Implementation of multi-expression programming (MEP), artificial neural network (ANN), and M5P-tree to forecast the compression strength cement-based mortar modified by calcium hydroxide at different mix proportions and curing ages

Abstract

In this study, four different modeling techniques, nonlinear regression (NLR), artificial neural network (ANN), M5P-tree, and multi-expression programming (MEP), are used for developing reliable models to predict the compressive strength of cement-based mortar modified with various calcium hydroxide (CH) content up to 45% (wt% dry cement). The developed accurate models are essential in the construction fields since the material properties prediction from the model is time-saving and cost-effective. The dataset for model development contained data from previous literature related to calcium hydroxide cement blended cement-mortar. The water/cement ratio (w/c) was ranged from 0.3 to 0.74, and the testing age of the sample was varied between 1 and 28 days. Nevertheless, the MEP model was better than other models based on statistical tool assessments. The M5P-tree model is the second-best technique for compressive strength prediction of cement-based mortar modified with calcium hydroxide. Based on the collected data, the compressive strength of the cement mortar decreases as the addition of calcium hydroxide increases.

Full text

Vol.:(0123456789)
1 3
Innovative Infrastructure Solutions (2022) 7:153
https://doi.org/10.1007/s41062-022-00761-8
TECHNICAL PAPER
Implementation ofmulti‑expression programming (MEP), artificial
neural network (ANN), andM5P‑tree toforecast thecompression
strength cement‑based mortar modified bycalcium hydroxide
atdifferent mix proportions andcuring ages
AsoAbdalla1· AhmedSalih1
Received: 11 December 2021 / Accepted: 31 January 2022
© Springer Nature Switzerland AG 2022
Abstract
In this study, four different modeling techniques, nonlinear regression (NLR), artificial neural network (ANN), M5P-tree,
and multi-expression programming (MEP), are used for developing reliable models to predict the compressive strength of
cement-based mortar modified with various calcium hydroxide (CH) content up to 45% (wt% dry cement). The developed
accurate models are essential in the construction fields since the material properties prediction from the model is time-saving
and cost-effective. The dataset for model development contained data from previous literature related to calcium hydroxide
cement blended cement-mortar. The water/cement ratio (w/c) was ranged from 0.3 to 0.74, and the testing age of the sam-
ple was varied between 1 and 28days. Nevertheless, the MEP model was better than other models based on statistical tool
assessments. The M5P-tree model is the second-best technique for compressive strength prediction of cement-based mortar
modified with calcium hydroxide. Based on the collected data, the compressive strength of the cement mortar decreases as
the addition of calcium hydroxide increases.
Keywords Calcium hydroxide· Compressive strength· Modeling· Sensitivity analysis
Introduction
Nowadays, many environmental issues are raised from
cement production and other pollutions, such as global
warming caused by carbon dioxide (CO2) emissions into the
atmosphere and landfilling by-products of factories. It is
believed that using those waste can solve many environmen-
tal problems while producing a sustainable material for con-
struction. Mineral admixture addition is one of the solutions.
By-products of silicon industries and power plants include
silica fume, calcium hydroxide, and fly ash; several studies
have been conducted on the use of these wastes in cement-
based concrete and mortars, exhibiting better mechanical
performance qualities and composite durability [1, 2]. Many
studies have been done on the influence of calcium hydrox-
ide powder on the mechanical characteristics of cement-
based mortar by replacing some Portland cement with cal-
cium hydroxide powder and changing the fresh and hardened
properties of cement mortar [3–5]. For many decades, con-
crete has been widely used as an essential material for con-
structing various infrastructures, including residential and
commercial buildings and civil engineering structures. It is
also used for the new generation of gravity-defying sky-
scrapers. It provides an opportunity for creativity and unlim-
ited engineering potential. Therefore, concrete is responsible
for many of the global construction industries. Aggregate
constitutes the major percent of the concrete which has a
high impact on its properties, as it typically constitutes
60–80% of the concrete volume. These aggregates directly
affect the fresh and mechanical performance of the concrete
[6]. Despite the global acceptance of concrete as a key con-
struction material, it has some shortcomings that usually
affect its quality and general performance. For instance, rela-
tively high density, brittleness, weak tensile strength, low
* Ahmed Salih
ahmed.mohammed@univsul.edu.iq
Aso Abdalla
aso.abdalla@univsul.edu.iq
1 Civil Engineering Department, College ofEngineering,
University ofSulaimani, Kurdistan Sulaimani - Kirkuk Rd,
Sulaymaniyah46001, Iraq

