Model Updating for SMART Load Rating of Bridges
Chang-Guen Lee / Won-Tae Lee
Korea 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
Deteriorated bridges
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)
P  Pr  RF  Kδ  Ki  Kr  Kt
Pr
: Design live load : DB-24 (43.2tonf)*
RF : Rating factor by static analysis using the initial FE model
Kd : 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
Advantages
Conventional method
using truck loading tests
Correction of analysis results using
static deflection (strain) data
SMART Load Rating
Correction of FE model
using dynamic characteristics of
bridges
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)
initial FEM
d analysis
Kd 
d measured
Conventional
proposed
Kd
model
updating
initial FEM
d analysis

updated FEM
d analysis
Proposed
*Other Correction Factors – Empirically Estimated (usually 1.0)
Procedure 1
Procedures
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.
Ambient vibration tests
Load Rating
Model updating
Updated FE model
Simulation of truck loading tests
3
6
T im e
Modal parameter ID
Modal Analysis
Initial FE model
Planning of Vibration Tests
Measuring Ambient Acceleration
Estimation of
Deflection Correction
Factor (Kδ)
Modal Parameter Identification
Updating Initial FE Model
No
Analysis = Exp. Modes
Yes
Updated FE model
Evaluation of Load
Carrying Capacity
Procedure 2
Modal Parameter ID Using Ambient
Vibration Tests
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.
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
  fi c  fi m  
min J    wi 

m
i 1 
 fi

Nm
2
subjected to
|  jic   jim | 
Downhill Simplex
SV functions in FDD
30
Model order
25
Unstable mode
20
Noise mode
15
10
1st singular values
5
0
0
Stable mode
20
40
60
Frequency(Hz)
80
Stabilization Chart in SSI
100
Genetic
Algorithms
Proof Tests
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.
Korea Expressway Corporation (KEX) Test Road
Ordinary Expressway
Yeoju JCT
Geumdang
Br.
Office
25 PCC Test Sections
2830m
Samseung Br. (SPG)
Yeondae Samseung Test Road
Br.
Br.
15 AC Test Sections
2710m
Geumdang Br. (PSCB)
Yeondae Br. (STB)
Proof Test 1 : Samseung Br.
Ambient Vibration Tests
FE Model of Samseung Br
Abutment
Abutment
1
2
3
Gamgok IC
4
5
Yeoju JC
LVDT
7
10
11
8
12
13
No. of accelerometers : 16EA
Sampling Frequency : 200Hz
9
14
Accelerometer
LDVT
6
15
16
Model Updating
Modal Parameter ID
25
Natural Frequencies and Mode shapes of initial FE model and
measured ones (Lower 6 modes)
F2=4.25Hz
(4.83)
F3=12.80Hz
(11.58)
Frequency (Hz)
F1=4.01Hz
(4.19)
initial
updated
measured
20
15
10
5
0
1
2
3
4
5
6
Mode
F4=13.37Hz
(12.90)
F5=17.24Hz
(14.74)
F6=21.60Hz
(18.37)
Comparison of Deflection Correction Factors (Kδ)
2.5
Load Test
AVT
Def. Correction Factor
2.0
1.5
Downhill Simplex Method
(Nelder and Mead, 1964) was used.
Kδ by the SMART Load Rating is
• in a reasonable range compared with Kδ
by the conventional method
• more consistent in seasonal variation
(summer and winter)
1.0
0.5
0.0
S1
S2
S3
W1
Test Set
W2
W3
Proof Test 2 : Geumdang Br.
