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ORIGINAL ARTICLE
Evaluation of mechanical properties of concretes containing coarse
recycled concrete aggregates using multivariate adaptive regression
splines (MARS), M5 model tree (M5Tree), and least squares support
vector regression (LSSVR) models
Aliakbar Gholampour
1
•Iman Mansouri
2
•Ozgur Kisi
3
•Togay Ozbakkaloglu
4
Received: 28 February 2018 / Accepted: 11 July 2018
ÓThe Natural Computing Applications Forum 2018
Abstract
This paper investigates the application of three artificial intelligence methods, including multivariate adaptive regression splines
(MARS), M5 model tree (M5Tree), and least squares support vector regression (LSSVR) for the prediction of the mechanical
behavior of recycled aggregate concrete (RAC). A large and reliable experimental test database containing the results of 650
compressive strength, 421 elastic modulus, 152 flexural strength, and 346 splitting tensile strength tests of RACs with no
pozzolanic admixtures assembled from the published literature was used to train, test, and validate the three data-driven-based
models. The results of the modelassessment show that the LSSVR model provides improvedaccuracy over the existingmodels in
the prediction of the compressive strength of RACs. The results also indicate that, although all three models provide higher
accuracy than the existing models in the prediction of the splitting tensile strengthof RACs, only the performance ofthe LSSVR
model exceeds those of the best-performing existing models for the flexural strength of RACs. The results of this study indicate
that MARS, M5Tree, and LSSVR models can provide close predictions of the mechanical properties of RACs by accurately
capturing the influences of the key parameters. This points to the possibility of the application of these three models in the pre-
design and modeling of structures manufactured with RACs.
Keywords Recycled aggregate concrete (RAC) Mechanical properties Least squares support vector regression
(LSSVR) M5 model tree (M5Tree) Multivariate adaptive regression splines (MARS)
1 Introduction
The high demand for concrete because of the rapid growth
in urbanization and industrialization has resulted in an
increase in the consumption of natural aggregates, which
typically makes up approximately 70% of the total volume
of concrete [1]. Furthermore, rapid industrialization and
urbanization have led to an increase in the generation of
construction and demolition (C&D) wastes, which conse-
quently resulted in the depletion of landfill space [2,3].
Over the past two decades, recycled aggregate concrete
(RAC), obtained by crushing concrete sourced from C&D
waste, has been considered as an alternative concrete
material to conserve natural aggregate resources and to
minimize the environmental impact of C&D waste [4,5].
During this period, a large number of studies have been
conducted to understand the mechanical behavior of RACs
&Togay Ozbakkaloglu
togay.ozbakkaloglu@adelaide.edu.au;
t.ozbakkaloglu@herts.ac.uk
1
School of Civil, Environmental and Mining Engineering,
University of Adelaide, Adelaide, SA 5005, Australia
2
Department of Civil Engineering, Birjand University of
Technology, P.O. Box 97175-569, Birjand, Iran
3
Faculty of Natural Sciences and Engineering, Ilia State
University, 0162 Tbilisi, Georgia
4
School of Engineering and Technology, University of
Hertfordshire, College Lane Campus, Hatfield AL10 9AB,
United Kingdom
123
Neural Computing and Applications
https://doi.org/10.1007/s00521-018-3630-y(0123456789().,-volV)(0123456789().,-volV)
(e.g., [6–9]). Existing studies confirmed that compressive
strength, elastic modulus, flexural strength, and splitting
tensile strength are the main mechanical properties for
design and analysis of RACs [10–12]. In addition, a
comprehensive literature review [1] revealed that a number
of models have been proposed either based on experi-
mental test results of the original study [13,37–48,65–69]
or compiled databases from the results of previous studies
[14–18] to predict the mechanical properties of RACs.
However, owing to the limitations in the number of input
parameters considered, as well as the use of relatively
small number of test results in the calibration of most
existing models, these models are not generalizable.
Therefore, additional studies are needed to investigate the
mechanical properties of RACs using computationally
economical techniques based on a comprehensive test
database containing key input parameters.
Machine learning-based models have been extensively
used to predict the properties of concrete [19–22]. Recently,
with the development of computer-aided modeling methods,
the use of artificial intelligence techniques has been consid-
ered to predict the mechanical behavior of RACs. Younis and
Pilakoutas [23] used multilinear and nonlinear regression
methods to develop a model for the prediction of the com-
pressive strength of RAC. Duan et al. [24]andSahooetal.
[25] predicted the compressive strength of RAC using artifi-
cial neural network (ANN) technique. Deshpande et al. [26]
used ANN, M5Tree, and nonlinear regression methods for the
prediction of the compressive strength of RAC. Duan et al.
[27] and Behnood et al. [28] used ANN and M5Tree tech-
niques for the prediction of the elastic modulus of RAC,
respectively. Gonzalez-Taboada et al. [29] applied genetic
programming and multivariable regression methods for the
prediction of the compressive strength, elastic modulus, and
splitting tensile strength of RAC. Recently, Ozbakkaloglu
et al. [2] and Gholampour et al. [30] predicted the compres-
sive strength, elastic modulus, flexural strength, and splitting
tensile strength of RACs with the use of nonlinear regression
and gene expression programming methods, respectively.
However, most of these techniques were either computa-
tionally complex, unable to handle a large number of data-
bases, or unable to accurately capture the influences of the
key input parameters for solving nonlinear problems. There-
fore, more robust and simple artificial intelligence techniques
should be applied to predict the properties of RACs.
