Prediction of bridge deck condition rating based on artificial neural networks

Journal of Science and Technology in Civil Engineering NUCE 2019. 13 (3): 15–25

PREDICTION OF BRIDGE DECK CONDITION RATING BASED ON
ARTIFICIAL NEURAL NETWORKS
Tu Trung Nguyena,∗, Kien Dinhb
a

Dept. of Civil, Construction, and Environmental Engineering, University of Alabama,
Tuscaloosa, AL 35487, USA
b
CONSEN INC., 5590 Avenue Clanranald, H3X 2S8, Montréal, QC, Canada
Article history:
Received 16/07/2019, Revised 08/08/2019, Accepted 12/08/2019

Abstract
An accurate prediction of the future condition of structural components is essential for planning the maintenance, repair, and rehabilitation of bridges. As such, this paper presents an application of Artificial Neural
Networks (ANN) to predict future deck condition for highway bridges in the State of Alabama, the United
States. A library of 2572 bridges was extracted from the National Bridge Inventory (NBI) database and used
for training, validation, and testing the ANN model, which had eight input parameters and one output being
the deck rating. Specifically, the eight input parameters are Current Bridge Age, Average Daily Traffic, Design
Load, Main Structure Design, Approach Span Design, Number of main Span, Percent of Daily Truck Traffic,
and Average Daily Traffic Growth Rate. The results indicated the obtained ANN model can predict the condition rating of the bridge deck with an accuracy of 73.6%. If a margin error of ±1 was used, the accuracy of
the proposed model reached a much higher value of 98.5%. Besides, a sensitivity analysis was conducted for
individual input parameters revealed that Current Bridge Age was the most important predicting parameter of
bridge deck rating. It was followed by the Design Load and Main Structure Design. The other input parameters
were found to have neglectable effects on the ANN’s performance. Finally, it was shown that the obtained ANN
can be used to develop the deterioration curve of the bridge deck, which helps visualize the condition rating of
a deck, and accordingly the maintenance need, during its remaining service life.
Keywords: condition rating; bridge deck; deterioration curve; artificial neural networks; sensitivity analysis.
/>
c 2019 National University of Civil Engineering

1. Introduction
According to the American Society of Civil Engineers’ 2017 Infrastructure Report Card [1], about
one in 11(9.1%) of the bridges in the United States were rated to be structurally deficient. “Almost four
in 10 (39%) are over 50 years or older, and an additional 15% are between the ages of 40 and 49. The
average bridge in the U.S. is 43 years old. Most of the country’s bridges were designed for a lifespan
of 50 years, so an increasing number of bridges will soon need major rehabilitation or retirement.”
[1]. It is known that, in order to have an optimum repair strategy, the future condition rating of the
bridges needs to be predicted with a high level of accuracy.
At present, the visual inspection technique is the most commonly used method to determine the
condition rating of a bridge structure in the United States [2]. During the examination, the inspectors
gather a large amount of information related to operational, geometric, and defects/condition of the
∗

Corresponding author. E-mail address: (Nguyen, T. T.)

15


Nguyen, T. T., Dinh, K. / Journal of Science and Technology in Civil Engineering

bridges. Those inspection data are then archived in the NBI database. For each bridge structure, such
data reflect the condition ratings of superstructure, substructure, and bridge deck. More specifically,
the deck condition rating is stored in item No. 58 of the NBI records.
The bridge deck is rated as an integer number between 0 and 9, in which 0 means a bridge being
in a failed condition while 9, on the other hand, indicates an excellent condition. The bridge with
a component’s condition rating of 4 or lower will be considered as structurally deficient. The deck
condition rating is performed for the entire deck, i.e., deck surface, sides and deck bottom. Table 1
shows a detailed description of the bridge deck in various ratings, which was taken from the Michigan
Department of Transportation’s guidelines [2]. Such an overall deck rating will be employed as the

prediction output of this study.
Table 1. Bridge deck condition rating (NBI item 58)
Code

Description

N

NOT APPLICABLE. Code N for culverts and other structures without decks, e.g., filled arch bridge.

9

NEW CONDITION. No noticeable or noteworthy deficiencies which affect the condition of the deck.

8

GOOD CONDITION. Minor cracking less than 0.8 mm wide with no spalling, scaling or delamination on the
deck surface or underneath.

7

GOOD CONDITION. Open cracks less than 1.6 mm wide at a spacing of 3 m or more, light shallow scaling
allowed on the deck surface or underneath. Deck will function as designed.

6

FAIR CONDITION. Deterioration of the combined area of the top and bottom surface of the deck is 2% or less
of the total area. There may be a considerable number of open cracks greater than 1.6 mm wide at a spacing of
1.5 m or less on the deck surface or underneath. Medium scaling on the surface is 6.4 mm to 13 mm in depth.
Deck will function as designed.

5

FAIR CONDITION. Heavy scaling. Excessive cracking and up to 5% of the deck area are spalled; 20–40% is
water saturated and/or deteriorated. Disintegrating of edges or around scuppers. Considerable leaching through
deck. Some partial depth fractures, i.e., rebar exposed (repairs needed).

4

POOR CONDITION. Deterioration of the combined area of the top and bottom surface of the deck is between
10–25% of the total area. Deck will function as designed.

3

SERIOUS CONDITION. The deck is showing advanced deterioration that has seriously affected the primary
structural components. Deterioration of the combined area of the top and bottom surface of the deck is more than
25% of the total area. Structural evaluation and/or load analysis may be necessary to determine if the structure
can continue to function without restricted loading or structurally engineered temporary supports. There may
be a need to increase the frequency of inspections.

2

CRITICAL CONDITION. Deterioration has progressed to the point where the deck will not support design
loads and is therefore posted for reduced loads. Emergency deck repairs or shoring with structurally engineered
temporary supports may be required by the crews. There may be a need to increase the frequency of inspections.

1

IMMINENT FAILURE CONDITION. Bridge is closed to traffic due to the potential for deck failure, but corrective action may put the bridge back in service.

0

FAILED CONDITION. Bridge closed.

