Machine Learning-Based Predictive Modeling of Sustainable Lightweight Aggregate Concrete

Abstract

Nowadays, lightweight aggregate concrete is becoming more popular due to its versatile properties. It mainly helps to reduce the dead loads of the structure, which ultimately reduces design load requirements. The main challenge associated with lightweight aggregate concrete is finding an optimized mix per requirements. However, the conventional material design of this composite is quite costly, time-consuming, and iterative. This research proposes a simplified methodology for the mix designing of structural and non-structural lightweight aggregate concrete by incorporating machine learning. For this purpose, five distinct machine learning algorithms, support vector machine (SVM), artificial neural network (ANN), decision tree (DT), Gaussian process of regression (GPR), and extreme gradient boosting tree (XGBoost) algorithms, were investigated. For the training, testing, and validation process, a total of 420 data points were collected from 43 published journal articles. The performance of models was evaluated based on statistical performance indicators. Overall, 11 input parameters, including ingredients of the concrete mix and aggregate properties were entertained; the only output parameter was the compressive strength of lightweight concrete. The results revealed that the GPR model outperformed the remaining four machine learning models by attaining an R² value of 0.99, RMSE of 1.34, MSE of 1.79, and MAE of 0.69. In a nutshell, these simplified modern techniques can be employed to make the design of lightweight aggregate concrete easy without extensive experimentation.

1. Introduction

Concrete is considered to be the second most consumed material after water globally. Its remarkable binding property helps to support large structures, which increases its demand daily. Due to its numerous benefits, the consumption of concrete adds up to a giant figure of 30 billion tons per annum [1]. In concrete structures, the majority of stresses result from the action of heavy dead loads. These heavy dead loads can be reduced by using lightweight aggregate concrete. The weight of aggregate generally used in concrete is almost 70% of the composite, indicating that most of the weight in concrete is occupied by the aggregate [2]. Using natural or artificial lightweight aggregate instead of normal aggregate could reduce the weight of the concrete significantly.

Lightweight aggregate is broadly divided into two categories: (a) natural lightweight aggregate includes vermiculite, perlite, pumice, diatomite, scoria, etc. and (b) artificial lightweight aggregate includes expanded clay aggregate, expanded perlite, plastic aggregate, and expanded polystyrene beads, etc. [3]. The use of LWAC is increasing, especially in high-rise buildings and long-span bridges, due to its numerous benefits. These benefits include a lower gravity load, better heat insulation and sound insulation, a reduced risk of earthquake damage, improved fire resistance, and lower shrinkage and creep resistance as compared to conventional concrete [4,5,6,7,8,9,10]. LWAC is also a sustainable alternative for making energy-efficient buildings through heat insulation properties and cost-effective structures. The lower dead loads eventually lower the structural members’ design actions that help reduce the cross-section and reinforcement requirements [11]. Due to the lower self-weight, the cross-section of the structural members also decreases, leading to a lower use of the cement, which is a primary contributor of greenhouse gases as well as aggregate [12]. Furthermore, waste of the different sectors is utilized as lightweight aggregate such as crumb rubber, electric arch furnace slag, fly ash, etc. [12,13,14,15]. Artificial lightweight aggregate is also manufactured using local clays and fly ash, which is replacing the natural aggregate in order to reduce the usage of natural reserves [12,16,17].

Shaiksha et al. [18] reported that using artificial lightweight aggregate instead of natural aggregate could significantly reduce the cost by 18% due to a 22% reduction in the unit weight of the concrete. Lydon et al. [19] confirmed that the compressive strength of the LWAC is directly dependent on the density of the LWA used [4]. Furthermore, Huang et al. [20] confirmed that the mechanical properties of the LWAC are also a function of the rheological properties and water/binder ratio, as LWA has a high absorption capacity due to its porous microstructure. The main challenge of LWAC is to select the appropriate water/binder ratio owing to the high absorption capacity of the LWA [15]. This ultimately leads to rapid slump loss and decreases the setting time of concrete.

