Analysis of compressive strength of nanostructure pyrolytic carbon enhanced nanocomposite mortar and forecasting using machine learning models

ABSTRACT

Utilization of Nano-structure pyrolytic carbon (NSPC) particles holds significant potential in developing nanocomposites. Consequently, compressive strength is a crucial characteristic which stipulates the efficiency of NSPC particles in cementitious composites. Nevertheless, predicting the compressive strength of this nanocomposite is a significant challenge due to distorted responses and complex structures. The main novelty of this research is to predict the compressive strength of the developed NSPC nanocomposite. Therefore, the machine learning (ML) model is the first-time proposed for predicting the compressive strength of nanocomposite mortar incorporated with various dosages of NSPC particles. In addition, the bound water of the nanocomposite mortar is determined to understand the efficiency of NSPC particles in the hydration process. This work highlights a comprehensive comparison of six ML algorithms, such as linear regression, random forest regression, extra trees, gradient boost regressor, extreme gradient boost, and LightGBM, for prediction accuracy of compressive strength of NSPC nanocomposites. Furthermore, it is evaluated through multiple statistical error analysis. Seventeen parameters were considered input variables to predict the compressive strength of nanocomposite mortar. According to the coefficient of determination analysis, the gradient boost regressor model attained the highest R² value of 0.87, while the extreme gradient boost and extra trees achieved R² values of 0.86 and 0.85, respectively. In addition, a low mean absolute error of 3.229 was earned for the extreme gradient boost. Overall, the gradient boost regressor was reliable and performed better in predicting the compressive strength and mapping the interplay between input variables and compressive strength.

Keywords:
Nanoparticles; Compressive strength; Cement mortar; Machine learning algorithm

1. INTRODUCTION

Concrete is an essential and heterogeneous building material used worldwide for construction. Within the realm of construction materials, cementitious composites are the most extensively utilized materials [¹, ²]. It is anticipated that further development in infrastructure construction necessitates effective building materials with elevating performance [²]. In this context, research has been conducted to discover innovative and efficient strategies for improving the performance of cementitious composites without environmental constraints [³]. Incorporating reinforcing additive material is an advanced investigation of cementitious composites [⁴]. Moreover, reinforcing nanostructure material is more efficient in preventing the propagation of cracks at the nanoscale and enhancing mechanical properties. Consequently, there has been a high interest in reinforcing nanomaterials in cementitious composites [⁵,⁶,⁷].

Nanotechnology is known for its unique properties, which have captivated a lot of interest over the past decade. The investigation of nanomaterials in cement composites has gained significant attention due to their potential to revolutionize the development of cementitious composites [⁸]. Aside from ongoing research, nanomaterials play an essential role in increasing the working properties of cement composites by improving their multifunctional properties, including mechanical, thermal, durability, and electrical capabilities [⁸, ⁹]. When compared with traditional cementitious composites, the performance of nanocomposites is significantly enhanced because of their surface area, physical effect, and chemical reaction. Numerous forms of carbon-based nanomaterials, including carbon nanofiber, graphene, carbon black, and carbon nanotubes (CNT), were extensively used throughout the research [¹⁰, ¹¹]. Utilization of these nanomaterials has attracted the researcher’s attention owing to their prodigious nanoscale and the characteristics they constitute in improving the performance of cementitious composites. Despite the benefits of using nanomaterials in the construction sector, their actual application has substantial limitations, such as being uneconomical, being hazardous due to their tiny size, and causing more significant problems, among others. This has spurred the goal of adopting sustainable nanomaterials instead of commercial nanomaterials, notwithstanding their inconsistent results.

Nanocomposite materials comprise nanosheets, nanofibers, nanotubes, or membrane nanostructures. These nanocomposites exhibit multiple phases, with at least one phase consisting of nanoparticles ranging from 1 to 100 nm in size. A nanocomposite constitutes a matrix that is reinforced by the integration of two or more distinct materials. Nanomaterials are frequently employed as reinforcement agents due to their nanoscale dimensions, extensive surface area, and complex phase interactions. Nanocomposites are advancing as a noteworthy alternative to various engineering materials [¹²]. The classification of nanocomposites is determined by the characteristics of their parent matrix and the specific nanomaterials utilized. The field of nanotechnology has significantly progressed material science, facilitating the development of distinctive nanocomposites through the implementation of efficient dispersion techniques [¹³]. Nanocomposite materials seek to enhance various properties, including physical, chemical, electrical, mechanical, hydrophobic, and conductive attributes [¹⁴, ¹⁵]. Nanocomposites composed of polymers, cement, and ceramics are indeed present.

ML approaches are a subset of artificial intelligence (AI) methodologies that employ iterative learning methods, which obviate the necessity for explicit, manually constructed algorithms. Further, ML is a notable expert in enhancing the accuracy of compressive strength predictions [¹⁶, ¹⁷]. The training portion of these approaches includes utilizing datasets that contain ‘n’ instances and characteristics to fine-tune their parameters. Nevertheless, testing datasets typically contain specific cases (n) and attributes (m) that are not accessible by the models. Furthermore, ML algorithms can deal with unresolved barriers or domains with numerous contingent parameters in current solutions.

2. LITERATURE REVIEW

In this research, we delve into the potential of sustainable carbon nanomaterials, specifically tyre char yielded through the pyrolysis process (500–550°C) of end-of-life tyres. With excellent physical and mechanical properties, Tyre char has piqued researchers interest in construction material [¹⁸, ¹⁹]. Tyre char is utilized as a phase change material [²⁰], concrete additive [²¹], electromagnetic interference shielding [²²], and bitumen binder [²³]. Moreover, the nano-size tyre char, when used as a reinforcing additive in cement composites, significantly enhances the mechanical behavior and reduces the porosity [²⁴]. When the tyre char is ground through ball milling, the particle size is reduced to less than 100 nm. It transforms into a new nanomaterial, which is introduced as Nano-Structure Pyrolytic Carbon (NSPC). With a rich carbon content (>90%) and having a similar nanostructure to commercial carbon black, NSPC particles are a promising nanomaterial for developing effective and sustainable construction materials [²⁵]. Meanwhile, tyre char (NSPC particles) is also proposed as an alternative nanomaterial to commercial carbon black [²⁶]. Structural properties of NSPC particles, such as particle size, bulk density, percentage of carbon, and surface area and content of NSPC, are the features that directly influence the mechanical properties of cement composites. Since NSPC is a newly formulated nanoparticle, it is crucial to experimentally establish the relationship between the properties of NSPC–cement composites and the optimal concentration of NSPC particles. However, the insufficient or excessive dosage of NSPC in cementitious composites might result in detrimental mechanical properties. Subsequently, compressive strength is the most critical parameter that indicates the performance of cementitious composites. Additionally, performing compression testing on nanocomposites may rely on empirical data, which is costly and time-consuming [²⁷]. Moreover, testing multiple samples with different NSPC concentrations at various curing ages is also impossible. Accordingly, developing a predictive model or conventional statistical methods such as response surface methodology or empirical/analytical formula are not sufficiently accurate in predicting the mechanical characteristics of complex materials [²⁸, ²⁹]. To resolve the issue, many recent studies have extensively utilized ML approaches to forecast the strength characteristics of cementitious composites [³⁰, ³¹]. Figure 1 depicts the scientometric network and density visualization exhibiting ML’s impact on predicting the compressive strength of cement composites. The figure indicates that most studies are connected to mechanical properties and compressive strength, which shows a strong interplay between the compressive strength and various input variables. In addition, the density visualization shows the impact of multiple keywords linked to compressive strength and ML.

