhou-hong，BIJAYA．J，LIN You-qin，et al．Experimental and analytical modal analysis of a CFT arch bridge over Xining Beichuan River [J]．Journal of the China Railway Society， 2003，25(4)：89-96．
[10] MEVEL．L，GOURSAT．M，BASSEVILLE．M．Stochastic subspace-based structural identification and damage detection and localisation--application to the Z24 bridge benchmark [J]． Mechanical Systems and Signal Processing，2003，17(1)：143-151．
[11] 徐良，江见鲸，过静珺． 随机子空间识别在悬索桥实验模态分析中的应用[J]．工程力学，2002，19(4)：46-49．
XU liang，JIANG Jian-jing，GUO jingjun． Application of stochastic subspace method to experimental modal analysis of suspension bridge， 2002，19(4)：46-49．
[12] BROWNJOHN．B，MAGALHAES．F，CAETANO．E，et al． Ambient vibration re-testing and operational modal analysis of the Humber Bridge [J]．Engineering Structures，2010，32(8)：2003-2018．
[13] Andersen P. Estimation of modal parameters and their uncertainties[R]. Dept. of Building Technology and Structural Engineering, Aalborg University, 1998.
[14] Sim J, Qiu Z, Wang X. Modal analysis of structures with uncertain-but-bounded parameters via interval analysis[J]. Journal of Sound and Vibration. 2007, 303(1–2): 29-45.
[15] REYNDERS．E，DEROECK．G．Uncertainty bounds on modal parameters obtained from stochastic subspace identification [J]．Mechanical Systems and Signal Processing，2008，22(4)：948-946.
[16] Pintelon R, Guillaume P, Schoukens J. Uncertainty calculation in (operational) modal analysis[J]. MECHANICAL SYSTEMS AND SIGNAL PROCESSING. 2007, 21(6): 2359-2373.
[17] Carden E P, Mita A. Challenges in developing confidence intervals on modal parameters estimated for large civil infrastructure with stochastic subspace identification[J]. Structural Control and Health Monitoring. 2011, 18(1): 53-78.
[18] VAN OVERSCHEE P，DE MOOR B．Subspace Identification for Linear Systems：Theory Implementation Applications [M]．Dordrecht，The Netherlands：Kluwer Academic Publishers，1996：57-91．
[19] PEETERS．B，DEROECK．G．Reference-based stochastic subspace identification for out-put only modal analysis [J]．Mechanical Systems and Signal Processing，1999，13(6)：855-878．