Innovative Infrastructure Solutions (2022) 7:153
1 3
153 Page 2 of 15
resistance to chemical attacks, etc. For these reasons,
research is continuously conducted to seek alternative
sources of concrete ingredients that are technically satisfac-
tory, cost effective, environmentally friendly, and materials
that resist an aggressive environment. Concrete materials,
including cement mortar, sand, and coarse aggregates, are
becoming expensive and sometimes not commonly found in
some locations. The need to find another source of construc-
tion materials is desirable. More durable and recyclable
materials are needed, utilization of waste and natural or agri-
cultural by-products. This may reduce the exploitation of
natural resources and reduce the effect of environmental pol-
lution. The utilization of recycled aggregate and natural
resources as coarse aggregate in concrete production mini-
mizes landfill waste. Many research on the properties of
concrete has been conducted [6, 7]. It was shown from the
literature that minerals recycled and agricultural by-products
are paved as alternative substitutes to aggregates. Ferro-
chrome slag replaced a certain amount of fine aggregate and
yielded a promising result for concrete production. Maxi-
mum strength was achieved when incorporated with 75%
steel slag as coarse aggregate. Incorporating copper waste
slag at 10–100% replacement as coarse aggregate enhanced
the mechanical performance of self-compacting concrete by
26–29%. Nowadays, machine learning has been used by the
researcher in civil engineering fields which includes fitness
monitoring of structural engineering system, mechanical
properties of concrete, the interface of composite members,
fire resistance of reinforced concrete elements, residual
properties of concrete subjected to fire [7]. Support vector
regression (SVR) is a type of machine learning technique
that works based on the rule of structural risk minimization.
The SVR can be used in regression and classification. The
behavior of high- and ultra-high-performance concrete
beams was estimated by developing an SVR-based model.
The characteristic parameters include fracture energy, ulti-
mate load, and so forth. SVR-and ANN-based models have
been developed and applied to predict the concrete behavior
based on mix design using experimental data. The compres-
sive strength was successfully predicted with high accuracy
based on SVR models [5, 6]. Another interesting block-
oriented model, which includes linear dynamic blocks and
non-memory blocks, is useful in nonlinear system modeling
responsible for simple block-oriented structures and efficient
structural ensemble. Hammerstein–Wiener model consists
of two static nonlinear blocks confining dynamic linear
blocks are generally employed for a nonlinear system. The
Hammerstein–Wiener model can describe or approximate
the complicated nonlinear industrial process than the Ham-
merstein model or Wiener model [7]. The statistical tech-
niques and machine learning algorithms are very strong tools
that are commonly used in engineering design. These tech-
niques are specifically used in complex engineering systems,
including composite materials and structures, and solved
technically. Therefore, this study has paid attention to pre-
dicting the compressive strength of concrete modified with
jujube seed as a partial substitute to coarse aggregate by
employing SVM and HWM models. The durability of con-
crete structures is essential [3]; thus, concrete must be ade-
quately compacted during the casting of fresh concrete to
achieve durable concrete leading to SCC development.
Improved segregation resistance translates aggregate parti-
cles’ distribution in the concrete mixtures relatively at all
locations and different levels [6]. Most importantly, SCC can
easily be poured into the formwork of congested reinforced
structures with no vibration, reducing construction time,
feasible design work, and enhancing product and working
environment quality. Therefore, contractors are motivated to
utilize industrial by-products and construction waste such as
recycled concrete aggregates that can be used as a partial
replacement for aggregates in concrete [4]. Calcium carbide
waste (CCW) is a by-product of the acetylene gas (C2H2)
production process. CCW is obtained through a chemical
reaction between water and calcium carbide. CCW is highly
alkaline (pH > 12) and contains a high proportion of
Ca(OH)2, which is about 92% of its mass fraction [6]. There-
fore, when it is combined with other pozzolanic materials,
the Ca(OH)2 will react with the silicon oxide or silicon and
aluminum oxides present in pozzolans to yield more calcium
silicate hydrates (C–S–H) responsible for strength develop-
ment [6]. Adamu etal. [7] also replaced fly ash with CCW
at 0, 10, 20, and 30% levels in alkali-activated fly ash sus-
tainable material using sodium hydroxide and sodium sili-
cate as activators. Their findings showed that the setting time
of mortar decreases, while the
CaC2 + 2H2O → C2H2 + Ca(OH)2 compressive strength and
shear bond strengths increase with increment in CCW con-
tent. CCW also densified the microstructure of the mortar
and increased the peaks of calcium hydroxide and calcium
silicate hydrates, leading to the strength increment. Haruna
etal. [6] used a hybrid of CCW and silica fume via a new
combustion technique to produce a new supplementary
cementitious material (SCM) in concrete, where they
replaced 5% cement with the new SCM. The findings
showed that the new SCM prolonged the hydration process
of the concrete, thereby increasing the setting times,
improved the compressive strength at later ages (45days),
and lower drying shrinkage value at the same age compared
to reference concrete. Adamu etal. [7] reported the effect of
RHA and Al2O3 nanoparticles on concrete’s mechanical and
durability properties. They replaced 10% cement with RHA,
and 1, 2, 3, and 4% cement with Al2O3 nanoparticles. Their
results showed that replacing 10% cement with RHA identi-
fied the concrete microstructure and increased the compres-
sive strength, flexural strength, tensile strength, and durabil-
ity properties in terms of resistance to hydrochloric acid and

