Road Materials and Pavement Design
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Prediction of asphalt pavement condition using
FWD deflection basin parameters and artificial
neural networks
Vidhi Vyas, Ajit Pratap Singh & Anshuman Srivastava
To cite this article: Vidhi Vyas, Ajit Pratap Singh & Anshuman Srivastava (2021) Prediction of
asphalt pavement condition using FWD deflection basin parameters and artificial neural networks,
Road Materials and Pavement Design, 22:12, 2748-2766, DOI: 10.1080/14680629.2020.1797855
To link to this article: https://doi.org/10.1080/14680629.2020.1797855
Published online: 27 Jul 2020.
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ROAD MATERIALS AND PAVEMENT DESIGN
2021, VOL. 22, NO. 12, 2748–2766
https://doi.org/10.1080/14680629.2020.1797855
Prediction of asphalt pavement condition using FWD deflection
basin parameters and artificial neural networks
Vidhi Vyas, Ajit Pratap Singh
and Anshuman Srivastava
Civil Engineering Department, Birla Institute of Technology and Science, Pilani, India
ABSTRACT
ARTICLE HISTORY
Applications of non-destructive testing devices such as Falling Weight
Deflectometer (FWD) provide crucial estimates of pavement health that
assist in the optimisation of pavement management systems. However,
regularly conducting these tests at a network level and post-processing
of the collected data is cumbersome, which requires technical expertise,
significant time, funds, and other resources. Due to this structural aspect
of pavements during the selection of maintenance or repair, decisions
are often ignored. This study attempts to develop reliable correlations for
estimates of two different deflection basin parameters using a number
of structural, functional, environmental, and subgrade soil attributes as
input. The data has been obtained through field tests over a 124 km long
pavement network. Different artificial neural network-based models are
trained by varying the number of hidden layers and neurons in these layers, for the above-mentioned purpose. The coefficient of determination and
mean square error is decisive for the selection of best network architecture.
These outcomes are also compared to the results of the classical multiple
linear regression method, and the superiority of neural networks over nonintelligent approaches for non-linear problems of pavement engineering is
appreciated. In addition to this, the results justify the fact that the properties
of the asphalt layer predominantly impact the entire pavement condition.
The proposed approach is an alternative way to facilitate quick pavement
condition assessment by reducing the frequency of deflection testing without compromising with the accuracy of its estimates. It would encourage
the increased application of structural condition data in pavement maintenance and rehabilitation necessities with ease. However, the study does
not intend to completely avoid conducting deflection testing and serve as
a base for future studies.
Received 6 October 2019
Accepted 13 July 2020
KEYWORDS
Artificial neural networks;
pavement condition
assessment; falling weight
deflectometer;
non-destructive testing;
pavement management
systems
Introduction
Failure of pavements pre-maturely or towards the end of their design life, due to poor design, construction, or maintenance practices, necessitates a robust decision-making strategy to meet their maintenance or rehabilitation needs. Pavement Management Systems (PMS) involves a holistic approach
towards the activities concerned with planning, design, evaluation, and maintenance of pavements
to provide economical, serviceable, and safe pavements at a network and project level. The key components of PMS include condition assessment surveys, robust databases, analysis schemes, judgment
criteria, and implementation techniques (AASHTO, 1993; Peterson & Shepard, 1972). The prerequisite
to maintain the high quality of pavements within the optimum budget is to update databases regularly
CONTACT Ajit Pratap Singh
aps@pilani.bits-pilani.ac.in
© 2020 Informa UK Limited, trading as Taylor & Francis Group
ROAD MATERIALS AND PAVEMENT DESIGN
2749
with the estimates of pavement performance parameters. The collection of these diverse parameters
requires a rational assessment of pavements, and thus, the condition assessment surveys form the
backbone of PMS. The concerned factors can be broadly categorised as those related to serviceability
(roughness), structural capacity (surface deflection), surface distress (variety of pavement distresses),
and safety (skid resistance). Evaluation of structural capacity can be conducted either by destructive
or Non-Destructive Testing (NDT). For in-situ structural assessment of pavements and to cover their
vast network, NDT methods based on deflection testing such as FWD are preferred.
FWD assesses not only the structural adequacy but also provide substantial information about
pavement layers and its subsurface conditions, including subgrade. Thus, most of the highway agencies perform FWD testing as a part of their routine pavement assessment procedures that are usually
scheduled at periodic intervals. However, the estimation of layer moduli demands back-calculation of
FWD data, and its accurate analysis requires technical expertise with exact estimates of pavement layer
thicknesses, which is either done through coring or Ground Penetrating Radar (GPR) scans. The use of
GPR is not a common practice in India, and coring practices require considerable time and resources.
Furthermore, the practice of data acquisition at frequent intervals is indeed time-consuming, labourintensive, interrupts traffic, and expensive, hence, it is difficult to be performed repeatedly. These are
possibly a few of the contributing reasons in neglecting the structural aspect of pavements during the
selection of maintenance or repair decisions. Therefore, to cope up with these limitations, many efforts
have been made by the researchers to find relatively quick alternative analysis methods and obtain a
thorough knowledge of pavement condition, without performing rigorous back-calculation procedures. The application of Deflection Basin Parameters (DBP), which are FWD basin derived strength
indicators, provides one such method of delivering rapid estimates of pavement’s structural state.
