Developments in the Built Environment 13 (2023) 100113
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Formulation of estimation models for the compressive strength of concrete
mixed with nanosilica and carbon nanotubes
Sohaib Nazar a, b, c, Jian Yang a, b, d, *, Muhammad Nasir Amin e, Kaffayatullah Khan e,
Mohammad Faisal Javed c, Fadi Althoey f
a
State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, 200240, PR China
Shanghai Key Laboratory for Digital Maintenance of Buildings and Infrastructure, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong
University, Shanghai, 200240, PR China
c
Department of Civil Engineering, Comsats University Islamabad-Abbottabad Campus, Pakistan
d
School of Civil Engineering, University of Birmingham, Birmingham, B15 2TT, UK
e
Department of Civil and Environmental Engineering, College of Engineering, King Faisal University, Al-Ahsa, 31982, Saudi Arabia
f
Department of Civil Engineering, Najran University, Najran, Saudi Arabia
b
A R T I C L E I N F O
A B S T R A C T
Keywords:
Nanomaterials
Decision tree
Random forest
Compressive strength
Carbon nanotubes
Nano silica
New concepts for improving the performance of cementitious materials have recently surfaced due to the
advancement in nanotechnology. In this context, nano silica (NS) and carbon nanotubes (CNTs) have been widely
used in recent years. These nanomaterials significantly enhance the mechanical and durable performance of
cement mixtures, although there are a few drawbacks related to high cost and workability issues. As a result,
these components must be consumed at specific rates in order to achieve the desired qualities. This study aimed
to create models to forecast the compressive strength (CS) for concrete mixed with two types of nanomaterials
utilizing machine-learning-algorithms (MLA), such as the decision tree algorithm (DTA) and random forest al­
gorithm (RFA). The results of both models were compared and verified by external K-fold cross-validation. A
comprehensive database was collected containing 72 and 55 data points for the CS of CNTs and NS-modified
concrete respectively. Four input variables such as fine aggregate (FA), cement content (CC), coarse aggregate
(CA) and water-to-cement ratio (W/C) were used for the calibration of the models. Additionally, predicted results
were checked through k-fold-cross-validation and other performance gauges such as mean-absolute-error (MAE),
mean-squared-error (MSE), correlation coefficient (R2), root-mean-square-error (RMSE), relative-root-meansquare-error (RRMSE) and performance-index-factor (Pif). The RFA (CNTs and NS) models were found with
better performance and accuracy than the DTA models by having the lowest MAE of 3.51, 4.17 RRMSE of 0.0783,
0.0584, and Pif of 0.0398 and 0.0299 respectively. In addition, the value of R2 for RFA models was observed
higher such as 0.90 (CNTs) and 0.93 (NS), while for DTA models R2 was found as 0.88 (CNTs) and 0.86 (NS)
respectively. The ensembled ML methods demonstrated a better generalization capability, which indicates their
better ability for future prediction of CNTs and NS mixed concrete.
1. Introduction
dioxide in the environment, cement production contributes around 7%
of all CO2 emissions (Burhan et al., 2019). Concrete has considerably
aided in the expansion and development of human civilization (Zhang
et al., 2021). It starts with a weak strength rating (Crainic and Marques,
2002). The demand for strong, powerful, long-lasting, and tensile con­
crete is increasing as modern construction projects get closer to
long-span bridges and big water conservation projects. However, the
development of nanoscale pores and cracks is a serious drawback that
On a global scale, concrete is frequently used in building materials. It
uses most nonrenewable raw materials, including freshwater, sand,
crushed stone, and gravel, and yearly uses around 1.6 billion tons of
Portland and modified Portland cement (Abdalla et al., 2019). An
essential component of concrete, Portland cement, requires a lot of en­
ergy and is a scarce resource. As one of the two main producers of carbon
* Corresponding author. State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University,
200240, PR China.
E-mail address: j.yang.1@sjtu.edu.cn (J. Yang).
https://doi.org/10.1016/j.dibe.2022.100113
Received 4 October 2022; Received in revised form 15 December 2022; Accepted 20 December 2022
Available online 23 December 2022
2666-1659/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/bync-nd/4.0/).
S. Nazar et al.
Developments in the Built Environment 13 (2023) 100113
reduces the durability and strength of concrete. To enhance the me­
chanical characteristics and crack endurance of concrete, the concept of
dispersed nanoparticles in the construction industry has recently
developed.
The addition of nanomaterials improves the strength and durability
and also enhances the hydration reactions, which reduces the pressure
on formwork. Nanomaterials act as the seed for nucleation, which leads
to dense and less porous CSH-hydrated products (Piro et al., 2021; Du
et al., 2019). CNTs and NS are the most fascinating materials with
distinctive CS and electrical, thermal, and chemical abilities. To
generate more resilient and high-strength composite materials, these
components are combined with cement. The outcomes of earlier in­
vestigations are incongruent. NS has a high specific surface area, which
leads to significant enhancement in a hydration reaction. NS usually
contains sizes from 10 nm to 200 nm. It is amorphous with tetrahedral
SiO4 attached at the corners of its 2-dimensional colloidal network.