Test Vehicle
Adjacent Bridge
Ambient Vibration Tests
1
2
Test Bridge
3 4 5 6 7 8 9 10 11 12
13
Gamgok IC
Abutment
Accelerometer
LDVT
Yeoju JC
LVDT
14
Pier
15
Pier
No. of accelerometers : 16EA
Sampling Frequency : 200Hz
16
Pier
Modal Parameter ID
Natural Frequencies and Mode shapes of initial FE model
and measured ones (Lower 4 modes)
Model Updating
10
8
Frequency (Hz)
F1=2.89Hz (2.99)
F2=4.02Hz(4.47)
initial
updated
measured
6
4
2
0
1
2
3
4
5
Mode
F3=4.69Hz(5.03)
Downhill Simplex Method
(Nelder and Mead, 1964)
F4=7.61Hz(7.51)
Comparison of Deflection Correction Factors (Kδ)
2.5
Load Test
AVT
Def. Correction Factor
2.0
Geumdang
Kδ
Conventional
1.11
SMART-LR
1.18
1.5
1.0
0.5
0.0
S1
S2
S3
S4
S5
Test Set
W1
W2
W3
6
Applications to Highway Bridges
Palgok III Br.(1996)
STB
L=230m
(40+3@50+40)
Dundae IV Br.(1996)
STB
L=310m
(45+4@55+45)
Measurement system installed at the inside of
the steel box girder
Ambient Vibration Tests
Inside of the steel box girder
Gahwacheon (1992)
PSCB
L=290m
(60+120+60+50)
Sensor Installation along the sideway
Yeondong Br.(1996)
PSCB
L=170m
(35+50+50+35)
Sensor Installation inside the box
Integrated GUI-based SMART Load Rating
Integrated GUI
Ambient vib. tests Using smart
sensors
Automated
Modal Parameter ID
Model updating
FE model using Commercial
S/W (SAP2k or MIDAS)
SMART
Load Rating
Selection of updating variables
Integrated GUI-based SMART Load Rating System
Field Test on NJ Bridge
SB-Span2
FE Model
Frame 1448
Shell 1401
Field Test on NJ Bridge
SB-Span2
Field Test on NJ Bridge
Test Equipments
Product Type: Accelerometer, Vibration Sensor
Accelerometer
Seismic, high sensitivity, ceramic shear ICP® accel., 10 V/g, 0.15 to
( Model 393B12 (PCB) )
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.
http://www.pcb.com/spec_sheet.asp?model=481A&item_id=
DAQ Card
16-Bit, 200 kS/s E Series Multifunction DAQ for PCMCIA
(DAQCard-6036E (NI))
http://www.pcb.com/spec_sheet.asp?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
SB-Span2
Test set #1
Lateral
Vertical
Test set #2
Field Test on NJ Bridge
SB-Span2
Test1. Sensor No. 1
Test1. Sensor No. 1
-2
0.15
10
0.1
Amplitude
acceleration
-4
10
0.05
0
-0.05
-0.1
-6
10
-8
10
-0.15
-0.2
0
-10
2000
4000
6000
8000
10
10000
time
Test1. Sensor No. 6
0
5
10
Frequency
15
20
Test1. Sensor No. 6
-2
10
0.4
-4
10
Amplitude
acceleration
0.2
0
-6
10
-8
10
-0.2
-10
-0.4
0
10
2000
4000
6000
8000
10000
time
Test1. Sensor No. 9
5
10
Frequency
Test1. Sensor No. 9
15
20
5
10
Frequency
15
20
15
20
-4
0.4
10
0.2
-6
Amplitude
acceleration
0
0
10
-8
10
-0.2
-0.4
0
-10
2000
4000
6000
8000
10
10000
0
time
Test1. Sensor No. 11
0.1
-6
Amplitude
acceleration
Test1. Sensor No. 11
-4
10
0.2
0
10
-8
10
-0.1
-0.2
0
-10
2000
4000
6000
time
8000
10000
10
0
5
10
Frequency
Field Test on NJ Bridge
SB-Span2
Test set #1
Test set #2
Stabilization Chart
Stabilization Chart
100
100
80
80
60
60
`
40
40
20
20
0
0
5
10
0
0
15
Result for Singluar Value Decomposition
0
-1
Singular Value
Singular Value
-2
10
-4
10
-6
0
10
15
Result for Singluar Value Decomposition
10
10
10
5
-2
10
-3
10
-4
5
10
Frequency (Hz)
15
10
0
5
10
Frequency (Hz)
15
Field Test on NJ Bridge
SB-Span2
Natural Frequencies [Hz]
1
-
2
-
3
4
5
6
FEA (initial)
2.615
X
3.70
X
6.15
10.59
7.66
12.13
SSI
2.705
3.176
3.383
4.365
5.144
7.851
8.986
11.423
FDD
2.722
3.137
3.577
5.139
7.825
8.972
11.426
SSI
2.767
3.14
3.321
4.353
5.165
7,647
8.856
11.416
FDD
2.734
3.113
3.54
X
5.114
7.703
8.862
11.377
Avg.