The mix design process for lightweight aggregate concrete is a bit complicated due to the inclusion of different properties of the lightweight aggregate. The main problem associated with the proper mix design of lightweight aggregate concrete is the variation in water absorbing capacity, and the density of the lightweight aggregate. To avoid the extensive mix design process, researchers have developed different types of machine learning (ML) models to predict the strength parameters of the concrete [21,22,23,24]. The use of artificial intelligence (AI) in concrete technology is not new; firstly, it was started simply to predict the compressive strength of the concrete and later also used to predict other properties of concrete due to its promising results [25]. Over the years, different approaches to machine learning have been made to predict the different parameters of a material or concrete. These include support vector machine (SVM), random forest (RF), decision tree (DT), gene expression programming (GEP), and artificial neural network (ANN) [4,26,27,28,29,30]. Aslam et al. [30] predicted the compressive strength of high-strength concrete using the GEP algorithm. Using the ANN algorithm, Siddique et al. [13] predicted the compressive strength of self-compacting concrete containing bottom ash [31]. Chithra et al. adopted an ANN model technique to predict the compressive strength of concrete containing nano-silica and copper slag [32].

Young et al. [23] adopted the ANN modeling technique to predict the compressive strength of lightweight aggregate concrete; however, this model lacked several important input parameters associated with the properties of aggregate, including water absorption, and the density of the LWA as well as the accuracy of the model was also compromised with an R² of 0.71. Tenza-Abril et al. [24] also developed an ANN model using ultrasonic pulse velocity as the input to predict the compressive strength of the segregated lightweight aggregate concrete. The model developed by Tenza-Abril was good in terms of accuracy with an R² of 0.82. These aforementioned purposed models for LWAC were limited in terms of their input parameters, along with compromised accuracies [24].

Therefore, there is a serious need for a comprehensive model involving all the important input parameters with high accuracy to predict the compressive strength of the lightweight aggregate concrete incorporating the properties of aggregate. This paper proposes a comprehensive approach to predict the compressive strength of structural and non-structural lightweight aggregate concrete. It is the first time that lightweight aggregate characteristics such as the water absorption capacity and density of the lightweight aggregate have been included in the dataset to predict the compressive strength of lightweight aggregate concrete based on input data that has not yet been utilized by the network. Additionally, the purposed machine learning model has a good accuracy as compared to already existing lightweight aggregate concrete compressive strength predictive models. Initially, a comprehensive dataset comprising 420 data points was extracted from the published journal articles [1,29,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72]. To make the dataset coherent, a detailed statistical analysis was performed for data cleaning to remove the outliers from the dataset. For the training of the models, a total of five ML-based algorithms were considered for comparative analysis. To avoid overfitting and underfitting the trained model, the dataset was divided into three separate parts, from which one was used for training, the second for testing, and the third for validation. Finally, the accuracies of the models were evaluated based on statistical error indicators, and then the best model was used to predict the compressive strength.

2. Data Collection and Analysis

2.1. Data Collection

This study utilizes 420 data points for the prediction modeling of lightweight aggregate concrete, which were collected from published literature. A dataset with 12 instances was used, from which 11 are input parameters and one is output. In the dataset, the input parameters are cement, sand, water-to-cement ratio (w/c), lightweight aggregate (LWA), normal aggregate (normal agg.), the density of lightweight aggregate, water absorption of lightweight aggregate, superplasticizer, curing time, fly ash (FA), and lightweight aggregate type. The output variable is compressive strength. The name, unit, minimum and maximum values, mean, mode, and standard derivation (SD) for training and testing are listed in

Table 1. Summary of dataset for ML models training.

Parameters	Unit	Minimum	Maximum	Median	Mode	SD	Type
Cement	kg/m3	156	1500	467	480	378.42	Input
Sand	kg/m3	0	1193	664	0	330.15	Input
Water-to-cement ratio	1	0.15	0.80	0.45	0.5	0.08	Input
LWA quantity	kg/m3	23.80	1191	308	37	297.28	Input
Density of LWA	kg/m3	415	1489	783	575	357.65	Input
Water absorption of LWA	%	0.92	58.30	25.20	40	13.83	Input
Normal aggregate	kg/m3	0	1326	0	0	353.98	Input
Superplasticizer	%	0	3	0	0	0.70	Input
Curing time	Days	1	120	28	28	14.27	Input
Fly ash	kg/m3	0	540	0	0	117.61	Input
Lightweight aggregate types	-	-	-	-	-	-	Input
Compressive strength	MPa	2.03	79	24.58	25	16.68	Output

and

Table 2. Summary of dataset for ML model testing.