In the current practice, the operational and physical characteristics of bridge components (superstructure, substructure, and deck) are evaluated visually by a bridge inspector based on his or her own
assessment. Such visual inspection requires the inspector to assign a subjective rating for each bridge
component. The overall rating of a bridge is then calculated through the integration of those component ratings. Since for each bridge, the instant rating indicates the immediate level of repair needed
for its structure, it is important to predict accurately the future ratings of a bridge, and accordingly, its
16


Nguyen, T. T., Dinh, K. / Journal of Science and Technology in Civil Engineering

components, so that bridge engineers can develop an effective bridge repair/rehabilitation plan.
In the literature, several deterioration models of bridge decks based on chemical and physical
processes have been proposed [3–6]. Other research applied stochastic models such as Markov chains,
or reliability-based methodology [7, 8]. In recent years, an alternative approach using an Artificial
Neural Network has been widely applied to structural condition assessment. For example, Cattan and
Mohammadi [9] used an ANN model to predict the condition rating of railway bridges in the Chicago
metropolitan area. Al-Barqawi and Zayed [10] predicted the condition of underground water main
pipes with the ANN model. The application of ANN model has also been expanded to predict the
condition rating of a certain component of a bridge such as abutment [11], bridge deck [12–15].
In this study, a supervised learning ANN model was developed and used to predict the condition rating of bridge decks using available information in the NBI database. In addition, a similar
methodology was also utilized to analyze the sensitivity of the input parameters in predicting the future condition of bridge decks. Dataset used for training, validation, and testing the proposed ANN
model is the NBI data from the State of Alabama in 2018. This dataset was downloaded from the
Federal Highway Administration (FHWA) website [16]. Original data were refined before being used
to develop the ANN model. The subsequent section provides details on the data refinement.
2. Database preparation
The original NBI data obtained from the FHWA website comprises valuable information about the
United States’ bridge network. However, based on the initial analysis, the NBI database also contained

multiple errors and data outside a normal range, i.e. outliners. In order to minimize the potential
negative effects of such data on the performance of the ANN model, the refinement of original data
was carried out. Specifically, the original data were filtered with consideration to a number of criteria
as discussed in the following paragraphs.
The initial refinement focused on removing the records containing flawed data. The original
dataset was checked for errors such as zero or negative Average Daily Traffic, zero Number of main
Span, negative Ages. The bridges with those errors were removed from the database. The refinement
also targeted at the bridges with reconstruction and repaired records. In this study, the authors used
the ANN model to predict the condition rating of bridge decks without previous intervention, i.e.,
previous repair or replacement. Thus, the bridges with repair and reconstruction activities were also
removed from the database. In another refinement step, the bridges with an overall deck rating of 1 or
2 or no rating were considered not being qualified for the inputs, and therefore they were also removed
from the database.
The next refinement was aimed to remove the input parameters those are likely not important.
According to the previous study [14], 11 NBI items were considered to have a significant influence
on concrete bridge deck performance. Those variables were: Age, Year Built, Average Daily Traffic,
Percent of Daily Truck Traffic, Average Daily Truck Traffic, Number of main Span, Region, Steel
Reinforcement Protection, Structure Design Type, Design Load, and Approach Surface Type [14].
However, due to the uncertainty in the NBI data, the number of items used in this study was reduced
to seven items as following: (i) Year Built (item 27), (ii) Average Daily Traffic (item 29), (iii) Design
Load (item 31), (iv) Main Structure Design (item 43B), (v) Approach Span Design (item 44B), (vi)
Number of main Span (item 45), (vii) Percent of Daily Truck Traffic (item 109).
The overall condition rating of bridge deck was the output of the ANN model, thus the Deck
Condition Rating (item 58) was utilized for a supervised learning of the ANN. In addition, the Current
Bridge Age item was created to replace the Year Built item from NBI database. The age of a bridge
17


Nguyen, T. T., Dinh, K. / Journal of Science and Technology in Civil Engineering

was equal to the subtraction of 2019 and the year that the bridge was built (Year Built, item 27).
Furthermore, a new item, Average Daily Traffic (ADT) Growth Rate, was added to the inputs. This
parameter and the Current Bridge Age item were used later as the variable parameters for constructing
the deterioration curve of bridges. The ADT Growth Rate parameter is the annual growth rate of ADT.
It was calculated by the following equation.
AGR =

FADT − LADT
100%
FDT − LDT

(1)

where AGR = Percent of annual ADT Growth Rate; FADT = Future ADT (item 114); LADT = Latest
ADT (item 29); FDT = Future year of ADT (item 115); LDT = Latest year of ADT (item 30).
In the last refinement, the old bridges with abnormal ratings were removed from the database.
This refinement was performed to ensure that the rating records reflect the reasonable typical deterioration for a bridge deck. To perform this refinement, the records were removed if they met one of the
following conditions: (i) age ≥ 30 and deck rating ≥ 6, (ii) age ≥ 25 and deck rating ≥ 7, (ii) age ≥ 20
and deck rating ≥ 8, and (iv) age ≥ 15 and deck rating ≥ 9 [14].
After performing refinement, the final dataset was a matrix that contains 2572 rows and 9 columns.
The range of the input and output parameters is listed in Table 2. Some bridges were forecast with a
reduction in the number of average daily traffic, and as a result, the value of the additional parameter
(ARG) was negative, as seen in Table 2. The classification of the deck condition rating is presented
in Table 3. This dataset was used for the ANN model with the inputs were the data from column 1 to
column 8 and the outputs were the data from column 9.
Table 2. Characteristics of input and output

No.

Parameter

Item

Contraction

Unit

Min.

Max.

