applied
sciences
Article
Using Statistical Analysis of an Acceleration-Based
Bridge Weigh-In-Motion System for Damage Detection
Eugene OBrien 1 , Muhammad Arslan Khan 1, * , Daniel Patrick McCrum 1
and Aleš Žnidarič 2
1
2
*
School of Civil Engineering, University College Dublin, D04 V1W8 Belfield, Ireland;
eugene.obrien@ucd.ie (E.O.); daniel.mccrum@ucd.ie (D.P.M.)
Slovenian National Building and Civil Engineering Institute (ZAG), 1000 Ljubljana, Slovenia;
ales.znidaric@zag.si
Correspondence: muhmmad.khan@ucdconnect.ie; Tel.: +353-7163-239
Received: 9 December 2019; Accepted: 14 January 2020; Published: 17 January 2020
Abstract: This paper develops a novel method of bridge damage detection using statistical analysis
of data from an acceleration-based bridge weigh-in-motion (BWIM) system. Bridge dynamic analysis
using a vehicle-bridge interaction model is carried out to obtain bridge accelerations, and the BWIM
concept is applied to infer the vehicle axle weights. A large volume of traffic data tends to remain
consistent (e.g., most frequent gross vehicle weight (GVW) of 3-axle trucks); therefore, the statistical
properties of inferred vehicle weights are used to develop a bridge damage detection technique.
Global change of bridge stiffness due to a change in the elastic modulus of concrete is used as a proxy
of bridge damage. This approach has the advantage of overcoming the variability in acceleration
signals due to the wide variety of source excitations/vehicles—data from a large number of different
vehicles can be easily combined in the form of inferred vehicle weight. One year of experimental
data from a short-span reinforced concrete bridge in Slovenia is used to assess the effectiveness of
the new approach. Although the acceleration-based BWIM system is inaccurate for finding vehicle
axle-weights, it is found to be effective in detecting damage using statistical analysis. It is shown
through simulation as well as by experimental analysis that a significant change in the statistical
properties of the inferred BWIM data results from changes in the bridge condition.
Keywords: bridge health monitoring; BWIM; structure dynamics; damage detection; vehicle-bridge
interaction; SHM
1. Introduction
Bridge structures are amongst the most critical components of transport infrastructure. Similar
to other structures, they deteriorate over their lifetimes due to aging, environmental conditions and
traffic loading [1–3]. Structurally deficient bridges may be unsafe, and continuous monitoring of
bridges is desirable in such situations. In the United States, 9.1% of the total number of bridges in
2016 were found to be structurally deficient and to require substantial investment and improvements
to operate [4]. Therefore, an effective method of bridge damage detection is important to detect
damage quickly when it occurs. In recent years, many methods of bridge damage detection have been
proposed for road authorities to maintain an acceptable level of bridge safety [5]. These methods
are classified using levels of damage identification. For example, Level I damage detection methods
identify the presence of damage in the structure, Level II methods identify the location of damage,
Level III methods quantify the extent of damage and Level IV methods predict the remaining service
life of the structure [6]. Visual inspection is the most frequently used method, but it can be expensive,
time-consuming and disruptive to traffic. Stochino et al. used a combination of visual inspection and
Appl. Sci. 2020, 10, 663; doi:10.3390/app10020663
www.mdpi.com/journal/applsci
Appl. Sci. 2020, 10, 663
2 of 20
non-destructive testing of materials to calculate a condition rating number (CRN) and hence develop
a low-cost SHM system [7]. This concept is tested on a set of real bridges to calculate the CRN and
assess the damage category of each bridge based on their visual inspection and assumed material
strength properties. Although the method is simple, low-cost and fast, it is less sensitive to small
changes in temperature and environmental conditions around the bridge.
Direct instrumentation is an approach to structure health monitoring (SHM) in which sensors
(typically accelerometers or strain transducers) are installed on the bridge. The most popular systems
are based on analysing bridge natural frequencies and modes extracted from sensors installed at
various locations on the bridge [8]. However, there tends to be a slight change in the bridge natural
frequencies, which are used to identify bridge damage (Level I) for a significant change in the bridge
condition. Cantero et al. proposed a bridge damage detection method (Level I) using a strain-based
weigh-in-motion (WIM) system which is sensitive to damage only if the location of damage is near the
sensor [9]. For that reason, arrays of distributed sensors are required to identify damage.
Indirect monitoring is an alternative approach, where an instrumented vehicle crossing the
bridge is used to infer information about its condition [10]. The most recent indirect monitoring
systems are able to detect changes in bridge damping [10] and natural frequency [11,12] using vehicle
accelerations. Zhang et al. estimated mode shape squares from vehicle accelerations and proposed
a new damage index of the bridge [13]. Malekjafarian et al. extracted full bridge mode shapes using
vehicle accelerations in segments of the bridge [14]. While the indirect SHM methods with instrumented
vehicles are easy to operate and are cost effective, the damage indicators are very sensitive to the
vehicle velocity, changes in road profile and environmental conditions [10].
In some of the latest SHM systems, unmanned aerial vehicles (UAVs) have measured bridge
displacements and mode shapes using vision-based techniques [15]. Although the use of UAVs is
convenient, low cost and can access remote parts of the bridge, the visual measurements may not
yet be accurate enough for short-span bridges, where the bridge deflections in response to passing
heavy vehicles are typically less than one millimetre. Another type of SHM system involves the use of
machine learning algorithms that process indirect measurements from the vehicle [16] or direct bridge
response measurements [17,18] to identify structural abnormalities. In these systems, the measurements
from the healthy bridge condition are analysed to build and train a model [16]. Yi et al. employed
a multi-stage energy-based method for damage assessment that uses a wavelet packet transform and
an artificial neural network (ANN) to detect local damages in steel frame structures [17]. A benchmark
structure of the American Society of Civil Engineers (ASCE) was tested in a laboratory to validate the
model. Jin et al. proposed an extended Kalman filter-based ANN model for SHM that estimates the
weights in a regression neural network to detect bridge damage under severe temperature changes [18].
They trained the neural network using one-year of measured bridge accelerations and temperature data
using a real bridge to test the concept. Although the machine learning models have shown promising
results, they require a great deal of bridge data to train the model effectively and are demanding of
computational resources due to the large number of unknown parameters.
Bridge weigh-in-motion (BWIM) is a technique for finding the gross vehicle and axle weights
of trucks crossing a bridge, using a measured bridge [19,20]. Any variation in the bridge structural
condition (stiffness) changes its behaviour and manifests itself in the form of changes in inferred BWIM
weights. Therefore, there have been some studies on the use of the BWIM system for bridge damage
detection [9].
The BWIM technique was first proposed by Moses, who found the vehicle axle weights by
minimising the sum of squared differences between the measured and calculated responses of
a bridge [19]. The gross vehicle weights (GVWs) were then calculated by summing the inferred axle
weights. BWIM systems generally consist of two sets of sensors: one for axle detection [21] and
a second to obtain the responses used to infer the axle weights [22]. Traditional BWIM systems use
strain responses which are measured by strain gauges, strain transducers or fibre Bragg grating (FBG)
sensors [9,23]. However, a BWIM system that uses strain measurements directly is not suitable for
Appl. Sci. 2020, 10, 663
3 of 20
bridge monitoring. Many bridges are statically determinate (single span simply supported), and the
bending moment is unaffected by stiffness. As a result, strain responses only change if the sensor is
located at (or very close to) the damaged point. If the bridge is damaged at another location, strain is not
affected, and any strain-based BWIM system becomes ineffective at detecting damage. Ojio et al. [24]
used bridge deflection instead of strain, measured without using any sensors attached to the bridge,
and developed a contactless bridge weigh-in-motion (cBWIM) system which has reasonably good
accuracy for GVWs [25].
Sekiya et al. proposed a portable BWIM system that uses acceleration rather than strain as the
bridge response. It integrates the acceleration signals twice to estimate the displacements and uses this
for the BWIM analysis [26]. In this integration process, the influence of initial conditions is significant,
and this adversely affects the accuracy. Specifically, pre-existing vibrations may be present and may
contaminate the calculations. To overcome this problem, large numbers of accelerometers are needed
and, even then, accuracy is relatively poor.
The effect temperature has on stiffness of concrete structures is a well-known phenomenon that
influences all health monitoring techniques and needs to be understood for a perfect structural health
monitoring system [27,28]. Concrete bridges are always subject to change in stiffness due to temperature
change as it affects the modulus of elasticity and compressive strength of concrete. Higher temperature
levels cause linear degradation in the modulus of elasticity and compressive strength of concrete,
which implies that any increase in temperature decreases the global stiffness of the bridge. Increases in
temperature affect the chemical bonds of concrete paste, causing breaking and disintegration of concrete
products and reducing the elastic modulus of concrete [26]. There is a consensus in the literature
that the relationship between the concrete modulus of elasticity and temperature is linear [27,28], but
there is no consensus on the slope of the linearity. Similar to concrete, glass material experiences
mechanical degradation due to long-term changes in humidity and temperature, which affect the
dynamic parameters of the structure [29]. Bedon illustrated the effect of changing ambient conditions
on bridge frequencies using a glass suspension footbridge [29]. Bedon et al. used a glass walkway
structure to demonstrate the correlation between the bridge frequencies and vibration comfort level [30].
In recent years, the application of smart sensors has gained interest among many researchers.
Chen et al. summarized the literature on smart SHM techniques for long-term monitoring of long-span
arch bridges [31]. Bridge strain and acceleration responses have been applied to a monitoring
system [31] commonly used to monitor traffic loading and extract modal parameters and bridge
frequencies to detect damage, respectively. Chen et al. also conducted a case study with the application
of five integrated subsystems for a smart SHM and assessed the advantages and disadvantages of
various signal processing techniques on bridge acceleration and strain responses [31]. They monitored
a long-span bridge in China for changing environmental and traffic load effects using an extensive
layout of fibre optic sensors and environmental sensors to develop an effective long-term SHM system.
Although the systems discussed in [31] have been found to be reasonably effective, they require a high
number of sensors on the bridge which makes the installation time-consuming and expensive.
In this paper, a novel smart approach to bridge damage detection, using a statistical analysis of
acceleration-based BWIM results, is proposed which not only identifies damage (Level I) but also
quantifies the extent of damage in the bridge. The acceleration responses are used directly to infer the
GVWs. This means that the proposed SHM system is able to monitor traffic loading as well as bridge
condition. A statistical analysis of the inferred GVWs allows the detection of damage. This approach is
shown to work with only one acceleration measurement, which can be measured using a portable
accelerometer, and information on axle configuration. Therefore, it can eliminate the requirement for
many sensors to be installed on the bridge. This will not only make the SHM system cost effective
but will also reduce the time to setup the system on the bridge. It is known that bridge accelerations
are sensitive to damage, i.e., loss of bridge stiffness [32,33]. Hence, a system that can reduce the
number of sensors will decrease the cost as well as time of installation. A statistical approach is
applied to the results to develop an effective method of bridge damage detection. To test the concept,
Appl. Sci. 2020, 10, 663
4 of 20
a one-dimensional vehicle model is simulated on a simply supported beam with a class ‘A’ road
profile [34] to obtain the bridge acceleration responses. Global stiffness loss due to a change in the bridge
modulus of elasticity is used as bridge damage. The BWIM results are calculated for various values of
vehicle parameters, and the statistical properties of the results are reviewed. Field measurements on
a reinforced concrete bridge in Slovenia are used as a complementary test of the concept.