Additionally, the techniques of Artificial Intelligence (AI) such as expert systems, Artificial Neural Networks (ANN), Genetic Algorithms (GA), and hybrid systems complement the analysis dealing with
complex interrelationships of traffic loading, climatic conditions, and material properties in providing
reasonable approximations.
A preliminary attempt is made in this paper to assess the structural condition of the pavements by
estimating the DBP through ANN. An alternative means is suggested for more efficient usage of DBP,
and the potential of ANN modelling to determine DBP is investigated. The superiority of ANN models
is highlighted by comparing their results with the multiple linear regression approach. The authors
have adopted a more holistic procedure by considering the impact of structural, functional, and environmental factors, as well as factors affecting subgrade condition on various DBP. To achieve these
objectives, different sets of ANN structures have been developed and tested. The intelligent approach
of ANN has been attested to offer such robust models to highway agencies which would facilitate
reliable decision-making of maintenance and rehabilitation treatments in a short span of time.
Literature review
Several studies have reported the use of NDT methods such as infrared thermography, impact echo,
GPR, and FWD to analyze pavement behaviour and its different aspects including back-calculation
of layer moduli, prediction of pavement strains, and layer interface bonding conditions (Bianchini,
2014; Elbagalati et al., 2018; Gopalakrishnan & Thompson, 2005; Park et al., 2005; Vyas et al., 2019).
Authors have utilised pavement deflection measurements under the FWD load to serve multiple purposes. Attempts to relate deflections under FWD load by developing linear and non-linear models with
parameters such as condition survey data, effective structural number, layer thickness, and equivalent
axle load was made (Gedafa et al., 2012; Wu et al., 2013). Determination of elastic moduli of layers and
critical strains has also been performed from FWD deflection measurements (Bilodeau & Doré, 2012;
Kumlai et al., 2014; Losa et al., 2008; Plati et al., 2016). Furthermore, the mechanistic-empirical pavement design guide also necessitates FWD testing for the assessment of in-situ pavement conditions
(ARA, 2004).
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V. VYAS ET AL.
Although FWD is nowadays used regularly for structural assessment of asphalt pavements, yet
it has been observed that the pavement prioritisation projects for reconstruction or rehabilitation
are still primarily based only on visual identification of distresses and functional condition surveys
(Papagiannakis & Masad, 2017). Assuming that poor structural health would be eventually reflected
by the deterioration in functional performance indicators, the consideration of structural aspect is
often ignored. In real field conditions, visual distresses usually get reflected after a major portion of
the pavement structure is deteriorated. In such cases, any sort of maintenance or rehabilitation activity would be expensive and would require a substantial amount of time, resources, and efforts. On
the other hand, the prior inclusion of structural condition during any decision-making process would
provide warning signs during the early stages of pavement deterioration and addressing them may
demand only minor repairs which would save huge funds. Vyas et al. (2019a) have made efforts in
this direction, by using structural as well as functional performance parameters to propose a decisionmaking approach for pavement prioritisation based on analytic hierarchy process and fuzzy theory.
In another study, the authors prioritised pavement sections on the basis of entropy weights and performed SWOT analysis for pavement maintenance and repair alternatives (Vyas et al., 2019b). However,
in order to encourage this practice at a larger scale, approaches providing quick judgments regarding
the deteriorated condition and its possible reasons or layers contributing to the distress generation
are obligatory.
In the view of the above conclusions, the most relevant and remarkable contribution of FWD testing is to encompass the DBP derived from deflections at different radial offsets, which are indicative of
pavement deflection basin and eventually its strength. The commonly proposed DBP include surface
curvature index, base curvature index, area under pavement profile, base damage index, base layer
index, middle layer index, and lower layer index (Horak, 1987; Horak, 2008; Horak et al., 2015; Kim,
2000; Losa et al., 2008; Park et al., 2005; Xu et al., 2002a, 2002b). The significance of using DBP has been
highlighted in the study carried by Kim (2000) in which these estimates were used to empirically evaluate individual layer moduli of pavements without undergoing complex back-calculation schemes.
More recent studies have also adopted these estimates of the deflection basin to analyze and report
the condition of pavements (Fakhri & Dezfoulian, 2019; Rabbi & Mishra, 2019; Sollazzo et al., 2017).
Saleh (2016) evaluated the structural condition of pavements using area ratio and normalised area
ratio from FWD deflections and concluded the normalised area ratio parameter to be highly appropriate for the structural condition of the pavements. In addition to this, researchers have also studied the
impact of critical factors such as those related to structure and temperature on pavement responses
using DBP (Xu et al., 2002a, 2002b). Surface distresses, and visual condition ratings were also reported
to affect deflection parameters, but no analytical or mathematical model was presented to determine
the relation (Horak, 2008; Horak et al., 2015). In similar works, functional performance rating indicators
of pavements were studied for their correlation with structural indices (Fakhri & Dezfoulian, 2019).