Parameters	Unit	Minimum	Maximum	Median	Mode	SD	Type
Cement	kg/m3	139	1350	384	450	197.70	Input
Sand	kg/m3	0	1178	630	0	294.92	Input
Water-to-cement ratio	1	0.23	0.8	0.42	0.35	0.07	Input
LWA quantity	kg/m3	0	950	155	0	270.29	Input
Density of LWA	kg/m3	406	1480	750	610	320.11	Input
Water absorption of LWA	%	0.92	56	20.5	20.5	13.54	Input
Normal aggregate	kg/m3	0	941.2	0	0	282.15	Input
Superplasticizer	%	0	2.5	0.5	0	0.687	Input
Curing time	Days	1	120	28	28	23.4	Input
Fly ash	kg/m3	0	540	0	0	111.38	Input
Lightweight aggregate types	-	-	-	-	-	-	Input
Compressive strength	MPa	4.28	65.14	27	25	15.54	Output

respectively. The statistical distribution of the parameters used in the dataset is shown in Figure 1. The box plot of input and output variables is shown in Figure 2.

2.2. Preprocessing of Dataset

The preprocessing data sample points initiate the development of the ML model. A correlation matrix was developed to determine the relationship between the dependent and independent variables and is shown in Figure 3. The Pearson correlation matrix is a comprehensive graph that shows the relationship between the variables in terms of Pearson correlation coefficients [73]. In the correlation matrix, the correlation coefficient range lies between +1 and −1. The correlation coefficient values range between −1 and +1 for the non-diagonal entries and exactly 1 for the diagonal entries since the relation of one variable with itself will always be perfect [74]. It is evident from the signs that the positive values show a direct relation and negative show an inverse relation between the variables [74]. The equation expressing the Pearson correlation coefficient is:

$$r=\frac{{\displaystyle \sum (x_i-\stackrel{\leftharpoonup }{x})(y_i-\stackrel{\leftharpoonup }{y})}}{\sqrt{{\displaystyle \sum {(x_i-\stackrel{\leftharpoonup }{x})}^2{{\displaystyle \sum (y_i-\stackrel{\leftharpoonup }{y})}}^2}}}$$

(1)

2.3. Dataset Normalization

The major challenge faced after data collection is processing the raw data to make them compatible with the ML models used. For instance, in our dataset, there was a considerable difference between the numerical values of cement, w/c, and normal aggregate used. This difference affected the accuracy of our model adversely. This issue was tackled using the data normalization technique. Data normalization means transforming data into the unit sphere or scaling down the actual values to numerical indexes between 0 and 1. It leads to data cleansing and convergence and significantly enhances the model’s efficiency. It also improves data execution by reducing the dataset’s redundancy. The governing equation taken into consideration for data normalization is mentioned below, where the normalized value of a certain input variable is a function of the actual, minimum, and maximum values of that variable in the dataset.

$$x_{norm}=\frac{x_i-x_{\min }}{x_{\max }-x_{\min }}$$

(2)

3. Methodology

3.1. Overview of Machine Learning

Implementing machine learning (ML) in civil engineering is considered a renaissance in this field. ML models have enhanced numerical computational power and higher accuracy. ML is a branch of artificial intelligence (AI) and can be used for several objectives such as classification, clustering, regression, etc. The basic working flowchart of machine learning is shown in Figure 4. Predicting the compressive strength of lightweight concrete is just one application of the ML models. ML follows certain algorithms that can learn from the input data themselves, and after hyperparameter tuning, it gives highly accurate results. An ML model that has been accurately trained and precisely calibrated has shown significant similarity with practical experimental data. The juggernaut behind this AI arena is that we allow the computer algorithms to learn from a given dataset rather than programing them conventionally. Hence, the algorithm comes up with a model that can interpret all the data fed to it.

Table 3. Recent uses of advanced machine learning modeling in research.