Figure 1
Scientometric network and density visualization for ML to predict compressive strength.

For instance, ML was used to detect cracks and recognize patterns in concrete beams [³², ³³]. It is used to predict the mechanical properties of concrete for sustainable construction [³⁴,³⁵,³⁶]. These ML algorithms outperformed empirical formulas and showed promising outcomes in predicting the compressive strength of cementitious mortar incorporated with secondary cementitious material (SCM) [³⁰, ³¹, ³⁷,³⁸,³⁹]. Similarly, the prediction of compressive strength of nanocomposite mortar (nano-silica/CNT) using Artificial Neural Network (ANN) [⁴⁰, ⁴¹], Genetic Expression Program (GEP) [⁴⁰], and Support Vector Machine (SVM) [⁴¹, ⁴²] outperformed response surface methodology (RSM). Moreover, multiple ML approaches, including Multi-Logistic Regression (MLR), Multi-variate Adaptive Regression Spline (MARS), Decision Tree (DT), SVM, and Adaptive Boost Algorithm (ABA), are efficiently employed to forecast the strength characteristics of cementitious composites. However, ML models relied on Ensemble Learning Algorithms (ELA), known for their efficiency in solving classifications and regression problems. Further, ELA was employed in several studies to predict the strength characteristics of cementitious composites. For instance, FENG et al. [⁴³] and HAN et al. [⁴⁴] predicted the compressive strength of concrete using AdaBoost and random forest, respectively. ZHANG et al. [⁴⁵] showed that the gradient boost algorithm was more accurate in predicting the mechanical properties of concrete than the standalone models. In another study, ZHANG et al. forecasted the penetration depth of a bullet in cement concrete using machine learning algorithms. They indicated that the K-Nearest Neighbors (KNN) model surpassed the LightGBM model. ASTERIS et al. [⁴⁶] predicted the compressive strength of cement mortar using different ML algorithms and showed that the AdaBoost and random forest have the highest prediction accuracy. Similarly, GAYATHRI et al. [³⁷] mapped the compressive strength of cement mortar using ML models and found that XGBoost is efficient in handling non-linearity problems. Moreover, ADEL et al. [⁴⁷] revealed that XGBoost is the most reliable and provides accurate results in predicting the compressive strength characteristics of CNT-reinforced nanocomposites. It is observed that most studies have predominantly utilized only ANN to develop prediction models for the compressive strength of mortar mixtures [⁴⁸]. It is noted that only a few comparative studies have been carried out using ML techniques to predict the compressive strength of mortar. However, no earlier comparison studies have been performed on the effective application of ML algorithms to predict the compressive strength of cementitious sustainable nanocomposites.

Therefore, the first scope of the investigation is to develop sustainable nanocomposites by adding NSPC particles at different dosages (0–3%) to the weight of the cement. The compressive strength of sustainable nanocomposite mortar is determined at different curing ages (1, 3, 7, 14, 28, 56, and 90 days). Additionally, the bound water of the nanocomposites is examined at different curing ages to validate the compressive strength characteristics. After the experimental investigation, the ML algorithms such as Extra Trees (ET), Gradient Boosting Regressor (GBR), Extreme Gradient Boost (XGBoost), LightGBM, Random Forest (RF), and Linear Regression (LR) models are analyzed and compared for developing superior metamodels to forecast the compressive strength of NSPC-based nanocomposite mortar. This endeavour elucidates the relationship between compressive strength and input parameters that enhance the significance of the findings.

2.1. Research significance

This study first experimentally examined the compressive strength of NSPC-reinforced cementitious composites. The main novelty of this research is to enable the ML approach to predict and validate the strength properties without the need for extensive assessments. The compressive strength of the NSPC-based cementitious nanocomposite is predicted and compared using six ML models: ET, GBR, XGBoost, LightGBM, RF, and LR. Therefore, applying the ML approach to predict the compressive strength of nanocomposite can result in enhanced quality and reliability in construction infrastructure. Eventually, the efficacy of each model is evaluated to discover the effective algorithm for predicting the compressive strength of NSPC-based cementitious nanocomposite.

3. MATERIAL PROPERTIES AND DESIGN METHODS

3.1. Materials

53-Grade, Ordinary Portland Cement (OPC) conforming to IS 12269:2013 was selected as the material of choice, purchased from Chettinad Cement Co. Ltd, India. This study used natural sand, a locally sourced material, as fine aggregate and sieved to less than 1mm. Silica fume containing 98% SiO₂ was used as SCM (10% wt. of cement) to improve the dispersion of nanoparticles. NSPC particles with average particle sizes of ~55 nm and a surface area of 29.5 m²/g representing high carbon (>90%) content were used as a sustainable carbon nanomaterial. Figure 2 shows the images of raw materials utilized in this study. Polycarboxylate ether (MasterGlenium SKY) with a density of 1.10 g/cm³ was used as a chemical admixture to promote the dispersion of nanoparticles in water and cementitious composites. The laboratory tap water was used throughout the experiment.

Figure 2
(a) OPC, (b) river sand, (c) silica fume, and (d) NSPC particles.

3.2. Material characterization

HR-SEM image of silica fume and NSPC particle is shown in Figure 3(a) and (b), respectively. It is observed that silica fume is irregular in shape and has a smooth surface with high purity. The NSPC particle exhibits a 2D structure with closely packed spherical morphology associated with adjacent particles. XRD graph for cement/silica fume and NSPC particle is illustrated in Figure 3(c) and (d), respectively. The detected diffraction peaks (2θ) were identified with JCPDS data.

Figure 3
Material characterization (a) HRSEM of silica fume, (b) HRSEM of NSPC, (c) XRD of cement and silica fume, (d) XRD of NSPC, (e) EDAX of silica fume, and (f) EDAX of NSPC.

