Modal Parameters Identification - WordPress.com

Modal Parameters IdentificationSteel Frame Bridge & Building

Zhongyuan Wo

Student Intern

August 26, 2016

1

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

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

3

ERA

4

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.

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

5

MARC Bridge*

Hammer Excitation

6

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

Spring Supports

7

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

Data process

8

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

Frequencies

9

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

1

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

10

0 2 4 6 8 10 120

50

100

150

200

250

Frequency (Hz)

Num

ber

of

pole

s

Stabilization Diagram

Mode shapes

11

SAP2000 mode shapes

ERA mode shapes

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

Steel Frame Building*

13

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

Steel Frame Building*

14

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

FE model

15

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

Measurements

16

At X1 & X2 on each story

Acceleration acquisition

Sensor points

Experimental data

Acceleration of X1 X2

In loading direction

X1

X2

Loading

Time history

17

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

Frequencies

18

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

Mode shapes

19

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

Animation

20

Mode 1: f = 0.92Hz Mode 2: f = 2.70Hz Mode 3: f = 4.57Hz Mode 4: f = 6.53Hz

SAP2000

ERA