2. Numerical Model
2.1. Bridge Model
The bridge model used in this paper is a 6 m long simply supported rectangular beam. The finite
element model of the beam contains 30 discretized beam elements having 4 degrees of freedom each for
translation and rotation at each end [35]. The mechanical properties of the bridge are shown in Table 1.
Table 1. Properties of the bridge.
Bridge Property
Notation
Value
Total no. of degrees of freedom
Young’s Modulus
2nd moment of area
Mass per unit length
Damping
1st natural frequency
Approach Length
N
E
J
µ
ξ
f1
Lapp
62
35 × 109 N/m2
0.114 m4
7000 kg/m
3%
32.2 Hz
100 m
The bridge accelerations at any location change with time depending on the vehicle position.
A sampling frequency (fs ) of 500 Hz is assumed. Nb is a (na × ns ) location matrix created for each axle
location on the bridge where ns is the total number of time steps and na is the number of axles. A road
profile, generated randomly according to the ISO standard [36], is added with a class ‘A’ roughness
to the MATLAB program [34], and an approach length is added to ensure that the vehicle degrees of
freedom are in equilibrium when the vehicle arrives on the bridge [37]. Dynamic responses of the
modelled beam to the moving vehicle are given by the system of equations at each time-step:
.
..
Kb yb + Cb yb + Mb yb = Nb fint
(1)
where Kb , Cb and Mb are the (n × n) bridge stiffness, damping and mass matrices, respectively,
.
..
and yb , yb and yb are the (n × ns ) vectors of bridge nodal displacements, velocities and accelerations,
respectively. fint is the vector of the total bridge and vehicle interaction forces containing static and
dynamic loads at an axle contact point. The dynamic loads are determined using the road profile and
the bridge displacement under each vehicle axle.
The damage considered in this paper is a percentage loss of bridge modulus of elasticity to
represent a global loss of bridge stiffness. The bridge stiffness, which is also related to the bridge
damage, changes proportionally with the change in the modulus of elasticity [27]. In the numerical
study in this paper, a percentage change in the concrete modulus of elasticity is used as a proxy of
damage due to temperature change.
2.2. Vehicle and System Models
Two types of vehicle model are used in this paper. The first one is a system of a quarter-car, and the
second one is a half-car crossing the bridge. A single quarter-car and two discrete quarter-cars are
used to assess the feasibility of the acceleration-based BWIM system as these models are not affected
by hop mass pitch rotation. The quarter-car model has 2 degrees of freedom (DOFs) which consist
of sprung mass bounce translation and axle hop translation [38]. The mechanical properties of the
quarter-car [39], other than its sprung mass, velocity and axle-spacing, are shown in Table 2.
of the quarter-car [39], other than its sprung mass, velocity and axle-spacing, are shown in Table 2.
Table 2. Properties of the quarter-car.
Appl. Sci. 2020, 10, 663
Quarter-Car Vehicle Property Notation
Value
Total degrees of freedom
nv
2
Table
2.
Properties
of
the
quarter-car.
Each unsprung mass
mu
750 kg
Each tyre
stiffness
Kt
3.5Value
× 106 N/m
Quarter-Car
Vehicle
Property
Notation
Each
suspension
stiffness
750 2× 103 N/m
Total
degrees of freedom
nv Ks
unsprung mass
mu
750 4kg
EachEach
suspension
damping
Cs
10 6 Ns/m
Each tyre stiffness
Each suspension stiffness
Each suspension
model,
showndamping
in Figure
Kt
Ks
isCsa
5 of 20
3.5 × 10 N/m
750 × 103 N/m
104 Ns/m representation
realistic
A half-car vehicle
1,
more
of a 2-axle
vehicle. This model has four DOF: sprung mass bounce displacement (ys,i), sprung mass pitch
half-car
model, shown inof
Figure
is aunsprung
more realistic
representation
2-axle
vehicle.
rotation (θ) Aand
axlevehicle
hop displacements
the 1,
two
axle
masses (yof
u,1aand
yu,2
). The vehicle
This model has four DOF: sprung mass bounce displacement (ys,i ), sprung mass pitch rotation (θ)
body is represented by a sprung mass (ms) and the suspension systems by the two unsprung axle
and axle hop displacements of the two unsprung axle masses (yu,1 and yu,2 ). The vehicle body is
masses (m
u,1 and mu,2). The sprung mass is connected to the axles through a combination of springs
represented by a sprung mass (ms ) and the suspension systems by the two unsprung axle masses
with linear
s,i)sprung
and viscous
dampersto with
damping
) andwith
to the road
(mu,1 stiffness
and mu,2 ). (K
The
mass is connected
the axles
through acoefficients
combination (C
of s,i
springs
stiffness (K
viscous
dampers with
coefficients
to the road surface
via
surface linear
via springs
with
linear
stiffnesses,
(Kdamping
t,i). Table
3 shows(Cthe
mechanical
properties
of the
s,i ) and
s,i ) and
springs with
stiffnesses,
(Kt,ito
). centre
Table 3 of
shows
the mechanical
properties
the model
[40,41].
model [40,41].
The linear
distance
of axles
gravity,
i.e., D1 and
D2, areoftaken
as half
of the total
The distance of axles to centre of gravity, i.e., D1 and D2 , are taken as half of the total axle spacing that
axle spacing that is chosen randomly in each simulation run using the typical two-axle traffic data.
is chosen randomly in each simulation run using the typical two-axle traffic data.
Figure 1. Section of a half-car vehicle model with general road profile on the bridge.
Figure 1. Section of a half-car vehicle model with general road profile on the bridge.
Table 3. Properties of the half-car model.
Table 3. Properties ofNotation
the half-car model.
Value
Half-Car Property
Total
degrees Property
of freedom
Half-Car
nv
4
Notation
Value
mu,1nv
750 kg
Total Unsprung
degreesmasses
of freedom
4
mu,2
1100 kg
mu,1
750 kg
Kt,1
1.75 × 106 N/m
Unsprung
masses
Tyre stiffness
mu,2
kg
Kt,2
3.5 ×1100
106 N/m
6
6
Kt,1
1.75
× 10
Ks,1
0.4 × 10
N/mN/m
Suspension
stiffness
Tyre stiffness
6
Ks,2
1 × 10
N/m
6 N/m
Kt,2
3.5
× 10
4
Cs,1
10 ×Ns/m
Ks,1
0.4
106 N/m
Suspension damping
Cs,2
20 × 103 Ns/m
Suspension stiffness
Ks,2
1 × 106 N/m
Cs,1
104 Ns/m
Equilibrium of forces
is used todamping
develop the equation of motion for the vehicle [33].
Suspension
Cs,2
20 × 103 Ns/m
.
..
Kv yv + Cv yv + Mv yv = fv
(2)
Appl. Sci. 2020, 10, 663
6 of 20
where Kv , Cv and Mv are the (nv × nv ) stiffness, damping and mass matrices of the vehicle respectively,
.
..
and yv , yv and yv are the (nv × ns ) vectors of vehicle displacements, velocities and accelerations,
respectively. The dynamic interaction forces applied to the vehicle DOFs through the road profile and
bridge displacements are contained in the vector, fv . The bridge and the vehicle models are coupled in
a global system at each axle contact point:
.
..
Kg u + C g u + M g u = F
(3)
where Mg and Cg are the coupled ((n + nv ) × (n + nv )) mass and damping matrices, respectively. Kg
is the time-varying coupled ((n + nv ) × (n + nv )) stiffness matrix and depends on the axle location
and the bridge static displacement due to vehicle loading. F is the force matrix of the coupled system
.
..
while u, u and u are the ((n + nv ) × ns ) vectors of displacements, velocities and accelerations of
the system, respectively. Equation (3) is solved in MATLAB using the Wilson-Theta integration
technique [42]. The Wilson-Theta value (θ) used in this method is 1.420815 for unconditional stability
in the integration process.
3. Statistical Approach Based on the Acceleration-Based BWIM System
3.1. Feasibility of the Concept
The idea of using the bridge acceleration response for a BWIM system was first proposed by
Sekiya et al. [26]. They derived the bridge displacements by integrating the acceleration responses
twice and used the derived signals in the conventional BWIM algorithm [26]. In this paper, the bridge
acceleration signals are used directly in the BWIM algorithm.
To simulate the acceleration response, the vehicle-bridge dynamic interaction model is programmed
in MATLAB using a quarter-car vehicle and the bridge model. Displacement, velocity and acceleration
at mid-span on the bridge are calculated. This location is chosen as it shows the maximum amplitude of
response. The influence line response, by definition, is the bridge acceleration due to a unit single-axle
load passing over the bridge and is required for the calibration of the BWIM system. The BWIM
algorithm [19] uses a comparison of the calculated and measured bridge responses. The calculated
response is found by summing the products of each axle weight and the influence line ordinate
corresponding to its location; see Equation (4). This assumes the principles of scaling: the acceleration
response to an axle with weight nW is n times the acceleration response to an axle with weight W
and superposition: the acceleration response to a multi-axle vehicle is the sum of the responses to its
individual axles. The calculated response for scan i is:
RTbi =
Xn a
j=1
W j I xi − d j
(4)
where Wj is the weight of axle j, I(x) is the influence line ordinate at distance x of unit-load from the
start of bridge, xi is the location of the first axle at scan i, dj is the distance of axle j from the first axle
(d1 = 0) and na is the number of axles.
Acceleration responses can be used effectively for BWIM if the relationship between the signal
amplitude and axle weight is linear or near to linear. This issue is explored by simulating the passage
of a single quarter-car over the bridge with masses ranging from 5 to 30 t. Accelerations on the bridge
are calculated and plotted for a constant vehicle velocity of 80 km/h. Using Monte Carlo simulation,
the vehicle mechanical properties are chosen randomly for each simulation run, assuming normal
distribution with standard deviations of 20%. To begin with, the bridge initial conditions are kept at
zero acceleration (static) in the model to represent ideal conditions, and a scanning frequency of 500 Hz
is assumed. All the acceleration responses are plotted in the time domain. The amplitude of the first
positive peak, which has the highest positive amplitude, is considered for the comparison. Figure 2
shows the bridge acceleration responses for different quarter-car masses (5 t to 30 t) using class ‘A’
road profile.