In recent years, data-driven techniques, such as multi-
variate adaptive regression splines (MARS), M5 model tree
(M5Tree), and least squares support vector regression
(LSSVR) models, have received a significant attention to
solve critical civil engineering problems. MARS is a
nonlinear and nonparametric regression method, and its
main advantages are efficiency and robustness to explore a
large number of intricate nonlinear relations and rapid
detection of interactions between them despite their com-
plexity [31]. M5Tree model is a binary decision tree with a
series of linear regression functions, and its main advan-
tages are the simple geometric structure and the ability to
efficiently handle a large number of datasets with different
attributes [32]. LSSVR is a statistical learning model,
which adopts a least squares linear system as a loss func-
tion instead of the quadratic program in the original support
vector machine (SVM) [33]. LSSVR solves a set of linear
equations by linear programming that is computationally
very simple [33]. Recent studies illustrated that because of
their main advantages of (1) easy handling of a large
number of databases, (2) computational simplicity, and (3)
strong ability of solving nonlinear problems, MARS,
M5Tree, and LSSVR models can be efficient alternatives to
existing artificial intelligence methods in solving key civil
engineering problems. Cheng and Cao [34] used MARS
model to predict the shear strength of reinforced concrete
beams. Behnood et al. [28] applied M5Tree model for the
prediction of the elastic modulus of RACs. Aiyer et al. [35]
applied LSSVR model to predict the compressive strength
of self-compacting concrete. Pham et al. [36] predicted the
compressive strength of high-performance concretes using
LSSVR model. However, no study has been reported to
date on the application of LSSVR and MARS models for
the prediction of the mechanical properties of RAC and
only a single study on the application of M5Tree model for
the prediction of the elastic modulus of RAC.
To address the above-mentioned research gaps, three
robust artificial intelligence techniques, namely MARS,
M5Tree, and LSSVR, were adopted in this study for the
prediction of the compressive strength, elastic modulus,
flexural strength, and splitting tensile strength of RAC.
Existing experimental test database of RACs is initially
presented, which is followed by the details of the three
models developed in this study. Subsequently, an assessment
of the prediction results of the three models is presented.
2 Experimental test database
The database of RAC, presented in Gholampour et al. [30],
was assembled based on 69 experimental studies published
in the open literature on RACs containing no pozzolanic
admixtures. The RAC database consisted of 332, 318, 421,
152, and 346 datasets, respectively, for compressive
strength of cube specimens (f
cm,cube
), compressive strength
of cylinder specimens (f
cm,cylinder
), elastic modulus (E
c
),
flexural strength (f
r
), and splitting tensile strength (f
st
).
Neural Computing and Applications
123
The cylinder specimens had either a 100 or 150 mm
diameter and a 200 or 300 mm height; the cube specimens
had a dimension of either 100 or 150 mm; and beams had a
dimension of either 100 9100 9500 mm or 150 9
150 9750 mm. Effective water-to-cement ratio (w
eff
/c)of
specimens varied from 0.19 to 0.87, coarse recycled con-
crete aggregate replacement ratio (RCA%) varied from 0 to
100, aggregate-to-cement ratio (a/c) varied from 1.2 to 6.5,
bulk density of recycled concrete aggregate (q
RCA
) varied
from 1946 to 2720 kg/m
3
, water absorption of coarse recy-
cled concrete aggregate (WA
RCA
) varied from 1.5 to 11.9%.
In addition, f
cm,cube
,f
cm,cylinder
,E
c
,f
r
, and f
st
in the database
ranged from 18.9 to 104.3 MPa, 26.6 to 61.2 MPa, 12.5 to
50.4 GPa, 1.9 to 10.2 MPa, and 1.1 to 6.3 MPa, respec-
tively. The distribution of the histogram of the key param-
eters (i.e., w
eff
/c, RCA%, a/c,q
RCA
, and WA
RCA
) for the
specimens in the database is illustrated in Fig. 1.
3 Existing models for the prediction
of mechanical properties of RAC
Models proposed to date for the prediction of the
mechanical properties of RACs were assembled from 21
different studies, as previously presented in Gholampour
et al. [30]. All models contained closed-form expressions
obtained from regression analysis of the test results. Fur-
thermore, two sets of expressions recently proposed by
Gholampour et al. [30] through the use of gene expression
programming (GEP) and Ozbakkaloglu et al. [2] using
regression analysis were also considered in the present
study. Existing models include 11 models for compressive
strength [2,15,16,23,30,37–39], 18 models for elastic
modulus [2,13–15,30,40–47,65,66], six models for
flexural strength [2,15,30,45–47], and eight models for
splitting tensile strength [2,15,16,30,43,46–48] of RAC.