Figure 3(c) shows that the cement is filled with Alite and Belite phases, whereas silica fume has high quartz (SiO₂). In Figure 3(d), the ZnS phase at 2θ values of 28.52°, 47.49°, and 56.12° correspond to the (111), (220), and (311) planes, respectively, which are oriented relative to ZnO. The scattering originating from the (110) plane adds to the presence of the pure carbon functional group at an angle of 29.37 degrees. The broad peaks indicate the existence of an amorphous carbon structure composed of randomly distributed microcrystalline graphitic carbon. The Energy Dispersive X-ray Analysis (EDAX) analysis for silica fume and NSPC particle is depicted in Figure 3(e) and (f). The EDAX technique enables quantitative chemical analysis by determining the weight percentage of different elements present in the material. Therefore, by estimating their concentrations, silica fume and NSPC nanoparticles contain more than 90% of Si and C atoms.

3.3. Mix proportion, specimen preparation, casting, and curing

A total of 7 mixes were designed to evaluate the compressive strength of cement mortar composites. The detailed mix proportion is represented in Table 1. NSPC particles were added to the cement at different percentages: 0.5%, 1%, 1.5%, 2%, 2.5%, and 3%. The preparation process was adopted based on the previous studies [¹⁴], as shown in Figure 4. NSPC particles were premixed with ethanal and then mixed with the aqueous solution. Further, the suspension is subjected to magnetic stirring and ultrasonication process. The binder ratio and superplasticizer (SP) were maintained constant in all the mixes to evaluate the lone effect of NSPC in the cement matrix. Silica fume was replaced for cement by 10% to assist the hydration and dispersion process. The combinations employed exact proportions of cement, sand, silica fume, and water for all the mixes. The prepared fresh mortar was cast in 50 mm × 50 mm × 50 mm cubes and cured under standard room temperature in water.

Table 1
Mix proportions for developing cementitious composites using NSPC particle.

MIX ID	CEMENT	SILICA FUME	SAND	w/b RATIO	NSPC (wt.% BINDER)	SP (wt. % BINDER)
CC	0.9	0.1	2	0.45	–	0.6
M 1	0.9	0.1	2	0.45	0.5	0.6
M 2	0.9	0.1	2	0.45	1	0.6
M 3	0.9	0.1	2	0.45	1.5	0.6
M 4	0.9	0.1	2	0.45	2	0.6
M 5	0.9	0.1	2	0.45	2.5	0.6
M 6	0.9	0.1	2	0.45	3	0.6

Figure 4
Preparation of nanocomposite cement mortar using NSPC particles.

4. DATA COLLECTION

Based on a comprehensive analysis of existing literature studies and the results of various characterization techniques on NSPC particles [⁴⁹], it is revealed that the NSPC particles closely resemble the structure of carbon black. This study meticulously accumulated an inclusive dataset on cementitious mortar composites reinforced with carbon black, tyre char, and pyrolytic carbon. Datasets were collected from relevant articles [⁵, ⁵⁰,⁵¹,⁵²,⁵³,⁵⁴,⁵⁵,⁵⁶,⁵⁷,⁵⁸,⁵⁹,⁶⁰,⁶¹,⁶²,⁶³,⁶⁴] on mortar samples to validate the real-time experimental dataset. The collected dataset functions as the fundamental basis for constructing ML models to forecast the compressive strength of cementitious nanocomposites. In this regard, seventeen parameters were selected as input data for each ML model, including size of specimen, cement grade, cement content, silica fume, nanoparticles, carbon content, surface area, particle size of nanomaterial, bulk density, SP, fine aggregate, water to binder ratio (w/b), curing age, and curing temperature. The prominent characteristic of these datasets is the inclusion of physical properties of nanomaterial (particle size, bulk density, & surface area), which were the significant parameters that affect the compressive strength of cementitious composites. Table 2 shows the feature descriptive statistics of collected datasets for compressive strength. Furthermore, these datasets were used for a robust and accurate prediction model to elucidate the relationships between inputs and outputs. The formulation of the training dataset ensures robustness by integrating the experimental sources from various research studies. The dataset is rigorously examined to substantiate the efficacy of the compressive strength of the nanocomposite. Subsequently, the testing dataset was collected after real-time compressive strength testing on mortar samples with NSPC particles. Further, the observed compressive strength was predicted and validated through the collected training dataset using different ML models.

Table 2
Feature description of parameters for compressive strength.

PARAMETERS	STATISTICS
	COUNT	MEAN	STD. DEV	MIN.	25%	50%	75%	MAX	SKEW
Height (mm)	213	47.06	14.82	20	40	50	50	100	0.08
Length (mm)	213	47.06	14.82	20	40	50	50	100	0.08
Breadth (mm)	213	54.64	16.97	20	50	50	70	80	0.29
Cement grade	213	40.78	6.75	32	33	42.5	43	53	0.25
Cement content (ratio)	213	0.96	0.07	0.7	0.9	1	1	1	1.78
Silica fume (ratio)	213	0.28	0.76	0	0	0.1	0.15	5	4.83
NSPC content (wt.%)	213	3.56	3.94	0	1	2.5	5	17.5	1.64
Carbon (%)	213	80.53	36.48	0	90	99	99	100	1.75
Surface area (m2/g)	213	141.70	257.28	0	29.5	95	120	1056	3.16
Particle size (nm)	213	2826.9	14093.12	0	20	50	100	74000	4.9
Bulk density (g/cm3)	213	0.81	0.74	0	0.37	0.41	1.70	2.1	0.63
SP (%)	213	1.60	1.57	0	0.6	1	1.60	9.8	2.25
Fine aggregate (ratio)	213	2.02	1.14	0.36	1	2	2.70	6	0.84
w/b (ratio)	213	0.43	0.07	0.27	0.38	0.43	0.45	0.65	0.39
Curing age (days)	213	27.98	26.4	1.0	7.0	28.0	28.0	180	3.13
Curing temperature (°)	213	22.77	1.90	20.0	20.0	23.0	25.0	25	0.38
Compressive strength (Mpa)	213	34.84	15.04	5.9	24.09	34.0	46.8	77.41	0.29

5. DATA PREPROCESSING AND MODEL DEVELOPMENT

To prepare the dataset for analysis, several key preprocessing steps were performed. A Pearson correlation heatmap, as shown in Figure 5, was used to visualize the relationships between input and output features. It aids in associating the pairs of highly correlated variables. Based on this analysis, the ‘Length’ feature was removed due to its high correlation with ‘Height,’ which reduced redundancy and mitigated potential multicollinearity. From the figure, the two most substantial correlation coefficients were observed at 0.56 and 0.43 for w/b ratio & compressive strength and carbon content & bulk density, respectively. Other strong correlations were also observed, such as cement content & cement grade, carbon content & NSPC dosage, and between the dimensions of 0.48, 0.42, and 0.51, respectively. In further steps, duplicate entries were removed to ensure that each data point was unique and contributed equally to the analysis, thereby maintaining the integrity of the dataset. A check for missing values confirmed no null values, ensuring the dataset was complete and suitable for further processing. The datasets were significantly preprocessed across the selected parameters. Besides, ML models function better under normal distribution. Therefore, feature scaling was applied to standardize the range of values across features. This normalization step ensured that all features were on a comparable scale, which is crucial for the effectiveness of many ML algorithms.

