sensors
ArticleSingle-Camera-Based Bridge Structural Displacement
Measurement with Traffic Counting
Zulhaj Aliansyah 1 , Kohei Shimasaki 2 , Taku Senoo 3 , Idaku Ishii 3, * and Shuji Umemoto 4
1

2

3

4

*

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Citation: Aliansyah, Z.; Shimasaki,
K.; Senoo, T.; Ishii, I.; Umemoto, S.
Single-Camera-Based Bridge

Graduate School of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-hiroshima,
Hiroshima 739-8527, Japan; aliansya@robotics.hiroshima-u.ac.jp
Digital Monozukuri (Manufacturing) Education Research Center, 1-3-2 Kagamiyama, Higashi-hiroshima,
Hiroshima 739-8511, Japan; simasaki@hiroshima-u.ac.jp
Graduate School of Advanced Science and Engineering, Hiroshima University, 1-4-1 Kagamiyama,
Higashi-hiroshima, Hiroshima 739-8527, Japan; taku-senoo@hiroshima-u.ac.jp
Keisoku Research Consultant Co., 1-665-1 Fukuda, Higashi-ku, Hiroshima, Hiroshima 732-0029, Japan;
umemoto@krcnet.co.jp
Correspondence: iishii@robotics.hiroshima-u.ac.jp; Tel.: +81-82-424-7692; Fax: +81-82-422-7158

Abstract: Vision-based structural displacement methods allow convenient monitoring of civil structures such as bridges, though they are often limited due to the small number of measurement points,
constrained spatial resolution, and inability to identify the acting forces of the measured displacement.
To increase the number of measurement points in vision-based bridge displacement measurement,
this study introduces a front-view tandem marker motion capture system with side-view traffic
counting to identify the force-inducing passing vehicles on the bridge’s deck. The proposed system
was able to measure structural displacement at submillimeter resolution on eight measurement
points at once at a distance of 40.8–64.2 m from a front-view camera. The traffic counting systemwith a side-view camera recorded the passing vehicles from two opposing lanes. We conducteda 35-min experiment for a 25 m-span steel road bridge with hundreds of cars passing over it andconfirmed dynamic displacement distributions with amplitudes of several millimeters when large
vehicles passed.

Structural Displacement
Measurement with Traffic Counting.
Sensors 2021, 21, 4517. https://

Keywords: bridge vibration; displacement distribution measurement; digital image correlation;
structural health monitoring; traffic counting; vehicle classification

doi.org/10.3390/s21134517
Academic Editor: Jesper Skottfelt

1. Introduction
Received: 1 June 2021
Accepted: 28 June 2021
Published: 1 July 2021

Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims inpublished maps and institutional affiliations.

Bridges have served a vital part in the transportation system by allowing road trafficand other loads to traverse over physical obstructions caused by topological and structural
conditions, e.g., rivers, valleys, railways, elevated roads. A bridge’s inability to serve
its purpose may result in a longer travel route or an isolated area removed from thetransport network. Bridge failures often result in casualties and large-scale monetary loss;
thus, such failures need to be prevented. A bridge is constantly subject to damages fromenvironmental factors or inherent usage loads during its service life. The damages to abridge can be categorized into three kinds of effects [1]:•Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.

•This article is an open access article
distributed under the terms andconditions of the Creative Commons
Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

•

Primary effects—related to the bridge’s material, construction type, shape, and design
considerations in relation to the bridge’s expected load and its dead weight under
static condition.
Secondary effects—identified from the time-bound dynamic structural response excited from forcing actions due to vehicular loads, wind, quake, or thermal expansion/shrinkage, which are often nonlinear and inelastic.
Tertiary effects—not directly related to static nor dynamic properties of the bridge,
which include environmental factors such as vegetation overgrowth, rust on metal
reinforcing members, paint decontamination, water ponding, deck spalling, erosion,
silting, etc. [2].