(a) (b)
(c) (d)
(e)
0
50
100
150
200
250
300
350
0.3 0.4 0.5 0.6 0.7 0.8 More
Frequency
weff /c
25 6
12
72
151
293
91
0
50
100
150
200
250
020 40 60 80 100
Frequency
RCA
139
237
18
130
58
68
0
50
100
150
200
250
300
350
Frequency
a/c
55 50
216
315
14
0
50
100
150
200
250
300
2345More 2000 2200 2400 2600 2800 More
Frequency
RCA
14
25
149
251
23
0
50
100
150
200
357911 More
Frequency
WARCA
26
1
20
42
162
178
Fig. 1 Histogram distribution
of: aw
eff
/c,bRCA%, ca/c,
dq
RCA
, and eWA
RCA
Neural Computing and Applications
123
4 Overview of MARS, M5Tree,
and LSSVR models
4.1 Multivariate adaptive regression splines
(MARS)
MARS is a form of regression analysis that was developed
by Friedman [31] for the prediction of continuous numer-
ical outcomes. Its algorithm consists of a forward and
backward stepwise procedure [49]. The backward proce-
dure removes the unnecessary variables among the previ-
ous selected set in the forward procedure to improve the
prediction accuracy. Therefore, the variable Xis transferred
to variable Yusing either of the following equations by an
inflection point along the input values [50]:
Y¼max 0;XcðÞor max 0;cXðÞ ð1Þ
in which cis a threshold value. In MARS, a function
applies for each input variable in forward–backward step-
wise procedure to find the location of the inflection point in
which the function value changes. MARS is a nonpara-
metric statistical technique in which piecewise curves and
polynomials give flexible results that can handle not only
linear but also nonlinear behavior [49]. Detailed informa-
tion about MARS is available in Ref. [50].
4.2 M5 model tree (M5Tree)
M5Tree model, which was originally proposed by Quinlan
[32], is based on a binary decision tree with a series of
linear regression functions at the terminal (leaf) nodes. In
the first stage, a decision tree is created by splitting the data
into subsets and assuming the standard deviation of class
values that reach a node as a measure of the error at that
node. Subsequently, the expected reduction in the error as a
result of testing each attribute at the node is calculated. The
standard deviation reduction (SDR), which is used to
describe the reduction in the error, is defined as follows
[51]:
SDR ¼sd TðÞ
XTi
jj
Tsd Ti
ðÞ ð2Þ
where T,T
i
, and sd represent a set of examples that reach
the node, subset of examples that have the ith outcome of
the potential set, and standard deviation, respectively.
Because of the splitting process, the standard deviation of
data in child nodes (i.e., lower nodes) becomes lower than
that of parent node. The split that maximizes the expected
error reduction is selected after examining all possible
splits [32].
4.3 Least squares support vector regression
(LSSVR)
LSSVR, proposed by Suykens and Vandewalle [33], is a
supervised learning method based on the principle of
structural risk minimization. By considering a given
training set of xk;yk
fg
N
k¼1with input data of xk2Rnand
output data of yk2Rwith class labels of yk21;þ1
fg
,
the linear classifier in the primal space is defined as:
yxðÞ¼sign wTuxðÞþb
ð3Þ
in which bis a real constant. LSSVR is defined in dual
space for nonlinear classification as:
yxðÞ¼sign X
N
k¼1
akykKx
T
k;x
þb
!
ð4Þ
in which akis a positive real constant and Kx
T
k;x
is a
kernel function that is defined as uxk
ðÞ;uxðÞ, where uxðÞis
a nonlinear map from original space to the high-dimen-
sional space. The following expression is used to estimate a
function:
yxðÞ¼
X
N
k¼1
akKx
k;xðÞþbð5Þ
In order to use radial basis function (RBF) kernel in the
modeling, two tuning parameters of cand rare added to
Eq. 5, in which cand rare regularization constant and
width of RBF kernel, respectively. The main advantage of
LSSVR compared to support vector regression (SVR) is the
use of the linear squares principle for the loss function in
the LSSVR. In the SVR, however, quadratic programming
is employed for this purpose, which is not computationally
efficient. Consequently, LSSVR is faster than the SVR in
computation [52]. Detailed information about LSSVR can
be obtained from Ref. [53].
5 Prediction of mechanical properties
of RAC
MARS, M5Tree, and LSSVR techniques were applied to
estimate the compressive strength, elastic modulus, flexural
strength, and splitting tensile strength of RAC. The main
parameters influencing the mechanical properties of RACs
were determined based on the accurate assessment of the
specimens in the database. Based on this assessment, it was
found that w
eff
/c, RCA%, a/c,q
RCA
, and WA
RCA
are the
most influential parameters on the mechanical behavior of
RACs. Therefore, these parameters were used as inputs to
the models. The number of data points available for the
validation and testing of the models was 171, 156, 224, 79,
Neural Computing and Applications
123
and 168 for f
cm,cylinder
,f
cm,cube
,E
c
,f
r
, and f
st
of RACs,
respectively. For each model, 80% of the database was
used for training and validation of the models and
remaining 20% was used for testing. The results of the
three models were subsequently compared with the exist-
ing models using the root-mean-square error (RMSE),
mean absolute error (MAE), and mean absolute percentage
error (MAPE) (also referred to as the average absolute
error, AAE, in previous studies) statistics to evaluate the
performance of the three models. Definitions of these sta-
tistical indicators are given as follows:
RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
nX
n
i¼1
ModiExpi
ðÞ
2
sð6Þ
MAE ¼1
nX
n
i¼1
ModiExpi
jj ð7Þ
MAPE ¼1
nX
n
i¼1
ModiExpi
jj
100
Expi
ð8Þ
where Mod
i
and Exp
i
are the estimated and experimental
values of mechanical properties of RAC and nis the
number of time steps.