Sr. No.	Machine Learning Algorithms	Datasets	Input Parameters	Output Parameters	Ref.
1.	GB_PSO, and SVR	721	Water content, aggregate content, RCA content, NA content, sand content, cement content, RCA water absorption, NA water absorption.	Compressive Strength	[75]
2.	Gaussian process regression, kernel transformations and regression, SVR	1681	Cement, fly ash, and water content	Compressive Strength	[76]
3.	GPR, ANN, SVR	406	Water, cement, slag, fine steel slag, coarse steel slag	Compressive Strength	[77]
4.	ELM, SVM, and GMDH	2028	Curing ages of 1, 3, 7, 28, and 90 days.	Compressive strength and ultrasonic pulse velocities	[78]
5.	RF (random forest)	-	FA, RM, and GP	Compressive strength, split tensile strength, and flexural strength	[79]
6.	ANN and DNN	335	Fly ash, water glass solution, sodium hydroxide solution, coarse aggregate, fine aggregate, water, concentration of sodium hydroxide solution, curing time, and curing temperature.	Compressive strength	[80]
7.	SVM, ANN, AdaBoost, CNN	380	C-G: cement strength class, W/B: water–binder ratio; S-R: sand ratio, P/A: paste–aggregate ratio, RA/A: recycled coarse aggregate replacement proportion, F/B: fly ash replacement proportion, SF/B: silica fume replacement proportion, S/B: slag replacement	Compressive strength	[81]
8.	RF, AdaBoost, GB, SVR, and XGB	220	W/C ratio and silica fume, silica fume content and fiber volume fraction	Compressive strength and flexural strength	[82]
9.	ANN, GB, XGB, SVR, KNN LR	630	Cement, fines, coarse aggregate, superplasticizer, and curing age	Compressive strength	[83]
10.	Least square support vector machine coupled simulated annealing CSA LSSVM-CSA, GP	-	W/C ratio, coarse–fine aggregate (CA/FA) ratio, proportion of CA to FA	Compressive strength	[84]
11.	Multiple linear regression, genetic algorithm-BPNN, backpropagation neural network, Gaussian process regression, radial basis function neural network.	2045	Water–cement ratio, water–binder ratio, aggregate–cement ratio, cement content (kg/m3), silica fume content (% cement mass), fly ash content (% cement mass), slag content (% cement mass), calcined clay content (% cement mass) (denoted as metakaolin), filler content (kg/m3), amount of superplasticizer (% cement mass), SAP content (% cement mass), SAP size (μm), SAP water uptake (g/g of SAP in cement slurry), and time since the beginning of shrinkage measurements (days)	Axial loading capacity	[85]
12.	Linear regression, K-nearest neighbors, support vector regression, XGBoost, decision tree, Gaussian process regression, gradient boosting, artificial neural network, random forest.	429	Wall features	The capacity of RC shear walls	[86]
13.	Data envelopment analysis	114	Superplasticizer, coarse aggregates, fine aggregates, water–binder ratio, fly ash replacement percentage, and the total binder content	Compressive strength, V funnel test, slump test, L box test	[87]
14.	Support vector machine	15	AE parameters	Compressive strength	[88]
15.	Gene expression programming	277	Binder content, fly ash, water–powder ratio, fine aggregate, coarse aggregate, and superplasticizer	Axial capacity	[73]
16.	Adaptive neuro-fuzzy inference system	7	Depth, thickness, yield strength of steel, the compressive strength of concrete and the length of the CFST	Compressive strength	[89]
17.	Conventional ANN	220	Mixtures incorporating 0%, 10 wt%, 20 wt%, 30 wt%, 50 wt%, 60 wt%, and 70 wt% wt 70% T-POFA as a replacement of ordinary Portland cement (OPC) at a constant water/binder (W/B) ratio of 0.35	Compressive strength	[90]
18.	Multivariate	21	W/c ratio, sand/cement ratio, curing days, and dry density	Compressive strength	[91]
19.	Intelligent rule-based enhanced multiclass support vector machine and fuzzy rules	114	Crumb rubber derived from end-of-life tires (grain size 0.5–3.5 mm) was replaced fine aggregate by 0%, 5%, 10%, 15%, 20%, 25%, and 30% of total aggregate volume. Silica fume replaced cement by 0%, 5%, and 10% of the total cement mass	Compressive strength	[92]
20.	Multivariate adaptive regression spline	114	Cement (kg), fly ash (kg), water–powder ratio (W/P), and superplasticizer (l/m3)	Compressive strength, slump test, L box test, V funnel test	[93]
21.	Gene expression programming	160	Fly ash as cement replacement	Post-fire behavior	[94]
22.	Gene expression programming (GEP), Random forest regression (RFR), and Support vector machine (SVM)	-	Temperature (T), recycled concrete aggregate (RCA) replacement level, and superplasticizer (SP) addition percentage	Compressive strength (f’c) of sugarcane bagasse ash (SCBA) concrete	[95]
23.	Extreme learning machine (ELM)	324	SCBA dosage (SCBA%), the quantity of fine aggregate (FA) and coarse aggregate (CA), water–cement ratio (W/C), and cement content (CC).	Compressive strength of high-strength concrete (HSC)	[91]
24.	Gaussian process regression (GPR)	414	Water, cement, fine aggregate, coarse aggregate, and superplasticizer	Compressive strength of Miscanthus	[96]
25.	Support vector regressor (SVR), random forest regressor (RFR), extra trees regressor (ETR), and gradient boosting regressor (GBR)	676	Curing time and pretreatment condition	Compressive strength	[97]
26.	Gaussian process regression (GPR)	414	Mixture proportions and the chemical compositions	Compressive strength of Miscanthus lightweight concrete (MLWC)	[98]
27.	Multiple linear regression (MLR), generalized linear modeling (GLM), quadratic polynomial regression (QPR), and support vector machine with linear kernel (SVML); non-linear models include artificial neural network (ANN), support vector machine with polynomial kernel (SVMP), support vector machine with radial kernel (SVMR), random forest (RF), and extreme gradient boosting (XGBoost)	12,107	Curing time and pretreatment condition	Compressive strength of field concrete at 7 days	[97]
28.	Support vector machine (SVM)	1000	Water, cement, coarse aggregate, fine aggregate, fly ash, superplasticizing admixture, and water-reducing admixture.	Compressive strength	[94]
29.	Support vector regression	115	Curing conditions	Compressive strength	[99]