Sensors 2021, 21, 4517. https://doi.org/10.3390/s21134517

https://www.mdpi.com/journal/sensors

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Although these three effects are in interplay with one another, addressing them isoften done separately. Primary effects should have been well-addressed in the design phaseand carried well throughout the construction. Secondary effects are to be evaluated using
finite-element simulation or direct measurements on the structure under a defined load.
Tertiary effects are usually assessed by routine visual qualitative inspection on the structure.
Condition assessment and maintenance need to be performed to maintain the safetyand durability of the bridge, especially to address the second and third effects of damage. Early damage detection from structural health monitoring (SHM) facilitates more
economical management and maintenance of modern infrastructure in the long run, given
the bridge’s longer expected service life, relative ease to address the early stage of thedamage, and prevention of damage accumulation [3]. A convenient method for structural
health monitoring should be realized to address the vast number of bridges in lieu of a
sophisticated arrangement of instruments [4,5], and ease of installation and flexibility of
deployment in the field should be taken into account to minimize social economic losses
with traffic regulation in addition to the resolution and accuracy of the measurements.
In this study, we introduce a single-camera-based deflection distribution measurement
method with subpixel digital image correlation (DIC) analysis for a dozens-of-meters-spanroad bridge; this is extended from the tandem-marker-based motion capture method [6] thatallows measurement of structural dynamic displacement from multiple tandem-distributed
points at once without decreasing measurement accuracy by installing a front-view camera
positioned with a small angular delineation to the bridge’s axis. It also enables easyinstallation bridge monitoring without traffic regulation. A traffic counting system with aside-view camera was additionally installed for identifying the dynamics response of thebridge specific to the passing vehicular traffic, and the relationship between the sizes ofpassing vehicles and their responses were quantified in bridge deflection measurement.
2. Related Works
2.1. SHM with Displacement Measurement
Bridges experience elastic vertical, lateral, and rotational displacement from the service
load combinations, and such load displacement may cause surface deterioration and local
cracking, impairing serviceability and durability [7]. Continuously unattended excessive
displacement may result in the accumulation of structural damages in the bridge, reflectedin the loss of stiffness of weakened parts of the bridge: bearings, joints, integral abutments,
and piers. To restrict excessive bridge deformations and vibrations, the displacement limit
is determined by linking with human psychological perceptions on structural safety due tothe occurring structural responses [8], as well as inspecting the appearance of sagging in
the bridge girders.
Structural damages are quantified with metrics derived from displacement, such asincrease of the frequency response in a specific frequency band, a shift of the bridge’s
modal frequency peaks toward a lower value, a discontinuity in the mode shapes, lower
damping coefficient, and other anomalies [9,10].
Frequency-domain analyses are usually employed on the extracted vibration signals
to evaluate the structural health of bridges [11,12]. The frequency response from a bridge’s
natural frequency and traffic load often resides at separate frequency bands [13]; thus,
identifying the frequency response specific to the structure would be possible. Statistics
of abnormal modal frequencies can infer structural damages [14]. Although the natural
frequencies may exhibit variance between multiple methods, measurement points, and ambient loading conditions [11,13], frequency-domain analysis gives reasonable estimatesfrom the extracted vibration signal. As the structural damage is often localized within aparticular member or joint, simultaneous measurement on multiple points on the bridge isalso important to pinpoint the damage’s approximate location.

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3 of 222.2. Drive-by Bridge Vibration Measurement
Vibration-based SHM refers to in-field nondestructive displacement sensing andanalysis of a structure in the time, frequency, or modal domains. Changes and irregularities
in these domains may indicate damage or degradation. Damage to a bridge may leadto some stiffness loss and, consequently, change its dynamic properties [15,16]. Loss ofstiffness could be reflected from a displacement larger than the design value or a drop in thevibration frequency response given a specified loading condition. In practice, the specificloading condition is performed either using heavily loaded trucks parked in specified
points along the span of the bridge [17]; large, controlled excitation devices attached to a
specific vehicle [18]; or, more recently, with drive-by methods utilizing ambient excitation
forces from the usual traffic [19,20].
Testing the vibration of a bridge from vehicular traffic is intuitive, as the bridge’s
service will still operate as usual and can potentially be conducted continuously in realtime. However, in practice, the interaction between vehicles and the bridge will vary due
to factors related to the bridge construction (length, dead mass, deck surface roughness,thermal stress on the members) [14], the passing vehicles (axle spread, weight, speed,
suspension) [21], or the superposition of multiple vibration sources [22].
The impact of vehicle load on bridge vibration varies by the weight on each axle,
the distances between axles, and the number of axles. Vehicles need to be configured
in such a way that the excitation force will result in dynamic displacement, which isdiscernible from ambient vibration from the bridge’s dead weight and environment [23];thus, heavy vehicles are often used for various tests on a bridge instead of common car
traffic. Vehicle speed and bridge deck roughness also affect the vibration profile of thebridge. At higher speeds, vehicle vibration dominates the observed vibration signal, hiding
the bridge vibration itself, and the vehicle speed needs to be relatively low to obtain
good separation between bridge and vehicle vibration frequency, as previously reported:
18 km/h [23], 36 km/h [24], and 40 km/h [19].
2.3. DIC Analysis
DIC is a method to infer subpixel deformation between two images using the correlation of defined facet [25] from the object’s normal surface, nonperiodic speckled pattern,or target marker apparatus. DIC evaluates various criteria from the facet in a single 2Dplane [26], such as cross-correlation, sum of absolute difference, and the squared sum ofdifference. The adjacent frames can also be evaluated in either the forward or backward
temporal direction [27]. DIC can be expanded for multiplane measurement using stereo
camera heads, beam-splitter prisms or mirrors, or wavelength separation of the exposures [28]. Measurement in the 3D-plane can be achieved with a digital projection of the
facet or oblique arrangement between the camera and object with known distances [29].
The latter is more common for displacement measurement of structures.
Various DIC applications have been demonstrated on a model bridge to measuredisplacement, strain, and modal responses [11,30–32]. DIC shows comparable results toconventional methods with accelerometers, laser vibrometers, or finite element simulation [11,33], despite its limitations regarding changes in facet appearance [31], image distortion and out-of-plane displacement or rotation [34], limited sampling rate [35], and strayfrequency responses from sensor aliasing or ambient vibration [33].
DIC has been implemented on actual bridges in several studies addressing the issuesof real-time performance, image degradation from optical turbulence, and subpixel accuracy [36–38]. Such implementation has yet to consider moving traffic and address theinaccuracy due to imprecise synchronization of multiple cameras [39]. There is a trade-off
between the field of view and spatial resolution due to finite sensor size and focal length.
Usage of a pan-tilt mechanism allows for a wider field of view without resorting to a lower
pixelwise spatial resolution [40], but the setup may introduce unwanted vibration andimage distortion from the varying object distances. A higher spatial resolution could beachieved by applying a complex filter to a downsampled subset of the image [30,36].