Innovative Infrastructure Solutions (2022) 7:153
1 3
Page 3 of 15 153
acid attack of the concrete. They further reported that replac-
ing cement with Al2O3 further densified the concrete micro-
structure and increased its strength and durability [8, 9].
Modeling the properties of materials can be performed in
various ways, including computational modeling, statistical
techniques, and newly created tools like regression analysis,
M5P-tree, and artificial neural networks (ANN) [10–18].
Also, Armaghani and Asteris [19] investigated the applica-
tion of ANN and adaptive neuro-fuzzy inference system
(ANFIS) models to predict the compressive strength of
cement mortar with or without metakaolin concluded that
ANFIS performed better than ANN. Moreover, Suba etal.
[20] employed ANN for mechanical properties prediction
and compared the result with linear regression, the forecast
of the ANN model was pretty close to actual work. Multi-
expression programming (MEP) was used to estimate the
mechanical properties of concrete and provide acceptable
results as implemented by Shah etal. [21]. The parametric
study revealed the accuracy of the MEP model, with a high
correlation coefficient (R). As a result, several techniques
were used in the literature to forecast the mechanical proper-
ties of cement-based mortar, but MEP has not been used for
that purpose.
Problem statement
i. There is no comprehensive study in the previous
research studies on the cement mortar modified with
the calcium hydroxide evaluating and quantifying the
effect of a wide range of mix proportions on the long-
term compressive strength of cement mortar.
ii. From now towards the researchers and the construc-
tion industry can use the developed models in this
study with high accuracy (low RMSE and high R val-
ues) to predict the compressive strength of the cement
mortar withoutany costand would save time for the
experimental lab work.
iii. Several new ideas were used in this study as follows:
iv. Collecting 215 tested data, statistical analysis to disci-
pline concerns the collection, organization, analysis,
interpretation, and presentation of data.
v. Long-term compressive strength prediction for the
cement mortar.
Objectives ofthis study
This study aims to determine the compressive strength of
cement mortar modified with calcium hydroxide (CH) with
various water to cement ratios and curing time using differ-
ent multiscale models. The models were subjected to sen-
sitivity analysis utilizing statistical evaluation tools. As a
consequence, experimental data from other research papers
were gathered and evaluated using a variety of statistical
modeling techniques to accomplish the following goals: (i)
To perform a statistical analysis and determine the impact of
mixture compositions of cement mortar (ii) To determine the
influence of calcium hydroxide on the compressive strength
of cement mortar (iii) Using statistical analysis, compare
and determine the most trustworthy model for measuring
the compressive strength of cement mortar modified with
calcium hydroxide.
Methodology
Figure1 presents the steps that have been followed during
this study.
Data collection
A comprehensive 215 data on compressive strength and 41
data on flexural strength of cement-based mortar modified
with calcium hydroxide were collected from different pre-
vious studies [2–4, 11, 17, 22–29, 48–51]. The dataset was
divided into three groups (training, testing, and validating)
randomly using the rand function in Microsoft Excel. The
largest group included 70% of the dataset (151 data), and
each of the other two groups included 15% of the dataset
(32 data). The training data is used to develop the model, an
algorithm is feeded with the training data and continually
evaluated to learn from the data and make a future predic-
tion while validating and testing data is provided to test the
developed model against unseen data and overfitting of the
developed model can be minimized [26]. The summary of
statistical analysis on the input and output parameters with
detail of the collected data is shown in Table1.
Statistical analysis
Water tocement ratio (w/c)
According to the statistical evaluation on the collected
data, w/c was ranged between 0.3 and 0.74, with mean and
median, standard deviation (SD), variance (Var), skew-
ness (Skew), and kurtosis (Kur) of 0.5, 0.08, 0.01, 0.67,
3.29, respectively (Table2). The relation between w/c and
compressive strength and the histogram for w/c is shown
in Fig.2.
Calcium hydroxide content (CH) (%)
Based on the collected data from previous literature, the
percentage of cement replacement with calcium hydroxide
was 45% maximum. With a median, SD, Var, Skew, and Kur
of 12, 10.83, 117.27, 0.82, 0.42, respectively (Table2). The

Innovative Infrastructure Solutions (2022) 7:153
1 3
153 Page 4 of 15
variation of compressive strength with the percentage of the
replacement of calcium hydroxide content and histogram for
CH content is displayed in Fig.3.
Curing time (t) (days)
The collected dataset contained experimental results from
previous research; curing time ranged from 1 to 28days,
with a median of 7days, SD, Var, Skew, and Kur of 12days,
143.45 0.5, and −1.67, respectively (Table2). The histo-
gram for curing time and variation of compressive strength
with curing time are presented in Fig.4.
Compressive strength (CS)
Compressive strength of cement-based mortar modified
with calcium hydroxide up to 28days was ranged from 3
to 75MPa, with a median of 28.85MPa, SD, Var, Skew,
and Kur of 13.5MPa, 182.36, 0.41, −0.34 (Table2). The
histogram of compressive strength of cement-based mortar
modified with calcium hydroxide and Weibull distribution
function is shown in Fig.4.
STEP 1
•Considering w/c, curing time, calcium hydroxide content as
independent variable (predictors) and compressive strength as a
target for the models.
STEP 2
•Data collection from previous researches related to modification of
cement mortar with calcium hydroxide.
STEP 3
•Statistical analysis, presentation of the data , and finding possible
correlation between independent and dependent variables.
STEP 4
•Data splitting randomly ,70% of the data for training the models,
the remaining 30% for validation and testing the developed models.
STEP 5
•Modeling using MEP, NLR, ANN, and M5P- tree models.
STEP 6
•Evaluation of the developed models based on R2, RMSE, MAE, SI,
and OBJ.
STEP 7
•Performing sensitivity analysis to find out the most influential
parameter in predicting the compressive strength of cement mortar
modified with calcium hydroxide.
Fig. 1 Flowchart of the methodology of the current study