1
2
3
4
5
6
7
8
9

Current Bridge Age
Average Daily Traffic
Design Load
Main Structure Design
Approach Span Design
Number of main Span
Percent of Daily Truck Traffic
ADT Growth Rate
Deck Condition Rating

29
31
43B
44B
45
109
58

CBA
ADT
DLD
MSD
ASD
NMS
PDT
AGR
DCR

year
No.
No.
%
%
-

2
4
0
0

0
1
1
−2.78
3

119
157350
6
22
22
48
75
26.5
9

Table 3. Number of records in each specific range the bridge deck rating

Condition Rating

3

4

5

6

7

8

9

Total

Number of records

9

65

1136

128

602

479

153

2572

3. Methods
As mentioned earlier, the ANN model was used to predict the condition rating for bridge decks.
Artificial Neural Network is an adaptive system using a number of fully connected neutrons to process the data and then establish the relationship between the inputs and outputs. A typical neutron
18

Table 3. Number of records in each specific range the bridge deck rating
Condition Rating

3

4

5

6

7

8

9

Total

Number of records

9

65

1136

128

602

479

153

2572

Nguyen, T. T., Dinh, K. / Journal of Science and Technology in Civil Engineering
3. Methods

often consists of five components as depicted in Fig. 1. The input section provides information (trigAs mentioned earlier, the ANN model was used to predict the condition rating for bridge decks. Artificial Neural Network
gering signals)
for
theusing
neutron.
information
is then
going
through
an evaluation
system
is an adaptive
system
a numberThe
of fully
connected neutrons
to process
the data
and then establish
the relationship

betweenwhere
and outputs.
A typical
neutron
often consistson
of five
as depicted
in Fig.
1. The input
section
provides
a weighttheisinputs
assigned
to each
input
depending
thecomponents
importance
of the
inputs.
After
that,
a summainformation
(triggering
signals)
for
the
neutron.
The
information

is
then
going
through
an
evaluation
system
where
a
weight
tion is performed to obtain a net input that comes to a neuron. The net input is then processed in the
is assigned to each input depending on the importance of the inputs. After that, a summation is performed to obtain a net input
determination
toThe
produce
value
in the inoutput
neuron section
[17].to produce value in the output neuron [17].
that comessection
to a neuron.
net input is
then processed
the determination
1. Input

x1

1

x2

2

w1

x3

3

w3

xn

n

2. Evaluation
3. Summation

4. Determination

5. Output

w2
Sum

Sigmoid

Output

wn
1. Components of
of aasimple
neuron
FigureFigure
1. Components
simple
neuron

Neural networks learn to map between input and output through a common learning process called error back-propagation.
Neural
networks learn to map between input and output through a common learning process called
It works by using the errors presented in the network output to adjust the weights between two adjacent layers. The error backerror back-propagation.
It works
usingin which
the errors
in theandnetwork
to adjust the
propagation consists of two
different by
processes,
one is a presented
feed-forward process
the other isoutput
a back-propagation
In thetwo
feed-forward
process,
the inputs
areerror

used to obtain
the outputs based onconsists
the weightsof
initially
or obtained
weightsprocess.
between
adjacent
layers.
The
back-propagation
twoassumed
different
processes,
from the previous adjustment. The errors are then passed backwards to the input layers through the back-propagation process,
in which one is a feed-forward process and the other is a back-propagation process. In the feed-forward
the weights are adjusted during this process to minimize the network errors to an acceptable level.
process, the inputs are used to obtain the outputs based on the weights initially assumed or obtained
The ANN model often contains multiple neutrons with an input layer, multiple hidden layers, and an output layer, as shown
from thein Fig.
previous
adjustment. The errors are then passed backwards to the input layers through the
2. In this study, the input layer consisted of eight parameters/neutrons, namely Current Bridge Age (CBA), Average
back-propagation
process,
theLoad
weights
are adjusted
during
thisApproach

process
to Design
minimize
network
Daily Traffic (ADT),
Design
(DLD), Main
Structure Design
(MSD),
Span
(ASD),the
Number
of main errors
Span (NMS),level.
Percent of Daily Truck (PDT), and ADT Growth Rate (AGR). The output of the ANN model was the Deck
to an acceptable
Rating (DCR). The dataset was divided arbitrarily into training, validation, and testing data subsets. The training
TheCondition
ANN model
often contains multiple neutrons with an input layer, multiple hidden layers, and
subset
consistedKien
of 70%,Dinh/
i.e. 1800 bridges, ofof
theScience
entire database.
validation subset
15%, i.e. 386 instances, of
Tu
T.

Nguyen,
andThe
Technology
incontained
Civileight
Engineering
an output
layer,
as
shown
in Fig.Journal
2.
study,
layer
consisted
the entire database. The remaining,
i.e.In
386this
samples,
werethe
usedinput
for testing
the proposed
ANNof
model. Theparameters/neutrons,
trained ANN model
was then utilized to develop a degradation curve for a specific bridge.

Input layer

1

CBA

2

ADT

3

DLD

4

MSD

5

ADS

6

NMS

7

PDT

8

AGR

hidden layer

output layer

DCR

Figure
2. Structure
of ANN
Figure
2. Structure
of ANN
model model
In addition, the ANN models were also employed to study the19
importance/effects of each input parameter to the output.
To perform this task, each ANN model was trained and used to predict the output with a single input parameter. The
performance of the model with that input was then evaluated and recorded. Repeated this task for all the input parameters. The
results were then ranked to explore the importance of each input to the output of the ANN model.


Tu T. Nguyen, Kien Dinh/ Journal of Science and Technology in Civil Engineering
Tu T. Nguyen, Kien Dinh/ Journal of Science and Technology in Civil Engineering
Input layer

hidden layer

output layer

Nguyen, T. T., Dinh, K. / Journal of Science and Technology in Civil Engineering
Input layer

hidden layer

output layer

namely Current Bridge Age (CBA),
1 CBA Average Daily Traffic (ADT), Design Load (DLD), Main Structure Design (MSD), Approach Span Design (ASD), Number of main Span (NMS), Percent of Daily
ADT
12 CBA
Truck (PDT), and ADT Growth Rate (AGR). The output of the ANN model was the Deck Condition
ADT
DLD
23 divided
Rating (DCR). The dataset was
arbitrarily into training, validation, and testing data subsets.
The training subset consisted 34of DLD
70%,
i.e.
1800 bridges, of the entire database. DCR
The validation subMSD
set contained 15%, i.e. 386 instances, of the entire database. The remaining, i.e. 386 samples, were
DCR
4 MSD
ADS
used for testing the proposed 5ANN
model. The trained ANN model was then utilized to develop a
ADS
56 bridge.

