2013 icossar sa_sm_fb_upload

Structural identification of the cable-stayed bridge
of the ANCRiSST SHM benchmark problem
Sapienza University of Rome – StroNGER s.r.l.
S. Arangio, S. Mannucci, F. Bontempi
email: stefania.arangio@uniroma1.it, franco.bontempi@uniroma1.it
New York, June19th 2013

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PartIPartIIConclusionsIntroduction
STRUCTURAL IDENTIFICATION OF THE CABLE STAYED BRIDGE
OF THE ANCRISST SHM BENCHMARK PROBLEM
S. Arangio, S. Mannucci F. Bontempi
Introduction
Part I
Conclusions
Part II
The ANCRiSST benchmark problem
Traditional ad soft computing approaches for
structural identification ad damage detection
Outline
Processing of monitoring data with
Enhanced Frequency Domain Decomposition and Bayesian neural networks

3/38
Introduction
Part I
Conclusions
Part II
The ANCRIiST benchmark problem
Outline

4/38
Introduction
The ANCRiSST benchmark problem
• Consortium of 20 research institutions
• Established in 2002 with the purpose of:
• assessing current progresses on smart materials and structures technology
• Developing synergies that facilitate joint research projects that cannot easily carried
out by individual centers
In October 2011 they opened for
researchers in the SHM community a
benchmark problem based on a real
bridge: the TianjinYonghe bridge
http://smc.hit.edu.cn/

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Description of the TianjinYonghe bridge
Tianjin Hangu
25.15 99.85 260 99.85 25.15
• Cable-stayed bridge
• Opened to traffic since December 1987
• After 19 years of operation damages were detected and the bridge was
retrofitted
• A sophisticated SHM system has been designed and implemented by the
Research Center of Structural Health Monitoring and Control of the Harbin
Institute of Technology
Introduction

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Structural Health Monitoring System
Tianjin Hangu
2515 5600 5885 5900 5600 5600 5900 5885 5600 2515
1 (3) 2 (4) 3 (5) 7 (9) 9 (10) 11 (12) 13 (14)
Uniaxial/biaxial accelerometers
Hygrothermograph
Anemometer
1, 3, 5, 7, 9 11, 13 2, 4, 6, 8, 10, 12, 14
During 2008:
• Continuous monitoring system
• 14 uniaxial accelerometers on the bridge deck (downward and upward)
• On the top of the tower: 1 biaxial accelerometer; 1 anemometer; 1 temperature
sensor
downward and upward
Introduction

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damaged area
Damage situation 1
Cracks at the closure segment
at both side spans
August 2008:
2 damages are detected
Introduction

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Damage situation 2
Damaged piers
Introduction

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Available data set
Health condition Damaged condition
• Time histories of the accelerations
recorded at the 14 deck sensors
on January 1st and January 17th 2008
(registration of 1 h for 24 h )
• Environmental information
(wind, temperature)
• Biaxial accelerations at the top of the
tower
• Time histories of the accelerations
recorded at the same 14 deck sensors
on July 30th 2008
(registration of 1 h for 24 h)
• Accelerations collected by field testing
August 7th to 10th 2008
Introduction

10/38
Introduction
Part I
Conclusions
Part II
Outline

11/38
PartI
Methods for structural identification ad damage detection
Input – output
techniques
• The structure has to be artificially excited
and in case of large structures it is not always
possible
• The operation of the structure has to be
interrupted
Only output
Techniques
• The excitation is given by the ambient
vibration
• Measurements in real operational
conditions
Traditional
methods
Soft computing
methods
• Time domain
approaches
• Frequency
domain
approaches
• Neural
networks
• Genetic
algorithms
• Fuzzy Logic

12/38
PartI
Enhanced Frequency Domain Decomposition
• Data collection and signal preprocessing
• Construction of the the Power Spectral
Density matrix (PSD)
• Whelch averaged modified periodgram method
• 50 % overlapping and periodic Hamming windowing
• Singular Value Decomposition (SVD) of the PSD
• Identification of modal frequencies and mode shapes
• Evaluation of the damping