Appl. Sci. 2020, 10, x FOR PEER REVIEW
Appl. Sci. 2020, 10, x FOR PEER REVIEW
7 of 20
7 of 20
domain. The amplitude of the first positive peak, which has the highest positive amplitude, is
domain. The amplitude of the first positive peak, which has the highest positive amplitude, is
considered for the comparison. Figure 2 shows the bridge acceleration responses for different
considered for the comparison. Figure 2 shows the bridge acceleration responses for different
Appl. Sci. 2020,
10, 663
7 of 20
quarter-car
masses
(5 t(5tot 30
t) using
quarter-car
masses
to 30
t) usingclass
class‘A’
‘A’road
road profile.
profile.
Figure 2. Bridge mid-span first-peak acceleration responses for single quarter-cars with different
masses
same
road profile
is used acceleration
inacceleration
each run of responses
the generalfor
road
profile).
Figure
2.(the
Bridge
mid-span
first-peak
single
quarter-cars
withwith
different
Figure
2. Bridge
mid-span
first-peak
responses
for
single
quarter-cars
different
masses
(the
same
road
profile
is
used
in
each
run
of
the
general
road
profile).
masses (the same road profile is used in each run of the general road profile).
The first positive peak amplitudes, normalised with respect to the 5 t axle value, are repeated
The
first positive
peak amplitudes,
normalised
with
respect
to
5 t axle value,
are
for
for
and plotted
against
axle
mass
in the
Figure
bestvalue,
fitsrepeated
of are
the plots
Thethree
firstdifferent
positivebridge
peak profiles
amplitudes,
normalised
with
respect
to the3.5 The
t axle
repeated
three
different
bridge
profiles
and
plotted
against
axle
mass
in
Figure
3.
The
best
fits
of
the
plots
in
in Figure 3 show that the amplitudes follow a reasonably linear trend for each road profile which
for three
different
bridge
profiles
and
plotted
against
axle
mass
in
Figure
3.
The
best
fits
of
the
plots
Figure
3 show
the amplitudes
followare
a reasonably
linearthat
trendthere
for each
profile
which
suggests
suggests
that that
the bridge
accelerations
scalable given
is a road
constant
road
profile.
The
in Figure
3
show
that
the
amplitudes
follow
a
reasonably
linear
trend
for
each
road
profile
which
that
theofbridge
are
given
that
theresystem.
is a constant
road
The BWIM
slopes of
these
slopes
these accelerations
fits are related
toscalable
accuracy
of the
BWIM
Ideally
for profile.
an accurate
system,
suggests
that
the
bridge
accelerations
are
scalable
given
that
there
is
a
constant
road
profile.
The
fits
related
to fit
accuracy
BWIM
Ideally
for anFigure
accurate
BWIMofsystem,
the are
slope
of the
shouldof
bethe
1 [43].
Assystem.
it can be
seen from
3, slope
the fitsthe
lessslope
thanof1
slopes
offitthese
fitsbeare
related
accuracy
of
theFigure
BWIM
for an
accurate
BWIM
system,
the
should
1 [43].
As ittocan
be seenBWIM
from
3,system.
slope
of Ideally
the fits less
than
1inferred
suggests
that the
suggests
that
the
acceleration-based
system
will underestimate
the
weights.
the slope
of
the
fit
should
be
1
[43].
As
it
can
be
seen
from
Figure
3,
slope
of
the
fits
less
than 1
acceleration-based
BWIM
system
will
underestimate
the
inferred
weights.
However,
because
of
However, because of the slope is constant for each given road profile, the underestimation willthe
be
slope
is
constant
each given road profile,
the system
underestimation
will be constant.the inferred weights.
suggests
that
the for
acceleration-based
BWIM
will underestimate
constant.
However, because of the slope is constant for each given road profile, the underestimation will be
constant.
Figure 3. Relationship between axle mass and normalised 1st peak amplitude
amplitude for
for 33 different
different profiles.
profiles.
To
of superposition,
the acceleration
response
to twotoquarter-cars
with 5 twith
axles5att
Totest
testthe
theprinciple
principle
of superposition,
the acceleration
response
two quarter-cars
4axles
m spacing
and
the
sum
of
two
individual
acceleration
responses
to
individual
5
t
axles
with
a
velocity
at 4 m spacing and the sum of two individual acceleration responses to individual 5 t axles
of
80 km/h
are plotted
inbetween
Figure
4.
It can
seennormalised
that
ofpeak
thethat
individual
responses
matches
Figure
3. Relationship
axle
mass
and
1stseen
amplitude
for
different
profiles.
with
a velocity
of 80 km/h
are plotted
inbeFigure
4. Itthe
cansum
be
the sumaxle
of 3the
individual
axle
very
well
with
the
response
to
the
two
axles
together
(superposition).
Figures
3
and
4
suggest
the3
responses matches very well with the response to the two axles together (superposition). Figures
feasibility
of
the
acceleration-based
BWIM
system
and
indicate
the
effect
of
the
road
profile
on
the
To test
the principle
of superposition,
the acceleration
toindicate
two quarter-cars
and
4 suggest
the feasibility
of the acceleration-based
BWIM response
system and
the effect ofwith
the 5 t
ofon
thethe
BWIM
system.
axlesinaccuracy
at 4profile
m spacing
and
the
sum
of two
individual
road
inaccuracy
of the
BWIM
system. acceleration responses to individual 5 t axles
with a velocity of 80 km/h are plotted in Figure 4. It can be seen that the sum of the individual axle
responses matches very well with the response to the two axles together (superposition). Figures 3
and 4 suggest the feasibility of the acceleration-based BWIM system and indicate the effect of the
road profile on the inaccuracy of the BWIM system.
Appl. Sci. 2020, 10, x FOR PEER REVIEW
Appl. Sci. 2020, 10, 663
8 of 20
8 of 20
Appl. Sci. 2020, 10, x FOR PEER REVIEW
8 of 20
Figure 4. Bridge acceleration response to a two quarter-car vehicle and sum of the individual axle
Figure
4. 4.
Bridge
acceleration
response
to
vehicleand
andsum
sumofofthe
theindividual
individual
axle
Figure
Bridge
acceleration
response
to aa two
two quarter-car
quarter-car vehicle
axle
responses
using
the
class ‘A’ road
profile.
responses
using
the
class
‘A’
road
profile.
responses using the class ‘A’ road profile.
3.2. The
The BWIM
BWIM Analysis
Analysis Using
Using the
the Half-Car
Half-CarVehicle
VehicleModel
Model
3.2.
3.2. The BWIM Analysis Using the Half-Car Vehicle Model
The acceleration-based
acceleration-based BWIM
BWIM system
system analysis
analysis is
is carried
carried out
out using
using the
the half-car
half-car vehicle
vehicle model.
model.
The
The acceleration-based BWIM system analysis is carried out using the half-car vehicle model.
Thebridge
bridgemidspan
midspanacceleration
accelerationresponses
responses
a half-car
4m
axle
spacing
a constant
velocity
of
The
forfor
a half-car
at at
4m
axle
spacing
at aatconstant
velocity
of 80
The bridge midspan acceleration responses for a half-car at 4 m axle spacing at a constant velocity of
80
km/h
and
using
1st
and
2nd
axle
weights
of
9
and
11
t,
respectively,
are
simulated
using
first
a
km/h
and using
1st and
of 9 and
t, respectively,
are simulated
using using
first afirst
smooth
80 km/h
and using
1st2nd
andaxle
2ndweights
axle weights
of 911and
11 t, respectively,
are simulated
a
smooth
profile,
then
a
class
‘A’
road
profile.
A
‘calculated’
bridge
acceleration
response
is
found
for
profile,
then
a class
‘A’a road
profile.
A ‘calculated’
bridgebridge
acceleration
response
is found
for for
each
smooth
profile,
then
class ‘A’
road profile.
A ‘calculated’
acceleration
response
is found
each simulated
‘measured’
acceleration
response
using
the
BWIMand
equations
and
the bridge
simulated
‘measured’
acceleration
response
using
the
BWIM
equations
the
bridge
influence
line
each simulated ‘measured’ acceleration response using the BWIM equations and the bridge
influence
line
response.
The
simulated
‘measured’
and
the
‘calculated’
bridge
accelerations
are
response.
The
simulated
‘measured’
and the
‘calculated’
bridge
accelerationsbridge
are shown
in Figureare
5a,b,
influence
line
response.
The simulated
‘measured’
and
the ‘calculated’
accelerations
shown
in
Figure
5a,b,
using
smooth
profile
and
class
‘A’
road
[27],
respectively.
To
simulate
realistic
using
smooth
profile
class
‘A’ road
[27],
simulate
realistic
bridge conditions,
shown
in Figure
5a,b,and
using
smooth
profile
andrespectively.
class ‘A’ roadTo
[27],
respectively.
To simulate
realistic
bridge
conditions,
pre-existing
bridge
vibration
is
assumed
on
arrival
of
the
vehicle
bridge.
pre-existing
bridge vibration
is assumed
on arrival
of the vehicle
on the
bridge.
bridge conditions,
pre-existing
bridge vibration
is assumed
on arrival
of the
vehicle onon
thethe
bridge.
(a)
(a)
(b)
(b)
Figure
5. Mid-span
‘simulated
measured’
and corresponding
‘calculated’
bridge acceleration
responses
Figure
5. Mid-span
‘simulated
measured’
and corresponding
‘calculated’
bridge acceleration
Figure 5. Mid-span ‘simulated measured’ and corresponding ‘calculated’ bridge acceleration
using:
(a) smooth
(b) class
‘A’(b)
road
profile.
responses
using:profile;
(a) smooth
profile;
class
‘A’ road profile.
responses using: (a) smooth profile; (b) class ‘A’ road profile.
During
many
repetitions
‘measured’and
and‘calculated’
‘calculated’responses
responses
were
During
many
repetitionsofofthis
thisexercise,
exercise, simulated
simulated ‘measured’
were
During
many
repetitions
of
this
exercise,
simulated
‘measured’
and
‘calculated’
responses
were
seen
to be
similar,
although
somesome
bias isbias
present
when using
road profile,
mentioned
seen
to consistently
be consistently
similar,
although
is present
when ausing
a road as
profile,
as
seen
to
be
consistently
similar,
although
some
bias
is
present
when
using
a
road
profile,
as
in
the
section
above.
The
BWIM
algorithm
is
tested
using
the
half-car
vehicle
model
with
smooth
and
mentioned in the section above. The BWIM algorithm is tested using the half-car vehicle model with
mentioned
in
the
section
above.
The
BWIM
algorithm
is
tested
using
the
half-car
vehicle
model
with
class
‘A’ road
Moses’
algorithm,
illustrated
in Equations
(6) for a(5)2-axle
vehicle,
is based
smooth
andprofile.
class ‘A’
road profile.