degradation curve for a specific
NMS
In addition, the ANN models
were also employed to study the importance/effects of each input
67 NMS
PDT
parameter to the output. To perform this task, each ANN model was trained and used to predict the
7 PDT
8 AGR The performance of the model with that input was then evaluated
output with a single input parameter.
8 AGR
and recorded. Repeated this task
for all the input parameters. The results were then ranked to explore
the importance of each input to the output of the ANN model.
Figure 2. Structure of ANN model

Gradient = 0.076679, at epoch 22
Gradient = 0.076679, at epoch 22

-3

Mu = 1e-05, at epoch 22
Mu = 1e-05, at epoch 22

Mean Squared Error (mse)

-4

10 -4
10

mu

mu

10 -3
10

-5

val fail

val fail

10 -5
10

Validation
epoch2222
Validation Checks
Checks == 6,6,atatepoch

1010

44

66

88

10
12
10
12
22 Epochs
Epochs
22

14
14

1616

1

10

0

10

10

-1

22

10

1

10

55
00
00

Train
Train
Validation
ValidationTest
Test
Best
Best

2

2

10

Mean Squared Error (mse)

5

10 5
10
0
10 0
10

-5
10 -5
10

gradient

gradient

2. Structure of ANN model
In addition, the ANN models were also Figure
employed
to study the importance/effects of each input parameter to the output.
4.
Results
and
discussion
To perform
this the
task,
each
ANNwere
model
trained
to predict the output
with
a single
input
parameter.
In addition,
ANN

models
alsowas
employed
to and
studyused
the importance/effects
of each
input
parameter
to the
output. The
performance
thetask,
model
with
thatmodel
input was
evaluated
andtorecorded.
Repeated
for allinput
the input
parameters.
To perform of
this
each
ANN
was then
trained
and used

predict the
output this
withtask
a single
parameter.
The The
The
model
this
has
eightevaluated
neutrons
inrecorded.
the
input
layer,
tenANN
neurons
hidden
layer,The
performance
of the
modeltoin
with
thatstudy
input
was then
Repeated
this
task

for
all in
thethe
input
parameters.
results
wereANN
then
ranked
explore
the importance
of each and
input
to the
output
of the
model.
results
were
then ranked
explore layer.
the importance
of each
to the activation
output of thefunction.
ANN model.
and one
neuron
in thetooutput
It employs

theinput
sigmoid
The regression method
4. Results and discussion
is
used
to
generate
output
for
the
ANN
model.
The
output
(condition
rating)
is
rounded up or down
4. Results and discussion
The ANN model in this study has eight neutrons in the input layer, ten neurons in the hidden layer, and one neuron in the
to the nearest
valid this
rating.
For instance,
if the
condition
ratingneurons
of a bridge
obtained

from
theneuron
ANNinisthe
ANN
model in the
study hasactivation
eight neutrons
in theThe
input
layer, tenmethod
inused
the hidden
layer, output
and onefor
outputThe
layer.
It employs
sigmoid
function.
regression
is
to generate
the ANN model.
6.51,
it
will
be
rounded
up
to

7.
Fig.
3
shows
some
information
about
the
training
and
performance
output
layer.
It employs
the sigmoid
activation
regression
method
is used
to generate
for the ANN
model.
The
output
(condition
rating)
is rounded
up orfunction.
down to The
the nearest

valid
rating.
For instance,
if output
the condition
rating
of a bridge
The
output
(condition
rating)
is it
rounded
or
downuptoto
the
valid
rating.
Forinformation
instance,
condition
of aperformance
bridge
of the
proposed
ANN
model.
After
training
was

completed,
the
ANN
modelif the
was
used
torating
predict
the
obtained
from
the ANN
is 6.51,
will
beup
rounded
7.nearest
Figure
3 shows
some
about
the training
and
from the
ANN
is 6.51,
it willtraining
beItrounded
tonoting
7. Figure

3 shows
information
the
and performance
ofobtained
the proposed
ANN
model.
After
wasupcompleted,
the
ANN
model
was
predict
the that
output
withnot
the testing
output
with
the
testing
dataset.
is worth
that
the some
testing
dataused
is about

atoset
oftraining
data
was
of
the
proposed
ANN
model.
After
training
was
completed,
the
ANN
model
was
used
to
predict
the
output
with
the testing
dataset.
It is in
worth
noting
thatset.
the A

testing
data is
a set of data
that was
not included inof
thethe
training
set.
A
detailed
discussion
included
the
training
detailed
discussion
about
the
performance
ANN
model
can
be
dataset. It is worth noting that the testing data is a set of data that was not included in the training set. A detailed discussion
about
the performance of the ANN model can be found in the subsequent sections.
foundtheinperformance
the subsequent
sections.
about

of the ANN
model can be found in the subsequent sections.

0

-1

10 10
0 0 2

1818 2020 22 22

(a) Training
(a) Training
Training

24

46

68

8
10

10
12

12
14

22 Epochs
22 Epochs

14
16

16
18

2018

2220

22

(b)Validation
Validation
(b)(b)
Validation

Figure
3.3.Information
thethe
proposed
ANN
model
Figure
Information
of

proposed
ANN
model
Figure
3. Information
ofofthe
proposed
ANN
model
4.1.Model
Modelperformance
performance
4.1.

4.1.
Model
performance
ordertotoevaluate
evaluate the
the performance
ANN
model,
a confusion
matrix
and and
a bubble
plot were
used. used.
The The
InInorder

performanceof
ofthe
theproposed
proposed
ANN
model,
a confusion
matrix
a bubble
plot were
confusionmatrix
matrix is
is often
often applied
applied for
classification
problems
to to
report
numerical
results
thanks
to itstoability
to show
the the
confusion
for
classification
problems
report

numerical
results
thanks
its
ability
to
show
In order
to evaluate
the performance
of the proposed
ANN plot
model,
a confusion
matrix
and a bubble
relationsbetween
between classified
classified outputs
The
bubble
(scatter
plot)plot)
provides
a visualization
of theof the
relations
outputs and
andthe
thetrue

trueones
ones[18].
[18].
The
bubble plot
(scatter
provides
a visualization
plot were
used.
The
matrix iswere
often
applied
for
classification
to report
numerical
confusion
matrix
with
theconfusion
number of
presented
viavia
the
diameter
of the
dotproblems
[19].