An open-source code (http://www.esat.kuleuven.be/
sista/lssvmlab/) was used for the LSSVR model. Various
numbers from 1 to 100 were tried for cand rcontrol
parameters. The optimal cand rvalues were calculated as
15.6 and 3.0 for f
cm,cube
, 17.1 and 3.3 for f
cm,cylinder
, 22.4
and 4.4 for E
c
, 7.9 and 1.5 for f
r
, and 16.8 and 3.3 for f
st
of
RAC, respectively. For MARS and M5Tree techniques,
open-source codes (http://www.cs.rtu.lv/jekabsons/regres
sion.html) were used.
5.1 Compressive strength
In order to assess the accuracy of the compressive strength
models, their performance was evaluated using the test
database. Based on the available input parameters in the
test database, only six compressive strength models
[2,15,30,38,39] could be used in the model assessments,
among which three of them were for cube specimens and
three for cylinder specimens. The remaining models
[16,23,37] required specific inputs that were not available
in the database.
Table 1shows the prediction statistics of MARS,
M5Tree, and LSSVR models and existing models for
f
cm,cube
of RAC. It can be seen in the table that the model
by Gholampour et al. [30] was the best-performing f
cm,cube
model in the literature. However, LSSVR model provided
improved accuracy over the existing models in predicting
f
cm,cube
. This observation can be attributed to the ability of
the model to accurately capture the influences of the key
input parameters (i.e., w
eff
/c, RCA%, a/c,q
RCA
, and
WA
RCA
) in the analysis. Figure 2shows the comparison of
MARS, M5Tree, and LSSVR model predictions with the
experimental f
cm,cube
at the validation stage. As can be seen
in the figure, LSSVR model developed a higher accuracy in
predicting f
cm,cube
of RACs than that of MARS and M5Tree
models.
Table 2shows the prediction statistics of MARS,
M5Tree, and LSSVR models and existing models for
f
cm,cylinder
of RAC. As can be seen in the table, those by
Gholampour et al. [30] showed the best performance
among the existing models. It can be seen in Table 2that
only LSSVR model performed better than the existing
models in predicting f
cm,cylinder
. Figure 3shows the com-
parison of MARS, M5Tree, and LSSVR model predictions
with the experimental f
cm,cylinder
at the validation stage. As
can be seen in the figure, similar to the case of f
cm,cube
,
LSSVR model exhibited a higher accuracy in the predic-
tion of f
cm,cylinder
of RACs compared to that of MARS and
M5Tree models. This is attributed to the fact that LSSVR is
based on a learning method that is dependent on the sta-
tistical learning theory. In this method, the use of a regu-
larization parameter helps to avoid over-fitting in the
modeling [54].
5.2 Elastic modulus
Table 3illustrates the prediction statistics of MARS,
M5Tree, and LSSVR models and existing models for E
c
of
RACs. As can be seen in the table, Ozbakkaloglu et al. [2],
Table 1 Model predictions of cube compressive strength (f
cm,cube
) of RAC
Model Number of all datasets RMSE (MPa) MAE (MPa) MAPE (%) Specimen type
Xiao et al. [15] 74 11.3 4.7 12.7 Cube
Pereira et al. [38] 157 11.8 9.4 22.2 Cube
Gholampour et al. [30] 156 8.9 5.5 12.7 Cube
MARS 156 9.1 5.4 13.0 Cube
M5Tree 156 8.3 5.9 14.2 Cube
LSSVR 156 7.7 4.6 12.6 Cube
Neural Computing and Applications
123
Rahal [40], Corinaldesi [41], and Zilch and Roos [14]
models showed the best performance among the models in
the literature to predict E
c
of RAC. As can also be seen in
Table 3, MARS, M5Tree, and LSSVR models provide
nearly identical accuracy to that of the best-performing
models in the literature in the prediction of E
c
of RACs.
Furthermore, MARS, M5Tree, and LSSVR models pro-
vided improved accuracy over Gholampour et al. [30]
model in the prediction of E
c
of RACs.
Figure 4shows the comparison of MARS, M5Tree, and
LSSVR model predictions with the experimental E
c
of
RACs at the validation stage. As can be seen in the figure,
LSSVR model developed a higher accuracy in predicting
the E
c
of RAC than that of M5Tree and MARS models,
confirming the suitability of the LSSVR model for this
application.
5.3 Flexural strength
Table 4illustrates the prediction statistics of MARS,
M5Tree, and LSSVR models and existing models for f
r
of
RACs. As can be seen in the table, the models by
Ozbakkaloglu et al. [2], Xiao et al. [15], and Gholampour
et al. [30] performed the best for the prediction of f
r
of
RAC among the existing models. It can be seen in
Table 4that LSSVR model provided slightly higher
accuracy than those of the best-performing models in the
literature in the prediction of f
r
of RACs. Comparison of
MARS, M5Tree, and LSSVR model predictions with the
experimental results shown in Fig. 5further illustrates the
better accuracy of the LSSVR model compared to that of
MARS and M5Tree models in the prediction of the f
r
of
RACs.