During hydration, a pozzolanic reaction occurs between NS and calcium
hydroxide which enlarges the CSH hydration products and fills the
entire space; thus, forming a less porous and dense structure with high
mechanical and durability properties (Yang et al., 2021). Wang et al.
found that 3% of NS is the most effective to increase the compressive
strength of lightweight aggregate concrete (Wang et al., 2018). Varghese
et al. found a significant increase in early-age compressive strength due
to the addition of NS in concrete (Varghese et al., 2019). Mostly
multi-walled CNTs are employed in cementitious composites due to
their amorphous nature, to achieve the desired properties (see Fig. 4).
The diameter of the CNTs was kept between 10 nm and 50 nm in most of
the research (Silvestro and Jean Paul Gleize, 2020; Du et al., 2020). Liew
et al. reported that CNTs can fill spaces from 10 to 103 nm spaces be­
tween the CSH hydration products (Liew et al., 2016). This improves the
densification and cracks formation is delayed in such cases. The most
effective length is reported between 10 μm and 20μm. Gao et al.,
employed multiwalled CNTs to improve the microstructure of concrete
interfacial transition zone through the expanded nucleation effect of
CNTs (see Fig. 2) (Gao et al., 2022). According to Glenn (2013) (Samui,
2013), particular unique properties like self-sensing, self-healing, and
electrical resistivity were attained by incorporating carbon nanotubes
(CNTs) and graphene oxide (GO).
In recent years, a range of fields have effectively used machine
learning techniques for the prediction of various attributes. Similar to
this, the use of such tactics in the civil engineering construction industry
could be more advantageous to eliminate time-consuming testing tech­
niques. has employed such tactics. Several methods have been used to
predict the mechanical strength and durability characteristics of cement,
including the Multivariate Adaptive Regression Spline (MARS) (Samui,
2013; Gholampour et al., 2020), Genetic Engineering Programming
(GEP) (Shahmansouri et al., 2020; Iqbal et al., 2020; Azim et al., 2020),
Support Vector Machine (SVM) (Kang et al., 2019; Ling et al., 2019;
Ahmed et al., 2022a), Multi-Logistic Regression (MLR) (Piro et al., 2022;
Ahmed et al., 2022b), Artificial Neural Networks (ANN) (Ahmed et al.,
2022b; Ababneh et al., 2020; Ahmad et al., 2021; Khan et al., 2021),
Decision Tree (DTA) (Nazar et al., 2022a, 2022b; Zhang et al., 2020),
Adaptive Boost Algorithm (ABA) (Feng et al., 2020; Rathakrishnan and
Ahmed, 2022). With variable importance measures (VIMs), a limited
number of model components, and effective resistance to errors, RF is
one of the most highly innovative ensemble algorithms (Auret and
Aldrich, 2012; Han et al., 2019). The DTA, as its name suggests, is the
fundamental estimator of RFA. However, RFA models are capable of
producing acceptable results even with default parametric parameters
(Svetnik et al., 2004). When utilizing RF, the whole set of base predictors
and parametric settings can be reduced to one. RFA has been utilized in
different engineering and non-engineering fields, including ecology
(Krkač et al., 2017; Dubeau et al., 2017; Fu et al., 2017) and bioinfor­
matics (Hanselmann et al., 2009; Schwarz et al., 2010; Boulesteix et al.,
2012), but it hasn’t been frequently used to forecast the performance of
special concrete. To predict the CS of long-lasting self-consolidating
concrete, Mohamed used the RF algorithm (Mohamed et al., 2017). The
author (Rao et al., 2017) tested a number of methods to predict the CS of
high-performance concrete (HPC) and found that the results provided by
the RF model were the best fitting. utilizing a RFA technique based on
beetle antenna search. The CS of self-compacting concrete was estimated
by the researchers (Zhang et al., 2019). The author obtained an unwa­
veringly a strong correlation with R2 = 0.97 by employing experimental
findings. An artificial neural network (ANN), an M5P-Tree (M5P), a
linear regression (LR), and a multi-logistic regression (MLR) model were
used by Ahmed et al. (2022c) to forecast the CS of blended ground
granulated blast furnace slag and fly ash based-geopolymer concrete
utilizing 220 data points. When four ML-techniques were used by Emad
et al. (2022) to estimate the CS of ultra-high-performance fiber rein­
forced concrete, they discovered that ANN was more effective. The
author (Han et al., 2019) used an RFA approach to predict the
compressive strength of HPC. The compressive strength of rubberized
concrete was predicted by the authors (Sun et al., 2019) using 138 data
samples from the literature and an advanced random forest method. This
advanced-based technique outperformed others with a good correlation
of R2 = 0.96. To forecast the CS of HSC, the author (Farooq et al., 2020)
created two models using RFA and GEP. The RFA model was found to be
more effective. The CS and durability qualities of concrete are improved
by the inclusion of nanomaterial. However, including the access quan­
tity could have a detrimental impact on workability. Therefore, the
estimation of such characteristics by machine algorithms may facilitate
their appropriate usage in the mix, saving time and money on experi­
mental labor. Additionally, utilizing ensemble and individual
ML-techniques, the estimation of the CS of the concrete that was
strengthened by the inclusion of CNTs, and NS has very seldom been
investigated.