The details
of those
two methods
confusion
matrix
with
the
number
ofinstances
instanceswere
presented
the
diameter
of the
dot [19].
The details
of those
two methods
were
presented
in
the
following
sections.
results
thanks
to
its
ability
to

show
the
relations
between
classified
outputs
and
the
true
ones
[18].
were presented in the following sections.
The bubble plot (scatter plot) provides a visualization of the confusion matrix with the number of
20


Nguyen, T. T., Dinh, K. / Journal of Science and Technology in Civil Engineering

instances were presented via the diameter of the dot [19]. The details of those two methods were
presented in the following sections.
a. Confusion matrix
The confusion matrices were created for both training and testing data sets. The columns of a
confusion matrix represent the true rating value from the manual inspection, and the rows show the
predicted rating values by the proposed ANN model. Two indicators, Correct Rating (CR) and Acceptable Rating (AR), were used to evaluate the performance of the network. The CR is the percentage of
predicted ratings that accurately matched the visual inspection rating. The AR is a ratio of predicted
values within a rating margin of error over the actual rating values.
Table 4. Confusion matrix of bridge deck rating in training

Manual Inspection
6

7

Prediction

3

4

5

3
4
5
6
7
8
9
SUM

1
0
0
0
0
0
0
1

0
3

0
0
0
0
0
3

3
40
810
1
0
0
0
854

0
1
5
49
19
0
0
74

CR (%)
AR (%)

100
100

100
100

94.8
99.6

66.2
98.6

8

9

SUM

0
0
1
37
254
88
0
380

0
0
0
8
138

222
88
456

0
0
0
0
1
12
19
32

4
44
816
95
412
322
107
1800

66.8
99.7

48.7
98.2

59.4
96.9

75.4
99.2

Table 5. Confusion matrix of bridge deck rating in the test set

Manual Inspection
6
7

Prediction

3

4

5

3
4
5
6
7
8
9
SUM

1
0
1

0
0
0
0
2

0
1
1
0
0
0
0
2

1
10
172
0
0
0
0
183

0
0
2
8
6
0

0
16

CR (%)
AR (%)

50.0
50.0

50.0
100

93.9
99.5

50.0
100

8

9

SUM

0
0
1
6
52
25

2
86

0
0
0
1
30
49
16
96

0
0
0
0
0
0
1
1

2
11
177
15
88
74
19
386

60.5
96.5

51.0
98.9

100
100

73.6
98.5

In the confusion matrix, the element ai j (i is the row, and j is the column) indicates that the
proposed ANN model predicted the rating as i while the true rating values as recorded in the database
is j. The elements in the diagonal of the confusion matrix (aii in the bold gray cells) are the elements
correctly classified by the network. These elements were used to calculate the CR for each individual
rating, and for the overall network. As presented in Table 4, the proposed ANN had an overall CR of
75.4% for the training data subset.
21


Nguyen, T. T., Dinh, K. / Journal of Science and Technology in Civil Engineering

The subjective rating of the visual inspection process is well recognized, therefore a margin error
of ±1 is selected
in this study
account
for of
that
subjectivity.

The light in
gray
cells
in the confusion
Tu T. Nguyen,
Kiento
Dinh/
Journal
Science
and Technology
Civil
Engineering
matrix represent
the
values
of
ratings
within
the
margin
of
error.
The
AR
indicator
was calculated
Tu
Tu
T.
T.

Nguyen,
Nguyen,
Kien
Kien
Dinh/
Dinh/
Journal
Journal
of
of
Science
Science
and
and
Technology
Technology
in
in
Civil
Civil
Engineering
Engineering
Tu T. Nguyen, Kien Dinh/ Journal of Science and Technology in Civil Engineering
for the overall network and for the individual ratings. Taking into account this margin, the overall
prediction
for the0 training data
significantly1 increased19to
9 ratings of0 the proposed
0 ANN model
0

2 subset 16
0
0
0
0
2
2
16
16
19
19
99.2%,999as shown in000Table 4. 000
0
0
2
16
111
19
SUM
2
2
183
16
86
96
1
386
Table
a confusion
matrix

deck 86
condition
ratings
in 1the
The
SUM
SUM 5 presents
183
183for the bridge
16
16
86
86
96
96
11 test set.
386
386
SUM
222
222
183
16
96
386
proposed
ANN model
the new/unseen
the testing
data set with

CR (%)
50.0 performed
50.0 well for
93.9
50.0 data in
60.5
51.0
100 the overall
73.6
CR
CR(%)
(%)
50.0
50.0
50.0
50.0
93.9
93.9
50.0
50.0
60.5
60.5
51.0
51.0
100
100
73.6
73.6
CR
(%)

50.0
50.0
93.9
50.0
60.5
51.0
100
73.6
CR of
73.6%,
5. When
the margin
error
was applied,
AR
AR
(%) as seen
50.0 in Table100
99.5
100 of ±1 96.5
98.9the overall
100value of98.5
AR(%)
(%)
50.0
50.0
100
100
99.5
99.5the great100

100
100
96.5
96.5
98.9
98.9
100
100
98.5
98.5
was AR
increased
to 98.5%.
The100
results show
potential of
the ANN98.9
model at 100
predicting
ratings
AR
(%)
50.0
99.5
96.5
98.5
4.1.2. Bubble plots
within
a ±1 plots
rating

