# Prediction of Mechanical Strength by Using an Artificial Neural Network and Random Forest Algorithm

Authors: Kamal Upreti; Manvendra Verma; Meena Agrawal; Jatinder Garg; Rekha Kaushik; Chinmay Agrawal; Divakar Singh; Rajamani Narayanasamy
Journal: Journal of Nanomaterials
 (2022)

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## Abstract

Geopolymer concrete could be the best alternative to ordinary Portland cement concrete due to its higher performance in any severe condition. It reduces the carbon footprints to a very higher level. Machine learning methods are the future of the construction industry because it predicts the mechanical strengths of concrete mix design on the basis of their constituents without destructive test conduction. This study is aimed at developing the models to predict the mechanical strengths and validate them with the actual results. After the experimental investigation, we found the results of the mechanical (including compressive, splitting tensile, and flexural tensile) strength. The M2 mix of geopolymer concrete got the highest mechanical strengths whereas the M5 mix gets the lowest mechanical strengths among all the mix designs. The machine learning methods ANN (artificial neural network) and random forest are used to develop the models based on mixed experimental results. Mechanical strength results are taken as outputs, and mixed constituents are taken as inputs for training and testing. The performance of predicted results is checked based onR2, MAE (mean absolute error), RMSE (relative mean square error), RAE (relative absolute error), and RRSE (root-relative square error). Random forest models show the best prediction to the ANN models because it shows the negligible error between actual and predicted values. The R2 value is 1 of 12 predicted results out of 15 by the use of random forest methods. So it is most suitable to predict the strength of geopolymer concrete based on their constituent’s material quantity.


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## Body

## 1. Introduction

Concrete is a very important material for our society and nation because the development of infrastructures is built primarily on concrete [1]. Concrete is the second most used material in the world after the water [2]. The production of concrete increases exponentially day by day [3, 4]. Portland cement is an essential and primary material for the production of ordinary concrete [5]. Around one ton of carbon dioxide is produced during the production of one-ton cement. The higher carbon dioxide emissions cause global warming [6, 7]. It deteriorates the ice of the Arctic and Antarctica mountains near the north and south poles of the earth [8]. Carbon dioxide shares around 50% of emissions among all greenhouse gases [9]. The cement industries contribute to around 8 percent of carbon dioxide emissions. So the production of concrete directly contributes to the increment in global warming.Geopolymer is highly effective over conventional concrete due to better strength, durability, and performance in various severe conditions also [10–12]. It shows better resistance to acid attack, sulphate attack, elevated temperatures, and freeze-thaw, wetting-drying, and seawater conditions [13–15]. It is eco-friendly, economic, and sustainable concrete over conventional concrete. It directly affects the circular economy through the usage of industrial symbiosis. The various factors that affect the properties of the geopolymer concrete would be curing condition and temperature, the molarity of sodium hydroxide, alkaline ratio, superplasticiser dosage and type, liquid to binder ratio, fly ash and GGBFS contents and composition, and gradation of aggregates [14–22].The above-defined problem could be reduced by the production of geopolymer concrete, because it would replace the cement content with pozzolanic materials like fly ash, GGBFS, rice husk ash, and calcined clay (metakaolin) [23–26]. The production of geopolymer concrete directly reduces the emission of carbon dioxides around 80 percent of ordinary concrete production [27]. The geopolymer is a name of bonding that is firstly stated by Prof. Davidovits in 1978. The geopolymer concrete is made with a different bonding pattern than the Portland cement bonding, in which the alkaline solution is used to activate the pozzolanic material to react with each other. Sodium or potassium hydroxide and sodium or potassium silicate are used as alkaline solutions in the geopolymer concrete [28–34]. It reacts with the alumino-silicates that are present in the pozzolanic material and make bonds. It makes the bond-like K+ or Na+‐Al‐O‐Si‐On–xH2O, whereas the calcium silicate hydroxide (C-S-H) bonds are made in the Portland cement reaction. Geopolymerisation is a process of reaction to build geopolymer bonds from the basic constituents. It occurs during the reaction of alumino-silicate to alkaline solution in the presence of water to make up to end products [35]. The geopolymer concrete is highly resistant to acid attack, sulphate attack, seawater conditions, freeze-thaw conditions, and other severe conditions compared to ordinary Portland cement concrete [36, 37]. The geopolymer concrete is easily usable in the construction of columns, beams, piles, and slabs. It can also be usable in the stabilization of soils by the mixing of materials with the weaker soils [38]. The geopolymer constituents are fly ash, GGBFS, sodium hydroxide, sodium silicate, superplasticiser, aggregates, and water. The mechanical property analysis is done over many years, in which various research stated the optimum point to get maximum strength and performance.The alkali-activated concrete and geopolymer concrete are different due to their reaction occurring during strength and hardenings. In both concrete, the constituents are the same, but the geopolymer concrete makes the geopolymer bonds but the alkali-activated concrete makes the C-S-H bonds, and it is the same bond constructed by the Portland cement in the geopolymer bond formation of silica and alumina bondsAl−O−Si−On. In the geopolymer concrete, all constituents have their unique importance. The pozzolanic materials are industrial solid wastes that reduce the waste storage area and reduce the pollution developing due to waste management and Portland cement production. The sodium hydroxide and sodium silicate work as catalysts to activate pozzolans to react and make bonds. A superplasticiser is used to make the concrete workable at less water content.Nowadays, the predictions of the mechanical strength of the geopolymer concrete are performed by the use of machine learning methods like ANN (artificial neural network), GEP (gene expression programming), multiple linear regression, generalized linear modelling, quadratic polynomial regression, support vector machine, random forest, and extreme gradient boosting [39–46]. The mechanical strength (compressive strength, splitting tensile, and flexural strength) would vary with the variation in the constituent’s material quantity. Machine learning methods develop a model to predict the compressive strength and other strengths on the basis of the quantity of the constituent material [47, 48]. The numerical models are developed by the machine learning methods, and the performance of the developed model is analysed by the R2 value [49–52]. If it is near 1, then the numerical models provide higher accuracy in the prediction of strength [53].


## 2. Research Significance

The geopolymer concrete samples were cast in the laboratories and get the mechanical (compressive, splitting tensile, flexural) strength via experimental analysis. The research significance of this study is to predict the mechanical strength of the geopolymer concrete by the use of artificial neural networks and random forest algorithm machine learning methods. The predicted values are validated by the experimental results, and we check the accuracy of the prediction of the results. The numerical models are developed by the ANN and random tree methods separately. The predicted result performance was evaluated by theR2, MAE (mean square error), RMSE (root mean square error), RAE (relative absolute error), and RRSE (root-relative square error).


## 3. Experimental Programme

### 3.1. Materials

In the geopolymer concrete mix, the GGBFS and fly ash were used as binding materials, whereas sodium hydroxide and sodium silicate are used as alkaline solutions. The coarse aggregates of 20 mm are used as maximum size aggregates, and the stone dust or m-sand is used as fine aggregates in the GPC. The SNF-based SP Conplast 430 is used as a superplasticiser in the GPC. SEM analysis was conducted on the fly ash and GGBFS, which clarified that the fly ash is spherical and porous, whereas the GGBFS particles are irregular in nature. Table1 depicts the mineral oxides present in the fly ash and GGBFS. Sodium hydroxide and sodium silicate were purchased from CDH Chemicals Private Limited, in which sodium hydroxide flakes have 98 percent of the minimum assay, whereas sodium silicates are alkaline in nature. Coarse aggregate and fine aggregates were collected from the locally available materials. Various tests were conducted on the coarse and fine aggregates to check their properties that meet the standards [49–52, 54–58]. Table 2 describes the properties of the fine aggregates that are found in the laboratory test analysis. Table 3 depicts the properties of the coarse aggregates that are found through the experiment tests conducted in the laboratories. After the laboratory’s tests, it is concluded that the coarse and fine aggregates are suitable for further investigation. Tap water is used in the mixing of geopolymer concrete that has a pH value of 7 [59].Table 1
Mineral composition of GGBFS and fly ash.
CharacteristicsSiO2Al2O3CaOFe2O3MgOSO3LOIFly ash (%)45.821.413.712.61.31.90.1GGBFS (%)34.5220.6632.430.5710.090.770.3Table 2
Properties of fine aggregate/stone dust (m-sand).
TestResultsZoneZone IIGradeWell gradedFineness modulus2.756 (medium sand)Specific gravity2.62Water absorption1.21%Silt content6%Bulk density1610 kg/m3Table 3
Properties of the coarse aggregate.
TestResultsFineness modulus7.29Specific gravity2.79Water absorption0.2%Crushing value23%Impact value22%Flakiness index24%Elongation index30%Abrasion value8%


