Modal Parameters Identification - WordPress.com
Transcript of Modal Parameters Identification - WordPress.com
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Modal Parameters IdentificationSteel Frame Bridge & Building
Zhongyuan Wo
Student Intern
August 26, 2016
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Outlines
The Eigensystem Realization Algorithm
Steel Frame Bridge
o FE model in SAP2000 & simulated data
o Comparison of modal parameters
Steel Frame Building*
o Real Experiment Plan
o Modal parameters identification
2* Project from Nakashima & Kurata Laboratory
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ERA & DIAMOND
ERA
o The Eigensystem Realization Algorithm (Juang & Pappa, 1985)
o Generating system realization using time-domain data
o Widely used as a modal analysis technique
DIAMOND
o An embedded MATLAB toolbox, (Doebling, Farrar, & Cornwell, 1997)
o Damage Identification, Model Update
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ERA
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Core code: MATLAB
DIAMOND*
* [1] S. W. Doebling, C. R. Farrar, and P. J. Cornwell, "DIAMOND: A graphical interface toolbox for comparative modal analysis and damage identification," in Proceedings of the 6th International Conference on Recent Advances in Structural Dynamics, Southampton, UK, 1997, pp. 399-412.
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Outlines
The Eigensystem Realization Algorithm
Steel Frame Bridge
o FE model in SAP2000 & simulated data
o Comparison of modal parameters
Steel Frame Building*
o Real Experiment Plan
o Modal parameters identification
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MARC Bridge*
Hammer Excitation
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Steel Frame Bridge
o FE model in SAP2000
o Hammer Impact
Simulated Data
o Sampling frequency: 5000Hz
o Total time: 4s
o DOFs: 463
* It’s called MARC bridge since it connected with the MARC building in Georgia Tech campus
0 0.002 0.004 0.006 0.008 0.01 0.012-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Time (s)
Forc
e (
kip
)
Hammer Excitation
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Spring Supports
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k0 = 8000 kip/in
k1 = 4000 kip/in
k2 = 400 kip/in
k3 = 4000 kip/in
k4 = 400 kip/in
Damping ratio 2%*
Rigid to Spring k1
k0 k2
k2
k4
* 1st & 3rd modal damping ratio in SAP2000 were set to 2%, using Rayleigh Damping
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Data process
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Hammer Excitation
Acc Data
Impulse Response
Filter
Butterworth Lowpass
Remove over 200Hz
Order=8
Down Sample
20000 points5000Hz, 4s
2000 points
500Hz, 4sFrequency Response
FFTDiamond
Compare Frequency & Mode Shape from Diamond & SAP2000 End
q=120,d=240Poles=80
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Frequencies
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Rigid FEM Spring FEM ERA Experiment*
1 4.92 4.07 4.07 4.07
2 5.42 4.53 4.53 4.64
3 7.36 6.73 6.73 6.65
4 10.45 8.75 8.75 8.77
5 11.89 10.70 10.70 10.94
Table 1. Comparison of the first 5 frequencies (Unit: Hz)
Modal frequencies 1-5
* D. Zhu, J. Guo, C. Cho, Y. Wang, and K.-M. Lee, "Wireless mobile sensor network for the system identification of a space frame bridge," Ieee/Asme Transactions On Mechatronics, vol. 17, pp. 499-507, 2012.
0 50 100 150 200 250 300 350 400 450 5000
5
10
15
Frequency (Hz)
FR
F
Frequency Response of Accy at point 61
Point 61Right end
4 5 6 7 8 9 10
2
4
6
8
10
12
14
X: 4
Y: 6.226
Frequency (Hz)
FR
F
X: 4.5
Y: 5.112
X: 6.75
Y: 14.28
X: 8.75
Y: 8.483
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23
4
5
1
2
3
4
5
0
0.2
0.4
0.6
0.8
1
Mode NumberMode Number
AU
TO
MA
CStabilization Diagram
Stabilization diagram
MAC Value
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0 2 4 6 8 10 120
50
100
150
200
250
Frequency (Hz)
Num
ber
of
pole
s
Stabilization Diagram
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Mode shapes
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SAP2000 mode shapes
ERA mode shapes
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Outlines
The Eigensystem Realization Algorithm
Steel Frame Bridge
o FE model in SAP2000 & simulated data
o Comparison of modal parameters
Steel Frame Building*
o Real Experiment Plan
o Modal parameters identification
12* Project from Nakashima & Kurata Laboratory
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Steel Frame Building*
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A Japanese steel frame building
Size
o Height: 76m 18 stories
o Dimension: 18m in loading direction
15m in orthogonal
Shake table test
o Scaled model: 1/3
* Project from Nakashima & Kurata Laboratory
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Steel Frame Building*
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A Japanese steel frame building
Size
o Height: 76m 18 stories
o Dimension: 18m in loading direction
15m in orthogonal
Shake table test
o Scaled model: 1/3
* Project from Nakashima & Kurata Laboratory
Loading direction
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FE model
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Built in SAP2000
Modeling without slab
o Slab stiffness Beam stiffness
o Discard slabs
Results
o Frequencies
o Mode shapes
(a). Beam with slab
(b). Beam without slab
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Measurements
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At X1 & X2 on each story
Acceleration acquisition
Sensor points
Experimental data
Acceleration of X1 X2
In loading direction
X1
X2
Loading
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Time history
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0 50 100 150 200 250
-100
-80
-60
-40
-20
0
20
40
60
80
100
Time (s)
Accele
ration (
cm
/s2)
Shake Table Accleration
0 50 100 150 200 250
-200
-150
-100
-50
0
50
100
150
200
Time (s)
Accele
ration (
cm
/s2)
Accleration of Story 12
(a). Shake Table Acceleration (b). Example acceleration of Story 12
Total time: 277t s
Sampling frequency: 200sf Hz
Story 12
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Frequencies
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Extra modes derived from our model
Japanese Simulation
ERA* FE model
1 0.87Hz 0.85Hz 0.92Hz
2 2.63Hz 2.69Hz 2.70Hz
3 7.14Hz 4.85Hz 4.57Hz
4 \ 7.10Hz 6.55Hz
*Experimental data to execute ERA is provided in .xlsx file provided by Japanese
Table 2. Comparison of the first 4 frequencies in the loading direction
An extra frequency in the loading direction
The 3rd frequency 7.14Hzshould be the 4th frequency in reality
Comparison of mode shape confirms our claim
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Mode shapes
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0
2
4
6
8
10
12
14
16
18
-1.5 -1 -0.5 0 0.5 1 1.5
1st 2nd 3rd 4th
Figure. Comparison of mode shapes in the loading direction
The 4th mode shape
(a). Japanese Results, first 3 mode shapes (b). ERA Results, first 4 mode shapes
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Animation
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Mode 1: f = 0.92Hz Mode 2: f = 2.70Hz Mode 3: f = 4.57Hz Mode 4: f = 6.53Hz
SAP2000
ERA