4.1.2.
4.1.2.Bubble
Bubble
plots
plots interval.
4.1.2.
Bubble

An alternative technique to present the classification results is a bubble plot. Figure 4 shows the bubble plots for the
performance of the ANN model in different data sets with an identical scaling factor. In those plots, the diameter of the dots
performance
performance
ofofthe
the
theANN
ANN
ANN
model
modelin
inindifferent
different
different
data
data
sets
sets
with
withananidentical
identical
scaling

scalingis
factor.
factor.
InInthose
those
those
plots,
plots,
the
thediameter
diameter
of
ofthe
the
the
dots
dots
performance
of
model
sets
with
scaling
factor.
plots,
the
dots
An alternative
technique
present

the
classification
results
a bubble
plot.
Fig.
4diameter
shows
the
bubrepresents
for
the number
of casesto
with
an data
identical
ratinganatidentical
each point.
Because
theInnumber
of samples
in the of
validation
and
represents
represents
for
for
the
the

number
number
of
of
cases
cases
with
with
an
an
identical
identical
rating
rating
at
at
each
each
point.
point.
Because
Because
the
the
number
number
of
of
samples
samples

in
in
the
the
validation
validation
and
and
represents
forsubset
the
of cases with
an of
identical
rating
each
point.
Because
theof
number
of samples
in the
validation
and
ble
plotsdata
for
thenumber
performance
ofhalf

the
ANN
in
different
data
sets
with
an
identical
scaling
factor.
testing
is approximately
the sizemodel
of theattraining
subset,
the size
the bubbles
in validation
and testing
plots
testing
testingdata
datasubset
subset
subsetis
isisapproximately
approximately
approximatelyhalf
half

halfof
ofofthe
the
thesize
size
sizeof
ofofthe
the
thetraining
trainingsubset,
subset,
subset,the
the
thesize
size
sizeof
ofofthe
the
thebubbles
bubbles
bubblesin
ininvalidation
validationand
and
andtesting
testingplots
plots
plots
testing
data

are
smaller.
Thethe
dots
on the diagonal
linedots
indicate
the training
number
ofthe
accurate
predictions,
andwith
the validation
dots
within thetesting
limit
of upper
In
those
plots,
diameter
of the
represents
for
number
of cases
an
identical
rating

at
are
are
smaller.
smaller.
The
The
dots
dots
on
on
the
the
diagonal
diagonal
line
line
indicate
indicate
the
the
number
number
of
of
accurate
accurate
predictions,
predictions,
and

and
the
the
dots
dots
within
within
the
the
limit
limit
of
of
upper
upper
are smaller. The dots on the diagonal line indicate the number of accurate predictions, and the dots within the limit of upper
and lower
error
margin the
line number
represent the
number of in
instances
within a ±1and
rating
interval.
each
point.
Because
of

samples
the
validation
testing
data
subset
is
approximately
and
andlower
lowererror
errormargin
margin
marginline
line
linerepresent
represent
representthe
the
thenumber
number
numberof
ofofinstances
instances
instanceswithin
within
withinaaa±1
±1
±1rating
rating

ratinginterval.
interval.
interval.
and
lower
error

b. Bubble
plots technique
An
Analternative
alternative
technique
techniqueto
totopresent
present
presentthe
the
theclassification
classification
classificationresults
results
resultsis
isisaaabubble
bubble
bubbleplot.
plot.
plot.Figure
Figure
Figure444shows

shows
showsthe
the
thebubble
bubble
bubbleplots
plots
plotsfor
for
forthe
the
the
An
alternative

8
88 8

88 8
Prediction
Prediction Ratings
Ratings
Prediction Ratings
Prediction Ratings

99 9

Prediction Ratings
Ratings
Prediction

Prediction
PredictionRatings
Ratings

9
99 9

7
77 7

77 7

6
66 6

66 6

5
55 5

55 5

4
44
3 333
33

4 44

44 4

Diagonal line
Diagonal
Diagonalline
line
line
Diagonal
Error
margin
Error
Errormargin
margin
margin
9
5 55
6 66
7 77
8 88
99 9
Manual
Inspection
Ratings
Manual
Manual
Inspection
Inspection
Ratings
Ratings

9

8
7
6
5
4

3
33 3 3
33 3

Diagonal line
Diagonal
Diagonal
line
line
Diagonal
line
Error
margin
Error
Error
margin
margin
Error margin
4
6
8
9
55
77

44 4
55Manual
66 6
77Ratings
88 8
99 9
Inspection
Manual
Manual
Inspection
Inspection
Ratings
Ratings
Manual
Inspection
Ratings

(a)
Training
(a)
Training
(a)
Training
(a)
Training

(b)
Validation
(b)
Validation

(b)
(b)
Validation
Validation
(b)
Validation

8 88

88 8 8
Prediction Ratings
Ratings
Prediction Ratings
Prediction Ratings

99 9 9

Ratings
Prediction Ratings
Prediction
Prediction Ratings
Ratings

9 99

7 77

77 7 7

6 66

66 6 6

5 55

55 5 5

4 44
3 33
3 33

44 4 4

Diagonal
line
Diagonal
Diagonal
line
line
Diagonal
line
Error
margin
Error
margin
margin
Error
margin
4 44

5 55
6 66
7 77
Manual
Inspection
Ratings
Manual
Inspection
Ratings
Manual
Inspection
Ratings

8 88

33 3 3
33 3 3

99 9 9

(c)
Testing
(c)
Testing
(c)
Testing
(c)
Testing

Diagonal

Diagonal
Diagonal
line
lineline
Diagonal
line
Error
margin
Error
Error
margin
margin
Error
margin
44 4 4

55 5 5
66 6 6
77 7 7
88 8 8
Manual
Inspection
Ratings
Manual
Manual
Inspection
Inspection
Ratings
Ratings
Manual

Inspection
Ratings

99 9 9

(d)
Overall
(d)
Overall
(d)
(d)
Overall
Overall
(d)
Overall

Figure
4.4.
Bridge
deck
deck
ratings
ratings
Bubble
plots
plots
Figure
Bridge
deck
ratings

–––Bubble
plots
Figure
4.4.Bridge
deck
ratings
Bubble
plots
Figure
Bridge
deck
ratings
–Bubble
Bubble
plots
4.2.
4.2.
Deterioration
curves
4.2.Deterioration
Deteriorationcurves
curves

22

for
bridge
deck
was
created

using
the
proposed
ANN
model.
This
curve
can
be
to
the
The
The
deterioration
curve
for
bridge
deck
was
created
using
using
the
the
proposed
proposed
ANN
ANN
model.
model.