Figure 5
Correlation heatmap of input parameters and output responses of compressive strength.

The preprocessed dataset was employed to train various ML models, including ET, GBR, XGBoost, LightGBM, RF, and LR. The performance of these models was assessed using multiple evaluation metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), R² score, Root Mean Squared Logarithmic Error (RMSLE), Mean Absolute Percentage Error (MAPE), and computation time (TT). The mathematical relations for these statistical metrics are represented in Chart 1. The datasets were precisely distributed into training (70%) and testing (30%) for performance evaluation and development of ML models. Meanwhile, the histogram graph and Pareto chart, as shown in Figures 6 and 7, offer comprehensive visualization of data distribution and frequency of data under variability, respectively. Noticeably, the data distribution shows that most of the dataset for NSPC content, superplasticizer dosage, fine aggregate content, and water-cement ratio were between 0–5 wt.%, 0–2.5%, 1:0.5 to 1:4, and 0.3–0.45, respectively. The dataset count for surface area and cement grade dominates specifically at 0-200 m²/g and 43-grade, respectively. In addition, the output value of compressive strength in most datasets is between 20 and 40 MPa. The frequency of data under variability is considered for all the input parameters before pre-processing.

Chart 1
Mathematical relations for statistical metrics.

STATISTICAL INDEX	STATISTICAL INDICATOR EQUATION
MAE	$\frac{{\displaystyle {\sum }_{i=1}^n\left|e_i\right|}}{n}$
MSE	$\frac{{\displaystyle {\sum }_{i=1}^n{e}_i^2}}{n}$
RMSE	$\sqrt{\frac{{\displaystyle {\sum }_{i=1}^n{e}_i^2}}{n}}$
R2	$1-\frac{{\displaystyle {\sum }_{i=1}^n{e}_i^2}}{{\displaystyle {\sum }_{i=1}^n(y_i-\overline{y})}}$
RMSLE	$\sqrt{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{[log(y_i+1)-log(e_i+1)]}^2}}$
MAPE	$\left(\frac{1}{n}{\displaystyle {\sum }_{i=1}^n\left|\frac{e_j}{y_j}\right|}\times 100\right)$

Figure 6
Histogram of the data for compressive strength.

Figure 7
Illustration of Pareto chart considering the data under variability for compressive strength.

6. TESTING METHODS

6.1. Peculiarities of the applied methods

Compressive strength and bound water represent essential yet separate characteristics in the realm of material science, each parameter representing its challenges in the context of predictive modelling. The compressive strength of a material and an essential measure of its durability are affected by numerous factors, including microstructure, curing conditions, and chemical composition, that result in significant variability and non-linear relationships. The presence of bound water, indicative of the chemically and physically integrated moisture within the material matrix, directly influences the compressive strength. Nonetheless, the indirect nature of its relationship with strength complicates the precise quantification of its influence. ML models provide a sophisticated means to uncover these complex relationships by discerning patterns in high-dimensional data that remain elusive through conventional methods. In contrast to traditional models, ML methodologies demonstrate a remarkable proficiency in navigating the intricacies of non-linearity, multicollinearity, and heterogeneous data. This capability renders them especially adept at elucidating the relationship between input variables and compressive strength. The application of these sophisticated algorithms, including LR, FR, ET, GBR, XGBoost, and LightGBM, can reveal intricate insights and enhance the predictive precision regarding material performance metrics.

6.2. Experimental methods

6.2.1. Compressive strength

The compressive strength of the NSPC-based cementitious composite was evaluated following the ASTM C109 on the 50 × 50 × 50 mm³ cube samples. SHIMADZU, Concrete 2000X, the compressive testing machine, was used to determine the compressive strength with a loading rate of 0.15 N.mm²/second, as shown in Figure 8. The average compressive strength was determined with three independent samples tested at 1, 3, 7, 14, 28, 56, and 90 days.

Figure 8
Compressive strength test set-up.

6.2.2. Bound water

Using the gravimetric approach, the amount of bound water (W_n, %) content in samples (50 g, <100 μm) of hardened cement mortar was ascertained by heating the sample to the temperature of 1000°C. The evolution of bound water in samples is evaluated using equation (1) at hydration ages of 1, 3, 7, 14, 28, 56, & 90 days.

$$w_n=\frac{M_{105}\times (100-LOI)-M_{1000}\times 100}{M_{1000}}$$

where M₁₀₅ is the mass of the samples after stopping hydration by ethanol exchange for 2 hours and dried at 105°C, (g); LOI is Loss on ignition; M₁₀₀₀ is the mass of the samples ignited to 1000°C for hours and cooled in a vacuum desiccator.

6.3. Machine learning models

6.3.1. Linear Regression (LR)

LR is a popular ML algorithm and has been extensively implemented as a statistical method in different ML techniques. Linear models are derived from LR algorithms where the model defines the dependent variable as a function of an independent variable. Equations (2) and (3) represent simple linear regression (SLR) and multiple linear regression (MLR), respectively. Meanwhile, SLR and MLR exhibit the equation of a straight line (one dependent variable) and a plane (more than one dependent variable), respectively.

$$y=b_0+b_{1}x$$

$$y=b_0+b_1{x}_1+b_2{x}_2+\dots \dots \dots \dots +b_n{x}_n$$

6.3.2. Random Forest (RF)

Leo Breiman introduced an ensemble technique called the RF algorithm in 2001. RF is a highly efficient method for predicting the strength properties of construction materials. RF performs a precise classifier and regressors by including appropriate randomness. The fundamental concept of RF is to utilize multiple decision trees and train them individually with smaller subsets which built through bagging (B) or bootstrap aggregation to assemble uncorrelated trees. Bagging techniques train decision trees by iteratively selecting B random samples from a set of training data (X). After training, these decision trees predict unknown samples (x′) using equation (4).