Moses’
algorithm,
illustrated(5)
inand
Equations
and (6)
for a 2-axle
smooth
and
class ‘A’
road
profile.
illustrated
in Equations
and
(6) ‘calculated’
for aand
2-axle
on
the minimization
the
sum of Moses’
squared
differences
between
the
‘measured’
and
the
vehicle,
is based
on of
the
minimization
of thealgorithm,
sum of squared
differences
between(5)
the
‘measured’
vehicle,
is[19].
based
on
the minimization
of weights
the sum
of squared
differences
between
the sum
‘measured’
the ‘calculated’
responses
[19]. The
are
inferred
by setting
the
partial
derivatives
of theand
responses
The
axle
weights
are axle
inferred
by setting
the partial
derivatives
of the
of squared
the
‘calculated’
responses
[19].
The
axle
weights
are
inferred
by
setting
the
partial
derivatives
sum of squared
to Equation
zero, as shown
in Equation
(6). This
results
in aequations
systemofofthe
differences
to zero,differences
as shown in
(6). This
process results
in process
a system
of linear
in
sum
of
squared
differences
to
zero,
as
shown
in
Equation
(6).
This
process
results
in
a system of
linear
in terms
the unknown
terms
of equations
the unknown
axle of
weights,
Wj . axle weights, Wj.
linear equations in terms of the unknown axle weights, Wj.
Xnsn m
s
22
(R
−((W
(5) (5)
(xii)) +
E =E = ∑i=1
Rm
W1 II(x
+W
W1 1I(x
I(ix−
2 )))
i −
2 ))
i −dd
i
i=
ns1
m
2
∑
)
)))
E = i=1(R i −
(5)
∂E(W1 I(x i + W1 I(x i − d2
= 0; j = 1,2
(6)
∂Wj
∂E
∂E
==0;0; j =
= 1,2
1, 2
(6)
(6)
∂W
∂W
j j
Appl. Sci. 2020, 10, x FOR PEER REVIEW
9 of 20
Appl. Sci. 2020, 10, 663
9 of 20
where Rm
i is the measured bridge acceleration response for scan i, and ns is the total number of
scans. The accuracy
of the acceleration-based BWIM system is found by comparing the actual gross
where Rm
measured bridge acceleration response for scan i, and ns is the total number of scans.
i is
weights
used
tothe
generate
the accelerations with the corresponding inferred values.
The accuracy of the acceleration-based BWIM system is found by comparing the actual gross weights
Because of the consistent biasness between the ‘measured’ and the ‘calculated’ responses, the
used to generate the accelerations with the corresponding inferred values.
accuracy of individual vehicle weights is poor. Therefore, a statistical approach to the
Because of the consistent biasness between the ‘measured’ and the ‘calculated’ responses,
acceleration-based
BWIM system is considered in this paper. The acceleration responses to three sets
the accuracy of individual vehicle weights is poor. Therefore, a statistical approach to the
of 500
half-car vehicles
are used
the acceleration-based
system
under healthy
bridge
acceleration-based
BWIM
systemtoistest
considered
in this paper. TheBWIM
acceleration
responses
to three sets
conditions
and
the
results
are
plotted
in
the
form
of
histograms
in
Figure
6a,b
using
a
smooth
profile
of 500 half-car vehicles are used to test the acceleration-based BWIM system under healthy bridge
andconditions
a class ‘A’
respectively.
The
axleform
weights,
velocities
and axle
of theprofile
half-car
androad,
the results
are plotted
in the
of histograms
in Figure
6a,b spacings
using a smooth
vehicles
randomly,
using
Carlovelocities
simulation,
normal
distributions
and aare
classchosen
‘A’ road,
respectively.
The Monte
axle weights,
and assuming
axle spacings
of the half-car
vehicleswith
are and
chosen
randomly,
using Monte
Carlo two-axle
simulation,
assuming
with
means and of
means
standard
deviations
of typical
traffic
data.normal
In this distributions
section, initial
free-vibration
standardisdeviations
typicalthe
two-axle
traffic data.
In thistosection,
initialpassing
free-vibration
of the bridge
is
the bridge
generatedofusing
acceleration
response
an earlier
two quarter-car
vehicle
generated
using
the
acceleration
response
to
an
earlier
passing
two
quarter-car
vehicle
with
randomly
with randomly chosen vehicle properties. A single random profile of class ‘A’ is used for the
chosen vehicle
single random
profile
of classweights
‘A’ is used
the simulations.
can be
simulations.
It canproperties.
be seen inAFigure
6a that the
inferred
arefor
fairly
accurate andIt consistent
seen
in Figure
6a that
the inferred
weights
are fairly
accurate
and consistent
when aGVW
smooth
road
when
a smooth
road
profile
is used in
the analysis
and
the average
of the inferred
accuracies
profile is used in the analysis and the average of the inferred GVW accuracies for each set are −5.9%,
for each set are −5.9%, −5.8% and −6%, respectively. In Figure 6b, it can be seen that the
−5.8% and −6%, respectively. In Figure 6b, it can be seen that the acceleration-based BWIM system
acceleration-based BWIM system underestimates the axle weights quite significantly but this
underestimates the axle weights quite significantly but this inaccuracy is very consistent. The averages
inaccuracy is very consistent. The averages of the 500 inferred GVW accuracies of the BWIM system
of the 500 inferred GVW accuracies of the BWIM system for each set in Figure 6b with the half-car
for each
set in Figure 6b with the half-car vehicle model are −61.5%, −61.8% and −61.7%, respectively.
vehicle model are −61.5%, −61.8% and −61.7%, respectively. The road profile has a significant influence
Theon
road
profile has
significant influence
onTherefore,
the accuracy
of the acceleration-based
BWIM.
the accuracy
of thea acceleration-based
BWIM.
the acceleration-based
BWIM system
is
Therefore,
the
acceleration-based
BWIM
system
is
not
accurate;
however,
importantly,
it
is
not accurate; however, importantly, it is very consistent. It is this consistency we will use to detectvery
consistent.
is this
consistency
weaxle
will
use to detect damage, not the accuracy of the axle weights.
damage,Itnot
the accuracy
of the
weights.
(a)
(b)
Figure
6. Histograms
actualsimulated
simulatedGVWs
GVWs and
and inferred
case
of of
a healthy
bridge
Figure
6. Histograms
of of
actual
inferredGVWs
GVWsfor
forthe
the
case
a healthy
bridge
with 500 half-car vehicles using: (a) smooth profile; (b) class ‘A’ road profile.
with 500 half-car vehicles using: (a) smooth profile; (b) class ‘A’ road profile.
Appl. Sci. 2020, 10, x FOR PEER REVIEW
10 of 20
Appl.
Appl. Sci. 2020, 10, 663
x FOR PEER REVIEW
10 of 20
4. Damage Detection Using the Statistical Approach
4. Damage Detection Using the Statistical Approach
The aim
of this paper
to detect
bridge
damage using statistical analysis of acceleration-based
4. Damage
Detection
Usingisthe
Statistical
Approach
BWIM
results.
thepaper
results
of detect
inferred
GVWs
are repeatable
(consistent
estimates
of axle weights),
The
aim ofAs
this
is to
bridge
damage
using statistical
analysis
of acceleration-based
The
aim
of
this
paper
is
to
detect
bridge
damage
using
statistical
analysis
of
acceleration-based
there isresults.
a potential
of the
BWIM
system to
detectare
any
change in(consistent
bridge condition
since
is
BWIM
As the
results
of inferred
GVWs
repeatable
estimates
of acceleration
axle weights),
BWIM
As the
results
of
GVWs
are
estimates
of acceleration
axlethe
weights),
sensitive
damage.
is inferred
represented
here
asrepeatable
achange
global loss
in bridge
stiffness.
Since
change
there
isresults.
a to
potential
ofDamage
the
BWIM
system to
detect
any
in(consistent
bridge
condition
since
is
there
is a to
potential
of Damage
the BWIM
system
to detect
inof
bridge
condition
since
acceleration
is
in global
stiffness
affects
the bridge
accelerations
all
types
bridges
[44],
the
proposed
sensitive
damage.
is represented
hereany
asofachange
global
loss
in
bridge
stiffness.
Since
themethod
change
sensitive
to
damage.
Damage
is
represented
here
as
a
global
loss
in
bridge
stiffness.
Since
the
change
could
be stiffness
expanded
to bridges
made
of differentof materials.
simulated
bridge
with method
various
in
global
affects
the bridge
accelerations
all types ofThe
bridges
[44], the
proposed
in
global
stiffness
affects
the half-car
bridge
accelerations
ofare
all types
bridges
[44],
the
proposed
damage
and
the
vehicle
model
tested of
numerically,
and
the
potential
of the
could
beconditions
expanded
to bridges
made
of different
materials.
The
simulated
bridge
with method
various
could
be
expanded
to
bridges
made
of
different
materials.
The
simulated
bridge
with
various
damage
statisticalconditions
approachand
for the
bridge
health
monitoring
is assessed.
A statistical
is applied,
damage
half-car
vehicle
model are
tested numerically,
andapproach
the potential
of the
conditions
and
the half-car
vehicle
model
are 7tested
the
potential
of the
comparingapproach
the mean
inferred
GVWs.
Figure
illustrates
a schematic
diagram
of the
methodology
statistical
for
bridge
health
monitoring
isnumerically,
assessed.
Aand
statistical
approach
isstatistical
applied,
approach
bridge
health
monitoring
is assessed.
A statistical
approach
is
applied,
the
for bridgefor
damage
using
a statistical
approach
to the
acceleration-based
BWIM
comparing
the
meandetection
inferred
GVWs.
Figure
7 illustrates
aapplied
schematic
diagram
of thecomparing
methodology
mean
inferred
GVWs.
Figure 7using
illustrates
a schematic
diagram
of theto
methodology
for bridge damage
system
data.
for
bridge
damage
detection
a statistical
approach
applied
the acceleration-based
BWIM
detection
using
a
statistical
approach
applied
to
the
acceleration-based
BWIM
system
data.
system data.
Figure 7. Schematic diagram of the methodology of bridge damage detection using the
Figure
7.7.Schematic
diagram
of the methodology
of bridge damage
detection
using detection
the acceleration-based
acceleration-based
BWIM
system.
Figure
Schematic
diagram
of the methodology
of bridge
damage
using the
BWIM
system.
acceleration-based BWIM system.
It is seen in Figure 6a that the acceleration-based BWIM system underestimates the axle weights
It
seen
6a
the
BWIM
system
underestimates
the
weights
and is
statistically
biased.
However,
this inaccuracy is
consistent,
therefore, it can
be used
as a
It is
is
seen in
in Figure
Figure
6a that
that
the acceleration-based
acceleration-based
BWIM
systemand
underestimates
the axle
axle
weights
and
is
statistically
biased.
However,
this
inaccuracy
is
consistent,
and
therefore,
it
can
be
baseline
for detecting
any change
in the
condition.