### 3.2. Synthesis

Table4 depicts the 10 mix designs of the geopolymer concrete, in which the GGBFS to fly ash ratio varies from 0 to 0.75 as binding materials, and after, the extra water varies from 5% to 30% of the binder. Sodium and sodium silicate solutions were made 20-24 hours before mixing and casting the samples. The pan mixer was used for the mixing of geopolymer concrete for 15 minutes [60]. After the mixing, the slump test was conducted on the mix to find their workability. The fresh mix geopolymer concrete was cast in the cubes, cylinders, and prism moulds of 150mm×150mm×150mm, 150mm×300mm, and 100mm×100mm×500mm, respectively, for the sample preparation [61–63]. The casted samples were demoulded after three days. The samples were cured in the oven at 60°C for 24 hours after demoulding.Table 4
Mix designs.
Mix designsFly ash (kg/m3)GGBFS (kg/m3)Coarse aggregate (kg/m3)Fine aggregate (kg/m3)NaOH solution (kg/m3)Sodium silicate (kg/m3)Superplasticiser (kg/m3)Extra water (kg/m3)M1405—126968381.0 (13 M)81.0—81M2303.75101.25126968381.0 (13 M)81.0—81M3202.5202.5126968381.0 (13 M)81.0—81M4101.25303.75126968381.0 (13 M)81.0—81M5303.75101.25126968381.0 (13 M)81.0—0M6303.75101.25126968381.0 (13 M)81.0—20.25M7303.75101.25126968381.0 (13 M)81.0—40.5M8303.75101.25126968381.0 (13 M)81.0—60.75M9303.75101.25126968381.0 (13 M)81.0—101.25M10303.75101.25126968381.0 (13 M)81.0—121.5


### 3.3. Experimental Test Setup

The mixed design specimens were tested to find the compressive strength, splitting tensile strength, and flexural tensile strength. All mix design samples were tested after 7 days, 14 days, 28 days, 42 days, and 56 days of casting. Cube samples were used to find compressive strength, cylindrical specimens were used to splitting tensile, and prism shape specimens were used for flexural strength. Cube samples were weighed after 28 of casting, which calculates the density of the samples.


## 3.1. Materials

In the geopolymer concrete mix, the GGBFS and fly ash were used as binding materials, whereas sodium hydroxide and sodium silicate are used as alkaline solutions. The coarse aggregates of 20 mm are used as maximum size aggregates, and the stone dust or m-sand is used as fine aggregates in the GPC. The SNF-based SP Conplast 430 is used as a superplasticiser in the GPC. SEM analysis was conducted on the fly ash and GGBFS, which clarified that the fly ash is spherical and porous, whereas the GGBFS particles are irregular in nature. Table1 depicts the mineral oxides present in the fly ash and GGBFS. Sodium hydroxide and sodium silicate were purchased from CDH Chemicals Private Limited, in which sodium hydroxide flakes have 98 percent of the minimum assay, whereas sodium silicates are alkaline in nature. Coarse aggregate and fine aggregates were collected from the locally available materials. Various tests were conducted on the coarse and fine aggregates to check their properties that meet the standards [49–52, 54–58]. Table 2 describes the properties of the fine aggregates that are found in the laboratory test analysis. Table 3 depicts the properties of the coarse aggregates that are found through the experiment tests conducted in the laboratories. After the laboratory’s tests, it is concluded that the coarse and fine aggregates are suitable for further investigation. Tap water is used in the mixing of geopolymer concrete that has a pH value of 7 [59].Table 1
Mineral composition of GGBFS and fly ash.
CharacteristicsSiO2Al2O3CaOFe2O3MgOSO3LOIFly ash (%)45.821.413.712.61.31.90.1GGBFS (%)34.5220.6632.430.5710.090.770.3Table 2
Properties of fine aggregate/stone dust (m-sand).
TestResultsZoneZone IIGradeWell gradedFineness modulus2.756 (medium sand)Specific gravity2.62Water absorption1.21%Silt content6%Bulk density1610 kg/m3Table 3
Properties of the coarse aggregate.
TestResultsFineness modulus7.29Specific gravity2.79Water absorption0.2%Crushing value23%Impact value22%Flakiness index24%Elongation index30%Abrasion value8%


## 3.2. Synthesis

Table4 depicts the 10 mix designs of the geopolymer concrete, in which the GGBFS to fly ash ratio varies from 0 to 0.75 as binding materials, and after, the extra water varies from 5% to 30% of the binder. Sodium and sodium silicate solutions were made 20-24 hours before mixing and casting the samples. The pan mixer was used for the mixing of geopolymer concrete for 15 minutes [60]. After the mixing, the slump test was conducted on the mix to find their workability. The fresh mix geopolymer concrete was cast in the cubes, cylinders, and prism moulds of 150mm×150mm×150mm, 150mm×300mm, and 100mm×100mm×500mm, respectively, for the sample preparation [61–63]. The casted samples were demoulded after three days. The samples were cured in the oven at 60°C for 24 hours after demoulding.Table 4
Mix designs.
Mix designsFly ash (kg/m3)GGBFS (kg/m3)Coarse aggregate (kg/m3)Fine aggregate (kg/m3)NaOH solution (kg/m3)Sodium silicate (kg/m3)Superplasticiser (kg/m3)Extra water (kg/m3)M1405—126968381.0 (13 M)81.0—81M2303.75101.25126968381.0 (13 M)81.0—81M3202.5202.5126968381.0 (13 M)81.0—81M4101.25303.75126968381.0 (13 M)81.0—81M5303.75101.25126968381.0 (13 M)81.0—0M6303.75101.25126968381.0 (13 M)81.0—20.25M7303.75101.25126968381.0 (13 M)81.0—40.5M8303.75101.25126968381.0 (13 M)81.0—60.75M9303.75101.25126968381.0 (13 M)81.0—101.25M10303.75101.25126968381.0 (13 M)81.0—121.5


## 3.3. Experimental Test Setup

The mixed design specimens were tested to find the compressive strength, splitting tensile strength, and flexural tensile strength. All mix design samples were tested after 7 days, 14 days, 28 days, 42 days, and 56 days of casting. Cube samples were used to find compressive strength, cylindrical specimens were used to splitting tensile, and prism shape specimens were used for flexural strength. Cube samples were weighed after 28 of casting, which calculates the density of the samples.


## 4. Modelling

Two machine learning methods were used to model: artificial neural networks (ANN) and random forest.


### 4.1. ANN (Artificial Neural Network)

ANN architecture is primarily composed of the following elements: the inputs, the weights, the sum function, the activation function, and the outputs. In the ANN work areas, the weights modify the input signals, which are summed with the bias term as shown in equation (1). One of the most important features of an ANN design is its sum function, which is comprised of the inputs and weights [46]. The ANN operates in the following ways. The input signals are changed by the weights, and the modified signals, combined with the bias term, are summed together as shown in
(1)y=f∑i=0nxiwi−b,where “f” represents the activation function and the xi weight of the ith input neuron n represents the number of neurons, and b is the bias term, with the result being denoted as y; the output of the neural network (equation (1)) includes an input for the activation function “f,” which is referred to as “sum” in the equation. Multiple feedforward artificial neural networks (ANN) use sigmoid functions, which are mathematical functions having “S”-shaped curves, to activate the network’s layers. When we look at equation (2), the variable ∝ serves as a constant for controlling gradient in the semilinear zone.
(2)ft=11+e−∝t,wheret=∑i=0nxiwi−b.The signals are sent to the next layers of the network until the required outputs are attained. If the computed output differs from the desired goal, the error is calculated and the error is propagated backwards through the network from the output layer to the input layer. The weights are adjusted in response to the signal that has been reflected back. The errors of the output nodes are propagated to all of the nodes of the hidden layers, resulting in each node in the hidden layers being given “blame” for the mistake that occurred.To produce an accurate forecast of the intended output, the ANN (artificial neural network) must be trained. Normally, data would be divided into two categories: training and testing. The coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root-relative square error (RRSE) may be used to assess the accuracy of the ANN created in predicting the intended output of the test data.