Innovative Infrastructure Solutions (2022) 7:153
1 3
Page 5 of 15 153
Modeling
The correlation matrix (Fig.5) shows that the correlation
coefficients (R) of CS with w/c, curing time, and calcium
hydroxide concentration are −0.516, 0.676, and −0.149,
respectively, indicating that there is no direct relationship
between cement-based-mortar compositions and compres-
sive strength. The correlation matrix (Fig.5) shows that the
correlation coefficients (R) of CS with w/c, curing time, and
calcium hydroxide concentration are −0.516, 0.676, and
−0.149, respectively, indicating that there is no direct rela-
tionship between cement-based-mortar compositions and
compressive strength.
Multi‑expression programing (MEP model)
Genetic algorithm (GA) was first introduced by Holland
[30], which was motivated through evolution theory, simi-
lar to that genetic programming (GP) proposed by Cramer
[30–32]. Several linear variations of GP have already been
proposed to deal with some difficulties (such as bloat)
caused by tree representations of GP. A few examples are
Cartesian genetic programming, grammatical evolution
(GE), linear GP, MEP, and gene expression programming
[33, 34]. Multiple solutions are stored in a separate chro-
mosome in MEP individuals. The most acceptable option is
usually chosen when it comes to fitness assignments. This is
Table 1 Summary of
model input parameters for
compressive strength prediction
and correlation between
compressive and flexural
strengths
References Water to cement ratio (w/c) Curing time, t (days) Calcium
hydroxide con-
tent, CH (%)
Com-
pressive
strength,
CS (MPa)
[23] 0.6 3, 7, and 28 0–20 3–33
[24] 0.43 3, 7, and 28 0 and 30 46–65
[25] 0.5 2, 7, and 28 0–15 9–55
[26] 0.3–0.5 7 and 28 0–45 18–65
[27] 0.5 1,3, 7, and 28 0–20 13.6–70
[28] 0.74 7 and 28 0–30 5–32
[29] 0.5 1 and 28 0–35 14–47.5
[48] 0.33 1, 3, 7, and 28 0–10 29–64
[49] 0.5 2, 7, and 28 0 and 30 16–60
[50] 0.5 3 and 28 0 and 30 17–60
[51] 0.5 2 and 28 0–35 6.7–62
[52] 0.5 3, 7, and 28 0–30 18–54
Remarks Ranged from 0.3 to 0.74 1, 3, 7, and 28days Varied between
0 and 45%
Ranged
from 3 to
70MPa
Table 2 Summary of statistical
analysis Statistical parameters Independent variables Dependent variables
Water to
Cement ratio,
w/c
Curing
time, t
(Days)
Calcium hydrox-
ide content, CH
(%)
Compressive
strength,CS
(MPa)
Flexural
strength, FS
(MPa)
No of data 215 215 215 215 41
Max 0.74 28 45 70 12
Min 0.3 1 0 3 4
Median 0.5 7 12 28.854 7.2
Mean 0.5 12 12.96 29.32 7.51
SD 0.085 12 10.83 13.5 1.934
Var 0.007 143.45 117.266 182.364 3.739
Skew 0.671 0.497 0.818 0.407 0.414
Kur 3.287 −1.674 0.424 −0.342 −0.244

Innovative Infrastructure Solutions (2022) 7:153
1 3
153 Page 6 of 15
known as strong implicit parallelism, and it is a distinctive
characteristic of MEP [35, 36]. This feature does not make
MEP more complex when compared with GE and GEP. The
MEP model incorporates different fitting factors to generate
a generalized relationship. Math operators were employed
to generate simple expressions in this investigation, and a
trial and error procedure was used to determine the fitting
parameters [37].
Nonlinear regression model (NLR)
The following formula (Eq.1) can be considered as a gen-
eral form for developing a nonlinear regression model [26,
27] to determine the compressive strength of the standard
cement mortar component and modified cement mortar,
Eq.1 represents the interrelationship between the independ-
ent variables,
CS, w/c, t, and L are compressive strength, water to
cement ratio, curing time, and calcium hydroxide content,
and a, b, c, d, e, f, and g are model parameters.
ANN model
The artificial neural network (ANN) is a computing system
that resembles the human brain and its information analy-
sis. In addition, this model is a machine learning system
employed in construction engineering for various numerical
forecasts and difficulties [1, 12, 13]. ANN consists of three
layers input, hidden, and output layer; these layers are con-
nected through biases and weights (Fig.6). The behavior of
an ANN network is influenced by the pattern of neurons’
connections, which also determines the network’s class.
As previously mentioned, it is possible to train a network
to enhance network performance. In more technical terms,
the network’s topology and connection weights change
(1)
CS
=a
(
w
c)b
(t)c+d
(
w
c)e
(t)f(L)
g
Fig. 2 a Scatter plot of compressive strength and water to cement
ratio and b histogram of water to cement ratio
Fig. 3 a Scatter plot of compressive strength and calcium hydroxide
content and b histogram for calcium hydroxide content

Innovative Infrastructure Solutions (2022) 7:153
1 3
Page 7 of 15 153
repeatedly such that the error at each output layer node is
minimized [19]. In this study, a multi-layer feed-forward
network was designed with mortar composition (w/c, t, CH)
as input and CS as output, and a sigmoid activation function
is used in the output layer.
where j is the number of input variables, xj is the input num-
ber j, and bias is the threshold for sigmoid activation func-
tion. The typical process of the result of ANN is illustrated
in Fig.7.
M5P‑tree model
Quinlan [38] first devised the M5 algorithm, which was
developed into the M5P-tree algorithm [39]. One of the
most significant advantages of model trees is their ability to
efficiently solve problems, dealing with many data sets with
a substantial number of attributes and dimensions. They are
also noted for being powerful while dealing with missing
data. The M5P-tree approach establishes a linear regression
at the terminal node by classifying or partitioning diverse
data areas into numerous separate spaces. It fits on each sub-
location in a multivariate linear regression model. The error
is estimated based on the default variance value inserted
into the node. The general formula for the M5P-tree model
is shown in Fig.8.
Performance criteria formodel evaluation
The developed models are evaluated based on different
assessment tools to choose the best model to predict the
CS of the mortar; the following are efficacy measurements
for the models. The evaluation formulas are illustrated in
Table3.
Analysis ofoutputs
Relation betweenpredicted andmeasured
compressive strength
MEP model
Comparison of measured with the predicted value of CS
using the MEP model is presented in Fig.9a. The model
had a good performance with R2 of 0.87, 0.87, and 0.897
for training, testing, and validating, respectively. Figure9a
contained −25 and + 25% error lines in the training, testing,
and validating datasets.
(2)
Output
=f
(n
∑
j=1
wjxj+bias
)
Fig. 4 a Scatter plot for compressive strength and curing time and b
histogram for compressive strength of cement mortar modified with
calcium hydroxide from 1 to 28days of curing
Fig. 5 Correlation matrix for independent variables and dependent
variable

