Model Updating for SMART Load Rating of Bridges

Model Updating for SMART Load Rating of Bridges

Chang-Guen Lee / Won-Tae LeeKorea Expressway Corporation

Jong-Jae Lee / Young-Soo Park

Sejong University, Korea

Smart Load Rating of Bridges Using Ambient Acceleration Data

Why Load Carrying Capacity?• Increase of the Number of Deteriorated Bridges• Prognosis of Remaining Lives• Widely Used as an Index for Bridge Integrity

Conventional Load Rating Test

Conventional loading tests

Controlled or Blocked Traffic

Measuring Deflection or Strain

Inconvenient & Increase of logistics cost A lot of time & cost for field tests

Load Carrying Capacity of a Bridge (MOCT, 2005, Korea)

Pr : Design live load : DB-24 (43.2tonf)*

RF : Rating factor by static analysis using the initial FE modelKd : the deflection correction factor - by static loading tests

Ki : the impact correction factor - by dynamic loading tests

Kr, Kt : the other correction factors - empirically estimated

*DB-24 : Korean design code for highway bridge about 1.3 times of HS-20, AASHTO

r r tP P RF K K δ iKK

Deteriorated bridges

SMART Load Rating

Correction of FE modelusing dynamic characteristics of

bridges

Conventional methodusing truck loading tests

Correction of analysis results using static deflection (strain) data

Advantages• No need to control or block traffics• Easier to measure acceleration rather than strain/deflection• High reliability by continuous measurements• Less time- and labor-consuming

Deflection Correction Factor (Kδ)

*Other Correction Factors – Empirically Estimated (usually 1.0)

initial FEManalysisproposedupdated FEManalysis

K

initial FEM

analysis

measured

K

Conventionalmodel

updating Proposed

Advantages

Procedures

3 6

T i m e3 6

T i m e3 6

T i m e

Updated FE model

Simulation of truck loading tests

Ambient vibration tests Model updating Load Rating

Modal parameter ID

Evaluation of Load Carrying CapacityModal Parameter Identification

Updating Initial FE Model

Estimation of Deflection Correction

Factor (Kδ)

Initial FE model

Measuring Ambient Acceleration

Modal Analysis

Planning of Vibration Tests

Updated FE modelAnalysis = Exp. ModesYesNo

Ambient acceleration data excited by ordinary traffic on a bridge without traffic control are measured. Based on the modal properties extracted from the ambient vibration data, the initial finite element (FE) model of the bridge can be updated to represent the current real state of a bridge. Using the updated FE model, the deflection akin to the real value can be easily obtained without measuring the real deflection. Based on the deflection values from initial and updated FE models, deflection correction factor can be obtained.

Procedure 1

Experimental modal analysis has drawn lots of attention from structural engineers for updating the analysis model and estimating the present state of structural integrity. Ambient vibration tests under wind, wave, or traffic loadings may be effective for large civil-infra structures. Several modal parameter identification methods without using input information in the frequency and the time domain are available, such as Frequency Domain Decomposition (FDD) and Stochastic Subspace Identification (SSI), etc.

0 20 40 60 80 1000

5

10

15

20

25

30

Frequency(Hz)

Mo

de

l o

rd

er

1st singular values

Stable mode

Unstable mode

Noise mode

SV functions in FDD

Stabilization Chart in SSI

Modal Parameter ID Using Ambient Vibration Tests

FE Model Updating

Using the extracted modal properties, the initial FE model is updated using various kinds of optimization algorithms. The objective function can be constructed using the differences between the measured and estimated natural frequencies, and the constraint equations were considered to limit the differences between the measured and estimated mode shapes as

2

1min | |

m c mNc mi i

i ji jimi i

f fJ w subjected to

f

Downhill Sim-plex

Genetic Algo-rithms

Procedure 2

Proof Tests

Yeoju JCT Test Road

25 PCC Test Sections2830m

15 AC Test Sections2710m

OfficeGeumdang

Br.Yeondae

Br.Samseung

Br.Yeoju JCT Test RoadTest Road





OfficeGeumdang

Br.Yeondae

Br.Samseung

Br.

Ordinary Expressway

Korea Expressway Corporation (KEX) Test Road

Geumdang Br. (PSCB) Yeondae Br. (STB)Samseung Br. (SPG)

The Korea Expressway (KEX) test road is a 2-lane one-way expressway built in parallel to Jungbu Inland Expressway in Korea. The total length of the test road is 7.7km, and there are three bridges along the test road. A series of conventional truck loading tests and ambient vibration tests were carried out to prove the proposed SMART Load Rating scheme.

Gamgok IC Yeoju JC

AbutmentAbutment

1 2 3

13121110

987

654

161514

LVDT

No. of accelerometers : 16EASampling Frequency : 200Hz

AccelerometerLDVT

Ambient Vibration Tests

FE Model of Samseung Br

Natural Frequencies and Mode shapes of initial FE model and measured ones (Lower 6 modes)

F1=4.01Hz(4.19)

F2=4.25Hz(4.83)

F3=12.80Hz(11.58)

F4=13.37Hz(12.90)

F5=17.24Hz(14.74)

F6=21.60Hz(18.37)

Modal Parameter ID

1 2 3 4 5 60

5

10

15

20

25

Fre

qu

en

cy (

Hz)

Mode

initial updated measured

Downhill Simplex Method (Nelder and Mead, 1964) was used.