summarizes some of the latest work conducted in the concrete domain with the integration of ML tools.

3.1.1. Artificial Neural Networks

An artificial neural network (ANN) is a data-driven ML-based approach inspired by the functioning of neural networks in the human brain [100]. ANN has versatile applications from speech recognition to medical diagnosis and data sorting to clustering. The working principle of ANN is based on its ability to learn from the data provided and find a certain connection between the input and output parameters through hidden functions. Neurons are the building blocks of ANN and there is a weight and bias associated with every neuron. The data proceed from the input layer towards the output layer through different intermediate hidden layers. All the corresponding layers are attached by discrete channels with distinct weights. In order to pass on the data through different layers, the input value of the preceding layer is multiplied by the weight of the channel attaching this neuron with the neuron of the succeeding layer. Then, finally, the product of these two is added to bias, which is a numerical value assigned to the succeeding layer neurons. Our model comprises 11 input layers, 10 hidden layers, and one output layer. The number of input and output layers is upon users’ discretion; however, the number of hidden layers is a variable that changes from data to data. The model is trained iteratively for the different number of hidden layers, and then the number of layers of the model with optimum accuracy are adopted [101]. The basic architecture of the ANN model is shown in Figure 5.

3.1.2. Regression Analysis

The regression analysis is a family of machine learning models that serves two primary purposes. Firstly, regression analysis is mainly used for the prediction in which their application has significant overlaps with the machine learning area. Secondly, regression analysis can identify the relationship between the dependent and independent variables [102]. According to the regression models, the independent variable ‘x’ predicts the dependent variable ‘Y’. Regression is further classified into two main domains: linear and non-linear regression analysis. When the relationship between the dependent and independent variables is non-linear, non-linear regression analysis is performed, which is frequently the case in most of the real-world applications. Similarly, when the relationship between the dependent and independent variables is linear, linear regression analysis is performed. The flowchart in Figure 6 illustrates the basic working flow of regression models which were used in this study.

Y = a + bx + cx² + dx³ + ex⁴ + …

(3)

Support Vector Machine

Support vector machines (SVMs) are supervised learning models for classification and regression analysis that examine data and identify patterns. SVM differentiates cases with different class labels by developing hyperplanes in a multidimensional space. Multiple continuous and categorical variables can be handled by SVM, which allows both regression and classification tasks [103,104].

Gaussian Process Regression

Gaussian process regression (GPR) is a Bayesian non-parametric technique that has been used widely in data-based modelling of a variety of systems, including those relevant to chemometrics. However, because it is challenging to formulate a covariance function for correlated multiple response variables that captures both the correlation between responses and the correlation between data points, most GPR implementations only simulate a single response variable [105,106].

Extreme Gradient Boosting Tree

A gradient boosting framework is used by the ensemble machine learning method XGBoost, which is decision-tree-based. Artificial neural networks frequently outperform all other algorithms or frameworks in prediction issues involving unstructured data (pictures, text, etc.). However, decision-tree-based algorithms are currently thought to be best-in-class for small- to medium-sized structured/tabular data [28,104,107].