Innovative Infrastructure Solutions (2022) 7:153
1 3
153 Page 8 of 15
Fig. 6 Typical procedure for
output of ANN network in a
single node
Fig. 7 Optimal ANN network structures, a two hidden layers and 4 hidden neurons, b two hidden layers and 5 hidden neurons, and c two hidden
layers and 7 hidden neurons
Fig. 8 Pruned M5P-tree model

Innovative Infrastructure Solutions (2022) 7:153
1 3
Page 9 of 15 153
NLR model
The variation of predicted compressive strength with meas-
ured compressive strength is displayed in Fig.9b. From the
modeling result, it is clear w/c and curing time are affect the
CS more than calcium hydroxide content. In comparison, the
effect of w/c is more significant on the compression strength
of cement-mortar. The model is developed, and the model
parameters are determined using the least square method
and solver technique [40–47]. The NLR model is presented
in Table4. Figure9a contained −25 and + 25% error lines
in the training, testing and validating datasets similar to the
MEP model.
ANN model
Figure8 shows the optimal ANN network structures, the
best network structure (Fig.8b) selected containing two hid-
den layers and five hidden neurons, with momentum, learn-
ing rate, learning time of 0.1, 0.2, and 2000, respectively.
Figure9c shows variation in predicted CS with measured
CS using the training, testing, and validating datasets and
error line −25 to + 25%, indicating the measurements and
predictions are in this limit with R2, RMSE of 0.901 and
4.234MPa.
M5P‑tree model
Figure8 shows the division of the input space by the algo-
rithm of the M5P-tree model into two linear regression func-
tions named LM 1 and LM 2. The relationship of predicted
and measured CS of the M5P-tree model showed in Fig.9d,
with R2 and RMSE of 0.81 and 5.219MPa. With error lines
of −20 to 25% for the training data set and −25 to 25% for
testing and validating datasets.
The error lines for the relationship between measured
compressive strength and the prediction using all the mod-
els were ranged between + 25 and − 25%, as shown in
Fig.10a. Also, the minimum and maximum values of the
ratio between the predicted compressive strength value and
the measured values range between 0.5 and 4.5 with the best
prediction of ANN and MEP models (Fig.10b).
Model evaluations
The MAE for MEP models is less than NLR and M5P-tree
by 15.6 and 15%, while greater than the ANN model by
12%. However, the MAE values of the MEP model for test-
ing and validating datasets are less than NLR, ANN, and
M5P-tree model. The OBJ values for the proposed models
are also evaluated; the OBJ for the MEP model is less than
Table 3 The criteria for measuring the efficiency of the developed models
where R2, RMSE, MAE, MBE, SI, OBJ, t test, U95, and ρ are coefficient of determination, root mean squared error, mean absolute error, an aver-
age of errors, scatter index, objective, t test, 95% confidence uncertainty, and performance index, respectively. yp, ye, and
ye
are predicted com-
pressive strength, measured compressive strength, and an average of measured compressive strength, respectively. n, tr, te, val are several data
in the training, testing, and validating dataset. For all of the assessment parameters, the ideal value is zero, while the best value for R2 is one.
Corresponding to SI, the performance of the model is excellent, good, fair, and poor if the SI<0.1, 0.1<SI<0.2, 0.2<SI<0.3, and SI>0.3,
respectively [46]
Formula Equation number Best value
R
2=1−
∑n
1(yp−ye)
2
∑
n
1(
ye−ye
)2
(3) 1
R=√
R2(4) 1
RMSE
=
√
SSE
n
(5) 0
MAE
=
∑n
1
�
yp−ye
�
n
(6) 0
SI
=
RMSE
ye
(7) 0
OBJ
=
(
ntr
n
to
∗RMSEtr+MAEtr
R2
tr
+1
)
+
(
nte
n
to
∗RMSEte+MAEte
R2
te
+1
)
+
(
nval
n
to
∗RMSEval+MAEva l
R2
val
+1
)
(8) 0

Innovative Infrastructure Solutions (2022) 7:153
1 3
153 Page 10 of 15
NLR, and M5P-tree models by 15 and 17%; in addition, the
OBJ of ANN is 6% less MEP model’s OBJ as displayed in
Fig.11. Also, the performance index for the MEP model was
less than other developed models for testing and validating
data which specifies better performance of the MEP model
over NLR, ANN, and M5P-tree models for unseen data
(Fig.11c). Summary of model evaluation for R2, RMSE,
and MAE of the developed models is presented in Table4.
Conclusions
Distinct soft computing techniques can be utilized to con-
struct useful and time-saving models; in this study, four dif-
ferent approaches were employed to develop a trustworthy
model for the prediction of compressive strength of calcium
hydroxide-modified cement mortar; the following are the
primary conclusions:
Fig. 9 Variation of CS Predicted with CS Measured using, a MEP model, b NLR model, c ANN model, and d M5P-tree model