The goal of the current study is to estimate the strength of CNTs and
NS in concrete in terms of CS by the application of AI-based ML tech­
niques i.e., random forest algorithm (RFA) and decision tree algorithm
(DTA). The robustness and accuracy of these algorithmic models are
directly related to the number of data points. A comprehensive dataset
of 72 and 55 data points for CNTs and NS, was formulated from the
experimental results of past studies. The four most influential factors
(water-cement ratio, cement content, coarse aggregate, and fine aggre­
gate quantity) were selected as input parameters for the modeling pur­
pose along with nano silica and carbon nanotubes. The results obtained
by the modeling from both individuals (DTA), and ensemble machine
algorithms (RFA) have been compared. The efficiency, modeling errors,
prediction, and generalization capability of both developed models were
checked, compared, and verified by statistical measures, sensitivity
analysis, and external K-fold cross-validation.
2. Used datasets
Datasets for concrete with nanotechnology modifications were
gathered from peer-reviewed publications (Yang et al., 2021; Wang
et al., 2018; Varghese et al., 2019; Murad, 2021; A et al., 2021;
Mohammed et al., 2017; Ren et al., 2022; Rehman et al., 2018; Sobol­
kina et al., 2012; MacLeod et al., 2020; Alhawat et al., 2019; Mukharjee
and Barai, 2020; Kumar et al., 2019; Mudasir and Naqash, 2021).
Compressive strength is shown in the data as a response parameter, and
two datasets with 72 and 55 data points for CNTs and NS, respectively,
were gathered. Cement content (C), coarse aggregate (CA), fine aggre­
gate (FA), water-to-cement ratio (W/C), and carbon nanotubes% (CNT),
or NS%, are the five input parameters that make up each dataset. To
create a numerically based empirical model for nano-modified concrete,
both datasets were trained and tested during the modelling process. The
earlier study (Behnood and Golafshani, 2018) found that 80% of data­
sets were utilized for training and 20% for testing. Fig. 1 depicts the
modified research process as a flowchart.
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S. Nazar et al.
Developments in the Built Environment 13 (2023) 100113
Fig. 1. Adapted research methodology chart.
(sets). The attributes that are given to each root node determine which
modelling is the most effective. The direction that each parent (Root)
node takes as it approaches the leaf determines the categorization
principle (see Fig. 2). These nodes are categorized as triangles, rect­
angle, or circle, three different geometric shapes. DTA is a generally
straightforward classification technique that is simple to understand and
apply (El Asri et al., 2022).
RFA is the classic parallel ensemble ML approach. It operates on the
idea of connecting different classifiers to address a more complex issue.
It is regarded as an improved categorization regression technique and
was first proposed by the researchers (Breiman, 2001) in 2001. Two of
RF’s key properties are the speed and tractability with which correlation
between input and output functions may be achieved. The primary
classification of supplementary data throughout the training phase de­
termines how variable the eventual projected outcomes will be. The
prediction accuracy is increased by taking the mean of all DTs, and the
outcome is anticipated based on the predictions of all these DT (Li et al.,
2022). The RF method is a mixture of different decision trees for each
subgroup of the dataset. The accuracy of the proposed model would
increase with the number of trees (El Asri et al., 2022; Shah et al., 2022).
The random forest’s schematic is depicted in Fig. 3. In this work, training
and testing subsets are created using 80% and 20%, respectively, of the
primary dataset. The RF algorithm is broken down into four parts in the
Python programming language, and as a result, better results are pro­
duced (Song et al., 2021).
Fig. 2. Leaves and nodes diagram of DTA (Nazar et al., 2022a).
3. Explanation of employed ML approaches
The DTA is a commonly used regression technique that, since it
simulates human decision-making, is easier to understand than other ML
algorithms. During modeling of potential outcomes, a fairly simple tree
shape structure with roots, branches, and leaf nodes is created (pre­
dictions) (Erdal, 2013). The leaf nodes (Karbassi et al., 2014), which
indicate the outcomes, are located at the conclusion of the flow chart of
the DTA, which begins with root nodes and further leads to branches.