However, parameters such as environmental factors, traffic, and subgrade soil conditions also have
leading impacts on pavement health, which are reflected in surface deflections and DBP. The inclusion of these diversified factors results in complicated pavement engineering problems, which are
challenging to solve using closed-form solutions or physics-based principles (Li & Wang, 2018). Soft
computing and AI based techniques including machine learning find their wide application in such
real-world problems (Meier, 1995; Shafabakhsh et al., 2015; Majidifard et al., 2019; Singh et al., 2018).
Alavi and Buttlar (2018) adopted genetic programming to formulate prediction model for PCI and
used smartphones to collect airport pavement condition data. Previous studies supported the usage
of ANN for back-calculation of pavement layer moduli and dynamic moduli of asphalt layer when pavements were subjected to FWD load (Gopalakrishnan et al., 2014; Pekcan et al., 2008; Varma & Kutay,
2016; Zaabar et al., 2014). Researchers have also adopted a hybrid of ANN and GA to develop backcalculation programme (Li & Wang, 2019; Tutumluer et al., 2009). The integration of the AI approach
and FWD derived parameters is found to be quiet successful in few studies (Fakhri & Dezfoulian,
2019; Sollazzo et al., 2017). The DBP surface curvature index and the thickness of the asphalt layer
were adopted to predict tensile strain in asphalt pavements (Plati et al., 2016). In another study,
ROAD MATERIALS AND PAVEMENT DESIGN
2751
Table 1. Threshold ranges of layer condition for SCI and BCI (Chang et al., 2014).
Layer condition threshold range (mils)
Parameter
Concerned layer
SCI
BCI
Asphalt layer
Base layer
Very good
Good
Fair
Poor
Very poor
<4
<2
4–6
2–3
6–8
3–4
8–10
4–5
> 10
>5
DBP were implemented to predict responses of asphalt pavements using ANN-based programme in
combination with GA optimisation (Li & Wang, 2018).
Although a lot of research has been done, the studies on the inclusion of diversified factors with AI
to address the real-life challenges of field testing in pavement prioritisation are limited. Therefore, this
study is an attempt to explore the amalgamation of DBP with neural networks to ease the task of data
analysis and offers an attractive way to inspire the practice of incorporating strength parameters in
pavement prioritisation projects. A thorough review of literature helped to ascertain typical deflection
basin parameters and range of their values, as proposed by the researchers (Chang et al., 2014). Finally,
to inculcate the effect of upper as well as lower pavement layers, two DBP, namely Surface Curvature
Index (SCI), and Base Curvature Index (BCI) are used in conjunction with eight decision variables in this
work. SCI is defined as the difference between the deflections measured by the sensor located at the
centre of the load plate and another sensor located at 300 mm from the centre. This is a measure of
the structural quality of the upper pavement layers, specifically asphalt layers (Kim, 2000). Similarly, BCI
infers the quality of lower layers and subgrade. It is defined as the difference between the deflections
measured by the sensor located 600 and 900 mm from the centre of the load plate. Thus, SCI = D0 –
D300 , and BCI = D600 – D900 , where D represents the deflection measured at sensor locations (in mm)
indicated at the subscript of D. Table 1 enlists threshold range of DBP used in this study, as found in
the literature. Once the values of SCI and BCI are computed from the developed prediction models,
the inferences about the pavement layer condition can be drawn directly by using the standard range
of threshold values classified into five categories namely, very good, good, fair, poor, and very poor, as
presented in Table 1. It can be concluded that small values of SCI and BCI indicate structurally sound
layers in the pavement structure, and vice versa. However, the range of threshold values varies for SCI
and BCI, as depicted in Table 1.
Objectives and scope
The study, as a whole, tries to address the problems faced by authorities of highway agencies while
implementing PMS on asphalt pavement network. Multiple challenges are faced during data acquisition and analysis pertaining to the structural condition of asphalt pavements. They include difficulty in
frequently performing FWD tests at a network level due to the concerns explained in the previous sections, the requirement of accurate layer thicknesses data for back-calculation of measured deflections,
and unpopularity of GPR usage in India owing to its high cost. Another challenge is to promote the use
of structural condition data rather than merely assessing the functional performance of pavements
while making maintenance decisions.
In order to address these concerns, the first objective is to reduce the frequency of conducting FWD
tests by developing analytical and reliable correlations using a set of ANN models for pavement’s structural health assessment. Secondly, to maintain the simplicity of these models by keeping the fewer
number of variables without causing a significant reduction in their accuracy, and alleviate the need
of performing rigorous back-calculation, DBP are used instead of deflections at all geophones. This
approach is relatively quick and, therefore, would encourage the usage of structural adequacy factors
in determining the maintenance and rehabilitation strategies. This would eventually assist in the optimum utilisation of available funds. Finally, the study proposes the best ANN architecture for dealing
with such problems.
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V. VYAS ET AL.