2.72
X
3.55
X
5.14
7.75
8.92
(11.4)
Test 1
Test 2
4.211
Field Test on NJ Bridge
SB-Span2
Comparison of identified modal properties
frequency : f=2.7674 Hz
Mode
FE Model
frequency : f=2.7049 Hz
Test 2
frequency : f=3.386 Hz
frequency : f=3.3209 Hz
Test 1
1
2.615
2.72
3.70
3.55
6.15
5.14
2
3
frequency : f=5.1436 Hz
frequency : f=5.1561 Hz
Field Test on NJ Bridge
SB-Span2
Comparison of identified modal properties
frequency : f=7.6468 Hz
Mode
FE Model
frequency : f=7.8439
Test
1 Hz
Test 2
4
10.59
7.75
7.66
8.92
12.13
11.4
frequency : f=8.9864 Hz
frequency : f=7.6468 Hz
5
6
frequency : f=11.423 Hz
frequency : f=11.415 Hz
Field Test on NJ Bridge
SB-Span2
Sensitivity of Updating Variables
Decrease
Initial
model
10%
30%
50%
1
2.615
2.59
2.53
2.46
2
3.699
3.64
3.52
3
6.15
6.09
5
7.662
4
6
Decrease
Initial
model
10%
30%
50%
1
2.615
2.594
2.543
2.473
3.36
2
3.699
3.668
3.589
3.475
5.96
5.79
3
6.15
6.106
5.988
5.824
7.61
7.49
7.31
5
7.662
7.570
7.337
6.997
10.59
10.47
10.21
9.91
4
10.59
10.536
10.327
10.067
11.12
11.03
10.82
10.51
6
11.12
10.972
10.588
10.373
Decrease
Initial
model
10%
30%
50%
1
2.615
2.610
2.596
2.576
2
3.699
3.691
3.670
3
6.15
6.038
5
7.662
4
6
Increase
Initial
model
10000
50000
100000
1
2.615
2.843
3.106
3.213
3.642
2
3.699
3.971
4.386
4.577
5.794
5.531
3
6.15
6.188
6.249
6.284
7.602
7.326
6.641
5
7.662
7.952
8.220
8.316
10.59
10.291
9.641
8.923
4
10.59
10.601
10.605
10.611
11.12
11.100
11.041
10.960
6
11.12
11.941
12.079
12.087
Field Test on NJ Bridge
SB-Span2
Design Variables
Parmeter
Initial
Updated
Slab Stiffness
1
0.523
Cross Beam
Stiffness
1
0.505
Spring at
Support(Ux)
1
12147ton/m
Web Stiffness
1
1.19
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
Field Test on NJ Bridge
SB-Span2
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
Field Test on NJ Bridge
SB-Span2
Variation of Natural frequencies
10
10
10
10
10
PSD of Accel.
10
10
10
10
10
s1
s2
s3
s4
-2
10
-3
-4
-6
2
10
10
-5
2.5
3
Freq. [Hz]
3.5
10
4
Ch.3
-1
10
s1
s2
s3
s4
-2
10
PSD of Accel.
PSD of Accel.
10
Ch.1
-1
PSD of Accel.
10
-3
10
10
Ch.2
-1
s1
s2
s3
s4
-2
-3
-4
-5
2
2.5
3
Freq. [Hz]
3.5
4
Ch.4
-1
s1
s2
s3
s4
-2
-3
-4
-4
10
-5
2
2.5
3
Freq. [Hz]
3.5
4
10
-5
-6
2
2.5
3
Freq. [Hz]
3.5
4
Field Test on NJ Bridge
SB-Span2
Lateral Motion
10
PSD of Accel.
10
10
10
10
10
Vertical vs Lateral
-1
Vertical - Ch.2
Vertical - Ch.3
Lateral at Ch.2
-2
-3
-4
-5
-6
2
4
6
8
10
Freq. [Hz]
12
14
Field Test on NJ Bridge
SB-Span2
DAQ System Check-up : Inner Clock
Output (V)
10
5
0
-5
0
50
100
150
Time (sec)
200
250
300
8
3
6
2
Output (V)
Output (V)
10
4
2
0
-1
0
-2
-2
-4
1
-3
0
0.5
Time (sec)
1
1.5
271.5
272
272.5
273
Time (sec)
273.5
274
Field Test on NJ Bridge
SB-Span2
Natural Frequencies [Hz]
1
-
2
-
3
4
5
6
FEA (initial)
2.615
X
3.70
X
6.15
10.59
7.66
12.13
SSI
2.705
3.176
3.383
4.365
5.144
7.851
8.986
11.423
5.139
7.825
8.972
11.426
Test 1
FDD frequency
2.722
3.137
: f=3.1756 Hz
3.577
4.211
frequency
: f=4.3651 Hz