As the accelerations
are itsensitive
toused
bridge
and
is statistically
biased.
However,
thisbridge
inaccuracy
is consistent,
and therefore,
can be used
asasa
abaseline
baselinefor
fordetecting
detectingany
anychange
changein
thebridge
bridgecondition.
condition.
Asthe
thewhen
accelerations
areissensitive
sensitive
to Global
bridge
damage,
the
statistical
properties
ofinthe
inferred
GVWs change
the bridge
damaged.
As
accelerations
are
to
bridge
damage,
the
statistical
properties
of
the
inferred
GVWs
change
when
the
bridge
is
damaged.
Global
loss of stiffness
is usedproperties
as a proxyofofthe
damage.
Loss
of stiffness
a concrete
bridge
generally Global
occurs
damage,
the statistical
inferred
GVWs
change in
when
the bridge
is damaged.
loss
as
Loss
of
in
bridge
generally
occurs
due of
tostiffness
change is
in
concrete
modulus
of elasticity
This change
in bridge
condition
affects
the
loss
of
stiffness
is used
used
as aa proxy
proxy of
of damage.
damage.
Loss[27].
of stiffness
stiffness
in aa concrete
concrete
bridge
generally
occurs
due
to
change
in
concrete
modulus
of
elasticity
[27].
This
change
in
bridge
condition
affects
the
bridge
bridge
response,
and hence
the[27].
accuracy
the acceleration-based
BWIM
system.
due
to acceleration
change in concrete
modulus
of affects
elasticity
This of
change
in bridge condition
affects
the
acceleration
response,
and hence
affects
the
accuracy
of mid-span
the acceleration-based
BWIM
system.
8
Figure acceleration
8 shows
theresponse,
effect
of and
bridge
damage
on
response
to a Figure
half-car
bridge
hence
affects
thethe
accuracy
of theacceleration
acceleration-based
BWIM
system.
shows
effect
bridge
on damage
theThe
mid-span
acceleration
response
to a8response
half-car
vehicle
using
vehiclethe
oneof
class
‘A’damage
road
profile.
velocity
ofmid-span
the vehicles
in Figure
is kept constant
at 80
Figure
8using
shows
the
effect
of bridge
on the
acceleration
to a half-car
one
class
‘A’
road
profile.
The
velocity
of
the
vehicles
in
Figure
8
is
kept
constant
at
80
km/h.
km/h. using one class ‘A’ road profile. The velocity of the vehicles in Figure 8 is kept constant at 80
vehicle
km/h.
Figure 8.
8. Effect of bridge damage in the mid-span bridge acceleration using the class ‘A’ road profile.
profile.
Figure
Figure 8. Effect of bridge damage in the mid-span bridge acceleration using the class ‘A’ road profile.
Appl. Sci. 2020, 10, 663
Appl. Sci. 2020, 10, x FOR PEER REVIEW
11 of 20
11 of 20
DueDue
to damage,
thethe
acceleration-based
uses the
the ‘calculated’
‘calculated’
to damage,
acceleration-basedBWIM
BWIMsystem
systemmalfunctions
malfunctions as
as it
it uses
response
(influence
line)
for for
thethe
healthy
bridge.
TheThe
gross
weights
inferred
by by
thethe
BWIM
system
are
response
(influence
line)
healthy
bridge.
gross
weights
inferred
BWIM
system
presented
in
Figure
9
for
500
trucks
using
the
half-car
vehicle
model.
The
relative
axle
weights,
are presented in Figure 9 for 500 trucks using the half-car vehicle model. The relative axle weights,
velocities,
axleaxle
spacings
and
pre-existing
forthe
thetrucks
truckswhich
which
velocities,
spacings
and
pre-existingbridge
bridgevibrations
vibrationsare
are chosen
chosen randomly
randomly for
are are
simulated
on the
bridge
withwith
a class
‘A’ profile
withwith
different
percentage
losses
of stiffness.
The
simulated
on the
bridge
a class
‘A’ profile
different
percentage
losses
of stiffness.
percentage
loss ofloss
stiffness
ranges
fromfrom
1% loss
(low)
to to
10%
loss
that
The percentage
of stiffness
ranges
1% loss
(low)
10%
loss(severe).
(severe). ItIt is
is acknowledged
acknowledged that
lossofofstiffness
stiffness isisa significant
change
in bridge
temperature;
however, however,
the higher loss
10%10%
loss
a significant
change
in bridge
temperature;
the percentages
higher loss
are shownare
to shown
demonstrate
the concept.the concept.
percentages
to demonstrate
Figure
9. Normal
distributioncurves
curvesfitted
fittedto
to inferred
inferred GVWs
model
using
the the
classclass
‘A’
Figure
9. Normal
distribution
GVWsusing
usinga ahalf-car
half-car
model
using
road profile
losses
of stiffness.
‘A’ road
profilewith
withdifferent
differentpercentage
percentage
losses
of stiffness.
seen in
acceleration-based
BWIMBWIM
results demonstrate
observableobservable
variation
As As
cancanbebeseen
in Figure
Figure9, the
9, the
acceleration-based
results demonstrate
in the statistical properties when there is global loss of bridge stiffness. The variations of the means
variation in the statistical properties when there is global loss of bridge stiffness. The variations of
and standard deviations of the inferred GVWs with loss of stiffness are calculated. The relationship
the means and standard deviations of the inferred GVWs with loss of stiffness are calculated. The
between the mean inferred GVWs and percentage loss of stiffness is found to be non-linear, but the
relationship between the mean inferred GVWs and percentage loss of stiffness is found to be
standard deviation shows a significant and roughly linear increase with increase in the percentage
non-linear, but the standard deviation shows a significant and roughly linear increase with increase
stiffness loss (about 17.5% increase for 3% increase in stiffness loss and a coefficient of determination
in the percentage stiffness loss (about 17.5% increase for 3% increase in stiffness loss and a coefficient
(R-squared) value of 99.6%) (see Figure 10a). The sensitivity of the standard deviation to loss of stiffness
of determination
(R-squared)
value
of 99.6%)
(seeforFigure
10a).
The sensitivity
of 10b.
the For
standard
is considerably greater
than first
natural
frequency,
example,
as illustrated
in Figure
each
deviation
to
loss
of
stiffness
is
considerably
greater
than
first
natural
frequency,
for
example,
percentage loss of stiffness, 1st bridge natural frequency is calculated using a fast Fourier transform ofas
illustrated
in (forced)
Figure 10b.
For eachdue
percentage
of The
stiffness,
1staxle
bridge
natural
frequency
the bridge
accelerations
to passing loss
trucks.
vehicle
weights
and velocities
areis
calculated
using a fast
transform
of shows
the bridge
(forced)
accelerations
duewith
to passing
trucks.
chosen randomly
forFourier
each run.
Figure 10b
an almost
linear
negative slope
an R-squared
Thevalue
vehicle
axle
weights
and
velocities
are
chosen
randomly
for
each
run.
Figure
10b
shows
an
of 96.7%. It can be seen that the bridge frequency decreases by about 1.2% for a 3% increase in
almost
linear negative
slope
an R-squared
value
of 96.7%.
can beGVW
seenisthat
the bridge
the percentage
stiffness
loss. with
Therefore,
the standard
deviation
of theItinferred
proposed
here
frequency
decreases
by loss
about
1.2% forofa the
3% bridge.
increase in the percentage stiffness loss. Therefore, the
as an indicator
of the
of stiffness
standard deviation of the inferred GVW is proposed here as an indicator of the loss of stiffness of the
bridge.
(a)
The vehicle axle weights and velocities are chosen randomly for each run. Figure 10b shows an
almost linear negative slope with an R-squared value of 96.7%. It can be seen that the bridge
frequency decreases by about 1.2% for a 3% increase in the percentage stiffness loss. Therefore, the
standard deviation of the inferred GVW is proposed here as an indicator of the loss of stiffness of the
Appl. Sci. 2020, 10, 663
12 of 20
bridge.
Appl. Sci.
2020,
x FOR
REVIEW
Appl.
Sci.10,
2020,
10, x PEER
FOR PEER
REVIEW
(a)
12 of 2012 of 20
(b)
Figure 10. Change in damage indicators with the
(b) percentage loss of bridge stiffness: (a) standard
deviation of inferred GVWs; (b) mean 1st bridge natural frequency.
10. Change
in damage
indicatorswith
with the
the percentage
bridge
stiffness:
(a) standard
FigureFigure
10. Change
in damage
indicators
percentageloss
lossof of
bridge
stiffness:
(a) standard
deviation of inferred GVWs; (b) mean 1st bridge natural frequency.
deviation
of inferred GVWs; (b) mean 1st bridge natural frequency.
5. Field Tests
5. Field
TheTests
statistical approach of the proposed bridge health monitoring technique is tested on a
healthy
concrete
culvertoftothe
assess
the repeatability
of monitoring
results under
field conditions.
Inathe
field
The statisticalslab
approach
proposed
bridge health
technique
is tested on
healthy
analysis,
the
global
change
in
stiffness
(due
to
temperature
change)
is
studied
to
investigate
the on a
concrete
slab culvert
to assess
resultshealth
under field
conditions.
In the fieldisanalysis,
The
statistical
approach
of the
therepeatability
proposed of
bridge
monitoring
technique
tested
change
in statistical
of BWIM
data. The Šentvid
bridge
(see
Figure
11),
used
theInfield
the
global
change
inproperties
stiffness
(due
tothe
temperature
change)
is studied
to investigate
thefor
change
in field
healthy
concrete
slab culvert
to assess
repeatability
of results
under
field
conditions.
the
testing,
is
a
6
m
long
frame/culvert
carrying
two
lanes
of
traffic
and
is
located
in
the
north
of
statistical
properties
of BWIM
data. The
Šentvid
bridge (see Figure
11),isused
for thetofield
testing,
analysis,
the global
change
in stiffness
(due
to temperature
change)
studied
investigate
the
Ljubljana,
Slovenia.
is
a 6 m long
frame/culvert carrying two lanes of traffic and is located in the north of Ljubljana, Slovenia.
5. Field Tests
change in statistical properties of BWIM data. The Šentvid bridge (see Figure 11), used for the field
testing, is a 6 m long frame/culvert carrying two lanes of traffic and is located in the north of
Ljubljana, Slovenia.
Figure 11. The Šentvid bridge in Slovenia.
Figure 11. The Šentvid bridge in Slovenia.
Each culvert structure is instrumented with a bridge weigh-in-motion system consisting of four
free-of-axle-detector (FAD) transducers [21] and 12 weighing strain transducers which are widely
used for a typical BWIM system. Figure 12 shows a plan layout of the transducers on the Šentvid
Figure
11. The Šentvid
in Slovenia.
bridge with dimensions in the
International
Systembridge
of Units.
