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: [email protected], [email protected]

New York, June19th 2013

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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

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Introduction

Part I

Conclusions

Part II

The ANCRIiST benchmark problem



Outline



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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

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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

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damaged area

Damage situation 1

Cracks at the closure segment

at both side spans

August 2008:

2 damages are detected

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Damage situation 2

Damaged piers

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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

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Introduction

Part I

Conclusions

Part II




Outline



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Part

I

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

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Part

I

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

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Part

II

Nonlinear feed-forward basis functions

( )

+

+= ∑∑

==

)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

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Traditional learning

tij

tij

tij www ∆+= − η1

ij

ijW

EW

∂

∂−=∆

η Learning rate

Weights updatingMinimization of a

sum of squares error function

Model fitting is obtained by modifications of the coefficients w

t = correct value

y = network value

( )

+

+= ∑∑

==

)2(0

1

)1(0

)1(

1

)2(, k

D

j

jiji

M

j

kjk bbxwgwfy wx

Gradient descent algorithm [traingd]

Conjugate gradient algorithm [traincg]Quasi – Newton algorithm [trainbfg]Levenberg – Marquardt algorithm [trainlm]

( ){ } ∑∑∑== =

+−=W

i

i

N

n

oN

t

tn

tn wxytE

1

2

1 1

2

2;

2

1 αw

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Probabilistic interpretation

( ){ }

−−∝

2;

2exp),,,( ww nn xytMxtp

ββ

1) Probabilistic interpretation

of the network output

2) Probability model

for the prediction error);( wxyt −=ε

Gaussian µ = 0

σD2 = 1/β

3) Predictive PDF

The output

approximates the

conditional average of

the target data

hyperparameter

4) Prior PDF

( )

−=

2

2exp

1),( w

ZMwp

W

α

αα

Gaussian µ = 0

σw2 = 1/α

hyperparameter

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Network learning as inference

16

=),,( MwDp β( )

( ){ }

−− ∑∑

=

N

n

N

t

nt

tn

D

o

xytZ

1

2;

2exp

1w

β

β

Likelihood

( ) ( )( )MDp

MwpMwDpDwp

,,

,,,)M,,,(

βα

αββα =Bayes

theorem

evidence

priorxlikelihoodposterior

=

( ) ( ){ } ∑∑∑==

+−=W

i

i

N

n

N

t

nt

tn wxytwE

o

1

2

1

2

2;

2

αβw

( ) ( ){ }∑∑=

−=−N

n

N

t

nt

tn

o

xytMwDp

1

2;

2,,log w

ββ

( ) ∑=

=−W

i

iwMwp

1

2

2,log

αα

max (posterior) = min (negative log posterior)

=− )M,,,(log βαDwp ( ) ( ) =−− MwpMwDp ,log,,log αβ

( )

−=

2

2exp

1),( w

ZMwp

W

α

αα

Prior

( )Mwp

( )MDwp ,

( )( )

( ){ }

−−= ∑∑

=

N

n

N

t

nt

tn

D

o

xytZ

MwDp

1

2;

2exp

1,, w

β

ββ

( )

−=

2

2exp

1),( w

ZMwp

W

α

αα

( ){ }∑ ∑ ∑= =

+−

=−

N

n

N

t

W

i

int

tn

o

wxyt

Dwp

1 1

2

2;

2

),,,(log

αβ

βα

w

M

DATA PRE- PROCESSING

OUTPUT

NETWORK ARCHITECTUREn°INPUT

n°UNIT IN THE HIDDEN LAYERS

POSTERIOR: BAYES’ THEOREM

( ) ( )( )MDp

MwpMwDpDwp

,,

,,,),,,(

βα

αββα =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

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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

Part

I

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 MiN HIDDEN = iN INPUT = k

POSTERIOR FOR w

yes


PROBABILISTIC MODEL

no

INPUT

CHOOSE INITIAL α, β

INITIALIZE WEIGHTS w

RE-ESTIMATION OF α, β

yes

noWγ ≈

yes

no

i= i+1

is α1,…,αk

‘very large’?

k= k-1

yes

no

( ) ( )( )MDp

MwpMwDpDwp

,,

,,,),,,(

βα

αββα =M

1st level

Model fitting

20



w = wMAP?