This
This
curve
curve
can
can
bebeused
used
used
totopredict
predict
predict
the
thethe
Thedeterioration
deteriorationcurve
curve
for
bridge
deck
was
created
using
the
proposed
ANN
model.
This
curve
can

be
used
to
predict
during
itsits
service
life.
InInIn
the
development
of
deterioration
curve
for
aaaspecific
bridge,
two
performance
performance
the
bridge
deck
during
service
life.
the
the
development
development

ofofthe
the
the
deterioration
deterioration
curve
curve
for
forfor
specific
specific
bridge,
bridge,
two
two
performanceofof
ofthe
thebridge
bridgedeck
deck
during
its
service
life.
the
development
of
the
deterioration
curve

a specific
bridge,
two
(CBA)
and
Average
Daily
Traffic
(ADT)
were
changed
in
step,
other
parameters
were
parameters,
parameters,
Current
Bridge
Age
(CBA)
and
Average
Daily
Traffic
Traffic
(ADT)
(ADT)
were

were
changed
changed
inineach
each
step,
step,
other
other
parameters
parameters
were
were
parameters,Current
CurrentBridge
BridgeAge
Age
(CBA)
and
Average
Daily
Traffic
(ADT)
were
changed
ineach
each
step,
other
parameters

were
ofof
bridge
age
was
1 1year,
the
change
of
daily
traffic
was
calculated
by
the
kept
kept
constant.
While
the
increment
bridge
age
was
year,
the
the
change
change
ofofaverage

average
average
daily
daily
traffic
traffic
was
was
calculated
calculated
by
byusing
using
using
the
thethe
keptconstant.
constant.While
Whilethe
theincrement
increment
of
bridge
age
was
1year,
year,
the
change
of

average
daily
traffic
was
calculated
by
using


Nguyen, T. T., Dinh, K. / Journal of Science and Technology in Civil Engineering

half of the size of the training subset, the size of the bubbles in validation and testing plots are smaller.
The dots on the diagonal line indicate the number of accurate predictions, and the dots within the limit
of upper and lower error margin line represent the number of instances within a ±1 rating interval.
4.2. Deterioration curves
Tu T. Nguyen, Kien Dinh/ Journal of Science and Technology in Civil Engineering
The deterioration curve for bridge deck was created using the proposed ANN model. This curve
can be used to predict the performance of the bridge deck during its service life. In the development
where
is the average
daily for
traffic
of the current
year;two
𝐴𝐷𝑇parameters,
dailyBridge
traffic of
the (CBA)
next year;
ARG

is the
1234 is the average
of theADT
deterioration
curve
a specific
bridge,
Current
Age
and
Averannual
average
daily
traffic
growth
rate.
To
obtain
the
deterioration
curve
for
the
deck
of
a
specific
bridge,
the
following

steps
age Daily Traffic (ADT) were changed in each step, other parameters were kept constant. While the
were applied.
increment of bridge age was 1 year, the change of average daily traffic was calculated by using the
1. Obtain equation
the initial value of inputs of the bridge of interest from the database.
following
ADTnext = (1 + ARG) ADT
(2)
2. Decide the number of years to be simulated
where
ADT
the to
average
dailyANN
traffic
of the
current
ADTnext is the average daily traffic of the
3. Apply
the is
inputs
the proposed
model
for the
rating year;
prediction
next year; ARG is the annual average daily traffic growth rate. To obtain the deterioration curve for
Increase
age by 1 bridge,

year and the
calculate
𝐴𝐷𝑇1234
the4.deck
of the
a specific
following
steps were applied.
Obtain
initial
of inputs
of the bridge of interest from the database.
5. 1.
Repeat
stepsthe
3 and
4 forvalue
the entire
life of simulation.
2. Decide the number of years to be simulated.
Figure 5 shows an example of the bridge deck rating projection using the proposed ANN model. In this figure, a circle dot
3. Apply
the inputs
to the
proposed
ANN
rating
represents
the overall
deck rating

predicted
by the
ANNmodel
model. for
Thethe
square
dotsprediction.
and diamond dots represent the upper limit
4.
Increase
the
age
by
1
year
and
calculate
ADT
.
nextbridge was seven years old with a current rating (DCR) of
and lower limit of the predicted condition rating, respectively. This
5. AGR
Repeat
stepsThe
3 and
4 for the
lifetoofpredict
simulation.
8 and an
of 2.5%.

simulation
wasentire
performed
the condition rating for the bridge deck over 60 years. Details
shows
an example
the can
bridge
deck
rating6. projection using the proposed ANN model. In
of the Fig.
initial5input
parameters
of this of
bridge
be seen
in Table
Fig. 5, a circle dot represents the overall deck rating predicted by the ANN model. The square dots and
Table 6. Initial input parameters from the database
diamond dots represent the upper limit and lower limit of the predicted condition rating, respectively.
Inputwas seven
CBA years ADT
MSD (DCR)
ASD
ARGsimulation
This bridge
old with aDLD
current rating
of 8 andNMS
an AGR PDT

of 2.5%. The
was performed
condition
60 years.
Value to 7predict the
17503
5 rating for
2 the bridge
0 deck over
2
10 Details
2.5of the initial
input parameters of this bridge can be seen in Table 6.
9
+1 error
-1 error
Rounded
Original

8

NBI rating

7

6

5

4

3

0

10

20

30

40

50

60

Deck Age, (Years)

Figure
5. 5.
Lifetime
ratingsprediction
prediction
Figure
Lifetimebridge
bridge deck
deck ratings
4.3 Input sensitivity analysis
To study the influence of a single input parameter to the23

overall deck rating for the bridges, the ANN model was used to
run the sensitivity analysis. In each case, a single input was used with the ANN model to predict the output. The performance
of each simulation instance was evaluated using the coefficient of determination (R2). The coefficient of determination
measures the correlation between input and output variables using equation (3)