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4 of 222.4. Video-Based Traffic Counting
A traffic counting system detects individual passing vehicle and infers their properties:
time of passage, travel direction, length, and estimated velocity. These information can beused for various purposes: congestion detection, automated tolling, road design, speed
limit enforcement, etc. The automated traffic counting system has been implemented withvarious detectors, e.g., induction loop, speed-trap laser, and surveillance camera. The
video-based traffic counting system is characteristically more robust with a long MTBF
(mean time between failures) compared with other detectors [41].
Video-based traffic detection of passing vehicles has been implemented with various
techniques: MoG (mixed of Gaussian) [42] and frame-history background subtraction [43]can filter out the nonstatic multi-modal background (e.g., shaking leaves, swaying branches,shadows), but both can still result in the false detection of slow-moving or stopping vehicles,
and overlapping vehicles (either from a single lane or adjacent lanes). Color-histogram
clustering addresses the issue with overlapping vehicles, but, in turn, exhibits inaccuracy
due to sudden changes in vehicle velocity, illumination changes, and color composition
variation [44].
The image segmentation method works to detect the presence of the vehicles bysubtracting each captured frame with a background image with no vehicle present. The
rolling average threshold for image segmentation proved to have good accuracy in various
weather and lighting conditions [45], with detection lines facilitating detection in multilane
settings with heterogeneous traffic [46]. This proves that a simple and adaptable image
processing routine will suffice if detection thresholds are adjusted properly.
Classification of the detected vehicles has been conducted to infer their properties.
SVM (support vector machine) classification is often inaccurate [42], and increased accuracy
comes with the added cost of computational complexity [47]. The CNN (convolutional neural network) method promises better accuracy [42] but requires prior supervised learningfor various different vehicle appearances, camera orientations, and lighting and weather
conditions [48–50], and generally performs slower compared to image-processing-based
methods. Thus, context-specific criteria should be applied to extract meaningful information from the passing vehicles to obtain better execution speed with acceptable accuracy.
3. Tandem Marker Motion Capture with Side-View Monitoring
3.1. Single-Camera-Based Bridge Displacement Measurement
Integration of structural health monitoring on a bridge and traffic identification allows
the measurement of structural dynamic response from traffic load to assess the structural
integrity of the bridge. Several studies have been carried out by integrating an array of
sensors (strain gauge, accelerometer, weigh-in-motion plate) and traffic monitoring video
cameras [51]. Video-based methods have also been applied in place of the sensors tofacilitate noncontact measurement of the bridge vibration under live load, measuring thedeflection of a portion of the structural members, e.g., girders [52] and cable stays [53]. Although such systems are generally comparable to finite simulation [54] and able to identify
simulated damages [55], they are still constrained due to the finite number of measurement
points, the requirement of synchronization between cameras [53], and the lack of generated
data from the traffic counting camera—especially in a real-time setting [56].
The suboptimal common placement of both displacement measurement (perpendicular to the bridge’s axis) and traffic counting cameras (high vantage point) resulted in a set ofissues: limited measurement field and the requirement of separate calibration/alignment
for each displacement measurement camera [52]; further, the difficulty to estimate thepassing vehicle’s details (size, type, speed) and susceptibility to errors are related to frontal
occlusion for the traffic counting camera [42,57,58].
Tandem arrangement of the optical markers along the span of a bridge with thefrontal placement of the displacement measurement camera has been found to facilitate
simultaneous capturing of multiple displacement measurement points from a single camera
viewpoint in its depth of field, requiring no synchronization module for multiple-point