13/38
PartII
Nonlinear feed-forward basis functions
( ) 



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
+

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+= ∑∑ ==
)2(
0
1
)1(
0
)1(
1
)2(
, k
D
j
jiji
M
j
kjk bbxwgwfy wx
∑=
+=
D
i
jijij bxwa
1
)1(
0
)1(
( )kk afy =
∑=
+=
M
j
kjkjk bzwa
1
)2(
0
)2(
( )jj agz =
NEURAL NETWORK
MODEL
( ) ( )







= ∑=
M
j
jjwfy
1
, xwx φ
output units
hidden units
activations
weights
bias
Neural network model

14/38
Traditional learning
t
ij
t
ij
t
ij www ∆+= −
η1
ij
ij
W
E
W
∂
∂
−=∆
η Learning rate
Weights updating
Minimization of a
sum of squares error function
Model fitting is obtained by modifications of the coefficients w
t = correct value
y = network value
( ) 
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1
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, k
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Gradient descent algorithm [traingd]
Conjugate gradient algorithm [traincg]
Quasi – Newton algorithm [trainbfg]
Levenberg – Marquardt algorithm [trainlm]
( ){ } ∑∑∑
== =
+−=
W
i
i
N
n
oN
t
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1
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2
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Probabilistic interpretation
( ){ } 



−−∝ 2
;
2
exp),,,( ww nn xytMxtp
β
β
1) Probabilistic interpretation
of the network output
2) Probability model
for the prediction error
);( wxyt −=ε
Gaussian µ = 0
σD
2 = 1/β
3) Predictive PDF
The output
approximates the
conditional average of
the target data
hyperparameter
4) Prior PDF
( )



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−=
2
2
exp
1
),( w
Z
Mwp
W
α
α
α
Gaussian µ = 0
σw
2 = 1/α
hyperparameter

16/38
Network learning as inference
16
=),,( MwDp β
( )
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N
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o
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2
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exp
1
w
β
β
Likelihood
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Dwp
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theorem
evidence
priorxlikelihood
posterior =
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o
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DATA PRE- PROCESSING
OUTPUT
NETWORK ARCHITECTURE
n°INPUT
n°UNIT IN THE HIDDEN LAYERS
POSTERIOR: BAYES’ THEOREM
( ) ( )
( )MDp
MwpMwDp
Dwp
,,
,,,
),,,(
βα
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βα =M
w = wMAP?
yes
INFERENCE OF NEW DATA
DATA POST PROCESSING
PROBABILISTIC MODEL
• NOISE MODEL
• PREDICTIVE PDF
• LIKELIHOOD
• PRIOR
),,,( Mxtp βw
( )MwDp ,, β
),( Mwp α
OPTIMIZATION
(MINIMUM OF )),,,(log MβαDwp−
no
INPUT
ED EW
( )Mwp
( )MDwp ,
1) Model fitting

18/38
Bayesian techniques for neural networks
• Level 1 Model fitting: inferring the model parameters given the
model and the data
• Level 2 Optimization of the hyperparameters α and β
• Level 3 Model class selection: optimal model complexity
• Level 4 Automatic relevance determination (ARD):
evaluation of the relative importance of different inputs
Network learning as inference (model fitting) is only one level in
which Bayesian inference can be applied in the neural network
field
Hierarchical multi-level approach
PartI

