Numerical verification on

Wavelet-based VRA method

for bridge damage detection
Yamamoto Lab., LAFEE, GSSIE,
Dept. of Eng. Mechanics and Energy

University of Tsukuba

Kyosuke YAMAMOTO Graduated from
Graduated School of Engineering,

Kyoto University

The 28th KKHTCNN Symposium
on Civil Engineering
16‐18/Nov, 2015, Thailand

Assistant Professor

Kyosuke YAMAMOTO
Undergraduate Student

Kosuke MORI
Graduate Student

Mikio ISHIKAWA

DEMAND OF OUR SOCIETY

1
Rough Screening
STEP:Engineers
INTACT

INTACTDAMAGE

Rapidly and EconomicallySensors on Vehicle2
Detailed Inspection only for “Suspicious Bridge”
STEP:

Strategic Allocation of Resourcesin bridge maintenance beyond
the boundary of local governments

Engineers & Money

Solution 1 | To change the way to observing bridge vibrations

Traditional monitoring:

New monitoring:Sensors on Bridge

Sensors on Vehicle
VRAHigh
CostlyVeterans
Few years

Accuracy
CostEngineersTime

For Detailed Inspection

Maybe Low
Cheap
Drivers & Analysts
10 sec. per one bridge

For Rough Screening

Traditional analysis:

New analysis:

Time Domain

Time-Frequency
DomainMaximum amplitude

Frequency

Solution 2 | To sophisticate signal processing method

Frequency Domain

TimePeak frequency

All information both in timeand frequency domain alive

Time‐Frequency Domain method

Frequency to scaleContinuous Wavelet Transform
Wavelet Coefficient

Signal𝒔Convolution

Mother Wavelet

Convolution
Lowscale

HighHigh

frequency

LowNumerical simulation

Direct calculation

Repeat calculation

Vehicle-Bridge
Interaction System

Vehicle Systemmodeled by

RBSM
Road
Unevenness

BridgeVibration

VehicleVibration

Contact Force

Non‐Linear system
System parameters depending on
the position of the vehicle(Un‐steady: memory‐consuming!)

Bridge Systemmodeled by

3D‐FEM

Model parameters

42Sensor
position0-2

Bridge Model
Global010203040Road Unevenness

Span Length [m]Width [m]ElementDeck
Axial Direction
Division
Cross Direction
Density [kg/m3 ]Thickness [m]Young’s Modulus [Pa]Density [kg/m3]
Young’s Modulus [Pa]Truss
Cross Section [m2]Member Second Moment of Area [m4]Shear Modulus of Rigidity
Second Polar Moment of Area [m4]40.06.020102400
0.40
25×1097800
200×109
0.020
1.0×10‐4
78×1091.0×10‐6

Vehicle Model
Sprung‐

Unsprung‐

Mass [kg]Damping [kg/s]
Stiffness [kg/s2]
Inertia Moment (Pitch) [kg m2]
Inertia Moment (Roll) [kg m2]
Length [m]Width [m]Mass [kg]Damping [kg/s]
Stiffness [kg/s2 ]Run speed [m/s]

18,00010,000
1.0×106
65,00015,000
2.750
1.800
1,100
30,000
3.5×106
10.0

Simulated vibrations and considered cases

Damage case(a) Intact(b) Mid-span(c) Edge(d) Upper

Normalized
Fourier’s PSD

Simulated Vibrationof the Vehicle
20-2
0

20-2
0
20-2
0

20-2
0

1

10.5Hz
2.0Hz

L/4

2L/4

3L/4

L005

101

15

20

1520

15

20

1520

10.5Hz
2.0Hz

L/42L/43L/4

L00

51

10
10.2Hz

2.0Hz

L/4

2L/4

3L/4

L005101

10.5Hz
2.0Hz

L/42L/4

3L/4Vehicle Position (m)L00510Frequency (Hz)Difficult to find change in Time and Frequency domain!

Result of CWTSpectrogram

Damage case(a) Intact

scale

10500
1000

51500(b) Mid‐spanscale

2000

0
10500
1000

51500(c) Edge

scale

2000
500
1000

scale

51500
2000

(d) Upper

0
10

100

10203040010500
1000

51500
2000

-100102030

40

Easy to find change in Time‐Frequency domain!

0Affect of mother wavelet
Complex Gaussian
Wavelet of order 2Damage case(a) Intact

Mexican hatscale

0010002000(b) Mid‐span

10-1001020304005-10010203040scale

0scale(c) Edge

1010002000

00-100102030

4005-100102030

4000101000

52000-100102030

40-10・Every mother wavelet can detect change
・The scale in which change appears is different

0102030400

Discussion

Traditional analysis:

New analysis:

Time Domain

Time-Frequency
DomainAcceleration

CWT
Frequency Domain

Bridge Damage

Fourier Transform

Local StiffnessDecreasing

Conclusion & Technical issues
Conclusion

I. CWT can detect the bridge damage in the High scale.
II. CWT can identify the damaged location.
III. Bridge damage affects the low frequency.
Technical issues

I. Impossible to measure the super low frequency of acceleration
II. Consider the appropriate mother wavelet for signal
𝑊𝑓 𝑡, 𝑠1· 𝑓 𝑡 ⨂𝜃 𝑡𝑠

500

101000

51500
2000

0500

10100051500
2000-100102030

400Experiment of actual bridge

Experiment of actual bridge

can Not detect
805050100100150

150200200

250250300300350

350

400

400

450

450

70
60

500

0.1

0.2

0.3

0.4

0.5

0.6

Intact

0.7

0.8

0.9

1500

50
40
30
20
10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Damage0.8

0.910