Nguyen, T. T., Dinh, K. / Journal of Science and Technology in Civil Engineering

Table 6. Initial input parameters from the database

Input

CBA

ADT

DLD

MSD

ASD

NMS

PDT

ARG

Value

7

17503

5

2

0

2

10

2.5

4.3. Input sensitivity analysis
To study the influence of a single input parameter to the overall deck rating for the bridges, the
ANN model was used to run the sensitivity analysis. In each case, a single input was used with
the ANN model to predict the output. The performance of each simulation instance was evaluated
using the coefficient of determination (R2 ). The coefficient of determination measures the correlation
between input and output variables using equation (3)
R2 = 1 −

n
ˆ i )2
i=1 (yi − y
n
¯ )2
i=1 (yi − y

(3)

where yi is the ith actual output, y¯ is the mean of the actual outputs, yˆ i is the ith predicted rounded
outputs, and n is the total number of samples. The results of the input analysis simulation are shown
in Table 7.
Table 7. Sensitivity analysis for the inputs

Input

R2

Ranking

CBA
ADT
DLD
MSD
ASD
NMS
PDT
AGR

0.93
0.18
0.60
0.52
0.23
0.08
0.14

0.05

1
5
2
3
4
7
6
8

As can be seen in Table 7, the most influential input parameter for the proposed ANN model
was the Current Bridge Age (CBA) with a value of R2 was 0.93. The Design Load (DLD) and Main
Structure Design (MSD) came in the second and third place with an R2 of 0.60 and 0.52, respectively.
The results were reasonable since the performance of a bridge deck was likely linearly dependent on
time. In addition, the design load was related to the type of load that applied to the bridge decks, thus
a strong relationship between the design load parameter and the performance of a bridge deck was
comprehensible. Other input parameters presented the limited correlation to the output.
5. Conclusions
In this paper, an ANN model was developed for predicting the condition rating of bridge deck
using the available information in the NBI database. The bridge data in the State of Alabama were
used to train, validate, and test the proposed ANN model. The model worked well with the new data
24


Nguyen, T. T., Dinh, K. / Journal of Science and Technology in Civil Engineering

in the testing data set with the percentage of prediction accuracy of 73.6%. Within the margin error
of ±1, the prediction accuracy of the model can achieve 98.5%. The trained ANN model can be
used effectively to develop the deterioration curve for the bridge deck. With such a curve, the future

condition rating of the bridge deck can be easily predicted. In addition, a sensitivity study of the input
parameters revealed that the Current Bridge Age (CBA) is the most important predicting factor to
the bridge deck condition rating/deterioration. Other factors such as Design Load (DLD) and Main
Structure Design (MSD) also had some significant effects on the deck deterioration.
References
[1] ASCE (2017). Infrastructure report card. American Society of Civil Engineers.
[2] MDOT (2011). NBI rating guidelines. Michigan Department of Transportation.
[3] Derucher, K., K. G., Ezeldin, S. (1994). Materials for civil and highway engineers. 3rd edition, PrenticeHall., Englewood Cliffs, N.J.
[4] Enright, M. P., Frangopol, D. M. (1998). Probabilistic analysis of resistance degradation of reinforced
concrete bridge beams under corrosion. Engineering Structures, 20(11):960–971.
[5] Bhargava, K., Ghosh, A. K., Mori, Y., Ramanujam, S. (2006). Analytical model for time to cover cracking
in RC structures due to rebar corrosion. Nuclear Engineering and Design, 236(11):1123–1139.
[6] Isgor, O. B., Razaqpur, A. G. (2006). Modelling steel corrosion in concrete structures. Materials and
Structures, 39(3):291–302.
[7] Markow, M. J. (2009). Bridge management systems for transportation agency decision making. NCHRP
Synthesis 397, Washington, DC: The National Academies Press.
[8] Frangopol, D. M., Kong, J. S., Gharaibeh, E. S. (2001). Reliability-based life-cycle management of
highway bridges. Journal of Computing in Civil Engineering, 15(1):27–34.
[9] Cattan, J., Mohammadi, J. (1997). Analysis of bridge condition rating data using neural networks.
Computer-Aided Civil and Infrastructure Engineering, 12(6):419–429.
[10] Al-Barqawi, H., Zayed, T. (2006). Condition rating model for underground infrastructure sustainable
water mains. Journal of Performance of Constructed Facilities, 20(2):126–135.
[11] Li, Z., Burgue˜no, R. (2010). Using soft computing to analyze inspection results for bridge evaluation and
management. Journal of Bridge Engineering, 15(4):430–438.
[12] Morcous, G. (2002). Comparing the use of artificial neural networks and case-based reasoning in modeling bridge deterioration. In Proc., 30th Annual Conference of Canadian Society for Civil Engineering,
Curran Associates, Inc, 2471–2479.
[13] Lee, J., Sanmugarasa, K., Blumenstein, M., Loo, Y.-C. (2008). Improving the reliability of a Bridge
Management System (BMS) using an ANN-based Backward Prediction Model (BPM). Automation in
Construction, 17(6):758–772.
[14] Emily, W. K. (2011). Artificial neural network models for the prediction of bridge deck condition ratings.

Master’s thesis, Michigan State University, USA.
[15] Huang, Y.-H. (2010). Artificial neural network model of bridge deterioration. Journal of Performance of
Constructed Facilities, 24(6):597–602.
[16] FHWA (2019). Federal highway administration. National Bridge Inventory.
[17] Topcu, I. B., Sarıdemir, M. (2007). Prediction of properties of waste AAC aggregate concrete using
artificial neural network. Computational Materials Science, 41(1):117–125.
[18] Diez, P. (2018). Smart wheelchairs and brain-computer interfaces, chapter 1 - Introduction, 1–21. Academic Press.
[19] Leban, G., Zupan, B., Vidmar, G., Bratko, I. (2006). Vizrank: Data visualization guided by machine
learning. Data Mining and Knowledge Discovery, 13(2):119–136.

25