The arrangement of the actual dataset begins with the fundamental root
node, which typically serves as a representation of the entire dataset
3.1. Development of the model and evaluation of its performance
The selection of various input factors from the existing database that
3
S. Nazar et al.
Developments in the Built Environment 13 (2023) 100113
variables. The non-uniform diffusion of frequency of input factors for
CNTs modified concrete is seen in the frequency histograms in Figs. 6
and 4, as well as in the descriptive analysis in Table 1. The statistical
results for the concrete mixed with NS are shown in Fig. 5 and Table 2.
4. Results and discussion
4.1. DTA model
Figs. 6 and 7 depict the statistical investigation of the actual and
forecasted values for the CS of concrete mixed with CNTs and NS for the
DTA-developed model. 20% of the acquired dataset was used for testing,
while the remaining 80% was used to train the algorithm. The NS
dataset’s error values were found using DT modelling to be 24.2 and
0.05 for the NS dataset and 15.7 and 0.08 for the CNTs dataset. A strong
correlation factor from DT effectively predicts the outcome, and little
error is discovered between actual and model outcome values. The R2
was found 0.86 for the values in the CNTs dataset and 0.88 for the values
in the NS dataset, indicating that the created DT model has higher
precision. Figs. 8 and 9 show how the DTA-based established model for
the CS of nano-modified concrete disperses investigational(actual)
values, predicted values, % errors and entire errors. R2 tests were per­
formed and determined to be 0.84 and 0.81 for the two datasets of
models generated by DTA.
Fig. 3. Random Forest Algorithm flow chart (Chou et al., 2014).
might significantly affect the strength of the concrete is the most
important phase before the synthesis of the model. Numerous nano­
particles have been used in concrete in earlier research to increase the
material’s compressive strength and durability. CNTs and NS are indeed
the most commonly used. Other than nanomaterials, coarse aggregate
(CA), sand (S), water/cement, and cement content (CC), all have a big
impact on the CS. Therefore, the following input factors have a signifi­
cant impact on the compressive strength (F’c) of nano-modified
concrete.
F’c = f(S, CA, W/C, CNT %, or NS% CC,)
Mean square error (MSE), root mean square error (RMSE), Nash
Sutcliff efficient (NSE), mean absolute error (MAE), performance index
factor (PiF), and correlation coefficient were used to evaluate the
effectiveness of the constructed model (R2). NSE has a range from − 1 to
1, with 1 denoting 100% efficiency. However, for better forecasted
outcomes, MAE must be lower than RMSE. A satisfactory connection
between the forecasted and actual values is indicated by an R2 value
greater than 0.8 (Chou et al., 2014; Mandeville et al., 1970). A perfor­
mance index of less than 0.2 denotes the model’s greater performance
(Iqbal et al., 2021).
The efficacy of the established model in terms of simplification
ability is significantly influenced by the distribution of the input
4.2. RFA model
The data analysis of the investigative (actual) and anticipated out­
comes for the CS of the concrete mixed with CNTs and NS using the
random forest algorithm is shown in Figs. 10 and 11. The output model
from RFA illustrated the less errors between real and expected values
and is very accurate. R2 values of 0.96 for the testing dataset (CNTs) and
0.90 for the training dataset (NS) show that the model is more accurate
at forecasting future outcomes when compared to the DTA method,
which therefore validates the fundamental premise behind using mul­
tiple decision trees in the RF algorithm. R2 for NS testing and training
was reported to be 0.91 and 0.93, respectively. The dispersion of actual
input values, anticipated output results, and total errors for the RFA
model for the CS of concrete mixed with CNTs and NS are illustrated in
Figs. 12 and 13. The largest inaccuracy for RFA was found to be 13.71
MPa and 12.11 MPa, respectively, in both datasets. While the CNT and
NS datasets modelled by the RFA method yielded the lowest error values
of 0.15 MPa and 0.10 MPa.
Fig. 4(a–e). Histograms indicating the dissemination of input and output variables for CNTs.
4
S. Nazar et al.
Developments in the Built Environment 13 (2023) 100113
Table:1
Numerical explanation of input parameters for CNTs mixed concrete.
Parameter
W/C
CNT
CC
CA
FA
CS
Mean
standard deviation
standard Error
Mode
median
Kurtosis
Skewness
maximum
minimum
Range
sample variance
0.4507
0.0553
0.0065
0.4500
0.4500
− 0.4145
0.1643
0.5500
0.3500
0.2000
0.0031
0.0832
0.0903
0.0106
0.0600
0.0600
17.7828
4.2324
0.5000
0.0100
0.4900
0.0082
440.3750
60.6443
7.0979
450.0000
380.0000
− 1.2410
0.4998
560.0000
380.0000
180.0000
3677.7306
927.3889
197.5766
23.1246
960.0000
952.0000
19.1985
− 4.4724
1050.0000
0.0000
1050.0000
39036.5227
753.7222
179.7506
21.0382
725.0000
757.0000
17.4491
4.1534
1580.0000
620.0000
960.0000
32310.2879
65.0934
16.6679
1.9508
60.7500
56.6756
− 0.7589
0.2776
102.9582
44.5
71.7082
277.8177
Fig. 5(a–e). Histograms showing the distribution of input and output variables for NS.
both developed models. Moreover, the performance index factor (Pif)
was calculated to check the performance of the DT and RF model.