$$f=\frac{1}{B}{\displaystyle {\sum }_{b=1}^B{f}_b(x^{\prime })}$$

6.3.3. Extra Trees (ET)

Extra Trees regression or Extremely Randomized Trees is an extended version of RF from a tree-based ensemble technique. The ET is a meta-estimator that may generate several random decision trees on subsets of data. Similar to RF, ET employs a sub-set of features to train the base estimators with the approach of random selection. In ET regression, each prediction tree is trained on total training data and does not use the bootstrap method. Moreover, it randomly selects a best-split point decision tree, unlike RF, which employs a discriminative split node. ET regression is less complex and faster than RF. The relative variance reduction used in the regression is expressed in Score as depicted in equation (5). Where T_i and T_j represent the subset of T (outcome of split, s).

$$Scor{e}_R(s,T)=\frac{\mathrm{var}\left\{z/T\right\}-\frac{\left|T_i\right|}{\left|T\right|}\mathrm{var}\left\{z/T_i\right\}-\frac{\left|T_j\right|}{T}\mathrm{var}\left\{z/T_j\right\}}{\mathrm{var}\left\{z/T\right\}}$$

6.3.4. Gradient Boost Regressor (GBR)

GBR is an ensemble learning algorithm that expresses dependent variables as a function of independent variables. The GBR approach conjugates weak learners (decision tree) to generate strong learners using the boosting principle. Here, the iterative model minimizes the cost function representing the prior model error. In each iteration, sample residuals are calculated, and the sample selection probability in the subset is updated. Predictions from weak learners to the present model are scaled by a learning rate (𝜂) controlling the contribution of each learner. The commonly used objective functions in this algorithm are square loss, absolute error, and Huber loss.

6.3.5. Extreme Gradient Boost (XGBoost)

The XGBoost algorithm is a powerful ML technique introduced by Chen et al. in 2016 for constructing organized regression models. XGBoost is computationally effective and efficient compared to the GBR framework. The XGBoost algorithm iteratively trains and features base learners to formulate an ensemble learning model, which subsequently performs the predictions. XGBoost addresses the bias-variance trade-off optimally. The objective function (equation (6)) contains the training loss function (L_(θ)) and regularization term (Ω_(θ)). Where ‘L’ is the squared error (equation (7)) for loss function, ‘T’ is weak learner (no. of leaves), and ${\displaystyle \sum {\omega }_i^2}$ is the score vector on weak learner for regularization (equation (8)).

$$Obj=L_{(\theta )}+{\Omega }_{(\theta )}$$

$$L={(y_i-{\widehat{y}}_i)}^2$$

$$\Omega =\gamma T+\frac{1}{2}\lambda {\displaystyle \sum {\omega }_i^2}$$

6.3.6. LightGBM

LightGBM is a novel Gradient Boost Decision Tree (GBDT) algorithm proposed by Guolin Ke in 2017. It is used for both regression and classification tasks. It allows parallel and large-scale data processing, which depends on the GBDT framework. This model diminishes memory consumption and enhances the efficiency of the training process. LightGBM employs a technique of feature parallelism, segmenting the dataset into smaller subsets to concurrently train multiple decision trees [⁶⁵]. LightGBM algorithm, based on a histogram which approximates the distribution of feature values, can outperform XGBoost with the help of GOSS (Gradient-based one-sided sampling) and EFB (Exclusive feature bundling) in terms of computational speed and memory consumption. LightGBM is a speed training process without a drop-in accuracy. The leaf-wise approach with depth limitation controls model complexity, guarantees efficiency, and prevents overfitting. The LightGBM model is characterized by several crucial hyperparameters, which include the number of leaves (num_leaves), maximum depth of the tree (max_depth), learning rate (learning_rate), number of weak learners (n_estimators), and the weight assigned to the L1 (reg_alpha) and L2 (reg_lambda) regularization term.

7. RESULTS AND DISCUSSION

7.1. Compressive strength

The mechanical properties of the cement mortar composites using different dosages of NSPC particles was performed in our previous investigation [¹⁴]. However, this study recapitulates the variations in the compressive strength of cement mortar composite for analysis and prediction using the ML algorithm. Figure 9 displays the compressive strength of sustainable nanocomposites at different curing ages. Generally, it is observed that the increase in curing age has improved the corresponding compressive strength of the nanocomposites. However, the high dosage of NSPC particles (i.e. with the trend of mix ID) has decreased trend. The initial compressive strength of plain cement mortar (CC) is as follows: 14.2 MPa on day 1, 15.53 MPa on day 3, 25.59 MPa on day 7, 28.39 MPa on day 14, 36.42 MPa on day 28, 37.63 MPa on day 56, and 39.64 MPa on day 90. Based on the findings, the compressive strength of mixes at 1 day and 3 days old exhibited a similar level of strength, with no significant variation seen across the mixtures. However, the composites containing 2 wt.% of NSPC particles (Mix 4) exhibited greater values compared to the CC mix when compared to other combinations. Including NSPC particles did not noticeably impact the compressive strength during the early stages. However, the role of NSPC particles in cement mortar composite at 7, 14, 28, 56, and 90 days was more distinct in comparison to early-age samples.

Figure 9
Compressive strength of mortar at different curing ages and strength comparison at 90 days [¹⁴].

The compressive strength exhibited a constant upward trend as the curing period progressed from CC to mix 4, validating the reinforcing impact of NSPC particles. Moreover, it has been noted that NSPC particles have significantly minimized the porosity in the cement mortar due to the filling effect of NSPC particles. In this context, silica fumes serve a crucial function by facilitating hydration and providing mechanical separation of the NSPC particles from aggregation. In the advanced stages of curing, the adhesive characteristics of silica fume effectively bond the layer of carbon nanoparticles to the hydration products, thereby enhancing the interfacial strength between the NSPC particles and the cementitious matrix. However, the interfacial zone is relatively affected by the high dosage of NSPC particles which is mainly due to water absorption and hydrophobic nature. The cement mortar composites with a particle concentration of 2wt.% NSPC exhibits the highest level of strength, surpassing that of the CC mix by 40.37%. Simultaneously, NSPC particles were added at concentrations of 0.5wt.%, 1wt.%, and 1.5wt.% to the CC resulted in strength improvements of 20.8%, 27.7%, and 34% in the specimen, respectively. Despite the similar structural properties of NSPC particles and commercial carbon black, the dosage amount is critical in determining compressive strength. The samples tested for compressive strength through experimental evaluation were validated through different ML algorithms as it is complex to investigate with high concentrations of NSPC particles at different curing ages. The more detailed aspect of the compressive strength of NSPC particles is detailed in our previous work [¹⁴]. Table 3 shows the compressive strength performance of NSPC cement mortar composites with previous studies. The comparison shows that the NSPC particles can provide better compressive strength than commercial carbon black.

Table 3
Performance comparison of compressive strength of NSPC composite with carbon black composites.