5.4 Splitting tensile strength
Table 5illustrates the comparison of prediction statistics of
MARS, M5Tree, and LSSVR models with those of existing
models in predicting the f
st
of RAC. As can be seen in the
table, Ozbakkaloglu et al. [2], Tavakoli and Soroushian
[46], Xiao et al. [15], and Gholampour et al. [30] models
performed the best among the existing models. It can also
be seen in Table 5that MARS, M5Tree, and LSSVR
models provided improved accuracy over these best-per-
forming models in the prediction of f
st
of RACs. The results
(a)
(b)
(c)
10
20
30
40
50
60
70
MARS (MPa)
Experimental (MPa)
RMSE=9.1 MPa
MAE=5.4 MPa
10
20
30
40
50
60
70
M5Tree (MPa)
Experimental (MPa)
RMSE=8.3 MPa
MAE=5.9 MPa
10
20
30
40
50
60
70
10 20 30 40 50 60 70
10 20 30 40 50 60 70
10 20 30 40 50 60 70
LSSVR (MPa)
Experimental (MPa)
RMSE=7.7 MPa
MAE=4.6 MPa
Fig. 2 Compressive strength estimates of cube RAC (f
cm,cube
)by
aMARS, bM5Tree, cLSSVR models at the validation stage. Circle-,
triangle-, and cross-shaped points are data points for validation set 1,
2, and 3, respectively
Table 2 Model predictions of cylinder compressive strength (f
cm,cylinder
) of RAC
Model Number of all datasets RMSE (MPa) MAE (MPa) MAPE (%) Specimen type
Ozbakkaloglu et al. [2] 257 8.0 4.7 14.5 Cylinder
Thomas et al. [39] 257 8.1 4.8 14.6 Cylinder
Gholampour et al. [30] 171 7.9 5.3 14.5 Cylinder
MARS 171 8.4 6.4 16.3 Cylinder
M5Tree 171 8.2 6.4 16.5 Cylinder
LSSVR 171 7.4 4.6 14.3 Cylinder
Neural Computing and Applications
123
suggest that all the three models are suitable for the pre-
diction of the splitting tensile strength of RACs, which
varies with the considered input parameters in a highly
nonlinear fashion. However, in some cases, data-driven
models (e.g., MARS) may over-fit the data in training
period and provide lower accuracy in test period compared
to the simple models (e.g., regression method).
Figure 6shows the comparison of MARS, M5Tree,
and LSSVR model predictions with the experimental f
st
results of RACs at the validation stage. It can be seen in
the figure that LSSVR model provided higher accuracy
than that of MARS and M5Tree models in estimating the
f
st
of RAC.
6 Variation of model predictions
with influential parameters
In order to illustrate the variations of the model predictions
with key input parameters within a physically meaningful
framework, the variations of MARS, M5Tree, and LSSVR
model predictions of f
cm,cube
,f
cm,cylinder
,E
c
,f
r
, and f
st
with
w
eff
/c, RCA%, a/c,q
RCA
, and WA
RCA
are investigated. As
was discussed in detail in Ref. [30], w
eff
/cand RCA% have
an accumulative effect on the mechanical properties of
RACs. Therefore, the datasets used at the validation stage
were divided into two subgroups based on their RCA%
(i.e., RCA% of 0–50% and 51–100%) to better isolate the
individual effects of w
eff
/cand RCA% on the mechanical
behavior of RACs.
Figures 7,8,9,10, and 11 show the variation of model
predictions of f
cm,cube
,f
cm,cylinder
,E
c
,f
r
, and f
st
of RACs
with w
eff
/cat each RCA% interval, respectively. As can be
seen in the figures and as expected, an increase in w
eff
/
cresulted in a decrease in each mechanical property of
(a)
(b)
(c)
10
20
30
40
50
60
70
MARS (MPa)
Experimental (MPa)
RMSE=8.4 MPa
MAE=6.4 MPa
10
20
30
40
50
60
70
M5Tree (MPa)
Experimental (MPa)
RMSE=8.2 MPa
MAE=6.4 MPa
10
20
30
40
50
60
70
10 20 30 40 50 60 70
10 20 30 40 50 60 70
10 20 30 40 50 60 70
LSSVR (MPa)
Experimental (MPa)
RMSE=7.4 MPa
MAE=4.6 MPa
Fig. 3 Compressive strength estimates of cylinder RAC (f
cm,cylinder
)
by aMARS, bM5Tree, cLSSVR models at the validation stage.
Circle-, triangle-, and cross-shaped points are data points for
validation set 1, 2, and 3, respectively
Table 3 Model predictions of elastic modulus (E
c
) of RAC
Model Number of all
datasets
RMSE
(GPa)
MAE
(GPa)
MAPE
(%)
Ozbakkaloglu et al.
[2]
351 3.09 2.23 10.8
Ravindrarajah and
Tam [13]
104 5.62 4.21 13.1
Kakizaki et al. [65] 33 4.51 3.64 10.9
Bairagi et al. [45] 104 6.76 5.55 19.1
de Oliveira and
Vazquez [66]
104 7.14 6.19 22.3
Tavakoli and
Soroushian [46]
104 6.55 5.29 16.8
Dillmann [67] 104 8.40 6.57 21.7
Dhir [68] 104 5.15 4.29 14.3
Zilch and Roos [14] 84 3.10 2.23 8.3
Kheder and Al-
Windawi [47]
172 6.76 8.12 18.7
Xiao et al. [15] 104 6.17 4.46 14.3
Rahal [40] 84 3.74 2.74 10.1
Corinaldesi [41] 172 3.85 3.13 10.1
Lovato et al. [16] 204 21.80 21.40 70.6
Hoffmann et al.
[42]
172 7.65 6.85 21.5
Pereira et al. [43] 82 10.54 9.07 31.1
Wardeh et al. [44] 104 5.79 4.86 17.2
Gholampour et al.