Model Updating

S1 S2 S3 W1 W2 W30.0

0.5

1.0

1.5

2.0

2.5

Load Test AVT

Def. C

orrectio

n F

acto

r

Test Set

Kδ by the SMART Load Rating is

• in a reasonable range compared with Kδ by the conventional method

• more consistent in seasonal varia-tion (summer and winter)

Comparison of Deflection Correction Factors (Kδ)

Proof Test 1 : Samseung Br.

No. of accelerometers : 16EASampling Frequency : 200Hz

AccelerometerLDVT

Ambient Vibration Tests

Proof Test 2 : Geumdang Br.

Natural Frequencies and Mode shapes of initial FE model and measured ones (Lower 4 modes)

Modal Parameter ID

Downhill Simplex Method(Nelder and Mead, 1964)

Model Updating

Comparison of Deflection Correction Factors (Kδ)

Test Vehic le

Test Bridge

Adjacent Bridge

Test Vehic le

Test Bridge

Adjacent Bridge

1 1312111098765432

161514

Gamgok IC Yeoju JC

Pier

Abutment

Pier Pier

LVDT

F1=2.89Hz (2.99) F2=4.02Hz(4.47)

F3=4.69Hz(5.03) F4=7.61Hz(7.51)

1 2 3 4 5 60

2

4

6

8

10

Fre

qu

en

cy (

Hz)

Mode

initial updated measured

S1 S2 S3 S4 S5 W1 W2 W30.0

0.5

1.0

1.5

2.0

2.5

Load Test AVT

De

f. C

orr

ectio

n F

acto

r

Test Set

Geumdang Kδ

Conventional 1.11

SMART-LR 1.18

Palgok III Br.(1996) STB L=230m (40+3@50+40)

Dundae IV Br.(1996) STB L=310m (45+4@55+45)

Gahwacheon (1992) PSCB L=290m (60+120+60+50)

Yeondong Br.(1996) PSCB L=170m (35+50+50+35)

Measurement system installed at the inside of the steel box girder

Ambient Vibration TestsInside of the steel box girder

Sensor Installation along the sideway

Sensor Installation inside the box

Applications to Highway Bridges

FE model using Commer-cial S/W (SAP2k or MI-DAS)

Selection of updating variables

Ambient vib. tests Using smart sensors

Automated Modal Parameter ID

Model updat-ing

SMARTLoad Rating

Integrated GUI

Integrated GUI-based SMART Load Rating System

Integrated GUI-based SMART Load Rating

Field Test on NJ Bridge SB-Span2

Frame 1448

Shell 1401

FE Model


Test Equipments

Accelerometer

( Model 393B12

(PCB) )

Product Type: Accelerometer, Vibration Sensor

Seismic, high sensitivity, ceramic shear ICP® accel., 10

V/g, 0.15 to 1k Hz, 2-pin top conn.

http://www.pcb.com/spec_sheet.asp?

model=393B12&item_id=9370

Signal Conditioner

(Model 481A03

(PCB))

Signal Conditioner, Modular Signal Conditioner

16-channel, line-powered, ICP® sensor signal cond.


model=481A&item_id=

DAQ Card

(DAQCard-6036E

(NI))

16-Bit, 200 kS/s E Series Multifunction DAQ for PCMCIA


model=393B12&item_id=9370

MUX

(Terminal Block)

(BNC-2090 (NI))

Rack-Mounted BNC Terminal Block

22 BNC connectors for analog, digital, and timing signals

28 spring terminals for digital/timing signals

http://sine.ni.com/nips/cds/print/p/lang/en/nid/1177

Field Test on NJ Bridge

Test set #1

Test set #2

Vertical Lateral



0 5 10 15 2010

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Frequency

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plitu

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Test1. Sensor No. 11

0 5 10 15 2010

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Test1. Sensor No. 9

0 5 10 15 2010

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Test1. Sensor No. 6

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plitu

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Test1. Sensor No. 1

0 2000 4000 6000 8000 10000-0.2

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time

accele

ration

Test1. Sensor No. 11

0 2000 4000 6000 8000 10000-0.4

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accele

ration

Test1. Sensor No. 9

0 2000 4000 6000 8000 10000-0.4

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time

accele

ration

Test1. Sensor No. 6

0 2000 4000 6000 8000 10000-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

time

accele

ration

Test1. Sensor No. 1


0 5 10 150

20

40

60

80

100Stabilization Chart

`

0 5 10 1510

-6

10-4

10-2

100

Frequency (Hz)

Sin

gula

r V

alu

e

Result for Singluar Value Decomposition

0 5 10 150

20

40

60

80

100Stabilization Chart

0 5 10 1510

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Frequency (Hz)