### 4.2. Random Forest Tree Algorithm

Random forests are a type of tree predictor in which the values of a random vector gathered independently and with the same distribution for all trees in the forest are used to forecast each tree’s behaviour. The generalisation error converges a.s. to a limit as the number of trees in a forest grows bigger. The generalisation error of a forest of tree classifiers is determined by the strength of individual trees in the forest and their association. The error rates are equivalent to AdaBoost when a random selection of features is employed to split each node, but they are more robust in terms of noise. Internal estimates are used to assess error, strength, and correlation as a response to increasing the number of features utilised in the splitting. Internal estimations are also used to establish whether or not variables are important. These ideas can be applied to regression as well. For predicting, random forests are a useful tool. The law of large numbers prevents them from overfitting. When the right kind of randomness is supplied, they become accurate classifiers and regressors. In addition, the framework sheds light on the random forest’s forecasting capacity in terms of the strength of individual predictors and their relationships. Using out-of-bag estimates, the otherwise theoretical values of strength and correlation become concrete [64].


## 4.1. ANN (Artificial Neural Network)

ANN architecture is primarily composed of the following elements: the inputs, the weights, the sum function, the activation function, and the outputs. In the ANN work areas, the weights modify the input signals, which are summed with the bias term as shown in equation (1). One of the most important features of an ANN design is its sum function, which is comprised of the inputs and weights [46]. The ANN operates in the following ways. The input signals are changed by the weights, and the modified signals, combined with the bias term, are summed together as shown in
(1)y=f∑i=0nxiwi−b,where “f” represents the activation function and the xi weight of the ith input neuron n represents the number of neurons, and b is the bias term, with the result being denoted as y; the output of the neural network (equation (1)) includes an input for the activation function “f,” which is referred to as “sum” in the equation. Multiple feedforward artificial neural networks (ANN) use sigmoid functions, which are mathematical functions having “S”-shaped curves, to activate the network’s layers. When we look at equation (2), the variable ∝ serves as a constant for controlling gradient in the semilinear zone.
(2)ft=11+e−∝t,wheret=∑i=0nxiwi−b.The signals are sent to the next layers of the network until the required outputs are attained. If the computed output differs from the desired goal, the error is calculated and the error is propagated backwards through the network from the output layer to the input layer. The weights are adjusted in response to the signal that has been reflected back. The errors of the output nodes are propagated to all of the nodes of the hidden layers, resulting in each node in the hidden layers being given “blame” for the mistake that occurred.To produce an accurate forecast of the intended output, the ANN (artificial neural network) must be trained. Normally, data would be divided into two categories: training and testing. The coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root-relative square error (RRSE) may be used to assess the accuracy of the ANN created in predicting the intended output of the test data.


## 4.2. Random Forest Tree Algorithm

Random forests are a type of tree predictor in which the values of a random vector gathered independently and with the same distribution for all trees in the forest are used to forecast each tree’s behaviour. The generalisation error converges a.s. to a limit as the number of trees in a forest grows bigger. The generalisation error of a forest of tree classifiers is determined by the strength of individual trees in the forest and their association. The error rates are equivalent to AdaBoost when a random selection of features is employed to split each node, but they are more robust in terms of noise. Internal estimates are used to assess error, strength, and correlation as a response to increasing the number of features utilised in the splitting. Internal estimations are also used to establish whether or not variables are important. These ideas can be applied to regression as well. For predicting, random forests are a useful tool. The law of large numbers prevents them from overfitting. When the right kind of randomness is supplied, they become accurate classifiers and regressors. In addition, the framework sheds light on the random forest’s forecasting capacity in terms of the strength of individual predictors and their relationships. Using out-of-bag estimates, the otherwise theoretical values of strength and correlation become concrete [64].


## 5. Results and Discussion

This section describes the experimental results and predicted results via machine learning methods and validates them together.


### 5.1. Experimental Results

The experimental section describes the slump, density, compressive strength, splitting tensile strength, and flexural strength of the all-mix designs. Slump tests were conducted before the casting of moulds of the plastic mix of the GPC. The density of the design mix of the GPC was calculated after the 28 days of the casting by the weight of the cube specimens before the compressive strength test. The mechanical strength including compressive strength, splitting tensile strength, and flexural strength was tested after 7 days, 14 days, 28 days, 42 days, and 56 days of the GPC mix casting. All the mechanical properties vary similarly with the mixed design. After 28 days, the compressive strength and all other strengths gained 95 percent strength of total strength. The mechanical strength varied from the ratio of GGBFS to fly ash from 0.00 to 0.75 and got the optimum point at a 0.25 ratio mix. The GPC mix varied the extra water from 5% to 30% of binder content. The optimum point of the mechanical properties was found at 20% of the binder content. The maximum compressive strength, splitting tensile, and flexural strength are 32.9 MPa, 4.8 MPa, and 5.3 MPa, respectively, after 56 days of casting. Tables5–7 depict the compressive strength, splitting tensile strength, and flexural strength values found after the experimental tests.Table 5
Compressive strength in MPa.
Mix designs7 days14 days28 days42 days56 daysM121.525.428.328.729.0M224.429.132.132.632.9M322.926.429.63030.2M421.725.128.429.029.3M516.218.119.920.320.8M621.323.826.927.327.7M723.627.630.831.231.6M824.128.931.932.432.6M924.028.431.632.032.4M1023.427.630.230.831.1Table 6
Splitting tensile strength in MPa.
Mix designs7 days14 days28 days42 days56 daysM12.32.83.13.23.2M22.93.84.64.74.8M32.73.64.34.54.6M42.63.43.94.14.2M51.92.22.82.93.0M62.22.93.63.83.9M72.63.44.04.24.3M82.83.84.44.64.7M92.73.64.34.54.6M102.53.23.94.24.3Table 7
Flexural strength in MPa.
Mix designs7 days14 days28 days42 days56 daysM12.53.03.53.63.6M23.14.05.05.25.3M32.93.74.54.74.9M42.73.64.24.44.6M52.12.43.03.23.3M62.53.13.73.94.0M72.83.54.24.44.5M83.03.84.64.74.8M92.93.64.44.64.7M102.73.24.04.24.3


### 5.2. Modelling Analysis

In the modelling analysis, ANN and random forest algorithm machine learning methods are used for the prediction of compressive strength, splitting tensile strength, and flexural strength. Figure1 shows the working flow chart of the regression model. It shows the total process of the regression work. It starts with data collection which includes the input and output data with their variables. After that, it shows the data preparation for training and testing separately. The training data process the input data with their parameters and classify them. After the completion of training, data were tested with the other remaining datasets. After the completion of training, testing of the data validates the results as output.Figure 1
Regression working flow chart.