Innovative Infrastructure Solutions (2022) 7:153
1 3
Page 11 of 15 153
1. Based on the collected data from literature maximum
percentage of calcium hydroxide is 45%, w/c was ranged
from 0.3 to 0.74. The addition of calcium hydroxide to
cement mortar decreases the compressive strength for
the same mixture and w/c.
2. Based on SI, the performance of MEP and ANN mod-
els are nearly the same, while the SI of MEP model for
validating data is 5% smaller than the SI value for the
ANN model. The objective value for the MEP model
is less than NLR and M5P-tree models by 17 and 16%.
95% Uncertainty value for MEP is smaller than other
developed models.
3. According to the statistical evaluation tools, the MEP
model is better than NLR and M5P-tree models for com-
pressive strength prediction after the ANN model.
4. Using several evaluation criteria, including the root
mean square error (RMSE), the coefficientof determi-
nation(R2), the OBJ, the SI, and the mean absolute error
(MAE). The sequence of models was ANN and M5P-
tree, suggesting that the ANN was the best model pro-
vided in this research based on data acquired from the
literature and producing a higher R2 and lower MAE and
RMSE. The most effective technique for the prediction
of CS of cement mortar is ANN, though the less com-
plicated model can be developed using multi-expression
programming.
5. The sensitivity analysis test was performed in order to
check the most effective dependent variables on inde-
pendent variables’ output performance. The results
indicated that the most effective parameters causing the
output result were curing time and CH content.
Table 4 Summary of developed models
Model Formula Eq. no R2RMSE (MPa) No. of data
MEP
CS =A+B+C−D
(9a) 0.87 4.857 215
A=2
(
w
c
)
2+2(t)+4
(w
c)−2
(
w
c
)
(t
)
(13b)
B
=
4
(w
c)2−4
(
w
c
)
2
(
w
c
)
2−t
(13c)
C
=
2
(w
c)−3
(
w
c
)2
2
(w
c)−3(w
c)2
−
4
(w
c)2−4(w
c)
2
(
w
c)
2−t
(13d)
D
=L
2
(
w
c
)
+2
+
2
t
(13e)
NLR
CS
=−129.25
(
w
c
)3.357
(t)−0.334 +19.63
(
w
c
)−0.532
(t)
0.1446
(
L+
0.001)−0.0161
(10) 0.84 5.39 215
M5P-tree
CS
=27.38 −15.67
(
w
c
)
+3.12(t)−0.46(CH
)
CS
=76.68 −92.69
(
w
c
)
+0.54(t)−0.30(CH
)
(11a)
(15b)
0.85 5.21 215

Innovative Infrastructure Solutions (2022) 7:153
1 3
153 Page 12 of 15
Fig. 10 Comparison of
developed model based on, a
variation between measured and
predicted CS values for testing
data and b Ratio of predicted
compressive strength to meas-
ured compressive strength

Innovative Infrastructure Solutions (2022) 7:153
1 3
Page 13 of 15 153
0.19
0.15
0.18
0.17
0.13
0.12
0.14
0.12
0.22
0.18
0.22
0.17
0
0.05
0.1
0.15
0.2
0.25
0.3
NLRANN M5P-tree MEP
Scater Index, SI
Training Te stingValidating
Fair
Good
Excele nt
3.83
2.89
3.80
3.23
3.35
3.03
3.47
2.77
4.95
3.76
4.53
3.35
0
1
2
3
4
5
6
NLRANN M5P-tree MEP
Mean Absolute Error, MAE (MPa)
Training Te stingValidating
(a)
(b)
(c)
Fig. 11 Comparing developed models based on, a SI, b MAE, c OBJ value
Declarations
Conflict of interest The authors declare that they have no known com-
peting financial interests or personal relationships that could have ap-
peared to influence the work reported in this paper.
References
1. Thongsanitgarn P, Wongkeo W, Sinthupinyo S, Chaipanich A
(2012) Effect of limestone powders on compressive strength and
setting time of Portland-limestone cement pastes. Adv Mater Res
343:322–326. https:// doi. org/ 10. 4028/ www. scien tific. net/ amr. 343-
344. 322
2. Qian J, Song M (2015) Study on influence of limestone powder on
the fresh and hardened properties of early age metakaolin based
geopolymer. Calcined clays for sustainable concrete. Springer,
Dordrecht, pp 253–259
3. Mohammed AS (2014) Characterization and modeling of poly-
mer-treated and nanoparticle modified sulfate contaminated soils,
drilling muds, and hydraulic fracturing fluids under groundwater
(Doctoral dissertation)
4. Piro NS, Mohammed AS, Hamad SM (2021) Multiple analytical
models to evaluate the impact of carbon nanotubes on the elec-
trical resistivity and compressive strength of the cement paste.
Sustainability 13(22):12544
5. Chen C, Habert G, Bouzidi Y, Jullien A (2010) Environmental
impact of cement production: detail of the different processes and
cement plant variability evaluation. J Clean Prod 18(5):478–485.
https:// doi. org/ 10. 1016/j. jclep ro. 2009. 12. 014
6. Haruna SI, Malami SI, Adamu M, Usman AG, Farouk AIB, Ali
SIA, Abba SI (2021) Compressive strength of self-compact-
ing concrete modified with rice husk ash and calcium carbide
waste modeling: a feasibility of emerging emotional intelli-
gent model (EANN) versus traditional FFNN. Arab J Sci Eng
46:11207–11222
7. Adamu M Haruna SI Malami SI Ibrahim MN Abba SI Ibrahim YE
(2021) Prediction of compressive strength of concrete incorpo-
rated with jujube seed as partial replacement of coarse aggregate:
a feasibility of Hammerstein–Wiener model versus support vector
machine. Model Earth Syst Environ 1–11
8. Pacheco-Torgal F, Faria J, Jalali S (2012) Some considerations
about the use of lime–cement mortars for building conservation
purposes in Portugal: a reprehensible option or a lesser evil. Con-
str Build Mater 30:488–494
9. Samiei RR, Daniotti B, Pelosato R, Dotelli G (2015) Properties
of cement–lime mortars vs. cement mortars containing recycled
concrete aggregates. Constr Build Mater 84:84–94. https:// doi.
org/ 10. 1016/j. conbu ildmat. 2015. 03. 042
10. Mahmood W, Mohammed A (2019) New Vipulanandan pq model
for particle size distribution and groutability limits for sandy soils.
J Test Eval 48(5):3695–3712. https:// doi. org/ 10. 1520/ JTE20
180606
11. Qadir W, Ghafor K, Mohammed A (2019) Evaluation the effect of
lime on the plastic and hardened properties of cement mortar and
quantified using Vipulanandan model. Open Eng 9(1):468–480.
https:// doi. org/ 10. 1515/ eng- 2019- 0055
12. Sihag P, Jain P, Kumar M (2018) Modelling of impact of water
quality on recharging rate of storm water filter system using vari-
ous kernel function based regression. Model Earth Syst Environ
4(1):61–68. https:// doi. org/ 10. 1007/ s40808- 017- 0410-0