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measurement [6]. This could enable a simpler method of whole-span bridge displacement
observation. The placement of traffic counting camera perpendicular to the bridge axis
could also allow a more reliable estimate of the passing vehicles’ dimensions.
This study aims to identify the structural dynamic response of an actual bridge fromvarious live traversing vehicular traffic, using a combination of the single-camera motion
capture DIC technique and traffic counting system. The dynamic displacement signals
from DIC analysis will be cross-referenced against traffic information using a synchronizedtimestamp. Figure 1 illustrates the general framework of the system.
‡‡

Marker-based motion
capture method
DIC analysis to extract
displacement

Physical markers
with tandem alignment

Vehicle-induced
structural response‡ Displacement‡ Frequency

Displacementmeasurement
Camera‡‡Evaluate displacementwith timestamp
Evaluate displacement
limitsTraffic-counting Camera

Traffic counting‡ Vehicle length‡ Speed‡ Lane/direction‡ TimeFigure 1. Framework of the SHM method for traffic-induced dynamic displacement measurement
using marker-based motion capture and traffic counting cameras. The method incorporates afrontal-positioned camera to measure displacement from multiple points simultaneously and aside-positioned traffic counting camera that allows more-accurate capturing of passing vehicles. DIC
and traffic counting algorithms are concurrently implemented to measure the displacement andfrequency response of the traffic-induced vibration.

3.2. Field Experiment
The field experiment was conducted on Hinotsume Bridge (34◦ 210 27.200 N 132◦ 430 17.400 E).
The structure incorporates two steel plate girder spans with a concrete deck spanning in the east–west direction, which allows both vehicles and pedestrians to cross. Each span is approximately
25 m-long with a support pier in the center connecting the two spans. The two-lane roadway on
top of the structure is 8.4 m-wide with adjacent sidewalks 2 m-wide on both sides. Guardrails
are featured on the edges of the bridge and also between the sidewalks and the roadway.
The speed limit in the vicinity is 50 km/h.
The displacement measurement camera was installed at the shoulder of the road to
the west of Hinotsume Bridge facing eastward. With its depth of field mostly parallel tothe bridge’s axis, this allows simultaneous capturing of tandem-layout markers installedon the bridge without occlusion. The traffic counting camera was installed north of thebridge by the riverbank to capture the whole span of the bridge from the perpendicular
direction, as shown in Figure 2. The perpendicular placement to the traffic direction may
allow more robust detection and length estimation of the individual passing vehicle.

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CAM2

CAM1
Hinotsume Bridge

Umaki Bridge

(a)

Dí

(b)

Dî

(c)
Figure 2. Field of view from the top view (a) of the displacement measurement camera (CAM1) (b)and traffic counting camera (CAM2) (c). The displacement measurement camera was positioned
64.2 m westward from the furthest marker installed on Hinotsume Bridge. The traffic counting
camera was placed northward by the riverbank away from the bridge’s side.

Cameras for the experiment are Panasonic HC-WZX2M at 1920 × 1080 px resolution.
Frame rate was 60 fps with 1 ms-exposure, short enough to eliminate motion blur while stillbright enough to detect the facets for DIC analysis reliably. Focal length of the displacement
measurement camera was set to 98.9 mm with F/16 aperture to obtain as much depthof field and the sharpest focus possible at maximum magnification. The duration of theexperiment was 35.4 min during afternoon hours (15:49 to 16:25 JST). The daylight during
the experiment provided enough light for proper exposure even at its narrowest apertureand no vignetting was observed in the captured frame of the displacement measurement
camera, as shown in Figure 3b.
The markers were installed on the edge guardrail of the eastern span approximately
3.9 m apart from each other using a magnet holder stand (MiSUMi-VONA MNMGBSHLD,Japan), as shown in Figure 3a. Markers’ displacement was evaluated relative to the fiducial
reference marker (M0), which was assumed to be static, installed on the abutment to theeast of the bridge isolated from the deck, providing a mechanism to cancel camera headvibration. The movement of all other markers is evaluated relative to the movement of
M0, as described in Equation (1). The markers were installed in a pattern such that all themarkers could be captured without occlusion from one another at different distances fromthe camera, as shown in Figure 3b.

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To camera
20 m

M7

M6

M5

M4 M3 M2 M1

M0 (ref)

(a)

M7
M1

M5

M3

M6
M4
M2

M0 (ref)(b)
Figure 3. Markers’ placement on the bridge’s outer edge guardrail (a) and the cropped field of view
from the displacement measurement camera with the markers’ facet assignment for DIC analysis (b).