The FAD transducers (7–8 and 15–16)
are located near the quarter points of each culvert and are used for vehicle axle detection and to find
Each
culvertbetween
structure
is instrumented
withtransducers
a bridge weigh-in-motion
of four
the spacing
axles.
The weighing strain
(1–6 and 9–14) are system
mountedconsisting
mid-span of
Appl. Sci. 2020, 10, 663
13 of 20
Each culvert structure is instrumented with a bridge weigh-in-motion system consisting of four
free-of-axle-detector (FAD) transducers [21] and 12 weighing strain transducers which are widely used
for a typical BWIM system. Figure 12 shows a plan layout of the transducers on the Šentvid bridge
with dimensions in the International System of Units. The FAD transducers (7–8 and 15–16) are located
near the quarter points of each culvert and are used for vehicle axle detection and to find the spacing
between axles. The weighing strain transducers (1–6 and 9–14) are mounted mid-span of the 6 m long
Appl. Sci. 2020,structure
10, x FOR[45].
PEER
TheREVIEW
sampling frequency of all sensors is 512 Hz.
13 of 20
Plan layout
the transducers on
on the
bridge
(dimensions
in m).
Figure 12.Figure
Plan 12.
layout
of theof transducers
theŠentvid
Šentvid
bridge
(dimensions
in m).
The acceleration-based BWIM can be applied to accelerometers or existing strain-based systems.
The acceleration-based
BWIM
can common
be applied
to accelerometers
or existing
strain-based
Strain-based WIM (SiWIM)
[43] is more
as the accelerometer
WIM is still in early
development.
For
the
field
tests,
one
year
of
data
of
passing
trucks
with
axle-weights
calculated
from
the
SiWIM
systems. Strain-based WIM (SiWIM) [43] is more common as the accelerometer WIM is still in early
system is used. The mid-span strain responses of the bridge are used to approximate the acceleration
development.
For the field tests, one year of data of passing trucks with axle-weights calculated from
responses as the difference of strain differences. It should be noted that these derived accelerations are
the SiWIM system
is used. The
mid-span rather
strainthan
responses
the bridge
arebeused
to approximate
the
oriented horizontally
(longitudinally)
vertically, of
as would
normally
measured
using
accelerometer.
remainder ofofthe
paper, differences.
acceleration response
means be
derived
accelerations
accelerationanresponses
as For
thethedifference
strain
It should
noted
that these derived
from the SiWIM.
accelerations are oriented horizontally (longitudinally) rather than vertically, as would normally be
The strain response at a sensor location 6 which is under one of the wheel tracks of the trucks
measured using
anin the
accelerometer.
For the
remainder
the paper,
means
traveling
slow lane of the bridge
is used
to derive the of
accelerations
in thisacceleration
way. Figure 13a response
shows
the strain response
a typical
5-axle truck. The peaks on the left side correspond to the passage of the
derived accelerations
fromtothe
SiWIM.
first
two
axles
while
the
peak
on
the right corresponds
tridemone
axleof
group.
derived
second
The strain response at a sensor location
6 which to
is the
under
the The
wheel
tracks
of the trucks
derivative of the strains is shown in Figure 13b.
traveling in the slow lane of the bridge is used to derive the accelerations in this way. Figure 13a
shows the strain response to a typical 5-axle truck. The peaks on the left side correspond to the
passage of the first two axles while the peak on the right corresponds to the tridem axle group. The
derived second derivative of the strains is shown in Figure 13b.
derived accelerations from the SiWIM.
The strain response at a sensor location 6 which is under one of the wheel tracks of the trucks
traveling in the slow lane of the bridge is used to derive the accelerations in this way. Figure 13a
shows the strain response to a typical 5-axle truck. The peaks on the left side correspond to the
passage of the first two axles while the peak on the right corresponds to the tridem axle group. The
Appl. Sci. 2020, 10, 663
14 of 20
derived second derivative of the strains is shown in Figure 13b.
Appl. Sci. 2020, 10, x FOR PEER REVIEW
14 of 20
(a)
(b)
Figure
Figure13.
13.Measured
Measuredresponse
responseof
ofthe
theŠentvid
Šentvidbridge
bridgeto
tothe
thepassage
passageof
ofaatypical
typical5-axle
5-axletruck:
truck:(a)
(a)Strain;
Strain;
(b)
Derived
acceleration.
(b) Derived acceleration.
5.1.Initial
InitialCalibration
Calibrationfor
forAcceleration-Based
Acceleration-BasedBWIM
BWIMAnalysis
Analysison
onField
FieldData
Data
5.1.
A BWIM
BWIManalysis
analysisisiscarried
carriedout
outusing
usingthe
thederived
derivedacceleration
accelerationresponses
responsesfrom
fromaayear
yearof
oftraffic
traffic
A
passing
over
the
bridge.
A
total
number
of
398,445
multi-axle
vehicles
crossed
the
bridge
in
passing over the bridge. A total number of 398,445 multi-axle vehicles crossed the bridge in 2014.2014.
As
As the
vehicle
velocity
a strong
impact
BWIM
analysis
[46],the
thevelocity
velocityrange
rangeofofdata
dataneeds
needs
the
vehicle
velocity
hashas
a strong
impact
onon
thethe
BWIM
analysis
[46],
to be
be selected.
data
areare
filtered
by using
only 5-axle
truckstrucks
passingpassing
within the
velocity
to
selected. Thus,
Thus,the
thetraffic
traffic
data
filtered
by using
only 5-axle
within
the
range
of
23.5
m/s
to
25.5
m/s,
which
covers
70%
of
vehicle
velocities,
and
the
GVW
range
of
15.75
to
velocity range of 23.5 m/s to 25.5 m/s, which covers 70% of vehicle velocities, and the GVW rangetof
16.75 tt.toAs
a result,
5208 trucks
across
theacross
full year
used
analysis.
15.75
16.75
t. As aa dataset
result, aofdataset
of 5208
trucks
the is
full
yearfor
is the
used
for the analysis.
To
implement
the
BWIM
concept,
an
influence
line
response
is
required
for calibration,
i.e.,
To implement the BWIM concept, an influence line response is required for calibration,
i.e., the
the
acceleration
response
corresponding
to
the
passage
of
an
axle
of
unit
weight.
In
this
section,
acceleration response corresponding to the passage of an axle of unit weight. In this section, the
the influence
is back-calculated
from
acceleration
responses
similar
thatshown
shownininFigure
Figure13b
13b
influence
line line
is back-calculated
from
acceleration
responses
similar
to to
that
using
the
matrix
approach
described
by
[47].
In
a
process
similar
to
that
used
to
estimate
masses
[19],
using the matrix approach described by [47]. In a process similar to that used to estimate masses [19],
OBrien et
et al.
al. found
foundthe
theinfluence
influencecurve
curvewhich
whichgives
givesaaleast
leastsquare
square fit
fit of
of calculated
calculated to
to measured
measured
OBrien
accelerations
[47].
accelerations [47].
The acceleration
acceleration responses
responsesto
to 10
10 trucks
trucks (all
(all 55 axle
axle trucks)
trucks) passing
passing the
the bridge
bridge with
with aa constant
constant
The
internalbridge
bridgetemperature
temperatureare
areused
usedto
tocalculate
calculate10
10influence
influenceline
lineresponses,
responses,as
asshown
shownininFigure
Figure14.
14.
internal
A
sample
of
10
trucks
from
the
5208
trucks
is
used
as
any
greater
sample
size
made
little
difference
A sample of 10 trucks from the 5208 trucks is used as any greater sample size made little difference
to the
the accuracy
accuracy of
of the
the influence
influence line.
line. All
All10
10runs
runs took
took place
place when
when the
the measured
measured internal
internal bridge
bridge
to
◦
temperaturewas
was20
20 °C,
C, to
to keep
keep the
the bridge
bridge environmental
environmental conditions
conditions consistent.
consistent. The
Theinfluence
influenceline
line
temperature
response
for
each
truck
passage
is
adjusted
by
shifting
the
phase,
i.e.,
aligning
the
highest
peak
points
response for each truck passage is adjusted by shifting the phase, i.e., aligning the highest peak
in the response.
Finally,Finally,
the influence
line usedline
for used
the analysis
taken asisthe
mean
themean
curves.
It is
points
in the response.
the influence
for theisanalysis
taken
asofthe
of the
shown
in
Figure
14
as
a
solid
black
line.
curves. It is shown in Figure 14 as a solid black line.
A sample of 10 trucks from the 5208 trucks is used as any greater sample size made little difference
to the accuracy of the influence line. All 10 runs took place when the measured internal bridge
temperature was 20 °C, to keep the bridge environmental conditions consistent. The influence line
response for each truck passage is adjusted by shifting the phase, i.e., aligning the highest peak
points
in the response. Finally, the influence line used for the analysis is taken as the mean
of the
Appl. Sci. 2020, 10, 663
15 of 20
curves. It is shown in Figure 14 as a solid black line.
Figure14.
14.Bridge
Bridgemid-span
mid-span acceleration
to to
unit-weight
axleaxle
fromfrom
10 truck
responses
and theand
Figure
accelerationresponses
responses
unit-weight
10 truck
responses
◦ C temperature.
Appl. Sci.
2020, 10, xline
FORresponse
PEER REVIEW
15 of 20
mean
influence
at
20
the mean influence line response at 20 °C temperature.
Figure
15. shows
the typical
measured
acceleration
response
to atruck
5-axle
and the
Figure
15. shows
the typical
measured
acceleration
response
to a 5-axle
andtruck
the corresponding
corresponding calculated response, calculated using the mean influence line. It can be seen from
calculated response, calculated using the mean influence line. It can be seen from Figure 15 that the
Figure15 that the calculated response matches the measured bridge response to a 5-axle truck fairly
calculated response matches the measured bridge response to a 5-axle truck fairly well, and the BWIM
well, and the BWIM system can be developed using the mean influence line (also shown in Figure
system
can be developed using the mean influence line (also shown in Figure 14).
14).
Figure
Typical
measuredbridge
bridge acceleration
acceleration response
truck
andand
corresponding
Figure
15. 15.
Typical
measured
responsetotoa a5-axle
5-axle
truck
corresponding
calculated
response.
calculated
response.
5.2. Effect
of Bridge
Temperature—StatisticalApproach
Approach to Damage
5.2. Effect
of Bridge
Temperature—Statistical
DamageDetection
Detection
In section,
this section,
the statistical
approach
for detecting
a change
in the
bridge
stiffness
to
In this
the statistical
approach
for detecting
a change
in the
bridge
stiffness
duedue
to change
change
in
temperature
is
investigated.