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
√∑
√n
√ (ei − mi )2
√
(1)
RMSE = i=1
n
n
∑
|ei − mi |
MAE = i=1
(2)
n
n
∑
(mi − ei )2
RSE = i=1
n
∑
(e − ei )2
(3)
i=1
∑n
(ai − pi )2
NSE = 1 − ∑i=1
n
2
i=1 (ai − pi )
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
√∑
√n
√ (ei − mi )2
1 √i=1
RRMSE =
|e|
n
Fig. 6. Correlation factor of actual and model values of DTA (for CNTs dataset).
5. Performance assessment of the established models
Generally, the performance of established models is measured in
terms of R2 (correlation factor); however previous studies recommend
the adaption of more statistical checks to measure the efficiency (Gan­
domi et al., 2013; Babanajad et al., 2017). Equations (1)–(7) shows the
seven statistical factors (relationship-coefficient R, coefficient of deter­
mination R2, mean absolute error MAE, Root mean square error RMSE,
and relative Root mean square error RRMSE, Nash-Sutcliffe efficiency
NSE, relative square error RSE) were used to compute the efficiency of
(4)
(5)
n
∑
(ei − ei )(mi − mi )
i=1
̅
R = √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
n
n
∑
∑
(ei − ei )2 (mi − mi )2
i=1
PiF =
5
RRMSE
1+R
(6)
i=1
(7)
S. Nazar et al.
Developments in the Built Environment 13 (2023) 100113
Table 2
Numerical explanation of input parameters for NS mixed concrete.
Parameter
W/C
CNT
CC
CA
FA
CS
Mean
standard deviation
standard Error
Mode
median
Kurtosis
Skewness
maximum
minimum
range
sample variance
0.3591
0.0807
0.0094
0.3800
0.4000
− 0.5036
− 0.8319
0.4500
0.2000
0.2500
0.0065
2.0945
0.9740
0.1140
2.0000
3.0000
1.0061
0.2280
5.0000
0.0000
5.0000
0.9487
437.8891
81.3051
9.5160
408.0000
380.0000
2.6676
1.8507
690.0000
352.0000
338.0000
6610.5228
878.4000
181.7814
21.2759
870.0000
760.0000
0.5528
0.5939
1307.0000
578.0000
729.0000
33044.4667
667.0000
161.6199
18.9162
602.0000
545.0000
− 0.2519
0.8142
1003.0000
465.0000
538.0000
26121.0000
91.4195
19.9000
2.3291
97.7683
58.977
− 0.6283
− 0.6590
122.4804
49.0000
73.4804
396.0090
Fig. 9. Distribution of fundamental errors between actual and model values by
DTA for NS dataset.
Fig. 7. Correlation factor for of actual and model values for DTA (for
NS dataset).
Fig. 8. Distribution of fundamental errors between actual and model values by
DTA for the CNTs dataset.
Fig. 10. Correlation factor for actual and model values for RFA (for
CNTs dataset).
where ei and mi illustrate the actual(tested) and model outcomes, ei , mi
and n shows the mean values of the composed actual dataset values and
model output values from the established model and an overall number
of specimens, respectively. A greater value of R and the value of the
performance index factor (PiF) closer to zero represents the better per­
formance of the developed model.
Previous research suggested that in order to get effective results from
built models, the ratio of the total number of datasets to the various
input variables must be at least three. [90–92]. In this investigation, the
ratio is maintained at about 12. The projected values for the DT and RF
algorithms are shown in Tables 5 and 3, respectively, along with a sta­
tistical analysis of the dataset. Overall, the RFA model outperformed the
DTA model in terms of the correlation between predicted and tested
values. The equations given above were used to statistically verify the
DT and RF models of CNTs and NS. In comparison to the DT models of
CNTs and NS, both RF models are found to have improved RSE, MAE,
RMSE, RRMSE, NSE, R, and PiF values. The results of the model show
that ensemble-based modeling, or the random forest model, is more
accurate and capable of generalization. The data points were found near
the ideal fit, and it can be shown that both RFA models have strong R2
values for both testing and training. The value of all errors RSE, MAE,
NSE, RMSE, and RRMSE was found lower for RF models as compared to
the DT models (see Table 3). Similarly, R values were found higher for
RF models. The values of PiF are observed lesser than 0.5, indicating a
better accuracy for all models. The capacity of the established RFA and
DTA models to forecast the compressive strength of concrete built mixed
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S. Nazar et al.