3.3. Implemented Algorithm
3.3.1. Tandem-Marker-Motion Capture from Frontal Camera
Displacement measurement was performed using a commercial DIC solution (GOM
Correlate 2019 Hotfix6 rev. 125216, GOM GmbH, Braunschweig, Germany), which features point-based and full-field displacements measurement. Only displacement in thevertical direction was evaluated in the analysis to emphasize the effect of vehicle loading on the bridge. Figure 4 explains the general workflow for the DIC displacement
measurement process.
As the facets’ vertical displacement was evaluated from only a single axial plane,
the calculated displacement of all markers was calibrated from the known object size of theprinted pattern marker (60 mm) of marker M1. Displacement of each marker would need
to be rescaled separately based on its respective distance to the camera. The approximate
scaling factor for each marker is evaluated from the ratio of its respective distance tothe distance of marker M1 from the camera, as specified in Figure 5, assuming no focal
distortion from the displacement measurement camera throughout its field of view and noout-of-plane movement of the markers. Thus, the displacement for marker number n attime t is given as
SFn
Sn,t =(1)( Pn,t − P0,t ),SF1where P is the captured pixelwise movement, SF is scaling factor for each marker, and S is
the measured displacement.
Given that the displacement limit of a bridge is often defined using static displacement
and the loading scenario during the experiment is entirely dynamic, single-point time-series
static displacement from the structure is approximated using differential displacement.

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Differential displacement evaluates single-point displacement between the center of the
span and abutment in the time domain, given as
Dt = S4,t − S7,t ,(2)

where S is the measured displacement of each marker at time t.
begin

load deformation
imagesDefine facet points:
position, size

Define calibration scale

For each
image

end

Calculate image
correlation criteria
For eachfacet point
Calculate Y-axis
facet displacement

Figure 4. General workflow of DIC displacement measurement from multiple facets in a single plane.
The deformation images were cropped beforehand to reduce the computational time of the DIC
process. The images would be discarded from DIC analysis if occlusion occurs between the cameraand markers due to traffic coming from the sides. Displacement of each facet is estimated based on
the position of the region of the image with the highest correlation criteria across multiple frames.
1.10

Vertical scaling factor (mm/px)

m1
m2

1.00
m3
0.90

m4
m5

0.80

m6
0.70

m7

0.60

36

40

44

48
52
56
Marker distance (m)

60

64

68

Figure 5. Scaling factor for each marker at different distances defines the ratio between actual physicaldisplacement and perceived pixelwise movement in the captured image. The value was calibrated
from the known object size of the printed marker (M1).

Differential displacement was calculated to compensate with the changing measurement baseline due to temperature, nonsteady traffic flow, and facet detection drift fromthe DIC process. Intermittent traffic jam and temperature changes have been shown toSensors 2021, 21, 4517

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exhibit drift in the structural responses [59]. Butterworth band-pass filter (10th order, 1 Hz
to 1.2 Hz band) was then applied on the differential displacement signal to suppress thevibration irregularities from the reverb vibration, vehicle suspension, road roughness,or superposition of vibration from other vehicles, and to better represent the first-mode
vibration. Such signal smoothing has been proved to better extract static component of thebridge response [60].
Displacement from all markers shall be evaluated not to exceed the displacement
limit set in the design to ensure structural safety. The displacement limit defined by
AASHTO (American Association of State Highway and Transportation Officials) will
be used for the evaluation. The limit considers the varying material, construction type,designated load, and perceived psychological safety of the structure [61], summarized inTable 1. Displacement over the specified limit indicates structural deficiency, although such
deficiency may not lead straight to a failure and the bridge may subsequently still be able
to serve typical loads within the limit. Nonetheless, repair or retrofit will be needed toensure structural safety in the long run to avoid accumulation of damage.
Table 1. Criteria for displacement limit on girder bridge. Compound load type (vehicular andpedestrian) has a stricter displacement limit criteria as pedestrian is more sensitive to movement due
to the absence of a direct suspension system.
Bridge Construction

Load Type

Displacement Limit

steel, aluminum, or concrete
steel, aluminum, or concrete
steel, aluminum, or concrete (cantilever)steel, aluminum, or concrete (cantilever)timbervehicular only
compoundvehicular only
compoundcompoundspan/800
span/1000
span/300
span/325
span/425