#### 5.2.1. ANN Result Analysis

Artificial neural networks are becoming more popular because they could be used to solve a broad variety of problems in science and engineering. Predictive statistical models of complex processes that are nonlinear in nature, such as biological systems, are often employed in this technique. It is possible to simulate a broad spectrum of complex system behaviour with the help of an ANN. Neuron components are used to describe the ANN’s functioning, which is much more like a normal human brain. To put it another way, “garbage in and garbage out” refers to a way of computer works, as input parameters are used to duplicate the system’s process in order to decide the output. To build an ANN model, the input and output components must be included with the latter being controlled by the former. The ANN principle is made up of a network of interconnected neurons, each of which carries its own weight. This means that the model’s answer is found by multiplying the weight by the network’s total number of signals. There are three layers in a basic ANN network: the input layer, the hidden layers, and the output layer. Before data training, the input and output layers are defined, and the hidden layer on the other hand is discovered by trial and error during data training. Figure2 represents a common ANN architectural model. It describes the initially put input of 10 datasets of 10-attribute numeric type and after applying the regression method multilayer perception on that. After the input is applied, target the 15 classes.Figure 2
ANN architecture that best models the performance of the geopolymer concrete.The model is composed of input factors (x1,x2,x3,x4⋯xn) and weights (w1,w2,w3,w4⋯wn), with weights (y1,y2,y3,y4⋯yn) for each factor. Singular value or sum function (sigmoid) processing is the ultimate processing method, and it has the final impact on the outputs. As a result, equation (1) provides a broad description of the analogy.It has been shown in the study that the ANN technique is capable of anticipating significant responses regardless of whether the data being processed is riddled with errors or missing information. The ANN method is divided into three stages which are learning, training, and model performance evaluation. The first of these efforts is education. The output variables are predicted correctly during the training stage, and the network’s weights and biases (supervised or unsupervised) are modified to ensure that the output variables are predicted reliably. The supervised training approach constructs a model using previously completed experimental data, while the unsupervised training method does not employ real-world input and output data. During the testing stage, the network may react to the input without modifying the overall network architecture.After a series of trials and errors, the best ANN model may be found at the end of each stage of development. At some point in the learning process, Alshihri realized that it was feasible to continue developing a large number of networks, at which time the process could be paused and evaluated at various points in the learning process. Use different random weights to reexamine the network, and keep going until you get the results you want. When it comes to selecting the best neural network model,R2 (result coefficient) and MSE (mean square error) are the most important metrics to consider. MATLAB software was used to evaluate the ANN model’s performance. The straining and recall techniques were used to build the model utilizing the error backpropagation approach. Lee claims that this approach can deal with issues involving several variables (multidimensional). Table 8 shows the datasets that were used for model development in this study. An LM multilayer feedforward backpropagation model was used to train the data, which is easily accessible in the MATLAB computing environment and is based on the feedforward backpropagation model. A total of 250 samples of data (including those from this study and others like it) were used to compile the database for this study’s findings. Seventy percent of the input data was utilized in the learning phase, and fifteen percent was used in each of the testing and validation stages. The data in MATLAB were automatically normalized rather than manually dividing using the maximum values, which was done by hand in MATLAB. The procedure was done multiple times until the best model that met the R2 and MSE conditions was found.Table 8
Input and output specification for the model development.
Input dataMinimumMaximumFly ash (kg/m3)405101.25GGBFS (kg/m3)0303.75Extra water (kg/m3)0121.5Slump (mm)0190Density (kg/m3)24062506Coarse aggregate (kg/m3)12691269Fine aggregate (kg/m3)683683NaOH solution (kg/m3)8181Sodium silicate (kg/m3)8181Superplasticiser (kg/m3)4.054.05Output dataCompressive strength (MPa)7 days16.224.414 days18.129.128 days19.932.142 days20.332.656 days20.832.9Splitting tensile (MPa)7 days1.92.914 days2.23.828 days2.84.642 days2.94.756 days34.8Flexural strength (MPa)7 days2.13.114 days2.4428 days3542 days3.25.256 days3.35.3Geopolymer concrete’s compressive strength, splitting tensile strength, and flexural strength may be calculated by using an empirical model. Input data of the geopolymer concrete that was formed included fly ash and GGBS as well as extra water, slump value, density, sodium hydroxide, sodium silicate, coarse and fine particles, and superplasticiser. The output data included the kind of concrete produced and the type of concrete produced. The most important output variables are compression strength, split tensile strength, and flexural strength. Various testing periods of 7, 14, 28, 42, and 56 days were included in the output data (age). To achieve the lowest feasible mean squared error (MSE), the ANN architecture shown in Figure2 has been optimized to represent the concrete’s behaviour. An estimated ten neurons are found in the input phase, twelve are in the hidden layer, and fifteen are in the output layer. For the selected model, the correlation and error analysis results are shown in Tables 9, 10, and 11. Results in Tables 5, 6, and 7 show that the model selected fits the criterion for error performance in a neural network model of artificial intelligence. In the case when a model’s R2 is near one and its MSE is modest, it shows that the predicted and actual data are perfectly correlated. When it comes to ANN models, it is widely accepted that the better the model, the better it is in foretelling the future behaviour of a system. Errors were calculated by using the following mathematical formulas to determine the R2, MAE, RMSE, RAE, and RRSE:
(3)R2=n∑xiyi−∑xi∑yi2n∑xi2−∑xi2n∑yi2−∑yi2,MAE=1n∑i=1nxi−yi,RMSE=1n∑i=1nxi−yi2,RAE=∑i=1nxi−yi∑i=1nxi−1/n∑i=1nxi,RRSE=∑i=1nxi−yi2∑i=1nxi−1/n∑i=1nxi2,where “x” represents the experimental value, “y” represents the predicted value, and “n” represents the total number of values.Table 9
Compressive strength performance analysis evaluation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANNR210.999210.99970.99990.99820.99990.99910.9984MAE00.088600.07390.020.25930.020.194300.258RMSE00.114600.1040.04470.31930.04470.237400.3088RAE05.19%0%3.14%0.81%10.47%0.81%7.82%0%10.54%RRSE04.98%0%3.33%1.30%9.30%1.29%6.87%0%9.08%Table 10
Splitting tensile strength performance analysis evaluation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANNR210.999410.997810.999110.998410.9983MAE00.010800.033300.026700.035900.0363RMSE00.01300.045900.035600.048400.05RAE04.56%08.40%06.15%07.77%07.63%RRSE04.50%09.52%06.50%08.44%08.49%Table 11
Flexural tensile strength performance analysis evaluation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANNR210.998510.998910.998710.999810.9999MAE00.015900.018800.031900.014400.0114RMSE00.018500.026900.042300.018800.0149RAE07.25%05.05%07.13%03.18%02.38%RRSE06.64%06.03%07.64%03.38%02.56%As shown by the chosen network architecture’s performance, the projected and actual testing results on geopolymer concrete are highly compatible. While maintaining a high degree of accuracy in its predictions, the chosen model can provide both input and output data for the tested concrete. A low matching percent error for the anticipated strength further supports the model’s usefulness, indicating that the prediction made by this model is statistically reliable. This conclusion shows that the model’s performance may be relied on in absolute terms because of the proximity of the datasets (predicted and actual). This demonstrates that the selected model is capable of accurately responding to a system with a high degree of confidence in its performance. Tables12, 13, and 14 show the validation of results between actual and predicted values by both the ANN model and the random tree method. Tables 9, 10, and 11 show the performance of the machine learning method model for the prediction of mechanical strength to the actual results found through experimental analysis.Table 12
Compressive strength validation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysActualPredictedActualPredictedActualPredictedActualPredictedActualPredictedRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANN21.521.521.4825.425.425.38828.328.328.26528.728.728.671292928.95924.424.424.17329.129.128.95532.13231.82232.632.532.36132.932.932.59922.922.922.90426.426.426.36729.629.629.39330302930.230.229.92621.721.721.53825.125.124.88228.428.427.806292928.54629.329.328.7716.216.216.20418.118.118.11119.919.919.92820.320.320.33820.820.820.83421.321.321.17723.823.823.65326.926.926.47827.327.326.9727.727.727.30823.623.623.4727.627.627.47730.830.830.4231.231.230.93731.631.631.20424.124.124.1928.928.928.93931.93231.95932.432.532.45232.632.632.683242423.88628.428.428.40131.631.631.156323231.71432.432.431.98223.423.423.38727.627.627.58830.230.230.05230.830.830.71631.131.130.99Table 13
Splitting tensile strength validation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysActualPredictedActualPredictedActualPredictedActualPredictedActualPredictedRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANN2.32.32.2972.82.82.8023.13.13.1033.23.23.2043.23.23.2032.92.92.8763.83.83.8144.64.64.6154.74.74.7164.84.84.8112.72.72.6933.63.63.6474.34.34.3324.54.54.5424.64.64.6412.62.62.5883.43.43.4453.93.93.9434.14.14.1624.24.24.2661.91.91.8992.22.22.222.82.82.8152.92.92.92333.0222.22.22.1832.92.92.9743.63.63.6423.83.83.8543.93.93.9552.62.62.5813.43.43.502444.0834.24.24.3144.34.34.4192.82.82.8093.83.83.7974.44.44.3994.64.64.5984.74.74.6992.72.72.6863.63.63.6134.34.34.3274.54.54.5324.64.64.632.52.52.5023.23.23.2133.93.93.9074.24.24.2134.34.34.316Table 14
Flexural strength validation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysActualPredictedActualPredictedActualPredictedActualPredictedActualPredictedRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANN2.52.52.498333.0023.53.53.5053.63.63.6023.63.63.6023.13.13.074444.014555.0285.25.25.2155.35.35.3122.92.92.9123.73.73.7284.54.54.544.74.74.7194.94.94.9142.72.72.7183.63.63.6214.24.24.2384.44.44.4154.64.64.6132.12.12.1112.42.42.412333.0163.23.23.2063.33.33.3052.52.52.5213.13.13.123.73.73.7623.93.93.928444.0222.82.82.8373.53.53.5724.24.24.2954.44.44.4424.54.54.533333.0123.83.83.7894.64.64.5994.74.74.74.84.84.82.92.92.9093.63.63.6024.44.44.434.64.64.6144.74.74.7122.72.72.7113.23.23.207444.0054.24.24.2034.34.34.302


