Home Technology Predictive modeling assessment of advanced concrete materials incorporating plastic waste as sand replacement
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Predictive modeling assessment of advanced concrete materials incorporating plastic waste as sand replacement

  • Hailong Tan , Zhixiong Yang EMAIL logo , Ali H. AlAteah , Raid S. Alrashidi , Mohammad Alharthai ORCID logo and Ahmed M. Maglad ORCID logo
Published/Copyright: November 24, 2025
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REVIEWS ON ADVANCED MATERIALS SCIENCE
From the journal REVIEWS ON ADVANCED MATERIALS SCIENCE Volume 64 Issue 1

Abstract

This research aims to contribute to the advancement of sustainable construction materials using a new composite of coated plastic waste as sand replacement material. This research assessed the predictive capabilities of Random Forest (RF), Particle Swarm Optimization-Support Vector Regression (PSO-SVR), and a Genetic Algorithm Optimized Artificial Neural Network (GA-ANN) that enable accurate, data-efficient prediction of compressive strength in plastic-waste foamed concrete, reducing experimental overhead and guiding sustainable mix optimization to forecast the compressive strength of foam concrete containing plastic waste. The models were evaluated using R2 metrics, where RF scored 0.9872 and 0.9005, and GA-ANN scored 0.9979 and 0.8853 for the training and testing sets, respectively. Sensitivity analyses of the RF and GA-ANN models were conducted to evaluate the compressive strength of the foam concrete and the impact of each associated input parameter. The findings confirmed that both models accurately predicted the compressive strength of the material. The R2 values for both models were calculated: for RF 0.9872 and 0.9005, and for GA-ANN 0.9979 and 0.8853. Sensitivity analysis indicated that the highest Permutation Importance values for cement, foam, sand, water-to-cement ratio, and plastic waste were 0.39, 0.34, 0.17, 0.11, and 0.39, respectively. In the GA-ANN case, the greatest Permutation Importance Values of 0.41, 0.31, 0.13, 0.11, and 0.05 were assigned to cement, sand, water-to-cement ratio, foam, and plastic waste, respectively, in that order concerning compressive strength. The PSO-SVR model in green maintained a good balance (AUC = 0.97 in training and AUC = 0.93) in testing. The PSO-SVR model achieved an average performance between those of the other two models. The MAE value was approximately 1.5 in training and 2.8 in testing, whereas the RMSE value was in the range of 4.5–5.0. The results showed the practicality of AI-based frameworks in the focus optimization of mix design and multi-criteria prediction of performance metrics of sustainable foam concrete containing recycled plastic waste.

Keywords: lightweight foamed concrete; compressive strength; gene expression programming (GEP); sensitivity analyses; waste plastic

1 Introduction

The adoption of ecological processes and materials has become increasingly important in the construction industry [1]. An exemplary approach is the creation of foamed concrete, which is a lightweight cementitious material with a low density (often between 400 and 1,600 kg/m3). Foamed concrete is highly flowable and has good thermal and acoustic insulation properties [2]. Owing to the multifunctionality of foam concrete, it is suitable for nonstructural walls, thermal insulation layers, subgrade layers in road construction, and even void filling [3]. The compressive strength of concrete has a significant impact on the performance of disparate applications and is significantly influenced by the mix design parameters of the water-to-cement ratio, curing regime, dosage of foaming agent, and additional constituents [4], [5], [6].The use of plastic waste in foam concrete has emerged as a leading option for addressing the problem of plastic pollution [7]. Recycled polyethylene terephthalate (PET), polystyrene (PS), and high-density polyethylene (HDPE) plastics contain fibers or granules incorporated into concrete mixtures [8]. Studies have shown that the inclusion of certain ratios of these wastes can enhance or retain the compressive strength of concrete while decreasing its density [9], 10]. This unpredictability makes it more difficult to accurately predict the mechanical properties using empirical methods because of the blending of many disparate components with unique characteristics [11].While conventional techniques such as plasma treatment, chemical grafting, or nanocoatings [12] often require sophisticated equipment and high costs, The polyester resin layer enhances compatibility between the hydrophobic plastic surface and the cementitious matrix [13], while the sand particles create a roughened texture that significantly improves mechanical bonding and composite density [14]. In addition, utilizing foundry sand as a coating material contributes to sustainability by valorizing an industrial by-product and promoting circular economy practices through the simultaneous recycling of plastic and sand waste [15]. This distinctive combination of improved performance, practicality, and environmental benefits highlights the novelty of the proposed treatment compared with other surface modification techniques.