FUNCTIONAL FILLER TYPE	COMPRESSIVE STRENGTH (MPa)	REFERENCES
NSPC particles	47.5	This study
Carbon black	31.1	OU et al. [5]
Activated carbon black	40.4	ABOLHASANI et al. [58]
Nano carbon black	38.1	WANG and ASLANI [50]
Carbon black	41.0	ZHANG et al. [66]

Figure 10 shows the failure cracks observed after 90 days of compressive loading. Due to the axial stresses, the typical vertical cracks along the loading axis are observed, which also propagated as the load increased. Moreover, localized crushing is also observed in some samples at the loading points. Moreover, no shear cracks formed as the NSPC particles filled the pores, making a compact and dense matrix.

Figure 10
Crack pattern of tested samples after compressive loading.

7.2. Bound water

In hardened cement mortar, the chemically bound water contributes to forming hydration products (Calcium Silicate Hydrate (CSH), ettringite, portlandite). Therefore, this study utilized chemically bonded water to examine the impact of NSPC particles on the hydration process of cement mortar composite at different curing stages. These results were used to support the compressive strength results in terms of bound water in capillary pores. The replacement of silica fume at a low level (10%) improved the W_n and was considered the optimum amount [⁶⁷]. Figure 11 exhibits the synergistic effect of silica fume and NSPC particle on the W_n of cement mortar samples with different curing ages. The interplay between silica fume and NSPC particles reveals a synergistic relationship that significantly improves hydration processes and refines the microstructural characteristics. Silica fume engages in a reaction with calcium hydroxide, resulting in the formation of secondary C-S-H, which enhances the amount of chemically bound water. Concurrently, NSPC particles function as fillers, augmenting the retention of physically bound water owing to their substantial surface area. This hybrid mechanism diminishes the presence of free water by converting it into bound forms, resulting in a denser and less permeable matrix. Furthermore, the enhanced interfacial transition zone (ITZ) facilitates a more effective distribution of hydration products and bound water, leading to superior overall performance. Moreover, from the figure, it is observed that the W_n of cement mortar composite increased with hydration age but decreased with the increase in NSPC particle (2%), corroborating with compressive strength results. Concurrently, it is also observed that the silica fume replacement offsets for the pernicious effect with the increased addition of NSPC particles up to 2%. Thus, the results demonstrate that silica fume assists in promoting pozzolanic reactions and hydration in hardened cement mortar composite at long curing days. The results depict that the mixture with 10% silica fume and 2% NSPC is the threshold due to the reduction in W_n beyond this substitution level.

Figure 11
Effect of the NSPC particle content on W_n with 10% silica fume and its comparison.

7.3. Predicting compressive strength of nanocomposite mortar

The compressive strength of sustainable cementitious nanocomposite mortar was predicted by deploying the different ML models on the collated dataset. Figure 12(a)–(f) exhibits the scatter plots of ML models of the actual values versus predicted values for training and testing predictions. The scatter plot by LR, as indicated in Figure 12(f), shows that the model is insufficient in apprehending all the variances in the training data. Consequently, it records the poor performance on testing data among all ML models. Meanwhile, the performance of ET, as shown in Figure 12(a), was nearly ideal for training data where all the datasets are almost within the ±30% error bound.

Figure 12
Scatter plots of true versus predicted compressive strength of sustainable cementitious nanocomposites (a) ET, (b) GBR, (c) XGBoost, (d) LightGBM, (e) RF, and (f) LR.

The effectiveness of the models was evaluated using statistical error metrics, including MAE, MSE, RMSE, R² score, RMSLE, MAPE, and computation time (TT). Table 4 summarizes the performance metrics for various ML models on the testing data. The GBR (Figure 12(b)) achieved the best overall performance with the highest R² score (0.8677) and lowest RMSE (5.2020) among the other algorithms, indicating an excellent fit to the data points. It also achieved the lowest MAE and MSE, reflecting its high accuracy in predicting the compressive strength of sustainable cementitious nanocomposite mortar. Additionally, its RMSLE (0.1692) and MAPE (0.1337) were among the lowest, signifying the minimal errors in logarithmic and percentage terms. GBR demonstrated the fastest computation time (0.061 seconds) next to ET and LR, which is competitive. Besides, XGBoost (Figure 12(c)) also exhibits remarkable performance with the second-best R² score (0.8621), and has the least RMSE (5.0939) compared to other algorithms. Meanwhile, the RMSLE (0.1727) and MAPE (0.1244) were close to those of GBR, reflecting low prediction errors. XGBoost was notably efficient, achieving a fast computation time of 0.058 seconds and the least MAE, which made it a strong contender. The ET regressor followed closely with an R² score of 0.8515 and showed low error metrics, including RMSE (5.4577), RMSLE (0.1758), and MAPE (0.1306). While its performance was slightly below that of GBR and XGBoost in terms of accuracy, reflecting a less accurate model fit than GBR and XGBoost. However, ET (Figure 12(a)) demonstrated reasonable computational efficiency with a moderate computation time (0.1230). The RF (Figure 12(e)) showed good performance with an R² score of 0.8136. Nevertheless, all statistical error metrics of RF were higher than those of GBR, XGBoost, and ET. It is observed that the computation time of RF (0.181 seconds) was also slower than the top-performing models. LightGBM (Figure 12(d)) achieved moderate performance, with an R² score of 0.7787 and an RMSE of 6.7981, which is higher next to LR’s most significant error in predictions. Similarly, the RMSLE (0.2273) and MAPE (0.1876) values were relatively high, demonstrating significant prediction errors. Despite these shortcomings, LightGBM’s computational efficiency (0.13) was relatively better but insufficient. Finally, LR (Figure 12(f)) had the lowest performance across all metrics, with the highest MAE (7.3468), MSE (86.7203), RMSE (9.1853), and the lowest R² score (0.5965), indicating a poorer fit to the data. Despite its performance limitations, LR was the most computationally efficient model, requiring the least computation time (0.03), but lagged significantly behind the other models in accuracy.

Table 4
Performance metrics for various ML models.