Innovative Infrastructure Solutions (2022) 7:153
1 3
153 Page 14 of 15
13. Marangu JMM (2020) Prediction of compressive strength of cal-
cined clay based cement mortars using support vector machine
and artificial neural network techniques. J Sustain Constr Mater
Technol 5(1):392–398. https:// doi. org/ 10. 29187/ jscmt. 2020. 43
14. Parsajoo M, Armaghani DJ, Mohammed AS, Khari M, Jahandari
S (2021) Tensile strength prediction of rock material using non-
destructive tests: a comparative intelligent study. Transp Geotech
31:100652
15. Mohammed A, Salih A, Raof H (2018) Vipulanandan constitu-
tive models to predict the rheological properties and stress–strain
behavior of cement grouts modified with metakaolin. J Test Eval
48(5):3925–3945. https:// doi. org/ 10. 1520/ JTE20 180107
16. Li Y, Hishamuddin FNS, Mohammed AS, Armaghani DJ, Ulrikh
DV, Dehghanbanadaki A, Azizi A (2021) The effects of rock index
tests on prediction of tensile strength of granitic samples: a neuro-
fuzzy intelligent system. Sustainability 13(19):10541
17. Mohammed A, Rafiq S, Sihag P, Mahmood W, Ghafor K, Sar-
war W (2020) ANN, M5P-tree model, and nonlinear regression
approaches to predict the compression strength of cement-based
mortar modified by quicklime at various water/cement ratios and
curing times. Arab J Geosci 13(22):1–16. https:// doi. org/ 10. 1007/
s12517- 020- 06199-5
18. Apostolopoulou M, Armaghani DJ, Bakolas A, Douvika MG,
Moropoulou A, Asteris PG (2019) Compressive strength of natu-
ral hydraulic lime mortars using soft computing techniques. Pro-
cedia Struct Integr 17:914–923. https:// doi. org/ 10. 1016/j. prostr.
2019. 08. 122
19. Armaghani DJ, Asteris PG (2021) A comparative study of ANN
and ANFIS models for the prediction of cement-based mortar
materials compressive strength. Neural Comput Appl 33(9):4501–
4532. https:// doi. org/ 10. 1007/ s00521- 020- 05244-4
20. Suba S (2009) Prediction of mechanical properties of cement
containing class C fly ash by using artificial neural network and
regression technique. Sci Res Essays 4(4):289–297
21. Emad W, Salih A, Kurda R, Hassan AMT (2021) Multivariable
models to forecast the mechanical properties of polymerized
cement paste. J Mate Res Technol 14:2677–2699
22. Liu J, Vipulanandan C (2005) Tensile bonding strength of epoxy
coatings to the concrete substrate. Cem Concr Res 35(7):1412–
1419. https:// doi. org/ 10. 1016/j. cemco nres. 2004. 06. 035
23. Moturi SV (2010) Evaluating the performance of cementitious
and epoxy coatings for concrete under acidic environment (Master
dissertation, University of Houston)
24. Mohammed AS (2017) Effect of temperature on the rheological
properties with shear stress limit of iron oxide nanoparticle modi-
fied bentonite drilling muds. Egypt J Pet 26(3):791–802. https://
doi. org/ 10. 1016/j. ejpe. 2016. 10. 018
25. Mohammed A, Mahmood W (2018) Statistical variations and
new correlation models to predict the mechanical behavior and
ultimate shear strength of gypsum rock. Open Eng 8(1):213–226.
https:// doi. org/ 10. 1515/ eng- 2018- 0026
26. Rai B, Kumar S, Satish K (2014) Effect of fly ash on mortar
mixes with quarry dust as fine aggregate. Adv Mater Sci Eng
2014:626425. https:// doi. org/ 10. 1155/ 2014/ 626425
27. Demircan E, Harendra S, Vipulanandan C (2011) Artificial neu-
ral network and nonlinear models for gelling time and maximum
curing temperature rise in polymer grouts. J Mater Civ Eng
23(4):372–377. https:// doi. org/ 10. 1061/ (ASCE) MT. 1943- 5533.
00001 72
28. Cai M Hocine O Mohammed AS Chen X Amar MN Hasanipanah
M (2021) Integrating the LSSVM and RBFNN models with three
optimization algorithms to predict the soil liquefaction potential.
Eng Comput 1–13
29. Sarwar W, Ghafor K, Mohammed A (2019) Modeling the rheolog-
ical properties with shear stress limit and compressive strength of
ordinary Portland cement modified with polymers. J Build Pathol
Rehabil 4(1):1–12. https:// doi. org/ 10. 1007/ s41024- 019- 0064-6
30. Mawlood Y, Salih A, Hummadi R, Hasan A, Ibrahim H (2021)
Comparison of artificial neural network (ANN) and linear regres-
sion modeling with residual errors to predict the unconfined
compressive strength and compression index for Erbil City soils
Kurdistan-Iraq. Arab J Geosci 14(6):1–14
31. Koza JR (1994) Genetic programming as a means for program-
ming computers by natural selection. Stat Comput 4:87–112.
https:// doi. org/ 10. 1007/ BF001 75355
32. Cramer N (1985) A representation for the adaptive generation of
simple sequential programs. In: Proceedings of the first interna-
tional conference on genetic algorithms, pp 183–187
33. Oltean M, Dumitrescu D (2002) Multi expression programming. J
Genet Program Evolvable Mach Kluwer Second Tour Rev. https://
doi. org/ 10. 21203/ rs.3. rs- 853086/ v1
34. Jiang H, Mohammed AS, Kazeroon RA, Sarir P (2021) Use of
the gene-expression programming equation and FEM for the high-
strength CFST columns. Appl Sci 11(21):10468
35. Brameier M, Banzhaf W (2001) A comparison of linear genetic
programming and neural networks in medical data mining. IEEE
Trans Evol Comput 5(1):17–26. https:// doi. org/ 10. 1109/ 4235.
910462
36. Handley S (1994) On the use of a directed acyclic graph to rep-
resent a population of computer programs. In: Proceedings of the
first IEEE conference on evolutionary computation. IEEE world
congress on computational intelligence, pp 154–159. https:// doi.
org/ 10. 1109/ ICEC. 1994. 350024
37. Mousavi SM, Gandomi AH, Alavi AH, Vesalimahmood M (2010)
Modeling of compressive strength of HPC mixes using a com-
bined algorithm of genetic programming and orthogonal least
squares. Struct Eng Mech Int J 36(2):225–241. https:// doi. org/
10. 12989/ sem. 2010. 36.2. 225
38. Quinlan JR (1992) Learning with continuous classes. In 5th
Australian joint conference on artificial intelligence. World Sci
92:343–348. https:// doi. org/ 10. 1142/ 97898 14536 271
39. Wang Y Witten IH (1996) Induction of model trees for predicting
continuous classes
40. Mohammed A, Mahmood W (2018) Vipulanandan failure mod-
els to predict the tensile strength, compressive modulus, fracture
toughness and ultimate shear strength of calcium rocks. Int J Geo-
tech Eng. https:// doi. org/ 10. 1080/ 19386 362. 2018. 14686 63
41. Mohammed AS (2018) Vipulanandan model for the rheological
properties with ultimate shear stress of oil well cement modi-
fied with nanoclay. Egypt J Pet 27(3):335–347. https:// doi. org/
10. 1016/j. ejpe. 2017. 05. 007
42. Vipulanandan C, Mohammed AS (2014) Hyperbolic rheological
model with shear stress limit for acrylamide polymer modified
bentonite drilling muds. J Petrol Sci Eng 122:38–47. https:// doi.
org/ 10. 1016/j. petrol. 2014. 08. 004
43. Vipulanandan C Mohammed A Ganpatye AS (2018) Smart
cement performance enhancement with NanoAl2O3 for real time
monitoring applications using Vipulanandan models. In: Off-
shore technology conference. OnePetro. https:// doi. org/ 10. 4043/
28880- MS
44. Aller-Rojas O, Moreno B, Aponte H, Zavala J (2020) Carbon stor-
age estimation of Lessoniatrabeculata kelp beds in Southern Peru:
an analysis from the San Juan de Marcona region. Carb Manag
11(5):525–532. https:// doi. org/ 10. 1080/ 17583 004. 2020. 18087 65
45. Telles JCF, Oliveira RF (1994) Third degree polynomial trans-
formation for boundary element integrals: further improvements.
Eng Anal Bound Elem 13(2):135–141. https:// doi. org/ 10. 1016/
0955- 7997(94) 90016-7
46. Li M-F, Tang X-P, Wu W, Liu H-B (2013) General models for
estimating daily global solar radiation for different solar radiation