For this purpose, AI and ML technologies have been implemented to assess the complex nonlinear interrelations of the input variables with the compressive strength variables [16], [17], [18], as shown in Figure 1. These approaches reject the linear constraints of traditional regression models and perform better than classical regression models on heterogeneous datasets that have many dimensions [18], [19], [20]. Among all AI technologies, the most commonly employed for predicting the compressive strength of concrete are artificial neural networks [21], 22]. Bilim et al. [23] were the first to implement artificial neural networks (ANNs) to forecast the compressive strength of ordinary concrete and achieved a remarkable predicted R2 value of 0.94, which was later extended to include lightweight and recyclable concrete. Moreover, it employed a multilayer perceptron artificial neural network model to predict compressive strength based on eight variables and achieved an R2 value of 0.93 in [24]. Jie Li et al. [25] created artificial neural network models aimed at predicting the strength characteristics of lightweight concrete modified with RPET and achieved a mean absolute error (MAE) lower than 2 MPa.

Figure 1: Scientometric analysis of ML applications in concrete [17].
Figure 1:

Scientometric analysis of ML applications in concrete [17].

Babatunde A. Salami et al. [26] employed three AI methodologies: Artificial Neural Network (ANN), Gene Expression Programming (GEP) shown in Figure 2 and a Gradient Boosting Tree (GBT) with a dataset of 232 experimental results. The models used easily measurable input parameters, such as the concrete density, water-cement ratio, and sand-cement ratio. 80 % of the data were used for training and the rest for testing. The hyperparameters were optimized using a trial-and-error method for each model. Among the three methodologies, the GBT model performed the best (R = 0.977, MAE = 1.817, RMSE = 2.69), outperforming ANN and GEP in prediction accuracy. However, the GEP showed some usefulness by providing a predictive equation that could be used in the field. The researchers concluded that the models could be relied upon within the ranges of inputs tested, and that they could accurately estimate the strength of foamed concrete.

Figure 2: GEP prediction of compression strength of foamed concrete using GeneXProTools software.
Figure 2:

GEP prediction of compression strength of foamed concrete using GeneXProTools software.

Soran A Ahmad, et al. [27] examined used three models to predict compressive strength of foam concrete – Linear Regression (LR), Non-Linear Regression (NLR), and ANN – and assessed their performance against a pool of 97 experimental datasets. The models were evaluated based on R2, RMSE, and MAE.The ANN and demonstrated the best performance with a 36 % improvement in R2 relative to LR, 22 % over NLR, and significantly lower RMSE and MAE values. This positions ANN as the most accurate technique among the three.Ali Ashrafian, et al. [28] developed a novel hybrid model, MARS-WCA (Multivariate Adaptive Regression Splines improved by Water Cycle Algorithm), to predict Foamed Cellular Lightweight Concrete (FCLC) compressive strength with high accuracy based on its mixture proportions. Through the best subset regression with Mallow’s P* (C) criterion, several significant explanatory variables were identified within 418 experimental datasets, including foam content, sand, binder, water-to-cement ratio, sand-to-cement ratio, and specimen age. The absolute model error, normalized model efficiency, and mean square error were calculated to assess the model efficacy against benchmarks including MLR, ANN, and SVR. The findings demonstrated that MARS-WCA provided the highest accuracy (NSE = 0.938), outperforming all other models by up to 41.7 %. These findings strongly support the MARS-WCA as an exceptionally effective and flexible tool for estimating the compressive strength of FCLC. Haji S Ullah et al. [29] studied the use of machine learning (ML) models to estimate the compressive strength of lightweight foam concrete (LFC), considering the challenges posed by the distribution of air voids.