Decision Tree

Decision tree analysis is a common, predictive modelling technique with applications bridging various areas. In general, decision trees are developed using an algorithmic method that defines how to divide a dataset based on several criteria. It is among the most widespread and useful techniques for supervised learning. Decision trees are a non-parametric supervised learning technique used for both classification and regression tasks. The aim is to learn straightforward decision rules derived from the data features to develop a model that predicts the value of a target variable [106,108,109].

4. Model Development and Construction

4.1. Anomalous Data

The data were collected from the previously published literature, including hypothetical trials of the different samples. In the collected data, some points were affecting the accuracy of the trained models. These data points are outliers called anomalous data. Twenty-two such types of data points were removed, e.g., a sample that included the water/cement ratio of 1 was removed as the anomalous data considering its unrealistic nature. In the same way, 130 MPa compressive strength of the lightweight aggregate concrete was reported without any additive and normal aggregate and was also included in outliers. Some data points did not even contain any lightweight aggregate, so those data points were also removed.

4.2. Hyperparameter Tuning

Hyperparameter tuning is the setting of a learning algorithm before training any ML model. Hyperparameter tuning is an iterative process where selecting appropriate model parameters determines the model’s accuracy. Model parameters vary from model to model as well as with dataset. The input variables and model parameters, such as number of hidden layers, learning rate, number of learners, leaf size, and percentage of the dataset for training, validation, testing, etc., were varied until the optimum model performance was achieved. Due to a large number of model parameters, only a few hyperparameters were tuned; the others were set to default. The hyperparameters of ML models that were optimized are shown in

Table 4. Optimized hyperparameter for ML models.

Methods	Hyperparameters	Range	Optimum Value
DT	Minimum leaf size	1–50	4
SVM	Kernel function		Cubic
	Epsilon	0.1–2	1.6
	Kernel scale	0.1–1.7	1
XGBoost	Minimum leaf size	1–20	8
	Number of learners	1–50	30
	Learning Rate	0.01–0.50	0.1
GPR	Kernel scale	1–80	52
	Sigma	1–15	12
ANN	Training algorithm	Bayesian regularization	10
	Hidden layer size	1–40

.

4.3. Model Performance Indicators

To assess the performance of the ML models, four types of statistical performance indicators were used. The performance indicators used were root mean square error (RMSE), mean absolute error (MAE), mean square error (MSE), variance account factor (VAF), performance index (PI), and coefficient of determination R-squared (R²). The coefficient of determination R² shows the variance in predicted values as compared to the actual values. The closer the value of R² is to 1, the higher the accuracy of the model is. On the other hand, RMSE and MSE indicate how many of the data points are converged on the regression line. MAE is a similar measure of errors in paired observations. The formulation of the statistical performance indicators is given as:

$$RMSE=\sqrt{\frac{1}{m}{\displaystyle \sum _{i=1}^m{(k_{act}-k_{pre})}^2}}$$

(4)

$$R^2=1-\frac{{\displaystyle \sum {(k_{act}-k_{pre})}^2}}{{\displaystyle \sum {(k_{act}-{\overline{k}}_{pre})}^2}}$$

(5)

$$MAE=\frac{{\displaystyle \sum _{i=1}^m|k_{act}-k_{pre}|}}{m}$$

(6)

$$MSE=\frac{{\displaystyle \sum _{i=1}^m{(k_{act}-k_{pre})}^2}}{m}$$

(7)

$$VAF=(1-\frac{\mathrm{var}{(k_{act}-k_{pre})}^2}{\mathrm{var}(k_{act})})\times 100$$

(8)

where K_pre and K_act are the predicted and actual values, respectively; m refers to the total number of sample points, and ${\overline{k}}_{pre}$ refers to the mean of the predicted values.

4.4. Training Process

Rigorous and repeated model training is performed to achieve higher accuracy. The selection of appropriate parameters during the training process determines the model’s accuracy. Therefore, the models were trained multiple times by changing input variables and parameters until the best model with the highest possible accuracy was obtained. Figure 7 gives a basic overview of the training process for the machine learning models adopted in this research.

