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Frontiers of Structural and Civil Engineering

Front Arch Civil Eng Chin    2011, Vol. 5 Issue (3) : 344-354     https://doi.org/10.1007/s11709-011-0124-8
RESEARCH ARTICLE |
Ambient vibration testing and updating of the finite element model of a simply supported beam bridge
Ivan Gomez ARAUJO(), Esperanza MALDONADO, Gustavo Chio CHO
School of Civil Engineering, Research Group INME, Industrial University of Santander, Santander, Colombia
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Abstract

An ambient vibration test on a concrete bridge constructed in 1971 and calibration of its finite element model are presented. The bridge is characterized by a system of post-tensioned and simply supported beams. The dynamic characteristics of the bridge, i.e. natural frequencies, mode shapes and damping ratios were computed from the ambient vibration tests by using the Eigensystem Realization Algorithm (ERA). Then, these characteristics were used to update the finite element model of the bridge by formulating an optimization problem and then using Genetic Algorithms (GA) to solve it. From the results of the ambient vibration test of this type of bridge, it is concluded that two-dimensional mode shapes exist: in the longitudinal and transverse; and these experimentally obtained dynamic characteristics were also achieved in the analytical model through updating. The application of GAs as optimization techniques showed great versatility to optimize any number and type of variables in the model.

Keywords modal analysis      parameter identification      ambient vibration test      Eigensystem Realization Algorithm (ERA) method      finite element method     
Corresponding Authors: Gomez ARAUJO Ivan,Email:igomez19@hotmail.com   
Issue Date: 05 September 2011
 Cite this article:   
Ivan Gomez ARAUJO,Esperanza MALDONADO,Gustavo Chio CHO. Ambient vibration testing and updating of the finite element model of a simply supported beam bridge[J]. Front Arch Civil Eng Chin, 2011, 5(3): 344-354.
 URL:  
http://journal.hep.com.cn/fsce/EN/10.1007/s11709-011-0124-8
http://journal.hep.com.cn/fsce/EN/Y2011/V5/I3/344
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Ivan Gomez ARAUJO
Esperanza MALDONADO
Gustavo Chio CHO
Fig.1  Superstructure cross section of the viaduct Garcia Cadena
Fig.2  Longitudinal section of the viaduct Garcia Cadena
Fig.3  Detailed plan of the viaduct Garcia Cadena
Fig.4  Vibration modes of the preliminary analytical model for B7 span without piers. (a) Mode 1; (b) mode 2; (c) mode 3; (d) mode 4
Fig.5  Setups of sensors
Fig.6  Correlation functions for setup 1 on the west side, span B7
Fig.7  Singular value diagram for setup 1, west side, span B7
symbolpairs of complex conjugate poles0<ξ<20%stable poles Δf relative<5%stable poles Δξ relative<5%stable poles with a MAC>0.9
-----
yes----
yesyesyes--
yesyesyesyes-
yesyesyes-yes
yesyesyesyesyes
Tab.1  Meaning of symbols used in the stabilizations diagrams
Fig.14  Stability diagram, ERA method, setup 1, west side, span B7
Fig.15  Stability diagram, ERA method, setup 1, central, span B7
Fig.16  Stability diagram, ERA method, setup 1, east side, span B7
Fig.17  Flowchart of the calibration process of the structure
modesfrequency identified/Hzdamping/%
13.484.95
24.256.01
34.933.84
47.263.30
511.422.84
612.211.75
713.472.52
814.391.55
914.941.85
1015.943.59
Tab.2  Frequencies and damping rates identified by the ERA method
frequencies/Hzeast sidecentralwest side
3.48
4.25
4.93
7.26
11.42
12.21
Tab.3  Vertical vibration modes identified, ERA method
Operatortypeparametervalue
selectionroulettepopulation size100
crossovertwo pointscrossover rate0.85
mutationjumpmutation rate0.005
otherselitismmaximum number of generations150
Tab.4  Operators and GA parameters used
run AGmain bean/(N·m-2)expansion beam/(N·m-2)slab/(N·m-2)brace beam/(N·m-2)
114.7736.2055.410.25
214.8335.9551.510.34
316.1832.0650.230.77
Tab.5  Modules of elasticity calibrated by the GA
modesfrequenc of FEM calibrated/Hzfrequenc identified (ERA method)/Hzerror/%
13.123.4810.26
24.014.133.08
35.054.834.64
47.477.193.87
511.5411.430.95
612.5012.192.58
713.1913.130.42
8-14.58-
916.22--
Tab.6  Comparison of frequencies of the calibrated finite element model and experimentally identified
Fig.30  Mode shapes of the calibrated finite element model. (a) = 3.12 Hz; (b) = 4.01 Hz; (c) = 5.05 Hz; (d) = 7.47 Hz; (e) = 11.54 Hz; (f) = 12.50 Hz; (g) = 13.19 Hz; (h) = 16.22 Hz
Fig.31  Fitness evolution of the best individual in the GA in the calibration. The best error is 0.3388
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