[30]
224 4.44 3.41 14.4
MARS 224 3.78 2.66 11.5
M5Tree 224 3.74 2.71 11.7
LSSVR 224 3.25 2.35 10.7
Neural Computing and Applications
123
(a)
(b)
(c)
15
25
35
45
55
MARS (GPa)
Experimental (GPa)
RMSE=3.78 GPa
MAE=2.66 GPa
15
25
35
45
55
M5Tree (GPa)
Experimental (GPa)
RMSE=3.74 GPa
MAE=2.71 GPa
15
25
35
45
55
15 25 35 45 55
15 25 35 45 55
15 25 35 45 55
LSSVR (GPa)
Experimental (GPa)
RMSE=3.25 GPa
MAE=2.35 GPa
Fig. 4 Elastic modulus (E
c
) estimates of RAC by aMARS,
bM5Tree, cLSSVR models at the validation stage. Circle-,
triangle-, and cross-shaped points are data points for validation set
1, 2, and 3, respectively
Table 4 Model predictions of
flexural strength (f
r
) of RAC Model Number of all datasets RMSE (MPa) MAE (MPa) MAPE (%)
Ozbakkaloglu et al. [2] 118 0.52 0.42 8.1
Bairagi et al. [45] 19 0.73 0.59 11.1
Tavakoli and Soroushian [46] 19 1.12 1.01 17.9
Kheder and Al-Windawi [47] 54 0.97 0.76 16.1
Xiao et al. [15] 19 0.52 0.45 8.1
Gholampour et al. [30] 79 0.54 0.45 8.3
MARS 79 0.58 0.49 9.2
M5Tree 79 0.55 0.48 8.6
LSSVR 79 0.52 0.41 8.0
(a)
(b)
(c)
2
4
6
8
MARS (MPa)
Experimental (MPa)
RMSE=0.58 MPa
MAE=0.49 MPa
2
4
6
8
8246
2468
M5Tree (MPa)
Experimental (MPa)
RMSE=0.55 MPa
MAE=0.48 MPa
2
4
6
8
2468
LSSVR (MPa)
Experimental (MPa)
RMSE=0.52 MPa
MAE=0.41 MPa
Fig. 5 Flexural strength (f
r
) estimates of RAC by aMARS,
bM5Tree, cLSSVR models at the validation stage. Circle-,
triangle-, and cross-shaped points are data points for validation set
1, 2, and 3, respectively
Neural Computing and Applications
123
RACs. It can also be seen in Figs. 7,8,9,10 and 11 that
these properties decreased with increasing RCA% at a
given w
eff
/c. It can be seen in the figures that all the three
models are able to accurately capture the effects of w
eff
/
cand RCA% on the mechanical behavior of RACs to well
reproduce the test results.
Figures 12,13,14,15 and 16, respectively, illustrate the
variation of f
cm,cube
,f
cm,cylinder
,E
c
,f
r
, and f
st
of RACs with
a/c,q
RCA
, and WA
RCA
. As can be seen in the figures, an
increase in a/cand q
RCA
resulted in an increase in each
mechanical property of RACs, whereas an increase in
WA
RCA
led to a decrease in the mechanical properties of
RACs. These observations are in agreement with the pre-
vious studies [41,55–64]. Therefore, all the three models
are capable of accurately predicting the trend of the vari-
ation of the mechanical behavior of RACs with key influ-
ential parameters.
7 Comparison of model predictions
with design code expressions
In order to investigate the agreement of predictions of
MARS, M5Tree, and LSSVR models of mechanical
properties of conventional concrete (RCA%= 0) with those
of existing design code and standard expressions, their
overall trends were compared, as shown in Fig. 17. Table 6
shows the existing code expressions given for the predic-
tion of E
c
,f
r
, and f
st
of conventional concrete based on
mean and characteristic cylinder compressive strength
(f
cm,cylinder
and f0
c,cylinder
). Figure 17 shows the variation of
the predictions of E
c
,f
r
, and f
st
by code expressions and
Table 5 Model predictions of splitting tensile strength (f
st
) of RAC
Model Number of all
datasets
RMSE
(MPa)
MAE
(MPa)
MAPE
(%)
Ozbakkaloglu et al.
[2]
307 0.51 0.48 15.9
Tavakoli and
Soroushian [46]
109 0.57 0.44 20.3
Kheder and Al-
Windawi [47]
139 0.77 0.65 23.1
Xiao et al. [48] 109 0.67 0.52 16.6
Xiao et al. [15] 109 0.52 0.46 16.6
Lovato et al. [16] 149 2.50 2.29 76.4
Pereira et al. [43] 58 0.78 0.57 17.3
Gholampour et al.
[30]
168 0.64 0.50 16.5
MARS 168 0.60 0.47 15.8
M5Tree 168 0.61 0.47 15.7
LSSVR 168 0.53 0.46 15.6
(a)
(b)
(c)
1
2
3
4
5
6
123456
MARS (MPa)
Experimental (MPa)
RMSE=0.60 MPa
MAE=0.47 MPa
1
2
3
4
5
6
M5Tree (MPa)
Experimental (MPa)
RMSE=0.61 MPa
MAE=0.47 MPa
1
2
3
4
5
6
612345
123456
LSSVR (MPa)
Experimental (MPa)
RMSE=0.53 MPa
MAE=0.47 MPa
Fig. 6 Splitting tensile strength (f
st
) estimates of RAC by aMARS,
bM5Tree, cLSSVR models at the validation stage. Circle-, triangle-,
and cross-shaped points are data points for validation set 1, 2, and 3,
respectively
20
30
40
50
60
70
f
cm,cube
(MPa)
weff /c
RCA%
MARS
LSSVR
M5Tree
10
20
30
40
50
60
0.4 0.5 0.6 0.4 0.5 0.6 0.7 0.8 0.9
fcm,cube (MPa)
weff /c
RCA%
MARS
LSSVR
M5Tree
(a) (b)
Fig. 7 Variation of model predictions of f
cm,cube
with w
eff
/c:
aRCA%= 0–50%, bRCA%= 51–100%. Data points show experi-
mental test results at the validation stage
Neural Computing and Applications
123
MARS, M5Tree, and LSSVR models with f0
c,cylinder
. The
comparison of the results shown in Fig. 17 indicates that
the trends of the MARS, M5Tree, and LSSVR models are
consistent with the overall trend of the existing code
expressions for conventional concrete.