The study utilized an assembled dataset of 191 experimental results that included input variables, such as cement concentration, sand content, water-cement ratio, and foam volume. This study used a Support Vector Machine (SVM) modeled alongside ensemble methods such as bagging, boosting, and Random Forest (RF). The model accuracy was evaluated by 10-fold cross-validation using R2, MAE, and RMSE as evaluation metrics. Random Forest performed the best out of all the models, reaching R2 = 0.96, MAE = 1.84 MPa, and RMSE = 2.52 MPa. This indicates that the ensemble methods greatly enhance the accuracy of forecasting the compressive strength of lightweight foam concrete (LFC).The evaluation of predictive models for concrete performance and behavior using RF model evaluation with sensitivity analysis is an important approach. RF is an ensemble learning technique that provides reliable predictions by aggregating the outputs from various decision trees [30], 31]. This results in reduced overfitting of the data while improving generalization. In particular, this methodology can assist in forecasting several concrete properties, including compressive strength, toughness, and slump, in relation to mixing ratios, curing conditions, and material specifications. Sensitivity analysis helps to identify the most influential factors. The water-cement ratio, aggregate dimensions, and quantities of the chemical admixtures are result-oriented variables. This understanding allows engineers to fine-tune the mixture design and boost the performance of materials. The combination of RF and sensitivity analyses offers a robust approach within concrete technology for assessing and refining predictive models, thereby fostering innovation and efficiency in construction practices. In alignment with green building objectives, natural materials can preserve or enhance the compressive strength, thermal insulation, and long-term durability of lightweight concrete [18], [19], [20].

The integration of waste plastics into the production of foam concrete still requires further research, despite the progress made in construction material sustainability. The goal of this study is to analyze the impact of waste plastic coated with fine foundry sand.Thus far, little attention has been devoted to investigating foamed concrete with integrated plastic waste. This has led to the development of reliable AI models focused on the type and amount of plastic incorporated into concrete, foam ratio, curing time, and ratios of all components. This study focuses on predicting the compressive strength of foamed concrete with varying concentrations of waste plastic by developing and validating AI-based models, including Random Forest (RF) and genetic algorithm-optimized Artificial Neural Network (GA-ANN) models. Model training utilizes data from lab experiments, while evaluation is performed on several performance metrics, such as R2, Root Mean Square Error (RMSE), and Mean Absolute Error (MAE). These results are expected to explain the fundamental factors determining the strength of the material and demonstrate the role of AI in facilitating an optimized eco-friendly mix design.

2 Dataset and methodology

Data was collected from previous works [15], 17], 32], 33] focus on coating plastic with polyester and foundry sand. The polyester used was an unsaturated cast-based polyester resin. Due to its good filler acceptance and low shrinkage properties, polyester is generally used in filled casting applications, such as artificial marble and in applications where fast curing and high thermal resistance are not required [34], rapid curing speed and excellent impact resistance [35] in addition to decreasing absorption [15]. Using recycled foundry sand instead of natural sand in concrete production can help preserve natural resources, minimize environmental problems, and provide certain economic advantages [36] in addition to the coating method is simpler to apply, require less specialized equipment, and are more suitable for large-scale applications in developing adhesion and mechanical performance of composite materials.

A total dataset of 191 samples, of which 151 were training data and 40 were test data, was prepared. The models were evaluated using R2 metrics, where RF scored 0.9872 and 0.9005, and GA-ANN scored 0.9979 and 0.8853 for the training and testing sets, respectively. Sensitivity analyses of the RF and GA-ANN models were conducted to evaluate the compressive strength of the foam concrete and the impact of each associated input parameter. The selection of RF, PSO-SVR, and GA-ANN in this study was based on both methodological suitability and problem-specific considerations. Random Forest (RF) was chosen due to its robustness in handling non-linear relationships, resistance to overfitting through ensemble averaging, and capability to provide variable importance, which is particularly useful in interpreting the influence of different mix design parameters on concrete properties. PSO-SVR combines Support Vector Regression with Particle Swarm Optimization, enabling effective hyperparameter tuning while preserving the strong generalization ability of SVR in small-to-medium datasets, where overly complex deep learning approaches may lead to overfitting and poor interpretability. Similarly, GA-ANN integrates Genetic Algorithms with Artificial Neural Networks to optimize network architecture and weights, ensuring improved convergence and predictive accuracy without the need for extremely large datasets. In contrast, algorithms such as XGBoost or deep learning architectures often require significantly larger datasets and computational resources to achieve stable performance, and their “black-box” nature makes them less interpretable in terms of understanding material behavior a critical aspect in materials science. Therefore, the chosen models strike a balance between predictive performance, interpretability, and feasibility given the available dataset size and the domain-specific need for explaining parameter influence.