Innovative Infrastructure Solutions (2022) 7:153
1 3
Page 15 of 15 153
zones in mainland China. Energy Convers Manag 70:139–148.
https:// doi. org/ 10. 1016/j. encon man. 2013. 03. 004
47. Mohammed A, Rafiq S, Sihag P, Kurda R, Mahmood W (2021)
Soft computing techniques: systematic multiscale models to pre-
dict the compressive strength of HVFA concrete based on mix
proportions and curing times. J Build Eng 33:101851. https:// doi.
org/ 10. 1016/j. jobe. 2020. 101851
48. De Weerdt K, Haha MB, Le Saout G, Kjellsen KO, Justnes H,
Lothenbach B (2011) Hydration mechanisms of ternary Portland
cements containing limestone powder and fly ash. Cem Concr Res
41(3):279–291. https:// doi. org/ 10. 1016/j. cemco nres. 2010. 11. 014
49. Türkel S, Altuntaş Y (2009) The effect of limestone powder,
fly ash and silica fume on the properties of self-compacting
repair mortars. Sadhana 34(2):331–343. https:// doi. org/ 10. 1007/
s12046- 009- 0011-3
50. Xu GQ, You ZG, Gao L, Han DL (2013) The influence of com-
bined admixture of super-fine limestone powder and low-quality
fly ash on the performance of cement mortar. Adv Mater Res.
https:// doi. org/ 10. 4028/ www. scien tific. net/ AMR. 652- 654. 1181
51 Zhang J, Li Z (2012) Impact of the limestone powder on the prop-
erties of cement paste and mortar. Appl Mech Mater. https:// doi.
org/ 10. 4028/ www. scien tific. net/ AMM. 174- 177. 236
52. Ayat A, Bouzerd H, Ali-Boucetta T, Navarro A, Benmalek
ML (2022) Valorisation of waste glass powder and brick dust
in air-lime mortars for restoration of historical buildings: case
study theatre of Skikda (Northern Algeria). Constr Build Mater
315:125681