#### 5.2.2. Random Forest Results

We provide a simple and effective random forest in this study. It is executed on the server to process the data collected from the input. The random forest algorithm illustrates the suggested model’s definition and process flow, respectively. Table12 shows the validation between the compressive strength of actual output vs. predicted output by both ANN and random tree. Table 9 shows the performance of prediction with their limited error of compressive strength. Similarly, Tables 13 and 14 show validation of splitting tensile and flexural strength between actual experimental and predicted values. Tables 10 and 11 show the performance of prediction with their limited error of splitting tensile and flexural strength.Table12 describes the compressive strength value at 7 days, 14 days, 28 days, 42 days, and 56 days, which includes the actual value and predicted value. ANN and random forest tree machine learning methods were used to predict the compressive strength. The random forest tree method predicted a more accurate compressive strength than the ANN method. Ten data are used at the same time for individual compressive strength. This table contains the 150 datasets of the compressive strength, whereas the actual data are 50 and the predicted data are 100.The analysis, known as the sensitivity analysis, was conducted to determine the impact of each variable on the prediction of the mechanical strength of GPC. It is important to understand how each of the input parameters will affect the projected outcome because they are crucial to the accuracy of the models that are used for prediction. Each input parameter contributed to the predicted output of the mechanical strength of GPC.Table9 depicts the coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root-relative square error (RRSE) values of predicted compressive strength to the actual experimental results of both machine learning methods. The random forest tree model is more relevant to the ANN model in all-day compressive strength. The random forest tree method shows a determination coefficient value of 1 at 7 days, 14 days, and 56 days, whereas the ANN model does not show a determination coefficient value of 1 in any day prediction.Table13 describes the splitting tensile strength value at 7 days, 14 days, 28 days, 42 days, and 56 days, which includes the actual value and predicted value. ANN and random forest tree machine learning methods were used to predict the splitting tensile. The random forest tree method predicted more accurate splitting tensile strength than the ANN method. Ten data are used at the same time for individual compressive strength. This table contains the 150 datasets of the compressive strength, whereas the actual data are 50 and the predicted data are 100.Table10 depicts the coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root-relative square error (RRSE) values of predicted splitting tensile strength to the actual experimental results of both machine learning methods. The random forest tree model is more relevant to the ANN model in all-day splitting tensile strength. The random forest tree method shows a determination coefficient value of 1 at 7 days, 14 days, 28 days, 42 days, and 56 days, whereas the ANN model does not show a determination coefficient value of 1 in any day prediction.Table14 describes the flexural strength value at 7 days, 14 days, 28 days, 42 days, and 56 days, which includes the actual value and predicted value. ANN and random forest tree machine learning methods were used to predict flexural strength. The random forest tree method predicted more accurate flexural strength than the ANN method. Ten data are used at the same time for individual compressive strength. This table contains the 150 datasets of the compressive strength, whereas the actual data are 50 and the predicted data are 100.Table11 depicts the coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root-relative square error (RRSE) values of predicted flexural tensile strength to the actual experimental results of both machine learning methods. The random forest tree model is more relevant to the ANN model in all-day flexural strength. The random forest tree method shows a determination coefficient value of 1 at 7 days, 14 days, 28 days, 42 days, and 56 days, whereas the ANN model does not show a determination coefficient value of 1 in any day prediction.


## 5.1. Experimental Results

The experimental section describes the slump, density, compressive strength, splitting tensile strength, and flexural strength of the all-mix designs. Slump tests were conducted before the casting of moulds of the plastic mix of the GPC. The density of the design mix of the GPC was calculated after the 28 days of the casting by the weight of the cube specimens before the compressive strength test. The mechanical strength including compressive strength, splitting tensile strength, and flexural strength was tested after 7 days, 14 days, 28 days, 42 days, and 56 days of the GPC mix casting. All the mechanical properties vary similarly with the mixed design. After 28 days, the compressive strength and all other strengths gained 95 percent strength of total strength. The mechanical strength varied from the ratio of GGBFS to fly ash from 0.00 to 0.75 and got the optimum point at a 0.25 ratio mix. The GPC mix varied the extra water from 5% to 30% of binder content. The optimum point of the mechanical properties was found at 20% of the binder content. The maximum compressive strength, splitting tensile, and flexural strength are 32.9 MPa, 4.8 MPa, and 5.3 MPa, respectively, after 56 days of casting. Tables5–7 depict the compressive strength, splitting tensile strength, and flexural strength values found after the experimental tests.Table 5
Compressive strength in MPa.
Mix designs7 days14 days28 days42 days56 daysM121.525.428.328.729.0M224.429.132.132.632.9M322.926.429.63030.2M421.725.128.429.029.3M516.218.119.920.320.8M621.323.826.927.327.7M723.627.630.831.231.6M824.128.931.932.432.6M924.028.431.632.032.4M1023.427.630.230.831.1Table 6
Splitting tensile strength in MPa.
Mix designs7 days14 days28 days42 days56 daysM12.32.83.13.23.2M22.93.84.64.74.8M32.73.64.34.54.6M42.63.43.94.14.2M51.92.22.82.93.0M62.22.93.63.83.9M72.63.44.04.24.3M82.83.84.44.64.7M92.73.64.34.54.6M102.53.23.94.24.3Table 7
Flexural strength in MPa.
Mix designs7 days14 days28 days42 days56 daysM12.53.03.53.63.6M23.14.05.05.25.3M32.93.74.54.74.9M42.73.64.24.44.6M52.12.43.03.23.3M62.53.13.73.94.0M72.83.54.24.44.5M83.03.84.64.74.8M92.93.64.44.64.7M102.73.24.04.24.3


## 5.2. Modelling Analysis

In the modelling analysis, ANN and random forest algorithm machine learning methods are used for the prediction of compressive strength, splitting tensile strength, and flexural strength. Figure1 shows the working flow chart of the regression model. It shows the total process of the regression work. It starts with data collection which includes the input and output data with their variables. After that, it shows the data preparation for training and testing separately. The training data process the input data with their parameters and classify them. After the completion of training, data were tested with the other remaining datasets. After the completion of training, testing of the data validates the results as output.Figure 1
Regression working flow chart.