Developments in the Built Environment 13 (2023) 100113
with CNTs and NS is thus confirmed by these output results.
6. Statistical and K-fold analysis
It is employed to assess the machine learning model’s effectiveness
and competence. It uses the Jack’s knife test’s basic tenets, which are
typically applied to prevent overfitting outcomes and lessen biases in
training set sampling. Because it is simple to understand and less
pessimistic in its assessment of the model’s skill, therefore it is widely
employed. The set of findings is distributed into k number of groups or
having equal folds of similar in size for K-fold cross-validation. However,
the classification based upon the statistical analysis affects the value of
these K groupings. The disparity between training and resampling sub­
sets will decrease with increasing K value. The following statistical tests
were also used to evaluate the effectiveness of the model.
K-fold cross-validation assesses the effectiveness of the constructed
model by the calculation of errors for the data chosen for test and train
data and coefficients of determination (R2) (MAE, MSE, RMSE). The
better prediction using a built model is demonstrated by the greater R2
value and lowest value of errors. Ten groups were created using the
experimental data that had been gathered; nine of these groups were
utilized for training and one for validation. After ten iterations, the
findings significantly improved with outstanding precision. Nearly 80%
of the values from the obtained dataset were used for training, while
20% were used for testing DTA and RFA models. As shown in Table 2,
and Table 3 for the choice tree and RFA-developed models, the error
analysis (MAE, RSE, RMSE, and RRMSE) can be used to explain the Kfold validation results. The findings unmistakably demonstrate that the
RFA created fewer errors than DTA. According to the available litera­
ture, equation 1 through 3 were used to compute each parameter’s
response (Selvaraj and Sivaraman, 2019).
The R2, MAE, MSE, and RMSE results that were determined after
analyzing both outputs using k-fold cross-validation are displayed in
Figs. 14–17. By using K-fold cross-validation, the created models for the
NS and CNTs datasets were both verified. Figs. 14–17 illustrate the
highest, smallest, and average MAE values for the DTA model in terms of
CS during the k-fold cross-validation process, which were 7.17 MPa,
1.54 MPa, and 4.91 MPa, respectively. 3.07 MPa was recorded as the
greatest value of the RMSE. The DTA model for CNT’s MSE was deter­
mined to have a value of 9.43 MPa. Additionally, Fig. 16 shows that the
Fig. 11. Correlation factor for actual and model values for RFA (for
NS dataset).
Fig. 12. Distribution of errors between actual and model values by RFA (for
CNT dataset).
Fig. 13. Distribution of errors between actual and model values by RFA (for
NS dataset).
Fig. 14. K-fold cross-validation indicators for DT1 (CNT).
Table 3
Statistical parameters of DTA and RFA models.
Model
RSE(MPa)
MAE(MPa)
NSE(MPa)
RMSE(MPa)
RRMSE(MPa)
R
PiF
DT(CNT) model
RF (CNT) model
DT(NS) model
RF (NS) model
0.9228
0.8303
0.9092
0.8633
4.086
3.513
4.311
4.170
0.143
0.090
0.096
0.077
5.61
5.187
5.58
5.33
0.08413
0.07831
0.06431
0.05844
0.9271
0.964
0.9380
0.953
0.0436
0.0398
0.0033
0.0299
7
S. Nazar et al.
Developments in the Built Environment 13 (2023) 100113
Fig. 18. Contribution of each input parameter on the CS (CNT dataset).
Fig. 15. K-fold cross-validation indicators for RF1(CNT).
Figs. 18 and 19.
Ni = qmax (xi − qmin (xi
SA =
qi
j
∑
qj
(8)
(9)
i=1
qmax (xi and qmin (xi illustrates the maximum and minimum predicted
model values, by keeping all input variables constant at their mean
values. Sensitivity analysis for each dataset was conducted separately.
Cement was found to be the most important influential factor on CS in
both datasets. In the case of the CNT dataset, W/B is found with a sig­
nificant effect on CS. It is because the dispersion capacity of CNTs is
better in high W/B ratios, while low W/B may lead to agglomeration.