In this work SCI and BCI are taken as output, and input variables include pavement structure-related
factors such as thickness of asphalt layer (La ), thickness of base layer (Lb ), and total thickness of pavement (Lt ); functional performance factor such as International Roughness Index (IRI); subgrade soil
strength depicting factors such as Maximum Dry Density (MDD) and California Bearing Ratio (CBR);
lastly environmental factors including atmospheric temperature (Ta ), and asphalt pavement surface
temperature at the time of testing (Ts ). Review of literature helped to ascertain the domains which
directly or indirectly affect the structural condition of pavements (Sollazzo et al., 2017). Accordingly,
the input variables are selected from the wide spectrum of important attributes. The selection also
depends upon the availability and ease of collecting data for these attributes. Pertaining to the ease
of conducting FWD or CBR test, it should be noted that FWD is limited in its availability while CBR is
widely available. Due to the limited availability of FWD for conducting field inspections anywhere in
the country, it needs to be transported from place to place. Performing this task repeatedly is neither
easy nor economical, and needs proper planning along with sufficient funds. On contrary, conducting
CBR tests is relatively easy and economical since it can be performed at multiple places due to its wide
availability. The advantage of developing a prediction model is that in case of difficulty in procuring
any particular device or conducting test, the particular parameter can be dropped off from the model.
Whereas no such flexibility would be available with FWD tests which would require to follow the entire
procedure everytime, from collecting the data to analyze it using back-calculation. The present study
aims to provide an approach to alleviate the need of conducting FWD tests repeatedly. It offers an
idea to incorporate the parameters from diverse field to develop the robust prediction models which
are highly flexible in nature since its parameters can be suitably varied or modified according to the
intended problem. The complete methodology is demonstrated by using the selected set of parameters. However, the input variables can be always varied according to the scope of work, equipment
availability, ease, and time constraints.
Field testing and generation of database
In order to create robust models using neural networks, a comprehensive and accurate database is
a prerequisite. Therefore, for this study, a vast road network of 124 km was selected for testing and
modelling purpose in India. The selection was primarily done on the basis of pavement condition, and
observation of visual distresses such as fatigue cracking, ravelling, rutting, and lane/shoulder drop off.
After the selection of pavement sections, detailed field surveys and testing were performed to collect
the required data.
Field tests to measure structural adequacy were conducted in accordance with the standards of
Indian road congress using Dynatest model 8000 FWD and load plate of diameter 300 mm (IRC 115,
2014). The geophone configuration is decided as per the need at the location and standards, which is
taken to be 0, 200, 300, 600, 900, and 1200 mm in this study (IRC 115, 2014). Three drops of mass were
taken at each testing point with loading time for each drop generally in the range of 0.015−0.050 s,
and the first drop being the seating load, was not recorded. The deflection data has been normalised
as per the standard load, and suitable corrections for temperature have been applied. FWD testing was
carried out at every 100 m intervals approximately. At a few locations where pavement condition was
poor, the testing interval was reduced to incorporate greater number of testing points to gain a better
understanding of the pavement structure. This resulted in a total of 1452 test records. Further details
of the FWD and testing procedure can be found elsewhere in the literature (ASTM D4694, 2015; ASTM
D4695, 2015; IRC 115, 2014).
Figure 1 shows a typical FWD deflection basin obtained from data recorded at a test location. The
position of load drop, radial geophone offsets, and deflections (D0 to D5 ) measured at the corresponding positions of sensor locations are also shown along with the expressions for estimation of SCI and
BCI.
In-situ asphalt surface temperature and air temperature were recorded at the time of FWD testing.
IRI is a standardised roughness measurement of the longitudinal profile of a travelled wheel path, and
ROAD MATERIALS AND PAVEMENT DESIGN
2753
Figure 1. A typical FWD deflection basin and geophone spacing used in this study.
Table 2. A sample of laboratory testing results on subgrade soil.
Grain size analysis
Test pit
number
1
2
3
4
5
Atterberg limits
4.75
mm IS
Sieve
425
mic IS
Sieve
75 mic
IS Sieve
LL
92
100
93
93
100
84
93
89
88
94
78
88
84
69
71
26
30
25
33
24
Heavy compaction test
PI
Soil
class
Field
moisture
content (%)
Field dry
density
(g/cm3 )
MDD
(g/cm3 )
OMC
(%)
CBR
(%)
20
14
6
9
6
CL
CL
ML-CL
ML
ML-CL
8.98
8.53
19.11
1.54
10.57
1.70
1.70
1.83
1.85
1.84
1.95
1.98
1.97
1.88
1.99
11.00
9.70
10.00
10.50
10.50
29.2
14.6
46.7
21.5
46.7
it is commonly measured in the unit m/km (Papagiannakis & Masad, 2017). The data was collected
using a bump integrator. A high value of IRI indicates increased roughness level and vice-versa. Subgrade soil parameters, including CBR and MDD, were determined through the laboratory tests on soil
samples collected from test pits. CBR test is a penetration test which intends to determine the strength
of subgrade soil, as compared to standard crushed rock (AASHTO T 193, 1993). High CBR value indicates a high strength of the soil. Soaked CBR values at 56 blows are taken in this study. MDD is the value
of dry density corresponding to optimum moisture content. Table 2 summarises a sample of laboratory testing results conducted on the subgrade soil. Coring operations along with test pits and field
surveys were performed to collect the facts about the type and thickness of layers, crack propagation
and delamination (if any), characterisation of materials, and subsurface drainage conditions. Measurement of deflections, IRI, and distresses was performed at the same location to maintain uniformity and
reliability in the results. The points at which data was missing, linear interpolation was adopted. It is
worth to mention here that the detailed explanation of these soil properties is beyond the scope of
this paper.