2.1 Data analysis

The parameters of the experiment along with the corresponding values of the name means, medians, modes, standard deviations, sample variances, and minimum and maximum are presented in Table 1. In the current case, these variables were cement, sand, water-to-cement ratio (w/c), foam, plastic waste, and compressive strength.

Table 1:

Features of descriptive statistics for modeling-relevant variables.

Statistical factors Cement Sand w/c Foam Plastic waste C.S
Median 699.7 724.3 0.40 0.22 0.0 24.56
Variance 30,533 54,122 0.01 14.06 1,419.6 178.3
Std error 12.4 17.0 0.007 0.27 2.68 0.95
95 % CI lower 631.8 661.0 0.41 0.38 0.0 21.96
95 % CI upper 680.3 728.5 0.43 1.44 10.7 25.67
Range 700.6 1,355.0 0.54 21.95 360.0 47.79
Q1 485.0 590.9 0.35 0.15 0.0 11.96
Q3 778.8 826.0 0.45 0.31 0.0 35.60
IQR 293.8 235.1 0.10 0.16 0.0 23.64
Skewness 0.5 0.1 0.9 5.3 4.2 0.0
Kurtosis −1.1 −0.8 1.1 30.0 19.2 −1.3

2.1.1 Initial data exploration and feature distribution analysis

Figure 3 shows the histogram plots of the concrete mix design, which show the distribution patterns with key features such as cement, sand, water-to-cement ratio (w/c), and foam. Compressive strength (C.S) was also applied. The concentration of cement content displays multimodal distribution with 500–800 kg/m3 having the greatest concentration showing conventional and high strength mix design variation. The sand content was positively skewed around 700–900 kg/m3, which suggests higher workability and packing density precision control. The w/c ratio is sharply inclined in the range of 0.35–0.45, mostly encompassing optimal workability/strength trade-offs; however, a few stragglers exceed 0.6 likely for flexibility during experimentation. Foam displays a severely right-skewed distribution, where most samples fall at zero value, indicating selectiveness in usage for aerated or lightweight concretes. Graphically similar to plastic waste submission, where only handfuls were sustainable exploratory derived from using high plastic amounts, showing minimal adoption of mainstream ratios in other mixes. Finally, a noteworthy observation is that the compressive strength evenly spans the range of 0–50 MPa, highlighting that regardless of the material combinations used while designing the mixes, their mechanical behaviors remained diverse across different performance levels throughout the engineered versions.

Figure 3: Distribution of cement content in concrete mixtures.
Figure 3:

Distribution of cement content in concrete mixtures.

2.1.2 Boxplot analysis of concrete mix features

Figure 4 presents boxplots of cement, sand, water-to-cement ratio (w/c), compressive strength (C.S), and foam and plastic waste contents of concrete. The distribution of cement and sand was fairly symmetric with moderate interquartile ranges. However, the sand variable exhibited several low-end outliers, which were probably experimental mixes with a lower fine aggregate portion. A few outliers above 0.6 and 0.8 in water to cement ratio suggest intentional alteration for workability or reduced strength targets, furthering its slight positive skew. Foam and plastic waste do not show much resemblance to traditional use; they cluster around zero but contain a few high-value outlier casts that indicate specialized or exploratory mixed applications. The C.S boxplot indicates strong symmetry centered at 25 MPa, while also capturing a broad range down to approximately 5 MPa and up to nearly 50 MPa, suggesting an intentional design to explore various performance grades of concrete. Overall, boxplots provide a succinct summary containing central measures as well as variability alongside disruptive values, which may impact the mechanical properties coupled with sustainability concerns in concrete frameworks.

Figure 4: Distribution of sand content across concrete mixes.
Figure 4:

Distribution of sand content across concrete mixes.