Frequency-domain analysis is conducted to measure load-specific structural response
from the bridge. The frequency spectrogram was evaluated using Fast Fourier Transform(FFT) from the measured displacement of M4 with a 128-samples bin at 33 ms step. The
spectrogram refers to the amplitude of each frequency band as it varies with time. Only
the lower-half of the frequency response band is presented for the analysis.
3.3.2. Traffic Counting from Side-View Camera
There was persistent occlusion from the guard rails captured by the traffic counting
camera which made capturing the vehicles’ full shape impractical. This may pose a challenge to neural-network-based object detection. Hence, in the experiment, vehicle detection
was performed using basic image segmentation to reduce complexity and increase the traffic counting system’s overall performance. The traffic counting system was implemented
on a laptop computer (HP Omen 15-dc1xxx, Intel i7-8750H, 32 GB RAM, python 3.8.6) andperformed at 80 fps, citing the possible real-time application for the video stream captured
from the camera at 60 fps.
Figure 6 explains the workflow of the image-processing routines for the traffic counting system. A random ID is assigned to the blob wider than 60 pixels, which is maintained
throughout the pass’ duration between two defined line segments. Smaller blobs are
regarded as nonvehicular traffic (pedestrian, motorcycle, etc.) or image noise from theenvironment. Figure 7 shows the images being handled from the traffic counting camera: captured image from the traffic counting camera, intermediate images in the image
segmentation process, and the resulting image with tagged vehicles.
Lane overlap occurs when two vehicles are coming from different directions and theright-going vehicle is occluded behind the left-going vehicle. At the first frame of such lane
overlap, the ID from the opposing vehicle is doubly assigned to each other. This ensuresthat a specific ID is retained for a vehicle throughout its pass duration despite momentarylane overlap with other vehicle(s), as shown in Figure 8. By the end of the pass, the IDof each vehicle is checked to match with its travel direction, assuming that no vehicle isSensors 2021, 21, 4517

10 of 22going in the reverse direction. Although this approach is fairly robust to identify eachvehicle during lane overlap, it limits the applicability to roads with no more than two
through lanes.
begin
end

end

For each frame

Crop the frame

Intersectright detection
line?

Background subtraction
Binarization
Detect blobs.
Merge closely-separated blobs.

false

true
Assign ID_right

For each blob
end
Has ID inprevious
frame?

false

true
Assign ID_right or ID_left fromprevious frame

Intersectleft detection
line?

false

true
Assign ID_left

Figure 6. Flowchart for the traffic detection algorithm. Closely spaced blobs within 10 px apartare merged to account for the occlusion from the guardrail. A unique ID is assigned to a sizable
blob (60 px-wide minimum) based on its initial position when crossing either of the detection lines.
A single-vehicle blob can be assigned with two IDs (right-going <100, left-going >100) to handle
momentary occlusion between left-going and right-going vehicles. The final ID is selected based onwhether the ID value matches the movement direction.

(a)

(b)

(c)

(d)

(e)
Figure 7. Captured frames from the video stream of traffic counting camera, cropped within theregion of interest covering the bridge’s deck (a). The background image for the image segmentation
process is captured when no vehicle is present on top of the bridge, updated with a 10-min interval (b).
Detected vehicle blob after background subtraction (c), the current background image is subtracted
from each frame to isolate only the moving objects. Detection frame with a unique ID assigned to thedetected vehicles’ blob (d). The blob selection was able to filter out nonvehicular objects such as awalking pedestrian from vehicle detection based on minimum blob width (e).

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Figure 8. Image sequence of lane overlap between right-going vehicle (ID 27) and left-going vehicle(ID 158) before, during, and after the lane overlap. Traffic count data during the duration of lane
overlap are discarded from the evaluation to ensure more representative data of respective vehicles.

4. Experiment Results and Discussion
The experiment looks to measure dynamic structural responses under normal traffic
flow. Several metrics (raw displacement, differential displacement, and frequency response)
are to be evaluated and associated with each of the passing vehicles based on its timestamp.
The displacement values should not exceed the defined limit at any occasion.
4.1. 35-min Displacement Monitoring
Figure 9 shows the markers’ displacement, derived differential displacement, and frequency spectrogram. The largest displacement during the experiment was 6.944 mm in M4
and still within the limit defined in Table 1 (25 mm, 1000th of the 25 m span). At any occasion during the experiment, neither measured raw displacement (Figure 9a) nor differential
displacement (Figure 9b) exceeded the load rating of Hinotsume Bridge. This indicates thatno overweight vehicle passed over the bridge and the displacement in the vertical direction
had all been within the range of elastic deformation. The constant low-amplitude vibrationin the displacement signals could be attributed to sensors’ noises and spatial aliasing in thecamera system and DIC process [33].
Passes of large vehicles resulted in large displacement in the markers that are clearlyobservable from the baseline. The displacement is dominated by first-mode curvature,
shown as a single, low-frequency peak in the spectrogram (Figure 9c). A notable lowfrequency response (peaks at ≈0.3 Hz) occurred at the same point as its differential displacement signal.
This could be useful to identify the bridge’s structural response to loading forces,
which was excited exclusively from large vehicular traffic. However, passes of large vehicles
might not always result in large structural displacement as the vehicle could possibly belightly loaded; the axle load may have been spread further apart; or the possibility ofvibration superposition from multiple vehicles/axles, which canceled each other.
The temporary drift observed in the baseline of differential displacement signal, i.e.,t = 1020–1200 s and t = 1650–1800 s, could be attributed due to image disturbance fromloose attachment, heat haze, or shadow cast on the markers [37]. Such occurrences simply
affect the accuracy of DIC facet position detection rather than imply constant load on
the bridge.