In
this
study,
the
internal
bridge
deck
temperature,
and
its
in temperature is investigated. In this study, the internal bridge deck temperature, and its subsequent
subsequent change over a year, is used as a proxy for the bridge condition; if the BWIM system
change
over a year, is used as a proxy for the bridge condition; if the BWIM system responds to
responds to changes in temperature, it should also be sensitive to damage. Figure 16 shows the
changes in temperature, it should also be sensitive to damage. Figure 16 shows the change in the
change in the internal temperature of the Šentvid bridge over one year. It can be seen in Figure 16
internal
temperature of the Šentvid bridge over one year. It can be seen in Figure 16 that while
that while there is considerable variability, there is a clear difference between summer and winter
theretemperatures.
is considerable
there is a clear
difference
summer
winter
temperatures.
Thevariability,
internal temperatures
are divided
intobetween
6 intervals
based and
on equal
numbers
of
The internal
temperatures
are
divided
into
6
intervals
based
on
equal
numbers
of
trucks,
i.e.,
868 trucks
trucks, i.e., 868 trucks per interval (i.e., 5208 in total). This approach resulted in the intervals of 6.5–22
per interval
(i.e.,
total).
approach
resulted
in the intervals of 6.5–22 ◦ C, 22–25 ◦ C, 25–30 ◦ C,
°C, 22–25
°C,5208
25–30in°C,
30–33This
°C, 33–35
°C and
35–44 °C.
◦
◦
◦
30–33 C, 33–35 C and 35–44 C.
The BWIM analysis is carried out to compare the change in the statistical properties of the inferred
steer-axle weights with the change in the mean internal bridge temperature. The influence line response
from Figure 14 is used for this analysis which is calculated using a constant internal bridge temperature
of 20 ◦ C. The reason for using the steer-axle weight is the low variability of this parameter; the steer
axle takes the weight of the engine and is therefore less variable than the weights of the other axles.
responds to changes in temperature, it should also be sensitive to damage. Figure 16 shows the
change in the internal temperature of the Šentvid bridge over one year. It can be seen in Figure 16
that while there is considerable variability, there is a clear difference between summer and winter
temperatures. The internal temperatures are divided into 6 intervals based on equal numbers of
trucks, i.e., 868 trucks per interval (i.e., 5208 in total). This approach resulted in the intervals of 6.5–22
Appl. Sci. 2020, 10, 663
16 of 20
°C, 22–25 °C, 25–30 °C, 30–33 °C, 33–35 °C and 35–44 °C.
Appl. Sci. 2020, 10, x FOR PEER REVIEW
16 of 20
bridge temperature of 20 °C. The reason for using the steer-axle weight is the low variability of this
parameter; the steer axle takes the weight of the engine and is therefore less variable than the
weights of the other axles.
5.3. Results and Discussion
The steer-axle weights are inferred from the derived acceleration responses to 5-axle trucks
crossing the Šentvid bridge. Figure 17a shows the histogram of actual steer-axle weights of trucks
internal
temperature
of the
the
Šentvid
bridgeinin2014.
2014.inferred weights
Figure16.
16.Measured
Measured
internalmean
temperature
of
Šentvid
bridge
that crossed theFigure
bridge
within
the interval
of 20 °C
and
the corresponding
the acceleration-based
BWIM system.
5.3.using
Results
Discussion
The and
BWIM
analysis is carried out to compare the change in the statistical properties of the
The same analysis is performed for different intervals of bridge temperature to assess the
inferred
steer-axleweights
weights withinferred
the change in the
internal bridge temperature.
The
influence
The steer-axle
the mean
derived
responses
to
5-axle
sensitivity
of the statistical are
properties of from
the BWIM
system acceleration
to temperature.
Figure 17b
showstrucks
the
line response
frombridge.
Figure Figure
14 is used
for
this the
analysis
whichofisactual
calculated
usingweights
a constanttrucks
internal
crossing
Šentvid
17athe
shows
histogram
steer-axle
that
normalthedistribution
curve fits to
histograms
of inferred
steer-axle
weights forof different
crossed
the bridge
withinItthe
interval
mean
of 20 ◦17b
C and
corresponding
inferred
weights
using
temperature
intervals.
can
be seen
in Figure
thatthe
there
are reasonable
changes
in both
thethe
mean and the standard
acceleration-based
BWIMdeviation
system. with temperature.
(a)
(b)
Figure
Histogramsof
ofactual
actual weights
weights and the
at at
2020
°C◦ C
Figure
17.17.(a)(a)Histograms
the inferred
inferredsteer-axle
steer-axleweights
weightsofoftrucks
trucks
internal
bridge
temperature;(b)
(b)Normal
Normal distribution
distribution fits
with
different
internal
bridge
temperature;
fits of
ofinferred
inferredsteer-axle
steer-axleweights
weights
with
different
mean
internal
temperatures.
mean
internal
temperatures.
The change in the standard deviation with temperature is illustrated in Figure 18. It can be seen
that the standard deviation of the inferred weights increases almost linearly with the increase in the
temperature, with an R-squared value of 89.7%. The standard deviation increases by about 10% due
to a 10 °C increase in the bridge internal temperature which means that statistically, the
acceleration-based BWIM data change with the change in bridge stiffness. Previously, the
Appl. Sci. 2020, 10, 663
17 of 20
The same analysis is performed for different intervals of bridge temperature to assess the
sensitivity of the statistical properties of the BWIM system to temperature. Figure 17b shows the
normal distribution curve fits to the histograms of inferred steer-axle weights for different temperature
intervals. It can be seen in Figure 17b that there are reasonable changes in both the mean and the
standard deviation with temperature.
The change in the standard deviation with temperature is illustrated in Figure 18. It can be seen
that the standard deviation of the inferred weights increases almost linearly with the increase in the
temperature, with an R-squared value of 89.7%. The standard deviation increases by about 10% due to
2020, 10, xinFOR
REVIEW
17 of 20
aAppl.
10 ◦Sci.
C increase
thePEER
bridge
internal temperature which means that statistically, the acceleration-based
BWIM data change with the change in bridge stiffness. Previously, the percentage change of standard
percentage
change in
ofthe
standard
deviation
obtained
in the numerical
analysis
thetoone-dimension
deviation
obtained
numerical
analysis
of the one-dimension
bridge
beamofdue
global loss of
bridge
beam
due
to
global
loss
of
stiffness
is
seen
to
be
more
significant
(Figure
10)
as compared
to
stiffness is seen to be more significant (Figure 10) as compared to the percentage change
in the field
the percentage
change
in the
analysis
(Figure it18).
Despite thetoreduced
is
analysis
(Figure 18).
Despite
the field
reduced
performance,
is encouraging
see fieldperformance,
evidence that it
this
encouraging
to
see
field
evidence
that
this
parameter,
through
most
of
the
temperature
range,
parameter, through most of the temperature range, provides a reasonable indication of a change in the
provides
a reasonable indication of a change in the bridge stiffness.
bridge
stiffness.
Figure 18. Inferred steer-axle weight standard deviation against the bridge internal temperature.
Figure 18. Inferred steer-axle weight standard deviation against the bridge internal temperature.
6. Conclusions
6. Conclusions
In this paper, a novel method of bridge damage detection using a statistical approach from
In this paper,BWIM
a novel
method
of bridge
using
a statistical
from
acceleration-based
data
is proposed
anddamage
its abilitydetection
to quantify
bridge
damage approach
is investigated.
acceleration-based
BWIM
data important
is proposed
and its
ability
to quantify
bridge damage
is investigated.
The
bridge accelerations
contain
bridge
health
condition
information.
As a result,
the inferred
The
bridge
accelerations
contain
important
bridge
health
condition
information.
As
result, the
BWIM weights are damage sensitive. Global uniform loss of bridge stiffness is used as aameasure
of
inferred
BWIM
weights
are
damage
sensitive.
Global
uniform
loss
of
bridge
stiffness
is
used
as
the damage, and statistical properties of the inferred BWIM results, specifically standard deviation,a
measure
and statistical
properties
of the
results, simulation,
specifically this
standard
are
shownoftothe
bedamage,
well correlated
with bridge
stiffness.
Ininferred
additionBWIM
to numerical
new
deviation,
are
shown
to
be
well
correlated
with
bridge
stiffness.
In
addition
to
numerical
simulation,
concept is tested in the field for global damage detection using one year of 5-axle truck data from
thisŠentvid
new concept
tested
in theIn
field
global
detection
usingofone
of 5-axleused
truck
data
the
bridgeisin
Slovenia.
thefor
field
tests,damage
the second
derivative
theyear
commonly
strain
from
the
Šentvid
bridge
in
Slovenia.
In
the
field
tests,
the
second
derivative
of
the
commonly
used
response is used as an estimate of acceleration, and temperature change is used as a proxy for damage.
strainstudies
response
is used as that
an estimate
of approach
acceleration,
and temperature
change
is used
as a proxy
for
Both
demonstrate
this novel
is effective
in detecting
changes
in bridge
stiffness
damage.
studiesthe
demonstrate
that
this novel
approach
is effective
in detecting
changes in
and
is ableBoth
to quantify
extent of that
change.
The main
findings
of this study
are as follows:
bridge stiffness and is able to quantify the extent of that change. The main findings of this study are
In numerical analysis, the relationship between the standard deviation of inferred GVWs and
1.
as follows:
bridge damage percentage is found in simulations to linearly increase. This change in the standard
1.
In numerical
analysis,
the relationship
the so
standard
deviation
inferred GVWs
deviation
due to bridge
damage
is significant,between
sufficiently
to be able
to detectofreasonably
small
andin
bridge
damage
percentage is found in simulations to linearly increase. This change in
changes
bridge
condition.
the standard
deviation
to bridge
damage
is significant,
to be ablethe
to
2.
Analysis
of the field
datadue
confirms
a linear
and
increasing sufficiently
relationshipso between
detectdeviation
reasonably
small changes
in bridge
condition.
standard
of inferred
steer-axle
weights
and the mean internal bridge temperatures.
2. temperature
Analysis ofaffects
the field
data the
confirms
increasing
relationship
As
stiffness,
ability ato linear
detect and
temperature
change
is strongbetween
evidencethe
of
standard
deviation
of
inferred
steer-axle
weights
and
the
mean
internal
bridge
an ability to detect a change in the damage state.
temperatures. As temperature affects stiffness, the ability to detect temperature change is
strong evidence of an ability to detect a change in the damage state.
Bridge accelerations are damage sensitive, and the possibility of using a statistical approach for
acceleration-based BWIM data for bridge damage detection has been shown to be promising using
both simulations and field testing. This method can be practically applicable for long-term bridge
Appl. Sci. 2020, 10, 663
18 of 20
Bridge accelerations are damage sensitive, and the possibility of using a statistical approach for
acceleration-based BWIM data for bridge damage detection has been shown to be promising using
both simulations and field testing. This method can be practically applicable for long-term bridge
monitoring and has a relatively low cost due to a smaller number of sensors being required than current
practice methods. This method has also been shown to be applicable to SiWIM systems. An initial
calibration of the bridge influence line using pre-weighed truck and a method of axle-detection is
an essential element in any such installation.