The analysis in this study is focused on asphalt pavements. To simplify the research, the dataset
does not include the particulars of maintenance or rehabilitation activities. In addition to this, due to
the limited accessibility to the previous records, time constraint, and scope of work; pavement construction history data, and estimation of traffic loading could not be included in the work, which can
be taken in future studies. Nevertheless, with the available resources itself, significant information was
collected, and a substantial amount of dataset for modelling purposes could be generated.
2754
V. VYAS ET AL.
ANN prediction model development
ANN models work on the principle of the biological neural network of the human brain and analogous to its thought process, which has the capability to learn and compensate for errors (Karayiannis
& Venetsanopoulos, 1993). The central processing units of ANN networks are called neurons which
have weighted connections between them to receive input data, process and transfer the data as
output to other neurons. They can learn input-output mapping and provide an easy approach to
estimate solutions of complex and non-linear problems without any need for preliminary conjectures. Improved performance of these models could be attained by defining more levels of input
processing based on trial-and-error methods, and repeatedly training the networks. Further, accurate
results can be obtained by comparing outputs from different training algorithms. However, generating a realistic ANN network requires empirical experiences; its effectiveness is entirely based on the
trial-and-error process, and repeatability of results is not assured (Zain et al., 2010). ANN follows the
black-box approach and therefore, the nature of the prediction equation is not known (Sollazzo et al.,
2017).
In this study, the ANN modelling is performed to obtain the desired outputs of deflection basin
parameters by taking eight input parameters. Despite the fact that the development of these models
is trial-and-error based, it is still essential to carefully select the critical governing parameters according
to the nature of the problem. The basis of the selection of various model parameters is presented in
the subsequent sub-sections.
Selection of ANN model parameters
Network
A set of layers and nodes form the major components of an ANN network structure. Commonly, a
multilayer feed-forward neural network is used. The network consists of an input layer, one or more
hidden layers which act as a boundary layer between the input and output layers and contains computational nodes called neurons, activation functions, bias, and output layer. The type of network
structure adopted in this study is exemplified in Figure 2. It has 8 neurons in the input layer corresponding to 8 decision variables (X): La , Lb , Lt , Ts , Ta , CBR, MDD, and IRI; used in this study, m, n, and p
represents neurons in the first, second, and ith hidden layer, respectively, and finally one neuron in the
output layer corresponding to SCI or BCI, as per the case under consideration. Assuming the multilayer
feed-forward network, its structure could be defined as 8-m-n-p-1 structure. Figure 2 also depicts the
processing inside a neuron, wherein the net input along with their respective weights (W) is summed
with respective biases, and the selected transfer function is applied over it (logsig in the present study).
The arrows show the forward flow of information and back-propagation of errors during the training phase. The back-propagation mechanism propagates the errors in the reverse direction, updates
biases and weights, and minimises error after every iteration (Karayiannis & Venetsanopoulos, 1993).
Literature shows that researchers have applied various structures for the ANN model to obtain the
best prediction performance (Amin & Amador-Jiménez, 2017; Shafabakhsh et al., 2015). The process
of selection of the best network structure is usually done by varying the two important parameters,
namely the number of hidden layers and number of neurons in the hidden layer(s), but it is subjected
to the complexity of various other parameters including computation memory and time. Authors of
similar previous studies varied the number of nodes of the hidden layer, such as 5, 10, and 25, based
on trial-and-error (Fakhri & Dezfoulian, 2019; Sollazzo et al., 2017). As far as this study is concerned, different network structures are developed by varying the two parameters mentioned above and their
results are compared to obtain the optimum structure. The best network structure is then recommended for such similar studies concerned with the computation of structural parameters of asphalt
pavements. Following the recommendation regarding the number of nodes in hidden layer to be i/2,
1(i), 2(i), and (2i + 1), where i is the number of input nodes, different structures are tried with number of nodes as 8/2 = 4, 1(8) = 8, 2(8) = 16 and (2*8 + 1) = 17 (Zhang et al., 1998). For the sake of
ROAD MATERIALS AND PAVEMENT DESIGN
2755
Figure 2. Illustration of ANN structure and its neuron.
avoiding complexity in the architectures, the hidden layers are kept up to a maximum number of two.
As depicted in Figure 3 (a-d) and Figure 4 (a-d), the different ANN architectures tried with one and two
hidden layers are 8-4-1, 8-8-1, 8-16-1, 8-17-1, 8-4-4-1, 8-8-8-1, 8-16-16-1 and 8-17-17-1.