(a)Figure 9. Cont.

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Figure 9. Displacement signal from the seven markers (a). Differential relative displacement between M4 (center of the span) and M7 (close to the support pier at the center of the bridge) with a
low-frequency band-pass filter (LPF) (b). Frequency spectrogram of the differential displacement
signal vibration with Hamming window (k = 128) (c). Short-duration peaks were observed in thedisplacement signals and the frequency response during large vehicle passes.

4.2. Traffic Counting
Traffic count during the duration of the experiment is shown in Figure 10. Among thedetected 336 vehicles passes, 188 were going eastbound (left-going) and 148 westbound(right-going) with calm traffic flow. The slight difference could be attributed to the fact thatthe bridge is located on a feeder road to Umaki Interchange (Japanese Expressway E75),
situated nearby to the east, which many vehicles head towards to reach other places.
In addition, vehicle speed and length were evaluated in relation to identify the vehicular loads, shown in Figure 11, further classified in Figure 12. Traffic was dominatedby small and compact cars with occasional large trucks. Besides, as the experiment was
conducted while the inspectors stood on the shoulder of the road, drivers might voluntarily
slow down slightly to ensure the safety of their surroundings.

Figure 10. Traffic count in a one-minute segment. Traffic was calm with an average of 4.13 vehicle/min eastbound and 3.25 vehicle/min westbound.

Sensors 2021, 21, 4517

13 of 22(a)(b)
Figure 11. Length of detected vehicles in both lanes on the bridge (a). The length was evaluatedfrom the passing vehicles’ pixelwise width in the frame, using different scaling factors for each laneas the left-going is closer to the camera: 36.55 mm/px (left-going) and 38.38 mm/px (right-going).
The speed of detected vehicles (b) was evaluated from the distance traveled and its duration from aparticular ID.

(a)

(b)
Figure 12. Vehicle length histogram (a) shows that Japanese light kei cars (<3.4 m) were most common.
Passing speed histogram (b) shows that drivers adhered to the enforced speed limit (50 km/h).

Displacement of markers obtained from DIC analysis, accompanied by its timestamp, was cross-referenced with the timestamp from the traffic counting process to obtaincorrespondence between the passing vehicles and induced displacement on the bridge.
Figure 13 shows the relationship between the markers’ displacement and passing vehicles’
length and speed. Large displacement was only observed during the passes of large vehi-

Sensors 2021, 21, 4517

14 of 22cles longer than 8 m. As there were no overspeeding large vehicles, the effect of speed in
the amplification of force dynamics could not be observed.

(a)

(b)
Figure 13. Bridge displacement according to vehicle lengths (a) and speeds (b). Most passes resulted
in displacement less than 1 mm. The vehicle needed to travel at substantial speed to induce substantial
structural displacement on the bridge. Several small vehicles were cross-recorded having large
displacement due to crossing the bridge at the same time as a large vehicle.

4.3. Structural Response from Large Vehicle Passes
Bridges will often only exhibit a notable structural displacement response from asizable vehicular load. AASHTO and FHWA (Federal Highway Administration, US)defined truck configurations and dimensions employed for load test on a bridge for trafficload [61,62], summarized in Table 2. These large vehicle configurations were incorporated
for detection in the traffic counting system to determine the bridge’s structural displacementfrom the traffic load.
Vehicle of interest (large vehicle) was classified based on the estimated vehicle length,
given that the weight of the trucks could not be directly measured from the video feed.
Although there is no exact specification on vehicle length for bridge live loading in Table 2,
AASHTO exemplifies that the standard load trucks’ total length are 3.66 m (120 ) longer
than their outside axle spread [61]. Considering that the shortest specified axle spreadin the list is 4.27 m, only detected vehicles longer than 7.9 m (260 ) were selected for
displacement analysis.
Table 2. Standard trucks for bridge impact testing. The three-axle truck (*) may have variable outside
axle spread up to 13.4 m (440 ) with the same tractor configuration as the two-axle truck. Longer
combination vehicles (**) are not allowed in Japan road networks.
Configuration

Gross Weight (ton)Outside Axle Spread (m)Two-axle truck
Three-axle truck *Four-axle trailer
Five-axle trailer
Six-axle trailer
Five-axle double trailer
Seven-axle double trailer **Eight-axle double trailer **Nine-axle double trailer **Seven-axle triple trailer **

13.64
24.55
29.09
36.36
40.91
36.36
54.55
56.36
67.27
60.00

7.85
10.67
11.13
20.21
20.37
23.26
32.41
27.84
40.03
33.29

Sensors 2021, 21, 4517

15 of 22

Table 3 shows four occasions of large vehicles’ passes among such passes, which
resulted in a differential displacement larger than 2.5 mm throughout the duration of
the experiment (Table A1). The corresponding raw displacement signal, differential displacement signal, and frequency response of those passes in a one-minute segment are
shown in Figure 14.
Table 3. Passing Large Vehicles.
Time (Vehicle ID)