### 5.2.1. ANN Result Analysis

Artificial neural networks are becoming more popular because they could be used to solve a broad variety of problems in science and engineering. Predictive statistical models of complex processes that are nonlinear in nature, such as biological systems, are often employed in this technique. It is possible to simulate a broad spectrum of complex system behaviour with the help of an ANN. Neuron components are used to describe the ANN’s functioning, which is much more like a normal human brain. To put it another way, “garbage in and garbage out” refers to a way of computer works, as input parameters are used to duplicate the system’s process in order to decide the output. To build an ANN model, the input and output components must be included with the latter being controlled by the former. The ANN principle is made up of a network of interconnected neurons, each of which carries its own weight. This means that the model’s answer is found by multiplying the weight by the network’s total number of signals. There are three layers in a basic ANN network: the input layer, the hidden layers, and the output layer. Before data training, the input and output layers are defined, and the hidden layer on the other hand is discovered by trial and error during data training. Figure2 represents a common ANN architectural model. It describes the initially put input of 10 datasets of 10-attribute numeric type and after applying the regression method multilayer perception on that. After the input is applied, target the 15 classes.Figure 2
ANN architecture that best models the performance of the geopolymer concrete.The model is composed of input factors (x1,x2,x3,x4⋯xn) and weights (w1,w2,w3,w4⋯wn), with weights (y1,y2,y3,y4⋯yn) for each factor. Singular value or sum function (sigmoid) processing is the ultimate processing method, and it has the final impact on the outputs. As a result, equation (1) provides a broad description of the analogy.It has been shown in the study that the ANN technique is capable of anticipating significant responses regardless of whether the data being processed is riddled with errors or missing information. The ANN method is divided into three stages which are learning, training, and model performance evaluation. The first of these efforts is education. The output variables are predicted correctly during the training stage, and the network’s weights and biases (supervised or unsupervised) are modified to ensure that the output variables are predicted reliably. The supervised training approach constructs a model using previously completed experimental data, while the unsupervised training method does not employ real-world input and output data. During the testing stage, the network may react to the input without modifying the overall network architecture.After a series of trials and errors, the best ANN model may be found at the end of each stage of development. At some point in the learning process, Alshihri realized that it was feasible to continue developing a large number of networks, at which time the process could be paused and evaluated at various points in the learning process. Use different random weights to reexamine the network, and keep going until you get the results you want. When it comes to selecting the best neural network model,R2 (result coefficient) and MSE (mean square error) are the most important metrics to consider. MATLAB software was used to evaluate the ANN model’s performance. The straining and recall techniques were used to build the model utilizing the error backpropagation approach. Lee claims that this approach can deal with issues involving several variables (multidimensional). Table 8 shows the datasets that were used for model development in this study. An LM multilayer feedforward backpropagation model was used to train the data, which is easily accessible in the MATLAB computing environment and is based on the feedforward backpropagation model. A total of 250 samples of data (including those from this study and others like it) were used to compile the database for this study’s findings. Seventy percent of the input data was utilized in the learning phase, and fifteen percent was used in each of the testing and validation stages. The data in MATLAB were automatically normalized rather than manually dividing using the maximum values, which was done by hand in MATLAB. The procedure was done multiple times until the best model that met the R2 and MSE conditions was found.Table 8
Input and output specification for the model development.
Input dataMinimumMaximumFly ash (kg/m3)405101.25GGBFS (kg/m3)0303.75Extra water (kg/m3)0121.5Slump (mm)0190Density (kg/m3)24062506Coarse aggregate (kg/m3)12691269Fine aggregate (kg/m3)683683NaOH solution (kg/m3)8181Sodium silicate (kg/m3)8181Superplasticiser (kg/m3)4.054.05Output dataCompressive strength (MPa)7 days16.224.414 days18.129.128 days19.932.142 days20.332.656 days20.832.9Splitting tensile (MPa)7 days1.92.914 days2.23.828 days2.84.642 days2.94.756 days34.8Flexural strength (MPa)7 days2.13.114 days2.4428 days3542 days3.25.256 days3.35.3Geopolymer concrete’s compressive strength, splitting tensile strength, and flexural strength may be calculated by using an empirical model. Input data of the geopolymer concrete that was formed included fly ash and GGBS as well as extra water, slump value, density, sodium hydroxide, sodium silicate, coarse and fine particles, and superplasticiser. The output data included the kind of concrete produced and the type of concrete produced. The most important output variables are compression strength, split tensile strength, and flexural strength. Various testing periods of 7, 14, 28, 42, and 56 days were included in the output data (age). To achieve the lowest feasible mean squared error (MSE), the ANN architecture shown in Figure2 has been optimized to represent the concrete’s behaviour. An estimated ten neurons are found in the input phase, twelve are in the hidden layer, and fifteen are in the output layer. For the selected model, the correlation and error analysis results are shown in Tables 9, 10, and 11. Results in Tables 5, 6, and 7 show that the model selected fits the criterion for error performance in a neural network model of artificial intelligence. In the case when a model’s R2 is near one and its MSE is modest, it shows that the predicted and actual data are perfectly correlated. When it comes to ANN models, it is widely accepted that the better the model, the better it is in foretelling the future behaviour of a system. Errors were calculated by using the following mathematical formulas to determine the R2, MAE, RMSE, RAE, and RRSE:
(3)R2=n∑xiyi−∑xi∑yi2n∑xi2−∑xi2n∑yi2−∑yi2,MAE=1n∑i=1nxi−yi,RMSE=1n∑i=1nxi−yi2,RAE=∑i=1nxi−yi∑i=1nxi−1/n∑i=1nxi,RRSE=∑i=1nxi−yi2∑i=1nxi−1/n∑i=1nxi2,where “x” represents the experimental value, “y” represents the predicted value, and “n” represents the total number of values.Table 9
Compressive strength performance analysis evaluation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANNR210.999210.99970.99990.99820.99990.99910.9984MAE00.088600.07390.020.25930.020.194300.258RMSE00.114600.1040.04470.31930.04470.237400.3088RAE05.19%0%3.14%0.81%10.47%0.81%7.82%0%10.54%RRSE04.98%0%3.33%1.30%9.30%1.29%6.87%0%9.08%Table 10
Splitting tensile strength performance analysis evaluation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANNR210.999410.997810.999110.998410.9983MAE00.010800.033300.026700.035900.0363RMSE00.01300.045900.035600.048400.05RAE04.56%08.40%06.15%07.77%07.63%RRSE04.50%09.52%06.50%08.44%08.49%Table 11
Flexural tensile strength performance analysis evaluation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANNR210.998510.998910.998710.999810.9999MAE00.015900.018800.031900.014400.0114RMSE00.018500.026900.042300.018800.0149RAE07.25%05.05%07.13%03.18%02.38%RRSE06.64%06.03%07.64%03.38%02.56%As shown by the chosen network architecture’s performance, the projected and actual testing results on geopolymer concrete are highly compatible. While maintaining a high degree of accuracy in its predictions, the chosen model can provide both input and output data for the tested concrete. A low matching percent error for the anticipated strength further supports the model’s usefulness, indicating that the prediction made by this model is statistically reliable. This conclusion shows that the model’s performance may be relied on in absolute terms because of the proximity of the datasets (predicted and actual). This demonstrates that the selected model is capable of accurately responding to a system with a high degree of confidence in its performance. Tables12, 13, and 14 show the validation of results between actual and predicted values by both the ANN model and the random tree method. Tables 9, 10, and 11 show the performance of the machine learning method model for the prediction of mechanical strength to the actual results found through experimental analysis.Table 12
Compressive strength validation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysActualPredictedActualPredictedActualPredictedActualPredictedActualPredictedRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANN21.521.521.4825.425.425.38828.328.328.26528.728.728.671292928.95924.424.424.17329.129.128.95532.13231.82232.632.532.36132.932.932.59922.922.922.90426.426.426.36729.629.629.39330302930.230.229.92621.721.721.53825.125.124.88228.428.427.806292928.54629.329.328.7716.216.216.20418.118.118.11119.919.919.92820.320.320.33820.820.820.83421.321.321.17723.823.823.65326.926.926.47827.327.326.9727.727.727.30823.623.623.4727.627.627.47730.830.830.4231.231.230.93731.631.631.20424.124.124.1928.928.928.93931.93231.95932.432.532.45232.632.632.683242423.88628.428.428.40131.631.631.156323231.71432.432.431.98223.423.423.38727.627.627.58830.230.230.05230.830.830.71631.131.130.99Table 13
Splitting tensile strength validation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysActualPredictedActualPredictedActualPredictedActualPredictedActualPredictedRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANN2.32.32.2972.82.82.8023.13.13.1033.23.23.2043.23.23.2032.92.92.8763.83.83.8144.64.64.6154.74.74.7164.84.84.8112.72.72.6933.63.63.6474.34.34.3324.54.54.5424.64.64.6412.62.62.5883.43.43.4453.93.93.9434.14.14.1624.24.24.2661.91.91.8992.22.22.222.82.82.8152.92.92.92333.0222.22.22.1832.92.92.9743.63.63.6423.83.83.8543.93.93.9552.62.62.5813.43.43.502444.0834.24.24.3144.34.34.4192.82.82.8093.83.83.7974.44.44.3994.64.64.5984.74.74.6992.72.72.6863.63.63.6134.34.34.3274.54.54.5324.64.64.632.52.52.5023.23.23.2133.93.93.9074.24.24.2134.34.34.316Table 14
Flexural strength validation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysActualPredictedActualPredictedActualPredictedActualPredictedActualPredictedRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANN2.52.52.498333.0023.53.53.5053.63.63.6023.63.63.6023.13.13.074444.014555.0285.25.25.2155.35.35.3122.92.92.9123.73.73.7284.54.54.544.74.74.7194.94.94.9142.72.72.7183.63.63.6214.24.24.2384.44.44.4154.64.64.6132.12.12.1112.42.42.412333.0163.23.23.2063.33.33.3052.52.52.5213.13.13.123.73.73.7623.93.93.928444.0222.82.82.8373.53.53.5724.24.24.2954.44.44.4424.54.54.533333.0123.83.83.7894.64.64.5994.74.74.74.84.84.82.92.92.9093.63.63.6024.44.44.434.64.64.6144.74.74.7122.72.72.7113.23.23.207444.0054.24.24.2034.34.34.302