Training, validation and testing dataset
Since ANN learns and adapts from the input data, a more accurate model will result from more number
of training data points. This seems to be a feasible solution for a synthetic database where the dataset
is generated from any simulation framework. However, the data used in the present study is taken
from the actual pavement testing, which is subjected to cost and time constraints. Recent studies have
helped to ascertain the division of input data (Fakhri & Dezfoulian, 2019; MATLAB & Simulink, 2020;
Sollazzo et al., 2017). Accordingly, the input data is divided into three sets by considering a typical
ratio of training (70%), validation (15%), and testing (15%) for 124 km of pavement with total 1452 data
points. Furthermore, it is advisable to perform normalisation of the data before the training and testing
process to bring the variables in the standard range of 0–1 or −1 to 1 in order to avoid computational
problems. Therefore, in the initial step, all the raw data has been normalised, using Equation (1) (Sanjay
& Jyothi, 2006):
xi =
0.8
∗ (xi − xmin ) + 0.1
(xmax − xmin )
(1)
where xmax and xmin are the maximum and minimum values of the data, respectively and xi is the ith
data point of the dataset.
2756
V. VYAS ET AL.
Figure 3. ANN architectures with one hidden layer for (a) 8-4-1; (b) 8-8-1; (c) 8-16-1; and (d) 8-17-1 networks.
Network algorithm and its associated functions
Many different network algorithms for ANN models are available, such as Radial Basis, Perceptron, Cascade-forward BP, Feed-forward time-delay, Feed-forward distributed time-delay, and selforganising map (Demuth & Beale, 2004). Feed-forward back-propagation (BP) algorithm is widely used
for its application in problems of pavement engineering (Elbagalati et al., 2018; Li & Wang, 2018;
Sollazzo et al., 2017). For the feed-forward BP algorithm, the widely-adopted transfer functions are
log-sigmoid transfer function (logsig), hyperbolic tangent sigmoid transfer function (tansig), and linear transfer function (purelin). Non-linear relationships between input and output variables would be
better addressed by using non-linear transfer function such as sigmoid function. Therefore, the logsig
transfer function is adopted in this study, as given by Equation (2):
z=
1
1 + e−y
(2)
ROAD MATERIALS AND PAVEMENT DESIGN
2757
Figure 4. ANN architectures with two hidden layers for (a) 8-4-4-1; (b) 8-8-8-1; (c) 8-16-16-1; and (d) 8-17-17-1 networks.
where z is the output from the hidden layer neuron after sigmoid function, and y is the net input to
the hidden layer neuron.
Eventually, the BP algorithm reduces the error and finds its lowest possible value, which is represented by performance function. This includes Mean Square Error (MSE), Sum Square Error (SSE), Mean
Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE).
Previous studies have mostly applied MSE performance function, and the same has been considered
in this study. MSE of n data points is given by Equation (3):
1
(Oi − Pi )2
n
n
MSE =
i=1
where Oi and Pi are the observed and predicted values of any data point, respectively.
(3)
2758
V. VYAS ET AL.
In order to reduce the error, as the number of iterations proceeds, the weights and biases are
continuously updated in which optimum values of learning rate, and momentum provides better
accuracy as well as faster convergence. The default values of these parameters is adopted. Training
function and learning function also govern the reduction in error. Training functions are based on
gradient descent algorithm (traingd, traingda, traingdx), Bayesian regularisation (trainbr) or Levenberg–Marquardt BP (trainlm), and learning functions such as learngd (gradient descent weight/bias
learning function), learngdm (gradient descent with momentum weight/bias learning function), etc.
are used. In this work, trainlm and learngd are used as training and learning functions, respectively.
Figure 5 presents the step-wise methodology adopted in this study and its explanation is covered in
the preceding paragraphs.
Results
In order to illustrate the efficacy of ANN models in predicting the structural parameters of asphalt
pavements, eight different models each for the two output variables are trained, resulting in a total of
sixteen models. The proposed structures differ in the number of hidden layers and neurons in these
layers, with the input and output layer fixed with eight and one nodes, respectively corresponding
to eight input and one output variable. The entire analysis is performed in MATLAB software, version
R2017a (Demuth & Beale, 2004). The data for modelling is collected through field testing.
The regression charts for training, validation, and testing phases along with error histograms for
selected ANN models are presented in Figures 6 and 7 for SCI and BCI, respectively. Similar plots are
obtained for the remaining cases. The error histograms plotted for each ANN architecture reveal that
their average is very close to zero, and in almost all the cases, 80% of the errors or more are confined
within one or two central bins. The performance of these models is summarised in Table 3.
Discussion
The feed-forward BP-ANN approach in this study has satisfactorily demonstrated the correlation of
input and output variables with varying coefficients of determination. It should be noted that the
data set used for modelling purposes has not been taken from any synthetic database, rather it has
been obtained experimentally by conducting extensive field testing which might have few manual or
instrumental errors associated during testing. Therefore, the R2 values obtained in 0.7–0.8 range can
be considered to be indicative of good correlation between the variables. Although it is concluded
that the correlation fits well, the R2 values may be further improved by modifying the non-linearity
aspects such as changing the transfer function or number of hidden layers and could be considered
in future scope of the study. The intelligent approach of neural networks has been concluded to be
felicitous for the complex problems of pavement response modelling, wherein numerous factors play
prominent roles. The development of similar robust models would assist the highway agencies in easing the decision-making exercises of pavement maintenance and rehabilitation treatments in a short
span of time.