2.1.3 Scatter plot analysis of feature-target relationships

The scatter plots are shown in Figure 5. explains the relationship between the compressive strength (C.S) and its major contributing components: cement, sand, w/c ratio, foam, and plastic waste. As expected, the correlation between the cement content and C.S exhibited a distinct positive trend, which confirmed the role of cement as a critical factor for strength development. The plot of sand versus C.S reveals that more intricacies-optimal sand contents of 600–900 kg/m3 are associated with higher strengths, but lower or excessively high sand contents tend to have disparate performance. The water-to-cement ratio maintains a strong negative relationship with compressive strength which aligns with theoretical expectations; “the greater the w/c ratio, the weaker the compressive strength.” In contrast, foam and plastic waste appear to bear no clear correlation to strength, as observed in their scatter plots, due to sparse and skewed usage. The corresponding data points for foam and plastic waste are close to zero, and only scant high values contribute to low or moderate strength, suggesting that such variables might be secondary factors affecting other properties, such as density or insulation, rather than directly enhancing strength. Overall, these scatter plots provide visual clarity into both strong and weak relationships as well as outlying behaviors within the dataset.

Figure 5: Scatter plots showing feature versus compressive strength relationships.
Figure 5:

Scatter plots showing feature versus compressive strength relationships.

2.1.4 Feature correlation analysis using hierarchical clustering heatmap

Figure 6 shows the heatmap resulting from hierarchical clustering in relation to a correlation matrix of the critical parameters of a concrete mix: cement, sand, water-to-cement ratio (w/c), foam, plastic waste, and compressive strength (C.S). The top- and left-hand clustering dendrograms grouped the variables according to their relatedness in terms of correlation. It can be noted that cement strongly influences the compressive strength, as it is positively correlated with r = 0.77. This confirms that the theory of cement contributes directly to mechanical performance. In contrast, the w/c ratio displays a sharp negative correlation with the C.S (r = −0.63), which is indicative of its concrete weakening properties when excessively high relative to the optimal value. Foam and plastic waste show a very strong correlation (r = 0.82), indicating that including one form is likely associated with including another form in a given mix, perhaps aimed at density reduction. Nevertheless, both have only a negligible direct correlation with C.S, confirming their subordinate role in strength development. This further illustrates that hierarchical clustering adding distinct value to cement’s relationship with strength is very close functionally, while foam and plastic waste fall within their own distinct grouping because of how differently they are used together separate from other components. In addition to visualizing specific correlations as individual data points contained within an overall construct framework, this heatmap portrays the relationships between these patterns, emphasizing the rationale behind selecting certain features to refine mixture designs.

Figure 6: Foam content distribution in lightweight concrete.
Figure 6:

Foam content distribution in lightweight concrete.

2.1.5 Quantifying linear relationships between features

The bar chart is shown in Figure 7 illustrates the correlations between the key feature pairs in the concrete dataset using Pearson’s correlation coefficient. Among the strongest correlations, cement exhibits a significant positive relationship with compressive strength (C.S) (r ≈ 0.77), which confirms that existing theories on cement content are critical for strength development. Foam and plastic waste also showed a very strong correlation (r ≈ 0.82), which may be indicative of their common occurrence in lightweight or sustainable concrete versions. On the negative side, the w/c ratio (w/c) is strongly correlated with the compressive strength (r ≈ −0.63). This is an intuitive relationship in concrete design theory; it is well known that higher ratios result in lower strength. Several other pairs, such as sand related to foam or plastic waste, demonstrated weak to negligible correlations, suggesting independence in their use and reinforcing their versatility within mixtures. Visualization enables better-informed decisions in model development, optimization of mixtures, and selection of features by providing clear summaries and intuitive overviews of statically related attributes. Table 1 shows features of descriptive statistics for modeling-relevant variables.

Figure 7: Usage distribution of plastic waste in concrete mixes.
Figure 7:

Usage distribution of plastic waste in concrete mixes.

2.1.6 Assessing data distribution with quantile-quantile analysis

Figure 8 shows the Q-Q (quantile-quantile) plots for six variables: cement, sand, water–cement ratio (w/c), foam, plastic waste, and compressive strength (C.S). It analyzes the extent of deviation from normality in the distributions with respect to a standard Gaussian distribution. The plots for cement, sand, and C.S show points approximately aligned with the red reference line, especially in the central regions, which indicates normality with only slight deviations at the extremes. The w/c plot appears to align reasonably, but exhibits clearly defined steps owing to its discrete nature. In contrast, foam and plastic waste exhibited strong deviations from the reference line, showing heavy right-skewness with outlier domination in the tails. These departures depict non-normal sparser, highly skewed distributions, consistent with their sparse experimental values within this dataset. Overall, visual assessments from Q-Q plots confirm that normality assumptions are justified for cement, sand, and compressive strength, but not foam and plastic waste. This is pertinent for statistical modeling, particularly when methods reliant on normality are used.