### 5.2.2. Random Forest Results

We provide a simple and effective random forest in this study. It is executed on the server to process the data collected from the input. The random forest algorithm illustrates the suggested model’s definition and process flow, respectively. Table12 shows the validation between the compressive strength of actual output vs. predicted output by both ANN and random tree. Table 9 shows the performance of prediction with their limited error of compressive strength. Similarly, Tables 13 and 14 show validation of splitting tensile and flexural strength between actual experimental and predicted values. Tables 10 and 11 show the performance of prediction with their limited error of splitting tensile and flexural strength.Table12 describes the compressive strength value at 7 days, 14 days, 28 days, 42 days, and 56 days, which includes the actual value and predicted value. ANN and random forest tree machine learning methods were used to predict the compressive strength. The random forest tree method predicted a more accurate compressive strength than the ANN method. Ten data are used at the same time for individual compressive strength. This table contains the 150 datasets of the compressive strength, whereas the actual data are 50 and the predicted data are 100.The analysis, known as the sensitivity analysis, was conducted to determine the impact of each variable on the prediction of the mechanical strength of GPC. It is important to understand how each of the input parameters will affect the projected outcome because they are crucial to the accuracy of the models that are used for prediction. Each input parameter contributed to the predicted output of the mechanical strength of GPC.Table9 depicts the coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root-relative square error (RRSE) values of predicted compressive strength to the actual experimental results of both machine learning methods. The random forest tree model is more relevant to the ANN model in all-day compressive strength. The random forest tree method shows a determination coefficient value of 1 at 7 days, 14 days, and 56 days, whereas the ANN model does not show a determination coefficient value of 1 in any day prediction.Table13 describes the splitting tensile strength value at 7 days, 14 days, 28 days, 42 days, and 56 days, which includes the actual value and predicted value. ANN and random forest tree machine learning methods were used to predict the splitting tensile. The random forest tree method predicted more accurate splitting tensile strength than the ANN method. Ten data are used at the same time for individual compressive strength. This table contains the 150 datasets of the compressive strength, whereas the actual data are 50 and the predicted data are 100.Table10 depicts the coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root-relative square error (RRSE) values of predicted splitting tensile strength to the actual experimental results of both machine learning methods. The random forest tree model is more relevant to the ANN model in all-day splitting tensile strength. The random forest tree method shows a determination coefficient value of 1 at 7 days, 14 days, 28 days, 42 days, and 56 days, whereas the ANN model does not show a determination coefficient value of 1 in any day prediction.Table14 describes the flexural strength value at 7 days, 14 days, 28 days, 42 days, and 56 days, which includes the actual value and predicted value. ANN and random forest tree machine learning methods were used to predict flexural strength. The random forest tree method predicted more accurate flexural strength than the ANN method. Ten data are used at the same time for individual compressive strength. This table contains the 150 datasets of the compressive strength, whereas the actual data are 50 and the predicted data are 100.Table11 depicts the coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root-relative square error (RRSE) values of predicted flexural tensile strength to the actual experimental results of both machine learning methods. The random forest tree model is more relevant to the ANN model in all-day flexural strength. The random forest tree method shows a determination coefficient value of 1 at 7 days, 14 days, 28 days, 42 days, and 56 days, whereas the ANN model does not show a determination coefficient value of 1 in any day prediction.


## 5.2.1. ANN Result Analysis

Artificial neural networks are becoming more popular because they could be used to solve a broad variety of problems in science and engineering. Predictive statistical models of complex processes that are nonlinear in nature, such as biological systems, are often employed in this technique. It is possible to simulate a broad spectrum of complex system behaviour with the help of an ANN. Neuron components are used to describe the ANN’s functioning, which is much more like a normal human brain. To put it another way, “garbage in and garbage out” refers to a way of computer works, as input parameters are used to duplicate the system’s process in order to decide the output. To build an ANN model, the input and output components must be included with the latter being controlled by the former. The ANN principle is made up of a network of interconnected neurons, each of which carries its own weight. This means that the model’s answer is found by multiplying the weight by the network’s total number of signals. There are three layers in a basic ANN network: the input layer, the hidden layers, and the output layer. Before data training, the input and output layers are defined, and the hidden layer on the other hand is discovered by trial and error during data training. Figure2 represents a common ANN architectural model. It describes the initially put input of 10 datasets of 10-attribute numeric type and after applying the regression method multilayer perception on that. After the input is applied, target the 15 classes.Figure 2
ANN architecture that best models the performance of the geopolymer concrete.The model is composed of input factors (x1,x2,x3,x4⋯xn) and weights (w1,w2,w3,w4⋯wn), with weights (y1,y2,y3,y4⋯yn) for each factor. Singular value or sum function (sigmoid) processing is the ultimate processing method, and it has the final impact on the outputs. As a result, equation (1) provides a broad description of the analogy.It has been shown in the study that the ANN technique is capable of anticipating significant responses regardless of whether the data being processed is riddled with errors or missing information. The ANN method is divided into three stages which are learning, training, and model performance evaluation. The first of these efforts is education. The output variables are predicted correctly during the training stage, and the network’s weights and biases (supervised or unsupervised) are modified to ensure that the output variables are predicted reliably. The supervised training approach constructs a model using previously completed experimental data, while the unsupervised training method does not employ real-world input and output data. During the testing stage, the network may react to the input without modifying the overall network architecture.After a series of trials and errors, the best ANN model may be found at the end of each stage of development. At some point in the learning process, Alshihri realized that it was feasible to continue developing a large number of networks, at which time the process could be paused and evaluated at various points in the learning process. Use different random weights to reexamine the network, and keep going until you get the results you want. When it comes to selecting the best neural network model,R2 (result coefficient) and MSE (mean square error) are the most important metrics to consider. MATLAB software was used to evaluate the ANN model’s performance. The straining and recall techniques were used to build the model utilizing the error backpropagation approach. Lee claims that this approach can deal with issues involving several variables (multidimensional). Table 8 shows the datasets that were used for model development in this study. An LM multilayer feedforward backpropagation model was used to train the data, which is easily accessible in the MATLAB computing environment and is based on the feedforward backpropagation model. A total of 250 samples of data (including those from this study and others like it) were used to compile the database for this study’s findings. Seventy percent of the input data was utilized in the learning phase, and fifteen percent was used in each of the testing and validation stages. The data in MATLAB were automatically normalized rather than manually dividing using the maximum values, which was done by hand in MATLAB. The procedure was done multiple times until the best model that met the R2 and MSE conditions was found.Table 8
Input and output specification for the model development.
Input dataMinimumMaximumFly ash (kg/m3)405101.25GGBFS (kg/m3)0303.75Extra water (kg/m3)0121.5Slump (mm)0190Density (kg/m3)24062506Coarse aggregate (kg/m3)12691269Fine aggregate (kg/m3)683683NaOH solution (kg/m3)8181Sodium silicate (kg/m3)8181Superplasticiser (kg/m3)4.054.05Output dataCompressive strength (MPa)7 days16.224.414 days18.129.128 days19.932.142 days20.332.656 days20.832.9Splitting tensile (MPa)7 days1.92.914 days2.23.828 days2.84.642 days2.94.756 days34.8Flexural strength (MPa)7 days2.13.114 days2.4428 days3542 days3.25.256 days3.35.3Geopolymer concrete’s compressive strength, splitting tensile strength, and flexural strength may be calculated by using an empirical model. Input data of the geopolymer concrete that was formed included fly ash and GGBS as well as extra water, slump value, density, sodium hydroxide, sodium silicate, coarse and fine particles, and superplasticiser. The output data included the kind of concrete produced and the type of concrete produced. The most important output variables are compression strength, split tensile strength, and flexural strength. Various testing periods of 7, 14, 28, 42, and 56 days were included in the output data (age). To achieve the lowest feasible mean squared error (MSE), the ANN architecture shown in Figure2 has been optimized to represent the concrete’s behaviour. An estimated ten neurons are found in the input phase, twelve are in the hidden layer, and fifteen are in the output layer. For the selected model, the correlation and error analysis results are shown in Tables 9, 10, and 11. Results in Tables 5, 6, and 7 show that the model selected fits the criterion for error performance in a neural network model of artificial intelligence. In the case when a model’s R2 is near one and its MSE is modest, it shows that the predicted and actual data are perfectly correlated. When it comes to ANN models, it is widely accepted that the better the model, the better it is in foretelling the future behaviour of a system. Errors were calculated by using the following mathematical formulas to determine the R2, MAE, RMSE, RAE, and RRSE:
(3)R2=n∑xiyi−∑xi∑yi2n∑xi2−∑xi2n∑yi2−∑yi2,MAE=1n∑i=1nxi−yi,RMSE=1n∑i=1nxi−yi2,RAE=∑i=1nxi−yi∑i=1nxi−1/n∑i=1nxi,RRSE=∑i=1nxi−yi2∑i=1nxi−1/n∑i=1nxi2,where “x” represents the experimental value, “y” represents the predicted value, and “n” represents the total number of values.Table 9
Compressive strength performance analysis evaluation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANNR210.999210.99970.99990.99820.99990.99910.9984MAE00.088600.07390.020.25930.020.194300.258RMSE00.114600.1040.04470.31930.04470.237400.3088RAE05.19%0%3.14%0.81%10.47%0.81%7.82%0%10.54%RRSE04.98%0%3.33%1.30%9.30%1.29%6.87%0%9.08%Table 10
Splitting tensile strength performance analysis evaluation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANNR210.999410.997810.999110.998410.9983MAE00.010800.033300.026700.035900.0363RMSE00.01300.045900.035600.048400.05RAE04.56%08.40%06.15%07.77%07.63%RRSE04.50%09.52%06.50%08.44%08.49%Table 11
Flexural tensile strength performance analysis evaluation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANNR210.998510.998910.998710.999810.9999MAE00.015900.018800.031900.014400.0114RMSE00.018500.026900.042300.018800.0149RAE07.25%05.05%07.13%03.18%02.38%RRSE06.64%06.03%07.64%03.38%02.56%As shown by the chosen network architecture’s performance, the projected and actual testing results on geopolymer concrete are highly compatible. While maintaining a high degree of accuracy in its predictions, the chosen model can provide both input and output data for the tested concrete. A low matching percent error for the anticipated strength further supports the model’s usefulness, indicating that the prediction made by this model is statistically reliable. This conclusion shows that the model’s performance may be relied on in absolute terms because of the proximity of the datasets (predicted and actual). This demonstrates that the selected model is capable of accurately responding to a system with a high degree of confidence in its performance. Tables12, 13, and 14 show the validation of results between actual and predicted values by both the ANN model and the random tree method. Tables 9, 10, and 11 show the performance of the machine learning method model for the prediction of mechanical strength to the actual results found through experimental analysis.Table 12
Compressive strength validation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysActualPredictedActualPredictedActualPredictedActualPredictedActualPredictedRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANN21.521.521.4825.425.425.38828.328.328.26528.728.728.671292928.95924.424.424.17329.129.128.95532.13231.82232.632.532.36132.932.932.59922.922.922.90426.426.426.36729.629.629.39330302930.230.229.92621.721.721.53825.125.124.88228.428.427.806292928.54629.329.328.7716.216.216.20418.118.118.11119.919.919.92820.320.320.33820.820.820.83421.321.321.17723.823.823.65326.926.926.47827.327.326.9727.727.727.30823.623.623.4727.627.627.47730.830.830.4231.231.230.93731.631.631.20424.124.124.1928.928.928.93931.93231.95932.432.532.45232.632.632.683242423.88628.428.428.40131.631.631.156323231.71432.432.431.98223.423.423.38727.627.627.58830.230.230.05230.830.830.71631.131.130.99Table 13
Splitting tensile strength validation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysActualPredictedActualPredictedActualPredictedActualPredictedActualPredictedRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANN2.32.32.2972.82.82.8023.13.13.1033.23.23.2043.23.23.2032.92.92.8763.83.83.8144.64.64.6154.74.74.7164.84.84.8112.72.72.6933.63.63.6474.34.34.3324.54.54.5424.64.64.6412.62.62.5883.43.43.4453.93.93.9434.14.14.1624.24.24.2661.91.91.8992.22.22.222.82.82.8152.92.92.92333.0222.22.22.1832.92.92.9743.63.63.6423.83.83.8543.93.93.9552.62.62.5813.43.43.502444.0834.24.24.3144.34.34.4192.82.82.8093.83.83.7974.44.44.3994.64.64.5984.74.74.6992.72.72.6863.63.63.6134.34.34.3274.54.54.5324.64.64.632.52.52.5023.23.23.2133.93.93.9074.24.24.2134.34.34.316Table 14
Flexural strength validation between actual experimental results and predicted results.
7 days14 days28 days42 days56 daysActualPredictedActualPredictedActualPredictedActualPredictedActualPredictedRandom treeANNRandom treeANNRandom treeANNRandom treeANNRandom treeANN2.52.52.498333.0023.53.53.5053.63.63.6023.63.63.6023.13.13.074444.014555.0285.25.25.2155.35.35.3122.92.92.9123.73.73.7284.54.54.544.74.74.7194.94.94.9142.72.72.7183.63.63.6214.24.24.2384.44.44.4154.64.64.6132.12.12.1112.42.42.412333.0163.23.23.2063.33.33.3052.52.52.5213.13.13.123.73.73.7623.93.93.928444.0222.82.82.8373.53.53.5724.24.24.2954.44.44.4424.54.54.533333.0123.83.83.7894.64.64.5994.74.74.74.84.84.82.92.92.9093.63.63.6024.44.44.434.64.64.6144.74.74.7122.72.72.7113.23.23.207444.0054.24.24.2034.34.34.302