MODEL	MAE	MSE	RMSE	R2 SCORE	RMSLE	MAPE	TT (Sec)
Linear Regression	7.3468	86.7203	9.1853	0.5965	0.3120	0.2812	0.0300
LightGBM	4.6950	48.0199	6.7981	0.7787	0.2273	0.1876	0.1300
Random Forest	3.7010	42.0389	6.0680	0.8136	0.1992	0.1542	0.1810
Extra Trees	3.3728	32.6528	5.4577	0.8515	0.1758	0.1306	0.1230
Extreme Gradient Boost	3.2293	30.0823	5.0939	0.8621	0.1727	0.1244	0.0580
Gradient Boost Regressor	3.4723	28.9770	5.2020	0.8677	0.1692	0.1337	0.0610

In addition, the performance metrics and statistical analysis show that MAE is robust to outliers and gives equal weight to all errors. MSE and RMSE emphasize more significant errors, which is helpful when large deviations are critical to identify. As seen in Table 4, XGBoost and Gradient Boosted Regression (GBR) exhibit lower values, signifying better error control. The R² score quantifies the model that explains the variance of the target variable. GBR and XGBoost achieve the highest R² scores (0.8677 and 0.8621, respectively), showing that the variability in the data is most effective. RMSLE benefits datasets with significant value ranges or when penalizing underpredictions is more critical. XGBoost and GBR outperform other models with RMSLE values of 0.1727 and 0.1692, respectively. MAPE is helpful in comparing models across datasets, as it provides a percentage-based error. GBR achieves the lowest MAPE (0.1337), indicating its consistent accuracy. Computational efficiency matters when training models, especially for large datasets. XGBoost and GBR have relatively low training times (0.0580 and 0.0610 seconds), making them more efficient compared to other models like Random Forest (RF) and Extra Trees (ET).

GBR performed better compared to models such as Extra Trees, XGBoost, Random Forest, Linear Regression, and LightGBM because the GBR model frequently demonstrates superior performance. This is primarily attributed to its sequential error-correction methodology, which adeptly captures intricate, nonlinear relationships in a manner that surpasses the capabilities of bagging techniques like RF and ET. The capacity of GBR to refine its performance via residual learning effectively mitigates the risk of overfitting, provided it is appropriately calibrated, thereby enhancing its resilience in the presence of noisy or imbalanced datasets. It necessitates a more lenient approach to feature scaling than techniques such as XGBoost and LightGBM. It often delivers robust performance immediately, particularly in scenarios where the connections between features and the target are complex.

The results from Table 4 indicate that the GBR outperformed other models in terms of accuracy and efficiency, showing the lowest MAE, MSE, RMSE, and highest R² score. Therefore, GBR is highly effective for predicting the compressive strength of sustainable nanocomposite mortar. XGBoost and ET also demonstrated strong performance but with relatively higher error metrics compared to the GBR algorithm. On the other hand, LightGBM and LR showed less favorable performance, particularly in terms of prediction accuracy, as indicated by their higher MAE, MSE, and RMSE values. While LR was the most computationally efficient, its accuracy limitations suggest it may not be the best choice for this specific application. Meanwhile, Table 5 exhibits the comparison of performance metrics achieved for the best ML model between the current and previous studies.

Table 5
Comparison of performance metrics for best ML model between current and previous studies.

DATA SET	ML MODEL	R2	RMSE	MAE	MSE	MAPE	RMSLE	PREDICTION	REFERENCE
202	GBR	0.87	5.20	3.47	28.97	0.13	0.16	NSPC nanocomposite	This study
−	XGB	0.94	2.78	2.21	−	−	0.08	CNT nanocomposite	LI et al. [68]
261	XGB	0.93	3.99	2.93	16.23	0.05	−	CNT nanocomposite	ADEL et al. [47]
424	XGB	0.97	−	2.00	11.25	−	−	Metakaolin cement mortar	GAYATHRI et al. [37]
−	AB	0.95	1.27	1.57	2.44	−	−	Biochar cement mortar	SOBUZ et al. [31]
132	RFR	0.98	1.55	1.09	−	−	−	GGBS geo-composites	GAD et al. [69]
287	GBR	0.96	1.56	1.18	2.95	0.02	−	Alkali-based concrete	SEKI et al. [70]
90	RF	0.98	2.63	1.83	−	7.16	−	Recycled aggregate concrete	DABIRI et al. [71]

In addition to evaluating the overall performance of the models, assessing the significance of various features is essential for analyzing the factors that influence the compressive strength of sustainable nanocomposite mortar. To facilitate this analysis, we present plots of feature importance for the top-performing models such as ET Regressor, XGBoost, GBR, and RF Regressor. These visualizations illustrate the relative importance of each feature, providing insights into their impact on model predictions and aiding in identifying key variables influencing the compressive strength of nanocomposite mortar.

Figure 13(a)–(d) depict the feature importance for each of these models, which includes only ET, GBR, XGB, and RF, offering a comprehensive aspect of different features that contribute to the prediction of compressive strength. The GBR model prioritizes the water-to-binder ratio (w/b) and curing age (days) as the most influential features, indicating their critical role in the model’s predictions. Accordingly, powder to fine aggregate ratio (fine aggregate content) and NSPC dosage also contribute to compressive strength as the influential features are relatively high. Similarly, the RF model underscores the importance of the water-to-binder ratio (w/b) and curing age (days) as crucial predictors. However, the fine aggregate content has limited emphasis on the strength parameters, while NSPC particles still relatively influence the compressive strength. XGBoost highlights the water-to-binder ratio (w/b) as a crucial feature, with fine aggregate content and curing age (days) being significant, though slightly less so. Despite this, fine aggregate influence is relatively high compared to curing age and aggregate content in XGBoost. Notably, the ET model aligns with GBR and RF in emphasizing the water-to-binder ratio (w/b) and curing age (days) but additionally shows notable importance for fine aggregate content and NSPC content (wt.%), indicating a broader scope of influential features. Compared to ET, XGBoost, GBR, and RF have higher feature importance values.

Figure 13
Relative feature importance analysis in model predictions (a) ET model, (b) GBR, (c) XGBoost, and (d) RF.

A significant interplay was observed between compressive strength and input parameters, including w/b ratio, carbon content, bulk density, cement content, and NSPC dosage. At the same time, the w/b ratio facilitates hydration, resulting in an improvement in strength. NSPC particle dosage assists in filling the voids and enhancing the density of the matrix. Meanwhile, the physical characteristics of NSPC particles, such as carbon content and bulk density, promote compressive strength. Such parameters have a strong interplay with the output compressive strength.

Overall, forecasting the compressive strength of NSPC nanocomposites by utilization of ML in the field of civil engineering is transforming the discipline, enabling precise predictions and enhancements of the characteristics of nanocomposite materials for sophisticated infrastructure development. This facilitates the advancement of construction materials that are durable, lightweight, nanoscale and possess self-healing or self-sensing with multifunctional properties, thereby diminishing maintenance needs and extending their longevity. The development of NSPC nanocomposites having complex microstructure and exhibiting remarkable bound water properties, thermal insulation, waterproofing, and corrosion resistance can be significantly enhanced through the application of ML techniques. These nanocomposites exemplify an ideal solution for constructions that prioritize energy efficiency and durability. The optimization of nanomaterials content, which might resist impact load, leads to enhanced seismic resilience, while the use of environmentally benign and recycled materials fosters sustainability.