Figure 8: Distribution of compressive strength (C.S) among mixes.
Figure 8:

Distribution of compressive strength (C.S) among mixes.

2.1.7 Combined histogram-boxplot analysis for univariate feature exploration

In Figure 9, distribution histograms with kernel density estimation curves and boxplots are compared for the six key features of cement, sand, water-to-cement ratio (w/c), foam, plastic waste, and compressive strength (C.S). The boxplots for cement and sand revealed symmetrical data spread with minimal outliers. Their corresponding histograms displayed approximately bell-shaped distributions with some skewness. The distribution of the w/c ratio was right-skewed, with a dense peak at approximately 0.4. This is corroborated by the boxplot, which reveals several high-end outlier values, suggesting a deviation from optimal ranges in a limited sample set. Foam and plastic waste showed highly skewed distributions, featuring extreme outliers in their respective boxplots. These two parameters support the notion of limited use coupled with a non-normally distributed statistical nature, as confirmed by their long right tails dominated by near-zero values. The C.S distribution appears fairly uniform across the tested strength range, whereas the boxplot indicates a wide interquartile range without extreme outliers, suggesting targeted testing through controlled spanning across various levels of compressive strength beyond the mid-range values. The tandem histogram and boxplot provide comprehensive characterization, including central tendency summary statistics, variation measurement, skewness assessment, and anomaly detection for each parameter, thus providing a basis for advanced modeling or optimization tasks.

Figure 9: Correlation matrix between mix components and compressive strength.
Figure 9:

Correlation matrix between mix components and compressive strength.

2.1.8 Multivariate relationship visualization

Figure 10 shows that the pair plot matrix offers an overview of the critical features in the dataset and their interrelations, including cement, sand, water-to-cement ratio (w/c), foam, plastic waste, and compressive strength (C.S). As with each variable histogram on the diagonal of the plot, we confirm that prior observations of cement and sand are normally distributed, whereas overflow control sand and plastic waste are skewed. The off-diagonal scatter plots show the interactions or correlations among the pairs of variables. A strong positive linear trend was noted for both cement and C.S, whereas a pronounced negative relationship was observed for w/c versus C.S, which aligns well with the concrete strength theory. Other foam-related relationships exhibit sparse presence without discernible trends, owing to the limited non-zero presence. Moreover, moderate clustering was observed in the cement-sand and sand-CS plots, suggesting potential secondary influences or interaction effects. This matrix serves as a primary graphical approach to check the data structure for multiquadrics before machine learning or statistical modeling is applied to identify data multicollinearity as well as some nonlinear dependencies hidden within the fold-structured outline.

Figure 10: Regression coefficients of mix components for predicting strength.
Figure 10:

Regression coefficients of mix components for predicting strength.

2.2 K-fold cross-validation

K-fold cross-validation continues to be a popular method for assessing the performance of machine-learning models. Figure 4 illustrates the flowchart for 5-fold cross-validation. In this method, the training set comprises k-1 subsets, and one subset is used for validation. This step was performed k times, using different validation subsets. The model predicted the mean of the metrics obtained over all validation sets. K-fold cross validation does not just mitigate the bias and variance problems from poorly divided datasets; it also provides a better estimate of the model’s capability to generalize. Here, the aim for overfitting and underfitting was to split the training dataset into five folds, as shown in Figure 11.

Figure 11: K-fold cross-validation process [37].
Figure 11:

K-fold cross-validation process [37].