8 Conclusions
This paper has presented an investigation into the capa-
bility of three artificial intelligence models, including
MARS, M5Tree, and LSSVR, for the prediction of the
20
30
40
50
60
70
80
fcm,cylinder (MPa)
weff /c
RCA%
MARS
LSSVR
M5Tree
10
20
30
40
50
60
70
0.4 0.5 0.6 0.7 0.3 0.4 0.5 0.6 0.7 0.8
f
cm,cylinder
(MPa)
weff /c
RCA%
MARS
LSSVR
M5Tree
Fig. 8 Variation of model predictions of f
cm,cylinder
with w
eff
/c:
aRCA%= 0–50%, bRCA%= 51–100%
10
20
30
40
50
E
c
(GPa)
weff /c
RCA%
MARS
LSSVR
M5Tree
10
20
30
40
50
0.2 0.3 0.4 0.5 0.6 0.7 0.1 0.3 0.5 0.7 0.9
E
c
(GPa)
weff /c
RCA%
MARS
LSSVR
M5Tree
(a) (b)
Fig. 9 Variation of model predictions of E
c
with w
eff
/c:
(a) RCA%= 0–50%, (b) RCA%= 51–100%
2
4
6
8
f
r
(MPa)
weff /c
RCA%
MARS
LSSVR
M5Tree
2
4
6
8
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.2 0.3 0.4 0.5 0.6 0.7
f
r
(MPa)
weff /c
RCA%
MARS
LSSVR
M5Tree
(b)(a)
Fig. 10 Variation of model predictions of f
r
with w
eff
/c:
aRCA%= 0–50%, bRCA%= 51–100%
1
2
3
4
5
6
f
st
(MPa)
weff /c
RCA%
MARS
LSSVR
M5Tree
1
2
3
4
5
6
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.3 0.5 0.7 0.9
fst (MPa)
weff /c
RCA%
MARS
LSSVR
M5Tree
(a) (b)
Fig. 11 Variation of model predictions of f
st
with w
eff
/c:
aRCA%= 0–50%, bRCA%= 51–100%
20
30
40
50
60
70
fcm,cube (MPa)
a/c
MARS
LSSVR
M5Tree
20
30
40
50
60
70
12345 2000 2300 2600 2900
fcm,cube (MPa)
RCA (kg/m3)
MARS
LSSVR
M5Tree
20
30
40
50
60
70
1357911
fcm,cube (MPa)
WARCA
MARS
LSSVR
M5Tree
(a) (b)
(c)
Fig. 12 Variation of model predictions of f
cm,cube
with: aa/c,bq
RCA
,
and cWA
RCA
20
30
40
50
60
70
fcm,cylinder (MPa)
a/c
MARS
LSSVR
M5Tree
20
30
40
50
60
70
1234567 1800 2300 2800
fcm,cylinder (MPa)
RCA (kg/m3)
MARS
LSSVR
M5Tree
20
30
40
50
60
70
135791113
fcm,cylinder (MPa)
WARCA
MARS
LSSVR
M5Tree
(a) (b)
(c)
Fig. 13 Variation of model predictions of f
cm,cylinder
with: aa/c,
bq
RCA
, and cWA
RCA
Neural Computing and Applications
123
compressive strength, elastic modulus, flexural strength,
and splitting tensile strength of RACs. The test database of
RAC was used to evaluate the performance of MARS,
M5Tree, and LSSVR models and existing models in the
literature. On the basis of assessment of modeling results,
the following conclusions can be drawn:
1. LSSVR model provides a higher accuracy for the
prediction of the compressive strength of cube and
cylinder RACs (MAPE = 12.6 and 14.3%, respec-
tively) compared to those of existing models.
2. The accuracy of MARS (MAPE = 11.5%), M5Tree
(MAPE = 11.7%), and LSSVR (MAPE = 10.7%)
models for predicting the elastic modulus of RAC is
nearly identical to that of best-performing existing
models.
3. MARS (MAPE = 9.2%) and M5Tree (MAPE = 8.6%)
models predict the flexural strength of RACs with a
slightly lower accuracy than that of the best-perform-
ing existing models, whereas LSSVR model (MAPE =
8.0%) performs better than the existing models.
4. All three models of MARS (MAPE = 15.8%), M5Tree
(MAPE = 15.7%), and LSSVR (MAPE = 15.6%) per-
form better than the existing models in the prediction
of the splitting tensile strength of RACs.
5. LSSVR model performs better than MARS and
M5Tree models in predicting the compressive strength,
elastic modulus, flexural strength, and splitting tensile
strength of RACs.