## 5.2.2. Random Forest Results

We provide a simple and effective random forest in this study. It is executed on the server to process the data collected from the input. The random forest algorithm illustrates the suggested model’s definition and process flow, respectively. Table12 shows the validation between the compressive strength of actual output vs. predicted output by both ANN and random tree. Table 9 shows the performance of prediction with their limited error of compressive strength. Similarly, Tables 13 and 14 show validation of splitting tensile and flexural strength between actual experimental and predicted values. Tables 10 and 11 show the performance of prediction with their limited error of splitting tensile and flexural strength.Table12 describes the compressive strength value at 7 days, 14 days, 28 days, 42 days, and 56 days, which includes the actual value and predicted value. ANN and random forest tree machine learning methods were used to predict the compressive strength. The random forest tree method predicted a more accurate compressive strength than the ANN method. Ten data are used at the same time for individual compressive strength. This table contains the 150 datasets of the compressive strength, whereas the actual data are 50 and the predicted data are 100.The analysis, known as the sensitivity analysis, was conducted to determine the impact of each variable on the prediction of the mechanical strength of GPC. It is important to understand how each of the input parameters will affect the projected outcome because they are crucial to the accuracy of the models that are used for prediction. Each input parameter contributed to the predicted output of the mechanical strength of GPC.Table9 depicts the coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root-relative square error (RRSE) values of predicted compressive strength to the actual experimental results of both machine learning methods. The random forest tree model is more relevant to the ANN model in all-day compressive strength. The random forest tree method shows a determination coefficient value of 1 at 7 days, 14 days, and 56 days, whereas the ANN model does not show a determination coefficient value of 1 in any day prediction.Table13 describes the splitting tensile strength value at 7 days, 14 days, 28 days, 42 days, and 56 days, which includes the actual value and predicted value. ANN and random forest tree machine learning methods were used to predict the splitting tensile. The random forest tree method predicted more accurate splitting tensile strength than the ANN method. Ten data are used at the same time for individual compressive strength. This table contains the 150 datasets of the compressive strength, whereas the actual data are 50 and the predicted data are 100.Table10 depicts the coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root-relative square error (RRSE) values of predicted splitting tensile strength to the actual experimental results of both machine learning methods. The random forest tree model is more relevant to the ANN model in all-day splitting tensile strength. The random forest tree method shows a determination coefficient value of 1 at 7 days, 14 days, 28 days, 42 days, and 56 days, whereas the ANN model does not show a determination coefficient value of 1 in any day prediction.Table14 describes the flexural strength value at 7 days, 14 days, 28 days, 42 days, and 56 days, which includes the actual value and predicted value. ANN and random forest tree machine learning methods were used to predict flexural strength. The random forest tree method predicted more accurate flexural strength than the ANN method. Ten data are used at the same time for individual compressive strength. This table contains the 150 datasets of the compressive strength, whereas the actual data are 50 and the predicted data are 100.Table11 depicts the coefficient of determination (R2), mean absolute error (MAE), root mean square error (RMSE), relative absolute error (RAE), and root-relative square error (RRSE) values of predicted flexural tensile strength to the actual experimental results of both machine learning methods. The random forest tree model is more relevant to the ANN model in all-day flexural strength. The random forest tree method shows a determination coefficient value of 1 at 7 days, 14 days, 28 days, 42 days, and 56 days, whereas the ANN model does not show a determination coefficient value of 1 in any day prediction.


## 6. Conclusion

After the experimental investigation, we found the results of the mechanical strength. The machine learning methods ANN and random forest develop the models based on experimental inputs and outputs. Conclusion is based on the following areas:(i)
In the experimental analysis, the M2 mix got the maximum mechanical (including compressive, splitting tensile, and flexural tensile) strengths whereas the M5 mix gets the minimum mechanical strengths among all the mix designs(ii)
ANN and random forest models check the performance of prediction based on theR2, MAE, RMSE, RAE, and RRSE(iii)
Random forest models show the best prediction to the ANN models because it shows the negligible error between actual and predicted values. TheR2 value is 1 of 12 predicted results out of 15 by the use of random forest methods. So it is most suitable to predict the strength of geopolymer concrete based on their constituent’s material quantity



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*Source: 7791582-2022-07-18.xml*