The advancement of nanocomposites exhibiting enhanced fire resistance and acoustic insulation, aimed at augmenting the safety and tranquility of buildings, is further facilitated by applying ML techniques. Moreover, it aids in forecasting the characteristics of nanocomposites employed in sophisticated coatings and adhesives while also facilitating the development of anti-fouling and antimicrobial surfaces for environments where hygiene is paramount. The integration of ML with advanced nanocomposites facilitates real-time structural health monitoring, while ML minimizes the necessity for extensive physical testing by allowing for rapid prototyping. These advancements advocate for infrastructure solutions that are robust, economically viable, and sustainable in their environmental impact.

7.4. Limitations

The incorporation of silica fume (SF) and NSPC particles in cement mortar presents certain limitations, including reduced workability, difficulties in attaining uniform dispersion of nanoparticles, and amplified production expenses. Furthermore, the enduring resilience of NSPC particles when subjected to environmental pressures is still ambiguous, and their manufacturing could entail energy-consuming procedures that counteract potential ecological advantages. The management of health and safety risks linked to the handling of fine nanoparticles necessitates meticulous oversight. It is imperative to consider these factors in order to harness the potential of this hybrid approach fully.

The synergistic influence of silica fume and NSPC particles on enhancing bound water presents specific limitations. The attainment of uniform dispersion of NSPC particles presents significant challenges and may result in agglomeration, thereby diminishing their efficacy in microstructural refinement. The diminished workability of the mortar, attributable to the elevated surface area of both silica fume and NSPC particles, may necessitate the incorporation of additional water or superplasticizers, potentially influencing the dynamics of hydration. Moreover, although silica fume improves the presence of chemically bound water, an overabundance of NSPC nanoparticles could impede hydration by obstructing water accessibility, thereby influencing the equilibrium between free and bound water. These factors underscore the necessity for meticulous optimization of their proportions.

The prediction of compressive strength of NSPC nanocomposites through machine learning encounters several obstacles, including the presence of limited and inconsistent datasets. The risk of overfitting stems from small sample sizes and the complexities involved in identifying pertinent features. The complexities inherent in modelling the nonlinear interactions between NSPC particles and cement components present significant challenges, compounded by scaling issues and the variability of environmental factors that reduce the generalizability of findings. Furthermore, “black box” models exhibit a deficiency in explainability, while computational complexity or noise present in experimental data further undermines the reliability of predictions. The constraints necessitate meticulous data curation, judicious model selection, and rigorous validation to guarantee precise and resilient forecasts.

8. CONCLUSIONS

This research comprehensively investigated the integration of NSPC particles in cement mortar to develop sustainable nanocomposites. The compressive strength and bound water of the sustainable nanocomposite mortar were determined experimentally at different curing ages. Further, this study paved the way for a paradigm shift by utilizing novel methodologies like the ML model to evaluate the compressive strength of sustainable nanocomposite mortar that incorporated NSPC particles. The compressive strength was estimated by implementing six ML algorithms, including ET, GBR, XGBoost, LightGBM, RF, and LR, which were devised utilizing a set of seventeen input variables. The compressive strength results obtained from ML models were compared with experimental results. The following conclusions were drawn from the experimental and computational findings:

• The compressive strength of sustainable nanocomposite mortar increased with curing age by the addition of NSPC particles. However, compressive strength was reduced with a high amount of NSPC particles (>2.5 wt.%). The highest compressive strength was achieved for the sustainable nanocomposites containing 2 wt.% of NSPC particles. Therefore, NSPC particles discovered in this study are innovative and sustainable nanoparticles that are alternative to commercial carbon black.

• The bound water results demonstrated that the nanocomposites with 2% NSPC particles were the threshold due to the reduction in W_n beyond this substitution level. Moreover, the replacement of 10% of silica fume offsets the pernicious effect with the increased addition of NSPC particles of up to 2wt.%.

• Two strongest correlation co-efficient was observed at 0.56 and 0.43, for w/b ratio & compressive strength and carbon content & bulk density, respectively. Another strong correlation was also observed, such as cement content & cement grade, carbon content & NSPC dosage, and between the dimensions 0.48, 0.42, and 0.51, respectively.

• The ML model based on the GBR algorithm evidenced enhanced performance by decreasing the variations between the true and predicted values. Notably, ET algorithm is ideal for testing data. Overall, the GBR model performed well compared to other models in forecasting the compressive strength of NSPC composites.

• LR records poor performance compared to other ML models. In terms of R² score, the GBR, XGBoost, XT, LightGBM, & RF algorithms are found to have 45.47%, 44.53%, 42.75%, 30.54%, and 36.4%, respectively, higher than the LR algorithm. On the contrary, the LR have the least computational time compared to other ML models, and it can be arranged as RF > LightGBM > ET > GBR > XGBoost > LR.

• However, the GBR and XGBoost have high R² and least MAE, MSE, and RMSE values. The XT algorithm demonstrated inferior error in all metrics (R², MAE, MSE, RMSE, RMSLE, MAPE & TT). It is observed that GBR is the optimized model from the statistical research to predict the compressive strength of sustainable nanocomposites.

• The feature importance of top-performing models such as GBR, XGBoost, ET, and RF prioritized the water-to-binder ratio (w/b), curing age (days), fine aggregate, and NSPC concentration as the most influential input features. Therefore, the interplay between the inputs and compressive strength was obviously correlated with improving the prediction performances.

• The comparative analysis using different ML models can be arranged from best to worst on the predicted results as GBR > XGBoost > ET > RF > LightGBM > LR.

Eventually, this study shows that a new nanocomposite using sustainable nanoparticles is developed for the first time, and their compressive strength is forecasted using an ML algorithm. Therefore, this novel investigation can be carried forward to future scientific research investigations to attain multifunctional properties for advanced applications.

9. FUTURE WORK

A future study can consider evaluating and predicting the electrical resistivity of NSPC composites using ML models. This nanocomposite could be assessed for multifunctional properties such as electromagnetic shielding and piezoresistivity properties. Moreover, this study is helpful in paving the way for forecasting the electrical properties of NSPC composites, which could be used in structural health monitoring applications.

10. ACKNOWLEDGMENTS

The authors would like to thank School of Civil Engineering, Vellore Institute of Technology, Chennai, India for providing support and lab facilities to carry out this research. We thank “School of Advanced Sciences, VIT-Chennai”, for providing the analytical services. The authors also express their gratitude for permitting to utilize the pyrolysis plant by “GS Pyro Enterprise Pvt. Ltd., India” and for the superplasticizer donated by “Master Builders Solutions, India”.

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Publication Dates

• Publication in this collection
  21 Feb 2025
• Date of issue
  2025

History

• Received
  11 Dec 2024
• Accepted
  15 Jan 2025