6. For conventional concrete, the predictions of the
MARS, M5Tree, and LSSVR models are in agreement
with those of the existing concrete design code
expressions.
20
30
40
50
Ec(GPa)
a/c
MARS
LSSVR
M5Tree
20
30
40
50
1234567 1800 2300 2800
Ec(GPa)
RCA (kg/m3)
MARS
LSSVR
M5Tree
20
30
40
50
135791113
Ec(GPa)
WARCA
MARS
LSSVR
M5Tree
(a) (b)
(c)
Fig. 14 Variation of model predictions of E
c
with: aa/c,bq
RCA
, and
cWA
RCA
3
4
5
6
7
8
f
r
(MPa)
a/c
MARS
LSSVR
M5Tree
3
4
5
6
7
8
f
r
(MPa)
RCA (kg/m3)
MARS
LSSVR
M5Tree
3
4
5
6
7
8
234567 2100 2400 2700
12345678
f
r
(MPa)
WARCA
MARS
LSSVR
M5Tree
(a) (b)
(c)
Fig. 15 Variation of model predictions of f
r
with: aa/c,bq
RCA
, and
cWA
RCA
1
2
3
4
5
6
fst (MPa)
a/c
MARS
LSSVR
M5Tree
1
2
3
4
5
6
456 2000 2400 2800
fst (MPa)
RCA (kg/m3)
MARS
LSSVR
M5Tree
1
2
3
4
5
6
123
1357911
fst (MPa)
WARCA
MARS
LSSVR
M5Tree
(a) (b)
(c)
Fig. 16 Variation of model predictions of f
st
with: aa/c,bq
RCA
, and
cWA
RCA
Neural Computing and Applications
123
The results of this study indicate that MARS, M5Tree,
and LSSVR models can provide close predictions of the
mechanical properties of RACs by accurately capturing the
influences of the key parameters, including the effective
water-to-cement ratio, recycled concrete aggregate
replacement ratio, aggregate-to-cement ratio, bulk density
of recycled concrete aggregate, and water absorption of
recycled concrete aggregate. These findings are promising
and point to the possibility of the application of these
techniques in the pre-design and modeling of structures
manufactured with RACs.
(a)
(b)
(c)
0
15
30
45
60
0 30 60 90 120
Elastic Modulus, E
c
(GPa)
Compressive Strength, f'
c,cylinder
(MPa)
MARS
M5Tree
LSSVR
ACI-11 [71]
CSA-04 [72]
EC2-04 [73]
JSCE-07 [74]
JCI-08 [75]
NZS-06 [76]
0
3
6
9
12
Flexural Strength, f
r
(MPa)
Compressive Strength, f'
c,cylinder
(MPa)
MARS
M5Tree
LSSVR
AS-09[70],CSA-04[72],NZS-06[76]
ACI-11 [71]
EC2-04 [73]
0
2
4
6
8
0 30 60 90 120
0 30 60 90 120
Splitting Tensile Strength, f
st
(MPa)
Compressive Strength, f'
c,cylinder
(MPa)
MARS
M5Tree
LSSVR
AS-09 [70]
ACI-11 [71]
EC2-04 [73]
JSCE-07 [74]
JCI-08 [75]
NZS-06 [76]
Fig. 17 Comparisons of models of the present study with models
given in design codes for conventional concrete: aelastic modulus,
bflexural strength, csplitting tensile strength
Table 6 Summary of conventional concrete mechanical property models given in current design codes
Model Elastic modulus (E
c
) (GPa) Flexural strength (f
r
) (MPa) Splitting tensile strength (f
st
) (MPa)
AS 3600-09 [70]Ec¼4:3105qh
ðÞ
1:5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
fcm;cylinder
pwhen fcm;cylinder 40MPa*
Ec¼2:4qh
ðÞ
1:5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
fcm;cylinder
qþ12
105when 40\fcm;cylinder 100 MPa
fr¼0:60 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f0
c;cylinder
qfst ¼0:4ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f0
c;cylinder
q
ACI 318-11 [71]Ec¼4:73 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f0
c;cylinder
qfr¼0:62 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f0
c;cylinder
qfst ¼0:53 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f0
c;cylinder
q
CSA A23.3-04 [72]Ec¼4:5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f0
c;cylinder
qfr¼0:60 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f0
c;cylinder
q–
Eurocode 2-04 [73]Ec¼22 fcm;cylinder=10
0:3fr¼0:435f0
c;cylinder
2=3
fst ¼0:3f0
c;cylinder
2=3
JSCE-07 [74]Ec¼4:7ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f0
c;cylinder
q–fst ¼0:44 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f0
c;cylinder
q
JCI-08 [75]Ec¼6:3f0
c;cylinder
0:45 –fst ¼0:13 f0
c;cylinder
0:85
NZS 3101:2006 [76]Ec¼3:32 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f0
c;cylinder
q
þ6:9fr¼0:60 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f0
c;cylinder
qfst ¼0:44 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f0
c;cylinder
q
f0
c,cylinder
,f
cm,cylinder
,f
r
, and f
st
are in MPa, E
c
is in GPa, and q
h
is in kg/m
3
*f
cm,cylinder
and f0
c,cylinder
are the mean and characteristic cylinder compressive strength, respectively (f0
c,cylinder
=f
cm,cylinder
-8 MPa as per Eurocode 2)
Neural Computing and Applications
123
Compliance with ethical standards
Conflict of interest The authors declare that they have no conflict of
interest.
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