19
POSTERIOR FOR α, β
TRAINING: OPTIMIZATION
w = wMAP?
?( ) ( )DMEVDMEV ii 1−>
CHOOSE MODEL Mi-1
?
POSTERIOR FOR Mi
α, β = αMP, βMP
OUTPUT
NETWORK MODEL Mi
N HIDDEN = i
N INPUT = k
POSTERIOR FOR w
yes
PROBABILISTIC MODEL
no
INPUT
CHOOSE INITIAL α, β
INITIALIZE WEIGHTS w
RE-ESTIMATION OF α, β
yes
no
Wγ ≈
yes
no
i= i+1
is α1,…,αk
‘very large’?
k= k-1
yes
no
( ) ( )
( )MDp
MwpMwDp
Dwp
,,
,,,
),,,(
βα
αβ
βα =M
1st level
Model fitting

20
w = wMAP?
CHOOSE MODEL Mi-1
?
POSTERIOR FOR Mi
α, β = αMP, βMP
OUTPUT
NETWORK MODEL Mi
N HIDDEN = i
N INPUT = k
POSTERIOR FOR w
yes
PROBABILISTIC MODEL
no
INPUT
yes
no
Wγ ≈
yes
no
i= i+1
is α1,…,αk
‘very large’?
k= k-1
yes
no
( ) ( )
( )MDp
MwpMwDp
Dwp
,,
,,,
),,,(
βα
αβ
βα =M
1st level
Model fitting
2nd level
Evaluating the hyperparameters α, β
( ) ( )
( )MDp
MpMDp
Dp
βαβα
βα
,,,
),,( =M

21/38
Issues in neural network design: selection of the optimal model
RULES OF THUMBS
-…between the input layer size and the output
layer size (Blum, 1992)
- (Software Neuroshell, 2000)
- (Berry and Lynoff, 1997)
- n = dimension needed to capture 70-80% of the
variance
(Boger and Guterman, 1997)
OPTIMAL NUMBER OF UNITS
)(
3
2
oI NNn +=
INn ⋅<2
examplesNn ⋅<
30
1
They aren’t rigorous methods
INPUT
LAYER
OUTPUT
LAYER
HIDDEN
LAYERS
PartI

22
w = wMAP?
CHOOSE MODEL Mi-1
?
POSTERIOR FOR Mi
α, β = αMP, βMP
OUTPUT
NETWORK MODEL Mi
N HIDDEN = i
N INPUT = k
POSTERIOR FOR w
yes
PROBABILISTIC MODEL
no
INPUT
yes
n
o
Wγ ≈
yes
no
i= i+1
is α1,…,αk
‘very large’?
k= k-1
yes
no
( ) ( )
( )MDp
MwpMwDp
Dwp
,,
,,,
),,,(
βα
αβ
βα =M
1st level
Model fitting
2nd level
3rd level
Model class selection
( ) ( )MpMDpDMp ∝)(
prior = constantevidence
( ) ( )
( )MDp
MpMDp
Dp
βαβα
βα
,,,
),,( =M

w = wMAP?
CHOOSE MODEL Mi-1
?
POSTERIOR FOR Mi
α, β = αMP, βMP
OUTPUT
NETWORK MODEL Mi
N HIDDEN = i
N INPUT = k
POSTERIOR FOR w
yes
PROBABILISTIC MODEL
no
INPUT
yes
n
o
Wγ ≈
yes
no
i= i+1
is α1,…,αk
‘very large’?
k= k-1
yes
no
( ) ( )
( )MDp
MwpMwDp
Dwp
,,
,,,
),,,(
βα
αβ
βα =M
1st level
Model fitting
2nd level
3rd level
Model class selection
( ) ( )MpMDpDMp ∝)(
prior = constantevidence
is α1,…,αk
‘very large’?
4th level
Automatic Relevance Determination
( ) ( )
( )MDp
MpMDp
Dp
βαβα
βα
,,,
),,( =M

24/38
Introduction
Part I
Conclusions
Part II
Outline

25/38
0
0,2
0,4
0,6
0 0,5 1 1,5 2 2,5 3
H6
H11
H15
H17
H19
H21
SingularValues(health)
f [Hz]
0
0,1
0,2
0,3
0 0,5 1 1,5 2
AverageSingularValues(health)
f [Hz]
EFDD: Singular Values Decomposition (undamaged)
PartII