In this research work, the possibility of appraising DBP, such as SCI and BCI, is exhibited using
pavement’s structural, functional, climatic, and subgrade strength attributes. The modelling has been
performed from the results of actual field testing with 1452 data points covering 124 km of the asphalt
pavement network, rather than from generation of any synthetic database. The large dataset and field
testing outcomes assure the robustness of these models, and their implementation presents practical
field implications. In a general sense, for a model with reasonable accuracy, the coefficient of determination (R2 ) value, which is a measure of the correlation between outputs and targets, is high (close
to one), and MSE which is the average squared difference between outputs and targets, is low (close
to zero). However, the acceptable values would differ from case to case and depend on the data availability and problem category. The R2 value of ANN models in this study is obtained to be as good
as 0.875, with the average value for all the three samples (training, validation, and test) being 0.784,
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2759
Figure 5. Flow chart showing ANN model development in the study.
0.810, and 0.768 for SCI; and 0.762, 0.674, and 0.717 for BCI (refer Table 3). The satisfactory R2 value in
all the sixteen models proves that the correlation developed in this work is significant, which can be
further attested by observing the low values of MSE, presented in Table 3. The error distribution plots
help to visualise the possible trends and also confirm the results, with an average value close to zero.
Another notable finding which compliments the outcomes from previous studies is that as compared
to other pavement layers, properties of asphalt layer have a more profound influence on the condition
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V. VYAS ET AL.
Figure 6. Regression results and error histograms for SCI using (a) 8-4-1; and (b) 8-4-4-1 networks.
of pavement (Schwartz et al., 2011). The finding is clearly evident from R2 values of SCI, which are higher
than the R2 values of BCI. It is worth to note that for the accuracy and acceptability of the model, low
values of MSE is not imperative since it is affected by the type of data, degrees of freedom, residual
space, and regression. Meticulous investigation of regression, MSE, and error plots should be made
before drawing any conclusion regarding the choice of the best network. Theoretically, as number of
neurons increases, the ANN model achieves better precision and prediction proficiency, but on the
contrary increases complexity and computation time. Nevertheless, with a view to select the best and
optimum network architecture from the sixteen structures containing a different number of computational neurons, apart from R2 and MSE values, the simplicity and computational ease are also taken
into consideration.
In accordance with the selection of the best network architecture, as seen from Table 3 and Figure 8,
the R2 values obtained for the network structure 8-8-1 and 8-16-1, i.e. for neurons equal to the number
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2761
Figure 7. Regression results and error histograms for BCI using (a) 8-4-1; and (b) 8-4-4-1 networks.
of input variables and twice of the number of input variables, are superior as compared to the R2 values
obtained for all other network architectures. On further increasing the number of neurons or number
of hidden layers, there is no significant improvement in the performance of the models. For one layer
models with SCI as an output parameter, increasing the number of neurons from 4 to 8, increases R2
value by 10.76%, whereas on further increment of neurons there is no significant change in R2 value,
and it eventually decreases. With BCI as an output parameter in one layer models, R2 value increases
by about 4% on increasing the neurons from 4 to 8, and 8 to 16 but decreases by additional neurons.
The general trend of MSE values in both the cases is such that it is maximum for 4-neuron models
and reduces (approximately by 37% for SCI and 45% for BCI) with the increase of neurons number to
eight. Additionally, it is evident from the R2 values of one layer models and two-layer models that the
overall performance of the two-layer models is less than the one layer models. One of the important
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V. VYAS ET AL.
Table 3. Performance results of different ANN models.
Input variables
Neurons
Output variables
MSE
Stag
R2
8-4-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
4
SCI
0.086
Training
Validation
Test
Total
0.719
0.771
0.786
0.734
8-8-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
8
SCI
0.054
Training
Validation
Test
Total
0.794
0.840
0.875
0.813
8-16-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
16
SCI
0.014
Training
Validation
Test
Total
0.789
0.862
0.874
0.812
8-17-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
17
SCI
0.0128
Training
Validation
Test
Total
0.779
0.846
0.853
0.798
8-4-4-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
4
SCI
0.096
Training
Validation
Test
Total
0.789
0.840
0.567
0.755
8-8-8-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
8
SCI
0.0513
Training
Validation
Test
Total
0.817
0.706
0.571
0.754
8-16-16-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
16
SCI
0.113
Training
Validation
Test
Total
0.773
0.868
0.849
0.794
8-17-17-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
17
SCI
0.078
Training
Validation
Test
Total
0.815
0.747
0.765
0.795
8-4-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
4
BCI
0.279
Training
Validation
Test
Total
0.702
0.705
0.775
0.712
8-8-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
8
BCI
0.151
Training
Validation
Test
Total
0.781
0.642
0.778
0.746
8-16-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
16
BCI
0.178
Training
Validation
Test
Total
0.802
0.652
0.800
0.777
8-17-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
17
BCI
0.0208
Training
Validation
Test
Total
0.793
0.662
0.681
0.762
8-4-4-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
4
BCI
0.148
Training
Validation
Test
Total
0.738
0.512
0.668
0.692
8-8-8-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
8
BCI
0.226
Training
Validation
Test
Total
0.752
0.775
0.727
0.753
Network
(continued).
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2763
Table 3. Continued.