Author Contributions: Conceptualization, E.O.; Formal analysis, M.A.K.; Funding acquisition, E.O.; Project
administration, E.O., M.A.K. and D.P.M.; Resources, A.Ž.; Software, M.A.K.; Supervision, E.O. and D.P.M.;
Visualization, E.O., M.A.K. and D.P.M.; Writing—Original draft, M.A.K.; Writing—Review & editing, E.O., M.A.K.
and D.P.M. All authors have read and agreed to the published version of the manuscript.
Funding: This research has received funding from the Science Foundation Ireland (SFI) under the US-Ireland R &
D partnership with the National Science Foundation (NSF) and Invest Northern Ireland (ID: 16/US/13277).
Conflicts of Interest: The authors declare no conflict of interest.
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
Lydon, M.; Taylor, S.E.; Robinson, D.; Mufti, A.; Brien, E. Recent developments in bridge weigh in motion
(B-WIM). J. Civ. Struct. Health Monit. 2016, 6, 69–81. [CrossRef]
Yu, Y.; Cai, C.; Deng, L. State-of-the-art review on bridge weigh-in-motion technology. Adv. Struct. Eng.
2016, 19, 1514–1530. [CrossRef]
Richardson, J.; Jones, S.; Brown, A.; OBrien, E.; Hajializadeh, D. On the use of bridge weigh-in-motion for
overweight truck enforcement. Int. J. Heavy Veh. Syst. 2014, 21, 83–104. [CrossRef]
U.S. Department of Transportation; Federal Highway Administration; Federal Transit Administration.
2015 Status of the Nation’s Highways, Bridges and Transit: Conditions and Performance; U.S. Department of
Transportation: Washington, DC, USA; Federal Highway Administration: Washington, DC, USA; Federal
Transit Administration: Washington, DC, USA, 2017.
Hester, D.; González, A. A bridge-monitoring tool based on bridge and vehicle accelerations. Struct.
Infrastruct. Eng. 2015, 11, 619–637. [CrossRef]
Doebling, S.W.; Farrar, C.R.; Prime, M.B. A summary review of vibration-based damage identification
methods. Shock Vib. Dig. 1998, 30, 91–105. [CrossRef]
Stochino, F.; Fadda, M.L.; Mistretta, F. Low cost condition assessment method for existing RC bridges.
Eng. Fail. Anal. 2018, 86, 56–71. [CrossRef]
Gomez, H.C.; Fanning, P.J.; Feng, M.Q.; Lee, S. Testing and long-term monitoring of a curved concrete box
girder bridge. Eng. Struct. 2011, 33, 2861–2869. [CrossRef]
Cantero, D.; González, A. Bridge damage detection using weigh-in-motion technology. J. Bridge Eng. 2014,
20, 04014078. [CrossRef]
Malekjafarian, A.; McGetrick, P.J.; OBrien, E.J. A Review of Indirect Bridge Monitoring Using Passing Vehicles.
Shock Vib. 2015, 2015, 16. [CrossRef]
Elhattab, A.; Uddin, N.; OBrien, E. Drive by bridge frequency identification under operational roadway
speeds employing frequency independent underdamped pinning stochastic resonance (fi-upsr). Sensors
2018, 18, 4207. [CrossRef]
Mei, Q.; Gül, M.; Boay, M. Indirect health monitoring of bridges using Mel-frequency cepstral coefficients
and principal component analysis. Mech. Syst. Signal Process. 2019, 119, 523–546. [CrossRef]
Zhang, Y.; Wang, L.; Xiang, Z. Damage detection by mode shape squares extracted from a passing vehicle.
J. Sound Vib. 2012, 331, 291–307. [CrossRef]
Malekjafarian, A.; OBrien, E.J. Identification of bridge mode shapes using short time frequency domain
decomposition of the responses measured in a passing vehicle. Eng. Struct. 2014, 81, 386–397. [CrossRef]
Spencer, B.F., Jr.; Hoskere, V.; Narazaki, Y. Advances in computer vision-based civil infrastructure inspection
and monitoring. Engineering 2019, 5, 199–222. [CrossRef]
Malekjafarian, A.; Golpayegani, F.; Moloney, C.; Clarke, S. A machine learning approach to bridge-damage
detection using responses measured on a passing vehicle. Sensors 2019, 19, 4035. [CrossRef]
Appl. Sci. 2020, 10, 663
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
19 of 20
Yi, T.H.; Li, H.N.; Sun, H.M. Multi-stage structural damage diagnosis method based on. Smart Struct. Syst.
2013, 12, 345–361. [CrossRef]
Jin, C.H.; Jang, S.A.; Sun, X.R.; Li, J.C.; Christenson, R. Damage detection of a highway bridge under severe
temperature changes using extended Kalman filter trained neural network. J. Civ. Struct. Health Monit. 2016,
6, 545–560. [CrossRef]
Moses, F. Weigh-in-motion system using instrumented bridges. J. Transp. Eng. 1979, 105, 233–249.
Jacob, B.; Feypell-de La Beaumelle, V. Improving truck safety: Potential of weigh-in-motion technology. Iatss
Res. 2010, 34, 9–15. [CrossRef]
OBrien, E.J.; Znidaric, A.; Baumgärtner, W.; González, A.; McNulty, P. Weighing-In-Motion of Axles and Vehicles
for Europe (WAVE) WP1. 2: Bridge WIM Systems; University College Dublin: Dublin, Ireland, 2001.
González, A. Development of a Bridge Weigh-in-Motion System; LAP Lambert Academic Publishing: Saarbruken,
Germany, 2010.
Jacob, B.; O’Brien, E.J.; Newton, W. Assessment of the accuracy and classification of weigh-in-motion systems.
Part 2: European specification. Int. J. Heavy Veh. Syst. 2000, 7, 153–168. [CrossRef]
OBrien, E.J.; Fitzgerald, P.C.; Malekjafarian, A.; Sevillano, E. Bridge damage detection using vehicle axle-force
information. Eng. Struct. 2017, 153, 71–80. [CrossRef]
Ojio, T.; Carey, C.; OBrien, E.J.; Doherty, C.; Taylor, S.E. Contactless bridge weigh-in-motion. J. Bridge Eng.
2016, 21, 04016032. [CrossRef]
Sekiya, H.; Kubota, K.; Miki, C. Simplified Portable Bridge Weigh-in-Motion System Using Accelerometers.
J. Bridge Eng. 2017, 23, 04017124. [CrossRef]
Shoukry, S.N.; William, G.W.; Downie, B.; Riad, M.Y. Effect of moisture and temperature on the mechanical
properties of concrete. Constr. Build. Mater. 2011, 25, 688–696. [CrossRef]
Kodur, V. Properties of concrete at elevated temperatures. ISRN Civ. Eng. 2014, 2014, 15. [CrossRef]
Bedon, C. Diagnostic analysis and dynamic identification of a glass suspension footbridge via on-site
vibration experiments and FE numerical modelling. Compos. Struct. 2019, 216, 366–378. [CrossRef]
Bedon, C.; Fasan, M. Reliability of Field Experiments, Analytical Methods and Pedestrian’s Perception
Scales for the Vibration Serviceability Assessment of an In-Service Glass Walkway. Appl. Sci. 2019, 9, 1936.
[CrossRef]
Chen, Z.; Zhou, X.; Wang, X.; Dong, L.; Qian, Y. Deployment of a smart structural health monitoring system
for long-span arch bridges: A review and a case study. Sensors 2017, 17, 2151. [CrossRef]
Fugate, M.L.; Sohn, H.; Farrar, C.R. Vibration-based damage detection using statistical process control. Mech.
Syst. Signal Process. 2001, 15, 707–721. [CrossRef]
Hester, D.; González, A. A wavelet-based damage detection algorithm based on bridge acceleration response
to a vehicle. Mech. Syst. Signal Process. 2012, 28, 145–166. [CrossRef]
Tyan, F.; Hong, Y.-F.; Tu, S.-H.; Jeng, W.S. Generation of random road profiles. J. Adv. Eng. 2009, 4, 1373–1378.
González, A. Vehicle-bridge dynamic interaction using finite element modelling. In Finite Element Analysis;
InTech: Terrebonne, QC, Canada, 2010; pp. 637–662.
ISO. Mechanical Vibration—Road Surface Profiles—Reporting of Measured Data; ISO 8608:1995; ISO: Geneva,
Switzerland, 1995; Volume 1, p. 29.
McGetrick, P.J.; Kim, C.-W.; González, A.; Brien, E.J.O. Experimental validation of a drive-by stiffness
identification method for bridge monitoring. Struct. Health Monit. 2015, 14, 317–331. [CrossRef]
McGetrick, P.; González, A.; O’Brien, E.J. Monitoring bridge dynamic behaviour using an instrumented two
axle vehicle. In Proceedings of the Bridge & Infrastructure Research in Ireland 2010 (BRI 10), Cork, Ireland,
2–3 September 2010.
Keenahan, J.; OBrien, E.J.; McGetrick, P.J.; Gonzalez, A. The use of a dynamic truck–trailer drive-by system
to monitor bridge damping. Struct. Health Monit. 2014, 13, 143–157. [CrossRef]
Harris, N.K.; González, A.; OBrien, E.J.; McGetrick, P. Characterisation of pavement profile heights using
accelerometer readings and a combinatorial optimisation technique. J. Sound Vib. 2010, 329, 497–508.
[CrossRef]
Cebon, D. Handbook of Vehicle-Road Interaction; Swets and Zeitlinger: Lisse, The Netherlands, 1999.
Bathe, K.-J.; Wilson, E.L. Numerical Methods in Finite Element Analysis; Prentice-Hall: Englewood Cliffs, NJ,
USA, 1976; p. 543.
Appl. Sci. 2020, 10, 663
43.
44.
45.
46.
47.
20 of 20
Žnidarič, A.; Igor, L.; Kalin, J.; Kulauzović, B. SiWIM Bridge Weigh-In-Motion Manual, 4th ed.; ZAG: Ljubljana,
Slovenia, 2011.
Cantero, D.; Hester, D.; Brownjohn, J. Evolution of bridge frequencies and modes of vibration during truck
passage. Eng. Struct. 2017, 152, 452–464. [CrossRef]
OBrien, E.J.; Zhang, L.; Zhao, H.; Hajializadeh, D. Probabilistic Bridge Weigh-in-Motion. Can. J. Civ. Eng.
2018, 45, 667–675. [CrossRef]
Yang, Y.-B.; Lin, C.; Yau, J. Extracting bridge frequencies from the dynamic response of a passing vehicle.
J. Sound Vib. 2004, 272, 471–493. [CrossRef]
OBrien, E.J.; Quilligan, M.; Karoumi, R. Calculating an influence line from direct measurements. Bridge Eng.
Proc. Inst. Civ. Eng. 2006, 159, 31–34. [CrossRef]
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).