USING WAVELETS ON THE RESPONSE OF A BEAM TO A CALIBRATED VEHICLE FOR DAMAGE DETECTION

David Hester

Arturo Gonzalez

Nantes, 2nd July 2009

Overview of presentation

• Rational behind research / Introduction to technique

• Computer models used• Description of Continuous Wavelet

Transform (CWT)• Performance of different wavelets• Approach for detecting small damage

01

Rational behind study

• Research in Structural Health Monitoring (SHM) increasing, typically requires Non Destructive Testing

• Bridges are a particularly interesting set of structures, in service for long period, traffic loads are steadily increasing

• Financially beneficial if service life of existing bridges can be maximised

• Reliable early damage detection technique significant step toward achieving this

02

Introduction to technique

• Ultimately would like to be able to detect damage in a bridge by monitoring it’s dynamic response

• Fundamental principal: Damage causes change in mechanical properties of structure

• Potential to use Wavelets to detect damage in a beam by performing a wavelet transform on the deflection signal of the beam

03Damage Deflection gauge

0 1 2 3 4 5 6 7 8 9 10-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5x 10

-3

Time

Def

lect

ion

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

x 10-4

Wav

elet

Coe

ffici

ent

Normalised Position of Load

Wavelet

Transform

04

Modelling of the Structural Response to a Moving Load

•Discretized model of a simply supported beam

[Kg], [Mg]

1

2 3

4

L

05

Crack Modelling

•Crack = Loss of Stiffness

Sinha’s method

•Sinha approximates the

exponential curve of

Christides and Barr with

a straight line.

•lc= 1.5d

06

Load ModellingVehicle modelled as a

constant moving Load

[Mg]{d2

y/dt2

}+[Kg]{y}={F}

Introduction to wavelets

• Wavelet transform was developed to extract Time-Frequency information from a signal

• A wavelet is a waveform of limited duration

07

Mexican hatDb 5

Gauss 2 Morlet

Figures taken from MATLAB

Outline of Wavelet Transform1. Wavelet compared to a section at start of

the original signal

2. Calculate wavelet coefficient ‘C’, which represents how closely correlated the wavelet is with this section of the signal.

3. Shift the wavelet to the right and repeat steps 1 & 2

4. Scale (stretch) the wavelet and repeat steps 1 through 3

5. Repeat steps 1-4 for all scales. Result of the WT are many wavelet coefficients ‘C’

08Figures taken from MATLAB

Using wavelets to detect damage

• Wavelets can detect local discontinuities in a signal

• Discontinuity in deflection-time response of a bridge as load passes over cracked section

• Basic principal is to use wavelet to detect the discontinuity in the signal and thereby locate damage

09

Mid-span deflection response of a beam cracked at the 1/3 point subject to moving P-Load (1st beam freq=0.9Hz)

0 0.2 0.4 0.6 0.8 1-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5x 10

-3

NORMALISED POSITION OF LOAD ON BRIDGE ( x(t)/L )

DE

FLE

CT

ION

AT

MID

-SP

AN

10

CrackDeflection sensor

WT applied to the midspan deflection signal of a beam subject to P-Load. Beam has a crack at 1/3rd point,

Increase in wavelet coefficients at 0.33L

→There is a localised discontinuity in deflection signal at 0.33L

→There is damage at 0.33L

WAVELET COEFFICIENTS AT DIFFERENT SCALES AND POSITIONS

NORMALISED POSITION OF LOAD ON BEAM ( x(t)/L )

SC

ALE

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 14 27 40 53 66 79 92105118131144157170183196209222235248

11

≈ 0.9HzScale=27

Wavelet

Transform

0 1 2 3 4 5 6 7 8 9 10-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5x 10

-3

Deflection Signal

Performance of different wavelets in detecting damageDamage

LevelWavelet Possible to detect Damage

(Yes/No)Damage

LevelWavelet Possible to detect Damage

(Yes/No)Pure

signalNoisy signal Pure signal Noisy

signala/h=0.1 db2 No No a/h=0.4 db2 Yes No

sym 2 No No sym 2 Yes Nocorfil 1 No No corfil 1 Yes Nogauss2 No No gauss2 Yes Yesmex hat No No mex hat Yes Yes

a/h=0.2 db2 Yes No a/h=0.5 db2 Yes Yessym 2 Yes No sym 2 Yes Yes

corfil 1 Yes No corfil 1 Yes Yesgauss2 Yes No gauss2 Yes Yesmex hat Yes No mex hat Yes Yes

a/h=0.3 db2 Yes NoDamage Level (a/h) = height of the crack / Depth of the beam

sym 2 Yes Nocorfil 1 Yes Nogauss2 Yes Yesmex hat Yes Yes

Gauss 2 Mex hat

12

Coefficient line plot

13

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5x 10

-3

NORMALISED POSITION OF LOAD ON BEAM ( x(t)/L )

WA

VE

LET

CO

EF

FIC

IEN

T

IDENTIFYING DAMAGE LOCATION FOR DIFFERENT LEVELS OF DAMAGE

Undamaged

delta=0.2delta=0.4

delta=0.6Delta=

Crack height / Beam depth

Delta=0.6

Delta=0.4

Delta=0.2

Damage at 1/3 point

WAVELET COEFFICIENTS AT DIFFERENT SCALES AND POSITIONS

NORMALISED POSITION OF LOAD ON BEAM ( x(t)/L )

SC

ALE

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 14 27 40 53 66 79 92105118131144157170183196209222235248

14

Improvement by using multiple measurements•

Use of one single measurement, delta=0.2

•Use of multiple measurements

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

-1.5

-1

-0.5

0

0.5

1x 10

-3 IDENTIFYING DAMAGE USING MIDSPAN DEFLECTION SIGNAL

NORMALISED POSITION OF LOAD ON BEAM ( x(t)/L )

WA

VE

LET

CO

FF

ICIE

NT

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1

-0.5

0

0.5

1x 10

-3

NORMALISED POSITION OF LOAD ON BEAM ( x(t)/L )

WA

VE

LE

T C

OE

FF

ICIE

NT

IDENTIFING DAMAGE USING A NUMBER OF MEASURING POINTS

1/5L

2/5L

3/5L

4/5L

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1

-0.5

0

0.5

1x 10

-3 AVERAGE COEFFICIENTS SEVERAL MEASURING POINTS

NORMALISED POSITION OF LOAD ON BEAM ( x(t)/L )

WA

VE

LET

CO

EF

FIC

IEN

T

Min not at damage location

Min at damage location

Average

Crack

Deflection Sensors

Conclusions

• Possible to use a moving load as a form of non destructive testing to detect damage

• Wavelet transform applied to Deflection-Time response can identify and locate damage

• In presence of noise detects large cracks relatively easily

• Multiple measuring locations give better results when detecting small cracks

Wavelet

Transform0 1 2 3 4 5 6 7 8 9 10

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5x 10

-3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

x 10-4

Locate DamageCrack

Deflection GaugeDeflection Signal

15

Acknowledgements

• This investigation has been carried out as part of work program 7 of the ASSET project, Sustainable Surface Transport

ASSET(Advanced Safety and Driver Support in Efficient Road Transport),

16