VehicleLength (m)Speed (km/h)

16:01 (24)

12.27

37.11

16:12 (171 and 57)

12.62
12.36

43.09
39.38

16:18 (25)

8.26

36.65

16:22 (42 and 87)

7.94
8.14

42.36
39.11

The largest peak displacement was consistently observed in M4 (center of the span)with the peak displacement tending to be smaller towards both ends of the span. Thisagrees with the prior finding that the first-mode curvature constantly comprises the largest
component of traffic-induced displacement at all various speeds and weights of the passing vehicles [63].
Consecutive passes of vehicles resulted in sustained vibration, which was initially
excited from the pass of a large vehicle. The vibration larger than baseline lingers until
the last trailing pass, as shown in Figure 14c, with distinct frequency response peaks
observed in Figure 14d despite the fact that its displacement signal has not returned tobaseline. Passes of left-going large vehicles resulted only in small displacement comparedto right-going ones, shown in Figure 14b. This could be attributed to the fact that thedisplacement markers were placed closer to the right-going lane and torsional vibration
occurs on the span.
The marker displacement signal from the four passes is presented in more detail in
Figure 15. All markers started to vibrate rather simultaneously after the initial excitationfrom the pass of a large vehicle. This could be attributed to the stiff plate-girder constructionof the span and the placement of the markers on the guardrail rather than directly on
the deck. The corresponding deck deflection of the span during the passes’ duration is
illustrated in Figure 16. Damped vibration with first mode at ≈0.3 Hz could be consistently
observed after the initial excitation.

Sensors 2021, 21, 4517

16 of 22

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(a)

(b)

/ îñ
/ í

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Figure 14. One minute segment of raw marker displacement, differential displacement between M4 and M7, and vibration
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in Table 3. Low-frequency vibration spectrum was observed during the passes of large, right-going vehicles while the passesof small vehicles did not result in notable vibration as in the earlier part of (a,b).

Sensors 2021, 21, 4517

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in a sustained, 3-Hz vibration.

Sensors 2021, 21, 4517

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Sensors 2021, 21, 4517

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5. Conclusions
Application of video-based displacement measurement and a traffic counting system was implemented on a plate-girder bridge to measure traffic-induced bridge deck
displacement and vibration. Owing to the inability to directly measure vehicles’ weight,
the system instead relies on the estimated vehicle length to classify the traffic-induced
structural displacement.
Notable displacement on the bridge could be observed from the passes of large
vehicles in the lane closer to where the markers were installed, and less so from smaller
vehicles and from the opposite lane. Vehicle-induced frequency response could be observed
more clearly from consecutive passes of large vehicles in the same lane.
Implementation with simpler image-based displacement measurement methods suchas marker centroid tracking or phase correlation could be employed in the future to achieve
real-time performance of the system for continuous in situ structural health monitoring.
Author Contributions: Conceptualization, I.I.; methodology, I.I. and Z.A.; software, Z.A. and I.I.;
validation, I.I. and T.S.; investigation, Z.A., K.S., and S.U.; resources, K.S., S.U.; data curation, K.S.
and Z.A.; original draft preparation, Z.A.; review and editing, I.I. and T.S.; visualization, Z.A. andI.I.; supervision, I.I.; project administration, K.S.; funding acquisition, I.I. All authors have read andagreed to the published version of the manuscript.
Funding: This work was partly supported through the TAOYAKA Program of Hiroshima University,
funded by the Program for Leading Graduate Schools, Japanese Ministry of Education, Culture,
Sports, Science and Technology.
Data Availability Statement: The data presented in this study are available on request from thecorresponding author. The data are not publicly available due to the large size of the video files andprivacy concern regarding the appearance of license plates of the passing vehicles.
Acknowledgments: Special thanks to Muhammad Fatkhurrozi from Institut Teknologi Sumatera
for the discussion on girder bridge loading capacity ratings.
Conflicts of Interest: The authors declare no conflict of interest.

Appendix A
Table A1. Passes with large displacement (>2.5 mm). The listed duration represents the duration
when differential displacement larger than set 2.5 mm was continuously observed throughout thepass. Small vehicle passes during such duration were being misdetected as having large displacement.
Time (ID)

Pass Duration [s]16:00 (24)1.12

16:06 (20)

1.82

16:07 (61)1.53

16:08 (81)1.38

16:15 (13)

1.58

16:18 (25)

1.67

16:22 (42)1.57

17:23 (87)

1.62

Traffic Counting Camera

Sensors 2021, 21, 4517

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