Numerical Verification ofBridge Screening Technology
based on Vehicle Vibration
University of Tsukuba

Kyosuke Yamamoto
Assistant Professor

Background:

Bridge Inspections based on Visual Checkby Veteran Engineers！

Social Matter:

The Training of Engineers requires several years,
though there is a Large Number of Aging bridges
Which bridge
should I check?

To implement the priorities of bridges
we need to know the soundness before the inspections!?

Solutions:

Bridge Screening (Roughly Quick Inspection)
enables Strategic Allocation of Resources！
Sensors
on Vehicle

Bridge Screening
based onvehicle responses

IntactIntactDetailedInspectionDamage

Technical issue:

How to estimate the bridge status only byusing vehicle vibrations?

12First ModeSecond Mode

3To measure the vibrations ofthe passing vehicle
To transform them tovibrations at the fixed points
To estimate the mode shapesof the bridge
Spatial Singular Mode Angle:

𝜃 = tan−1

𝐴21
𝐴11

𝐴
𝐴22

= tan−1 − 12

The Purpose:

To examine the applicability of SSMA
to the Bridge Screening
Bridge Vibration𝒚 𝑡 = 𝐀𝒒 𝑡
Bridge Vibrations measured
at Moving Positions

𝐍 𝑡 −1 𝒚 𝑡 = 𝐀𝒒 𝑡Vehicle Vibrations(1) Bridge vibrations(2) Road Roughness(3) Vehicle Body vibrations

𝐍 𝑡 −1 𝒛 𝑡 = 𝐀𝝈 𝑡

The Proposed Method:

Application of SVD method tothe spatially corrected vibration data
MeasuredVehicleVibrations

SVD: Singular Value Decomposition𝒛 𝑡

𝐍 𝑡 −1 𝒛 𝑡

𝒙 𝑡=

Spatially Corrected Vibrationsat assumed fixed points

𝐀𝒔 𝑡

Estimated Mode Shapes
Estimated Basis Coordinates
SVD assumes their non-correlation

×=The Methodology:

Experimental & Numerical Verification
Data Acquisition
Numerical Simulation
Field Experiment
Laboratory Experiment

Application ofthe proposed method

The Numerical Simulation:

RBSM Vehicle & FEM Bridge
1 23 45 678 910Vehicle Model

40600816243240Displacement[mm]20t (=200kN) 40m span Steel Truss Bridge Road Unevenness840-4-8-20020Position[m]4060The Procedure to calculate SSMA:

Acceleration[m/s2]

4201-2-4-100102030

40

Mode shapeAcceleration[m/s2]

Spatial Correction & Mode Decomposition
50

4𝑌002𝑋

L/3

2L/3Position [m]0-2-4-100102030
Wheel Position[m]4050𝑌First Mode

Second Mode𝑋LThe Results of Numerical Simulation:

SSMA Applicability to the damage detection
when varying velocity & road roughness

60

SSMA[deg]

SSMA[deg]

60
504030IntactDamaged51015
V elocity[m/s]Smooth Road

20

IntactDamaged50403051015
V elocity[m/s]

Rough Road20

The Robustness:

0.3
0.2
0.1
00.3
0.2
0.1
05151.5

5252.55151.552
SSMA[°]

52.5

Smooth Road

Frequency
割合
割合

Frequency
割合
割合

It is found that SSMA has the high sensitivity
to a local bridge damage

0.3
0.20.100.30.20.1
040.6

40.8

4141.2

40.6

40.8
41
SSMA[°]

41.2

Rough Road

The Field Experiment:

SSMA Applicability to the damage detection
on the actual steel truss bridge

1) ボルト固定

2) 切断3) ボルト除荷

車上計測

損傷検知

On-going Measuring
11000mm

Damage Detection

25t トラック
25ton
Truck

First
1 日目
Day

2 日目

SecondDay

5460mm

5460mm

5460mm

5460mm

5460mm

5460mm

5460mm

5460mm

5460mm

5460mm

5460mm

5460mm65m
span
65520mm
健全時
INTACT

損傷時
DAMAGE

前軸
Front

後軸
Rear

総重量
Total

(kN)

(kN)

(kN)

10(km/h)

20(km/h)

40(km/h)

87.4

165.8

253.21 回目
First

1回目
First

1First回目

87.8

170.6

258.4

2 回目

Second
2,3回目

SecondThird

10(km/h)

20(km/h)

40(km/h)

First
1～3回目

First
1～3回目

First
1～3回目

Second SecondThird
Third

SecondThird

The Results of Field Experiment:

High sensitivity to the damage detection
Low Accuracy to the damage identification〇 DAMAGE

SSMA〇 INTACT

Because the mode shape isindependent from thevehicle speed, it means thelow estimation accuracyof SSMA.
The high sensitivity todamage because the angle
changes distinctively afterdamage.

Speed (km/h)

The Lab. Experiment:

Statistical Validity of SSMA should be
examined for Engineering application
Damage Section
CH171560

アプローチ部
100

CH2CH35200
進行方向

2000

ピン支承
180 180500

ピン支承CH41040

Sensorセンサー
RailTruck
レール
RemovedRail
レール除去部

アプローチ部ワイヤー

The result of the Lab. Experiment:

SSMA probability density distribution
statistically changes after the bridge damage
0.95

Probability

SSMA
SSMA[rad]
[rad]

0.9
0.85
0.8
0.75
0.7
99.5
1010.5Run speed[rpm]
[rpm]
Speed

11SSMA [rad]Discussion:

Why does SSMA shows the high sensitivity tothe bridge damage?
𝐀𝒔 𝑡

0.4
Probability=

0.3

HistogramNormal distribution

0.2
0.1
Intact
04

4.5

55.5

66.5

77.580.4
Probability

𝒙 𝑡

0.3

HistogramNormal distribution

0.2
0.1
Damage
04

4.5

5
5.5
66.5
7
Kurtosis of reference coordinate

7.58

Discussion:

Why does SSMA shows the high sensitivity tothe bridge damage?
𝒙 𝑡

INTACT
Noise=Damage

DAMAGE𝐀𝒔 𝑡

INTACT

Damage

INTACTDAMAGE

Noise

Damage & SVD error

Mode Shape

What SVD can estimate is
the component of non-correlation
close to the signals

Basis Coordinate

DAMAGE

Conclusion:

1. SSMA is the bridge mode shape estimated only
by using the vehicle data.
2. The applicability and statistical validity is verified
numerically and experimentally.
3. It is applicable to the damage detection becauseof its high sensitivity.
4. It is still difficult to apply SSMA to the damage
identification, because of its low estimation
accuracy

University of Tsukuba
1-1-1, Ten-Nou-Dai, Tsukuba, Ibaraki, JAPAN