26/38
0
0,5
1
1,5
2
0 0,5 1 1,5 2
AverageSingularValues(damaged)
f [Hz]
0
0,5
1
1,5
2
0 0,5 1 1,5 2 2,5 3
H6
H9
H12
H15
H18
H20
H22
H23
H24
EFDD: Singular Values Decomposition (damaged)
PartII

27/38
Comparison of the mode shapes
PartII

28/38
PartII
Procedure for neural network training
time history of the
acceleration recorded at
sensor #
Structural system
Ambient excitation
1+−dtf 2−tf tf1−tf 1+tfTraining of the neural
network model in
undamaged condition
2+tf
Test of the trained neural
network model on a new time
history

29/38
PartII
Neural network based damage detection strategy
14 groups of networks have been created
(one for each measurement point e one for each hour of measurements)
14 (points) x24 (hours) = 336 neural network models
Tianjin Hangu
1 (3) 2 (4) 3 (5) 7 (9) 9 (10) 11 (12) 13 (14)
accelerometers

30/38
PartII
Detection of anomalies
If ∆e ≈ 0
the structure is considered as undamaged
If ∆e is large an anomaly is detected

31/38
PartII
Damaged area
Error in the approximation of the accelerations in the undamaged sections
Training Undamaged
Damage detection
Tianjin Hangu

32/38
PartII
Bayesian model class selection
The most plausible class can be obtained applying Bayes’ Theorem:
( ) ( )( , ) |j jj
p M D p D M p M∝M M
prior = costevidence
provided by D
The various model can be compared by evaluating their evidence
The chosen model has 3 hidden units:
N hidden units 1 2 3 4 5
evidence 20756 22603 24922 21944 23240

33/38
PartII
BAYESIANMODELSELECTION

34/38
PartII
Error in the approximation of the undamaged conditions
downriver
upriver
∆e at the various locations
Data for training: January 1st 2008 (H1 to H24)
Data for testing: January 17th 2008 (H1 to H24)
Undamaged conditions

35/38
PartII
Error in the approximation of the damaged conditions
∆e at the various locations
Data for training: January 1st 2008 (H1 to H24)
Data for testing: July 30th 2008 (H1 to H24
Damaged conditions!

36/38
PartII
Difference of the errors
The difference of error in the approximation suggests the presence of structural
anomalies around sensor #10

37/38
Introduction
Part I
Conclusions
Part II
Description of the bridge and available monitoring data
Outline
Neural network based damage detection strategy
Results

38/38
Conclusions
In the Performance based Design framework, monitoring is an
important tool for the verification of the accomplishment of the
expected performance during the entire life cycle
Different approaches for processing monitoring data exist.
A traditional approach (Enhanced Frequency Domain
Decomposition) and a soft computing approach (neural networks)
have been applied on the same data coming from the bridge of the
ANCRiSST SHM benchmark problem and both methods detected
the occurrence of an anomaly.
This work shows that the use of different methods is very important for
the cross validation of the obtained results
The current work is focused on the development of methods for the
localization of the detected damage
Conclusions

w = wMAP?
CHOOSE MODEL Mi-1
?
POSTERIOR FOR Mi
α, β = αMP, βMP
OUTPUT
NETWORK MODEL Mi
N HIDDEN = i
N INPUT = k
POSTERIOR FOR w
yes
PROBABILISTIC MODEL
no
INPUT
yes
n
o
Wγ ≈
yes
no
i= i+1
is α1,…,αk
‘very large’?
k= k-1
yes
no
email: stefania.arangio@uniroma1.it
stefania.arangio@stronger2012.com
This research was partially supported by StroNGER s.r.l. from
the fund “FILAS - POR FESR LAZIO 2007/2013 - Support for
the research spin off”.

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