CHOOSE MODEL Mi-1

?

POSTERIOR FOR Mi

α, β = αMP, βMP


OUTPUT


POSTERIOR FOR w

yes


PROBABILISTIC MODEL

no

INPUT




yes

noWγ ≈

yes

no

i= i+1

is α1,…,αk

‘very large’?

k= k-1

yes

no

( ) ( )( )MDp

MwpMwDpDwp

,,

,,,),,,(

βα

αββα =M

1st level

Model fitting

2nd level

Evaluating the hyperparameters α, β

( ) ( )( )MDp

MpMDpDp

βαβαβα

,,,),,( =M

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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

2oI NNn +=

INn ⋅< 2

examplesNn ⋅<30

1

They aren’t rigorous methods

INPUTLAYER

OUTPUTLAYER

HIDDENLAYERS

Part

I

22



w = wMAP?



CHOOSE MODEL Mi-1

?

POSTERIOR FOR Mi

α, β = αMP, βMP


OUTPUT


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

MwpMwDpDwp

,,

,,,),,,(

βα

αββα =M

1st level

Model fitting

2nd level


3rd level

Model class selection

( ) ( )MpMDpDMp ∝)(

prior = constantevidence

( ) ( )( )MDp

MpMDpDp

βαβαβα

,,,),,( =M



w = wMAP?



CHOOSE MODEL Mi-1

?

POSTERIOR FOR Mi

α, β = αMP, βMP


OUTPUT


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

MwpMwDpDwp

,,

,,,),,,(

βα

αββα =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

MpMDpDp

βαβαβα

,,,),,( =M

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Introduction

Part I

Conclusions

Part II




Outline



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0

0,2

0,4

0,6

0 0,5 1 1,5 2 2,5 3

H6

H11

H15

H17

H19

H21

Sin

gula

r V

alu

es

(healt

h)

f [Hz]

0

0,1

0,2

0,3

0 0,5 1 1,5 2

Avera

ge S

ingula

r V

alu

es

(healt

h)

f [Hz]

EFDD: Singular Values Decomposition (undamaged)

Part

II

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0

0,5

1

1,5

2

0 0,5 1 1,5 2

Avera

ge S

ingu

lar

Valu

es

(dam

aged)

f [Hz]

0

0,5

1

1,5

2

0 0,5 1 1,5 2 2,5 3

H6H9H12H15H18H20H22H23H24

EFDD: Singular Values Decomposition (damaged)

Part

II

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Comparison of the mode shapes

Part

II

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Part

II

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

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II

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

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Detection of anomalies

If ∆e ≈ 0

the structure is considered as undamaged

If ∆e is large an anomaly is detected

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Damaged area

Error in the approximation of the accelerations in the undamaged sections

Training Undamaged

Damage detection

Tianjin Hangu

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Bayesian model class selection

The most plausible class can be obtained applying Bayes’ Theorem:

( ) ( )( , ) |j jjp 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

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BA

YE

SIA

N M

OD

EL S

ELE

CT

ION

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Part

II

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

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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 H24Damaged conditions!

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II

Difference of the errors

The difference of error in the approximation suggests the presence of structural

anomalies around sensor #10

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Introduction

Part I

Conclusions

Part II


Description of the bridge and available monitoring data

Outline

Neural network based damage detection strategy

Results

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Conclu

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In the Performance based Design framework, monitoring is animportant tool for the verification of the accomplishment of theexpected performance during the entire life cycle

Different approaches for processing monitoring data exist.A traditional approach (Enhanced Frequency DomainDecomposition) and a soft computing approach (neural networks)have been applied on the same data coming from the bridge of theANCRiSST SHM benchmark problem and both methods detectedthe occurrence of an anomaly.

This work shows that the use of different methods is very important forthe cross validation of the obtained results

The current work is focused on the development of methods for thelocalization of the detected damage

Conclusions



w = wMAP?



CHOOSE MODEL Mi-1

?

POSTERIOR FOR Mi

α, β = αMP, βMP


OUTPUT


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

email: [email protected]

[email protected]

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”.

2013 icossar sa_sm_fb_upload

Technology

Transcript of 2013 icossar sa_sm_fb_upload