Overall, the variable importance of input parameters is found as Cement
> W/B > CNT > CA > Sand as shown in Fig. 18. In the case of the 2nd
dataset, both NS and W/B were found with approximately similar
importance factors. In both cases, the nanomaterials effect was reported
as more than 15% as both significantly accelerate the hydration process
of ordinary Portland cement (Nazar et al., 2020). The variable impor­
tance of coarse aggregate (CA) and fine aggregate (FA) was found at
13.4% and 11% in the 2nd dataset respectively (see Fig. 19). The overall
trend of Cement > W/B > NS > CA > Sand is observed. These results are
found in line with the experimental test results obtained by (Yang et al.,
2021; Mukharjee and Barai, 2020). Table 4 and Table 5 are made ac­
cording to the methodology adopted in (Abdalla and Salih Mohammed,
2022). Regression is repeated throughout the procedure each time one
input parameter is taken out of the training dataset. The trial with the
highest MAE (MPa) and RMSE (MPa) is selected, and the trials are sorted
based on the recorded MAE. The eliminated parameter from the trial
with the highest MAE is the more sensitive variable in predicting the
compressive strength of concrete modified with CNTs and NS.
Fig. 16. K-fold cross validation indicators for DT2 (NS).
Fig. 17. K-fold cross validation indicators for RF2 (NS).
MAE and R2 highest values for RFA in terms of CS were 5.73 MPa and
0.99 MPa, respectively. Similar to Figs. 16, Figure 17, Figs. 17 and 18
display the K-fold cross-validation ranges of R2, MAE, MSE, and RMSE.
MSE and R2 had the greatest values at 10.75 MPa and 0.91, respectively,
whereas RF had values of 9.12 MPa and 0.96. Fewer errors demonstrate
the RFA’s superior generalizability and predictability when compared to
the DTA for the estimation of new data.
7. Sensitivity analysis and discussion
The sensitivity analysis is conducted using Equations (8) and (9) to
measure each input parameter effect on the compressive strength of
nanomodified concrete. The significant effect of selected input variables
including nanomaterials on the compressive strength is shown in
Fig. 19. Contribution of each input parameter on the CS (NS dataset).
8
S. Nazar et al.
Developments in the Built Environment 13 (2023) 100113
Table 4
Sensitivity analysis CNTs modified concrete using RF model.
No
Combination
Removed
parameter
RMSE
(MPa)
MAE
(MPa)
Ranking
1
Cement, CNT, CA,
FA, W/B
CNT, CA, FA, W/B
Cement, CA, FA,
W/B
Cement, CNT, CA,
W/B
Cement, CNT, FA,
W/B
Cement, CNT, CA,
FA, W/B
–
5.187
3.513
–
Cement
CNT
11.2
8.31
8.91
6.93
1
3
FA
6.29
4.1
5
CA
7.41
5.34
4
W/B
9.62
7.29
2
2
3
4
5
6
Table 6
Statistical parameters and their ranges for the external validation of the models
developed by DT and RF.
S.
No
Equation
Condition
CS
(RF1)
CS
(DT1)
CS
(RF2)
CS
(DT2)
1
2
R
0.8 < R
0.85 < k
< 1.15
0.94
0.94
0.91
0.99
0.93
0.93
0.89
0.94
1.03
0.99
1.01
0.96
m<1
- 0.02
0.029
- 0.012
0.019
n<1
− 0.016
− 0.192
− 0.013
− 0.162
0.5 < Rm
00.71
0.54
00.61
0.67
R0 2 ≅ 1
0.991
0.931
0.989
0.930
0 0.923
0.958
00.911
0.908
3
4
5
Table 5
Sensitivity analysis NS modified concrete using RF model.
No
1
2
3
4
5
6
Combination
Cement, NS, CA,
FA, W/B
NS, CA, FA, W/B
Cement, CA, FA,
W/B
Cement, NS, CA,
W/B
Cement, NS, FA,
W/B
Cement, NS, CA,
FA, W/B
6
Removed
parameter
RMSE
(MPa)
MAE
(MPa)
Ranking
–
5.33
4.17
–
Cement
NS
9.49
8.72
8.11
7.46
1
2
FA
6.3
5.36
5
CA
7.11
5.97
4
W/B
8.29
7.14
3
7
k =
∑n (ei × pi )
i=1
ei 2
k =
′
∑n (ei × pi )
i=1
pi 2
R2 − R0 2
m =
R2
R2 − R0 2
n =
R′ 2
Rm = R2 (1 −
√̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅
⃒
⃒
⃒R2 − R0 2 ⃒
R0 2 = 1 −
∑n
∑ni=1
8
− pi 0 ) 2
2
R0 = 1 −
∑n
i=1 (ei
∑n
′
(pi − ei 0 )2
i=1 (pi
′
0.85 < k
< 1.15
2
R0 ≅ 1
′
− pi 0 )2
0 2
i=1 (ei − ei )
ei 0 = k × pi
pi 0 = k × ei
9. Conclusions
8. Structure of the model and performance
The research on the applications of nanomaterials in concrete to
enhance their compressive strength and durability has been widely
increased. The most frequently used nanomaterials in concrete to in­
crease their mechanical and durability performance are carbon nano­
tubes and nano silica. However, the addition of CNTs and NS from
certain limits may impart a negative impact on strength and workability
because of the dispersion issue. The current study utilizes the individual
and ensemble machine learning (ML) based algorithms, i.e., decision
tree algorithm (DTA) and the random forest algorithm (RFA) to estimate
the CS of concrete mixed with CNTs and NS. Based on the acquired data
set retrieved from published literature, the models were tested and
trained. The statistical checks have confirmed the superiority of the
ensembled ML RF algorithm, which has shown better generalization and
predictability than the individual DT algorithm.