Sin

gula

r V

alu

e

Result for Singluar Value Decomposition

Test set #1 Test set #2


1 - 2 - 3 4 5 6

FEA (initial) 2.615 X 3.70 X 6.15 10.59 7.66 12.13

Test 1

SSI 2.705 3.176 3.383 4.365 5.144 7.851 8.986 11.423

FDD 2.722 3.137 3.5774.211

5.139 7.825 8.972 11.426

Test 2SSI 2.767 3.14 3.321 4.353 5.165 7,647 8.856 11.41

6

FDD 2.734 3.113 3.54 X 5.114 7.703 8.862 11.377

Natural Frequencies [Hz]

Avg. 2.72 X 3.55 X 5.14 7.75 8.92 (11.4)

frequency : f=2.7049 Hz






Mode FE Model Test 1 Test 2

1

2

3


2.615

3.70

6.15

2.72

3.55

5.14

Comparison of identified modal properties

Mode FE Model Test 1 Test 2

4

5

6








10.59

7.66

12.13

7.75

8.92

11.4

Comparison of identified modal properties


Slab

Initial model

Decrease

10% 30% 50%

1 2.615 2.59 2.53 2.46

2 3.699 3.64 3.52 3.36

3 6.15 6.09 5.96 5.79

5 7.662 7.61 7.49 7.31

4 10.59 10.47 10.21 9.91

6 11.12 11.03 10.82 10.51

Cross beam

Initial model

Decrease

10% 30% 50%

1 2.615 2.610 2.596 2.576

2 3.699 3.691 3.670 3.642

3 6.15 6.038 5.794 5.531

5 7.662 7.602 7.326 6.641

4 10.59 10.291 9.641 8.923

6 11.12 11.100 11.041 10.960

Girder - web

Initial model

Decrease

10% 30% 50%

1 2.615 2.594 2.543 2.473

2 3.699 3.668 3.589 3.475

3 6.15 6.106 5.988 5.824

5 7.662 7.570 7.337 6.997

4 10.59 10.536 10.327 10.067

6 11.12 10.972 10.588 10.373

Spring at support (longitudinal dir.) ( ton – m )

Initial model

Increase

10000 5000010000

0

1 2.615 2.843 3.106 3.213

2 3.699 3.971 4.386 4.577

3 6.15 6.188 6.249 6.284

5 7.662 7.952 8.220 8.316

4 10.59 10.601 10.605 10.611

6 11.12 11.941 12.079 12.087

Sensitivity of Updating Variables


Initial Measured Updated

2.615 2.72 2.716

3.699 3.52 3.570

6.154 5.14 5.178

10.592 7.75 8.085

7.663 8.92 7.93

11.127 11.14 11.0

Parmeter Initial Updated

Slab Stiffness 1 0.523

Cross Beam Stiffness

1 0.505

Spring at Sup-port(Ux)

1 12147ton/m

Web Stiffness 1 1.19

Design Variables


Conclusions and Future Works

1. Application of Smart Load Rating Procedures

2. Modal parameter ID of the test bridge

3. Selection of Design Variables in Model Updating

4. Low lateral modes (butterfly modes) of the test bridge bad condition in concrete slab and cross beam require more detail investigations on FE model & test data

5. Verification of the updated FE model Truck loading tests

6. Effects of considered modes / design variables


2 2.5 3 3.5 410

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Freq. [Hz]

PS

D o

f Acc

el.

Ch.1

s1s2s3s4

2 2.5 3 3.5 410

-5

10-4

10-3

10-2

10-1

Freq. [Hz]

PS

D o

f Acc

el.

Ch.2

s1s2s3s4

2 2.5 3 3.5 410

-5

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Freq. [Hz]

PS

D o

f Acc

el.

Ch.3

s1s2s3s4

2 2.5 3 3.5 410

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10-5

10-4

10-3

10-2

10-1

Freq. [Hz]

PS

D o

f Acc

el.

Ch.4

s1s2s3s4

Variation of Natural frequencies


2 4 6 8 10 12 1410

-6

10-5

10-4

10-3

10-2

10-1

Freq. [Hz]

PS

D o

f Acc

el.

Vertical vs Lateral

Vertical - Ch.2Vertical - Ch.3Lateral at Ch.2

Lateral Motion


0 0.5 1 1.5-4

-2

0

2

4

6

8

10

Time (sec)

Ou

tpu

t (V

)

271.5 272 272.5 273 273.5 274-3

-2

-1

0

1

2

3

Time (sec)

Ou

tpu

t (V

)

0 50 100 150 200 250 300-5

0

5

10

Time (sec)

Ou

tpu

t (V

)

DAQ System Check-up : Inner Clock


1 - 2 - 3 4 5 6

FEA (initial) 2.615 X 3.70 X 6.15 10.59 7.66 12.13

Test 1

SSI 2.705 3.176 3.383 4.365 5.144 7.851 8.986 11.423

FDD 2.722 3.137 3.5774.211

5.139 7.825 8.972 11.426

Natural Frequencies [Hz]



Model Updating for SMART Load Rating of Bridges

Documents

real deflection

initial fe modelkd

rating factor

updated fe models

analysis model

deflection akin

deflection values

ambient vibration data