Network
Input variables
Neurons
Output variables
MSE
Stag
R2
8-16-16-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
16
BCI
0.029
Training
Validation
Test
Total
0.734
0.737
0.720
0.730
8-17-17-1
La, Lb. Lt, Tp, Ta, CBR, MDD, IRI
17
BCI
0.254
Training
Validation
Test
Total
0.797
0.710
0.586
0.751
Figure 8. Variation in regression and mean square error results for different ANN architectures for (a) SCI; and (b) BCI.
Table 4. Comparison of results from artificial neural networks and multiple linear regression approaches.
Model type
Artificial neural network (8-8-1 structure)
Input variables
Output variable
R2
MSE
La, Lb, Lt, Ts, Ta, CBR, MDD, IRI
SCI
BCI
0.813
0.746
0.054
0.151
Multiple linear regression
La, Lb, Lt, Ts, Ta, CBR, MDD, IRI
SCI
BCI
0.475
0.417
0.032
0.055
observation is that even for two-layer models, better performance (in terms of R2 and MSE values)
is obtained for the 8-8-8-1, and 8-16-16-1 structures, i.e. for neurons equal to the number of input
variables and twice of the number of input variables but the two layers make the system much more
intricate. However, since the results from both the structures are comparable and considering the need
to maintain the simplicity of the models by keeping fewer neurons and hidden layers, the network
configuration 8-8-1 can be selected as the best structure.
In order to further validate the suitability of ANN for such complex non-linear problems, the ANN
results have been compared with multiple linear regression approach, with the same number of input
records. Table 4 compares the results of multiple linear regression models for SCI and BCI, respectively,
with that of the ANN 8-8-1 model. The R2 from these models for the same number of records and input
variables are 41.60% and 44.10% lower for SCI and BCI, respectively than those obtained from ANN.
However, the p-values are almost equal to zero and less than the significance level of 0.05, therefore,
a significant linear regression relationship exists between the variables. This provides the evidence to
the higher applicability of ANN models for dealing with such non-linear behaviours.
The highway agencies may work on a similar fashion by training their own ANN structures using the
readily available or measurable data to obtain an accurate prediction of structural adequacy without
entirely depending on the deflection tests. However, the results are highly dependent on the number,
quality, and characteristics of the input variables. Therefore, the selection of these parameters should
be made scrupulously by understanding their connections/relationships.
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V. VYAS ET AL.
Conclusions
In this paper, the propriety of using ANN models for numerical predictions of structural performance
parameters in asphalt pavements and their assistance in providing vital conclusions to optimise PMS
are justified. The structural and functional performance parameters of asphalt pavements along with
environmental and subgrade soil characteristics, have been correlated to the results of FWD deflection basin derived parameters, namely SCI and BCI. Adopting a large dataset of 1452 records obtained
from field testing, authors have trained sixteen different ANN structures as 8-4-1, 8-8-1, 8-16-1, 8-17-1,
8-4-4-1, 8-8-8-1, 8-16-16-1, and 8-17-17-1, for each of the two output parameters separately to gain
better insights of modelling. The models show an accuracy with R2 values up to 0.875 and 0.868 in
testing, and validation phases, respectively. The best network structure based on the R2 , MSE, and
simplicity of the network for such studies is proposed to be 8-8-1. On a further note, the superior R2
values of SCI as compared to BCI rationalises the fact that properties of the asphalt layer predominantly
impact the entire pavement condition. The ANN outcomes are also compared to the classical multiple linear regression approach, and the results authenticate the superior performance of ANN models
as compared to multiple linear regression models for non-linear problems of pavement analysis and
design.
The preliminary approach presented in the study provides reliable correlations among the
attributes. The ease of approach for data analysis minimises the need to go through the cumbersome
process of back-calculation. The developed models would help to estimate the values of SCI and BCI of
the pavement, which are direct indicators of its structural condition, along with the clear understanding of pavement layers contributing to the current condition (refer Table 1). Therefore, by directly
knowing the structural health of pavements, need of conducting FWD surveys frequently to obtain
information about structural condition of pavement would reduce. At the same time, it would promote
the use of employing structural condition while making M&R decisions, due to the ease of obtaining
the information. Hence, the current practice of typically selecting pavement sections for M&R based
only on their functional condition assessment would improve, and detailed knowledge of structural
adequacy of individual pavement layer would assist in optimising the M&R strategies. However, it does
not intend to avoid conducting the deflection testing since the direct assessment of structural capacity would indeed increase the model accuracy. Accordingly, future studies can seek to incorporate
other significant input parameters such as traffic-related (like annual average daily traffic, equivalent
single axle load, etc.), additional climatic factors (like annual average daily temperature), rainfall data,
and other functional performance indicators such as pavement condition index, and present serviceability index. Consequently, the authors believe that this study can form a basis for future studies by
incorporation of additional parameters listed above, particularly at network levels where deflection
data acquisition and processing frequently is a challenge but the approach and methodology adopted
could be similar. It is worth mentioning here that the trained ANN models should be adopted for similar
cases only, otherwise the accuracy and quality of prediction could be affected significantly.
Disclosure statement
No potential conflict of interest was reported by the authors.
ORCID
Ajit Pratap Singh
http://orcid.org/0000-0001-5103-0486
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