The following conclusions, however, can be represented from the
data and analysis:
Although few studies were conducted previously to forecast the CS
nanomodified concrete (MacLeod et al., 2020). But the investigations
were limited by using only individual machine learning algorithms.
However, this study presents a comparative analysis of the imple­
mentation of the established models by engaging ensembled and indi­
vidual machine learning algorithms to forecast the CS of concrete mixed
with CNTs and NS. Statistical checks are used to check the efficacy of
established models. It is reported that a high correlation between the
experimental (actual) and predicted outcomes follows the order RF > DT
for the CS of. The average MAE is highest in the case of DT for
compressive strength (MPa) and lowest for RF. The average value of
RMSE was found higher for DT as compared to RF. These values indicate
better predictability and higher generalization capacity for unknown
data (Iqbal et al., 2020; Shah et al., 2020). Overall results indicate that
the model developed by RF gave a better performance than the DT
model.
Table 6 shows the external validation of both models by comparison
with the criterion available in previously published literature. RF1 and
DT1 show the models for the CNTs data set while RF2 and DT2 represent
the NS dataset. k′ or k explain the slope of the regression line (between
the experimental and predicted(by models) results) (Golbraikh and
Tropsha, 2002). R0′ 2 or R02 illustrates the coefficient of correlation
between forecasted and actual values, and actual and forecasted values
respectively. However, the values of both should be less and equal to 1.
Rm is the absolute difference between correlation coefficients(R0′ 2 and
R02) and which should not be less than 0.5 (Golbraikh and Tropsha,
2002). Also, the two factors m and n are the performance indexes fac­
tors, which must have a value less than 0.1. Both RF models have shown
better ranges of statistical parameters than DT models as shown in
Table 6.
• The ensemble ML algorithm RF algorithm-based model has illus­
trated improved performance with less variation between the actual
datasets and the anticipated results. Also, the accuracy level of the
RFA model was found to be higher with R2 values of 0.93, and 0.91,
than the DTA model with R2 of 0.86 and 0.88 for both datasets of
CNTs and NS.
• The values of MAE (3.51), RMSE (5.18) and RRMSE (0.078), Pif
(0.0398) for RF-model confirm better accuracy than the 4.08, 5.61,
0.084, and 0.0436 values for the DT-model for CNTs dataset.
Moreover, a similar trend in all statistical values is observed for a
developed model of NS.
• The effectiveness and superior performance of the RFA-based models
for both the CNTs and NS-developed models were confirmed by the
K-fold cross-validation results.
• The sensitivity analysis illustrated the variable importance of input
parameters in the following order Cement > W/B > CNT > CA >
9
Developments in the Built Environment 13 (2023) 100113
S. Nazar et al.
Sand for CNTs model and Cement > NS > W/B > CA > Sand for NSbased model.
• The output results showed the better accuracy and precision of both
models which depict that developed models can be employed
effectively in the future to forecast the CS of concrete mixed with
CNTs or NS. Thus, it proves the efficacy of machine learning tech­
niques in solving complex problems in the prediction of the
compressive strength of concrete mixed with carbon nanotubes or
nano silica.
• This study is however having the limitation of prediction of the CS in
the range of 44 MPa–102 MPa for CNTs modified concrete and 49
MPa to 122 MPa for NS-modified concrete. However, for compres­
sive strength in other ranges, the prediction models must be devel­
oped by using other software.
• Also, more experimental work is required to increase the datasets
and include the effect of dispersion techniques in the modeling.
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Author contributions
S.N., M.N.A— Conceptualization, data acquisition, Writing - orig­
inal draft & Validation; Software J.Y., K.K— Data curation, Supervision,
Software, Writing - review & editing; M.F.J., F.A—, Software, writing
original draft, validation,
Declaration of competing interest
The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.
Data availability
No data was used for the research described in the article.
Acknowledgments
This work was supported by the Deanship of Scientific Research, Vice
Presidency for Graduate Studies and Scientific Research, King Faisal
University, Saudi Arabia [Project No. GRANT2265]. The authors are
grateful for the financial support of the Science Research Plan of the
Shanghai Municipal Science and Technology Committee (Grant No.
20dz1201301, 21dz1204704), the Science and Technology Planning
Project of Guangdong Province (Grant No 2022A0505050077) and the
National Natural Science Foundation of China (Grant No. 52078293).
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