5. Results and Discussion

5.1. Predicted Results and Discussion

The five machine learning algorithms, support vector machine (SVM), artificial neural network (ANN), decision tree (DT), Gaussian process of regression (GPR), and extreme gradient boosting tree (XGBoost) were trained and tested. A model’s accuracy is measured in terms of R²; the larger the value, the more accurate the model will be, while in the case of the RMSE, the lower the value, the greater accuracy of the model [17]. Figure 8 compares the actual and predicted results of the output parameter. The trained model of GPR, which outperforms all other models, gives an RMSE of compressive strength for the training dataset of 1.34, while the RMSE for the testing dataset is 7.79, while the model’s accuracies for the testing and training datasets in terms of R² for compressive strength are 0.99 and 0.92, respectively.

5.2. Rank Analysis

To evaluate the overall performance of machine learning models, rank analysis is performed. Based on the results of the training and testing phases of the ML models summarized in

Table 5. Summary of trained models.

ML Models	Set	RMSE	R2	MSE	MAE	VAF
DT	Training	4.45	0.94	19.78	2.68	93.81
	Testing	6.58	0.87	43.37	4.32	86.34
SVM	Training	2.38	0.98	5.64	1.58	98.29
	Testing	7.43	0.84	55.26	3.61	85.56
XGBoost	Training	5.02	0.92	25.22	3.39	92.91
	Testing	7.79	0.82	60.82	4.81	83.09
GPR	Training	1.34	0.99	1.79	0.69	99.40
	Testing	5.06	0.92	25.62	3.01	95.65
ANN	Training	2.62	0.98	6.89	1.71	98.59
	Testing	8.4	0.9	70.58	5.13	94.19

, each model is rated based on the results of all statistical indices computed. The worst performing model is ranked as having a model value of 1, while the best model is ranked as having a model value of 5 (as five models are used in this study). The total rank is then calculated in this method by adding all the individual ratings. The model with the lowest rank is considered to be the best performing one, while the model with the highest rank is considered to be the worst performing one. The performance of the models is calculated by adding each model’s total rank of the training and testing sets to find their overall rank. As can be seen in

Table 6. Rank analysis of ML models.

ML Models	Set	RMSE	R2	MSE	MAE	VAF	Total Rank	Overall Rank
DT	Training	4	2	4	4	2	16	29
	Testing	2	3	2	3	3	13
SVM	Training	2	5	2	2	3	14	27
	Testing	3	2	4	2	2	13
XGBoost	Training	5	1	5	5	1	17	30
	Testing	4	1	3	4	1	13
GPR	Training	1	4	1	1	5	12	25
	Testing	1	5	1	1	5	13
ANN	Training	3	3	3	3	4	16	39
	Testing	5	4	5	5	4	23

, the performance of the GPR model stands out above all five models with an overall rank of 25. Following GPR, SVM has the second overall rank of 27, DT has the third overall rank of 29, XGBoost the fourth overall rank of 30, and ANN the fifth overall rank of 39.

5.3. Model Performance Analysis

Since it is evident from Table 6 that the GPR model was found to be the best fit for forecasting the compressive strength of lightweight aggregate concrete, a separate dataset was used to validate the predictive model. These data were not included during the model’s training and testing process. The output (compressive strength) was monitored by varying the type of LWA, the density of LWA, and the water absorption of LWA, which is the prime input of the model. The results were highly encouraging, and the predicted compressive strength was almost the same as that published in the literature. The summary of validation and the comparison of the predicted and actual data are shown in Figure 9.

6. Conclusions

This study used different machine learning tools to develop an optimized compressive strength predictive model of sustainable lightweight aggregate concrete including lightweight aggregate characteristics with 420 data points. Five ML models were trained with 11 input parameters and one compressive strength output.

• For the development of machine learning, the model’s dataset was divided into three parts: training, testing, and validation.
• A detail statistical analysis was performed on the dataset to make it coherent before training the machine learning models.
• Statistical indicators were used to evaluate the performance of ML models, including root mean square error (RMSE), mean absolute error (MAE), mean square error (MSE), and coefficient of determination R-squared (R²).
• To enhance the accuracy of the predictive models, optimal hyperparameter tuning was performed during the training process. After hyperparameter tuning, an optimized machine learning Gaussian process of the regression model for compressive strength prediction of sustainable lightweight aggregate concrete was developed.
• The R² and RMSE of the GPR model were above 0.99 and 1.34, respectively, indicating that the GPR model exhibited better performance in predicting the compressive strength of lightweight aggregate concrete.
• It is therefore concluded that extensive, uneconomical, and time-consuming work of finding an optimum mix design can be replaced by using these ML algorithms with maximum accuracy to predict the compressive strength of LWAC.