2.3 Model assessment using RF and GA-ANN and sensitivity analysis

The compressive strength of foam concrete was evaluated using random forest and genetic algorithm-artificial neural networks as predictive models. The efficacies of the RF and GA-ANN models were assessed by juxtaposing the experimental values with the anticipated values. The impact of the input on the RF model was elucidated by a sensitivity analysis, and a sensitivity analysis of the compressive strengths of the RF and GA-ANN models was conducted for each parameter. Sensitivity analysis underscores the impact of the input factors on the predictions [38]. The sensitivity analysis values assess a model’s predictions independently of the features, highlighting their significance. Sensitivity analysis evaluates a model’s predictions irrespective of the features, emphasizing their importance. Genetic algorithms that leverage Darwin’s natural selection were evaluated, chosen, crossed over, and mutated to enhance the predictive accuracy of the ANN model. Numerous studies have indicated that GA-ANN consistently enhances engineering selection and evolution. It probabilistically explores an extensive solution space for global optima as shown in Figure 12 [39].

Figure 12: Hybrid GA-ANN flowchart [39].
Figure 12:

Hybrid GA-ANN flowchart [39].

2.4 Performance assessment and sensitive analysis

To evaluate the prediction performance of the suggested ML models, six indicators were used: R, R2, MSE, MARE, RMSE, and α 20 index. The mathematical definitions of these performance metrics are as follows.

(1) R 2 = 1 − ∑ i = 1 n Actual i − Predicted i 2 ∑ i = 1 n Actual i − Predicted avg 2

(2) MSE =   1   n ∑ i = 1 n Actual i − Predicted i 2

(3) MARE =   1   n   ∑ 1 = 1 n Actual i − Predicted i Actual i

(4) RMSE =   1   n   ∑ i = 1 n Actual i − Predicted i 2

(5) a 20 = n 20 n

n 20 is the number of samples with a ratio of 0.8–1.2 between the expected and actual compressive strengths.

3 Results and discussion

An optimal replacement range of 20 % was identified, where the mixtures achieved a favorable balance between compressive strength and sustainability benefits. At lower replacement levels, the mechanical properties remained comparable to the control mix, while at higher levels, strength reduction became more pronounced despite the environmental advantages. This highlights the importance of selecting a replacement range that maximizes the valorization of waste materials without compromising structural performance which also reflects its impact on durability aspects Water absorption and sorptivity both decreased significantly for lightweight foamed concrete, enhancing durability, whereas shrinkage could be minimized. Increasing the replacement ratio with the same water content could leads to the filling of voids and the creation of denser microstructures by blocking the formation of large voids and improving the packing density, which can reduce the porosity and sorptivity [15]. Then this research also assessed the predictive capabilities of Random Forest (RF), Particle Swarm Optimization-Support Vector Regression (PSO-SVR), and a Genetic Algorithm Optimized Artificial Neural Network (GA-ANN) to forecast the compressive strength of foam concrete containing plastic waste.

3.1 Receiver operating characteristic and regression error characteristic

The performance evaluation of the GA-ANN, RF, and PSO-SVR models was demonstrated using the Receiver Operating Characteristic (ROC) and Regression Error Characteristic (REC) curves, as shown in Figure 13. The ROC curve illustrates the classification capability of both models in terms of the true positive rate versus the false positive rate [40]. Figure 13a was used to evaluate the ability of the model to distinguish between correct and incorrect outputs (even in regression models converted to binary classification). The horizontal axis represents the false positive rate, and the vertical axis represents the true positive rate. The closer the curve is to the top-left corner, the stronger the performance. The Random Forest (RF) model performed the best among all models. AUCs in training are 1.00 and 0.99, demonstrating near-perfect accuracy, with strong generalization ability to unseen data. The GA-ANN model, shown in blue, performed well in training (AUC = 0.97) but deteriorated in testing (AUC = 0.91). This significant decrease indicates overfitting [41]. The PSO-SVR model in green maintained a good balance (AUC = 0.97 in training and AUC = 0.93) in testing, which means it provides stable and balanced performance between accuracy and generalization. Figure 13b was used to analyze the accuracy of the regression models. The horizontal axis measures the “absolute error,” whereas the vertical axis shows the cumulative percentage of samples that fall within this error. The steeper the curve toward the upper-left corner, the more likely the model is to produce results that are very close to the actual values (i.e., lower error). The RF curve reached approximately 95 % of the samples with an absolute error of less than 2, indicating that most predictions were very accurate. In contrast, GA-ANN exhibited a weaker slope in the test curve, indicating less accurate predictions when faced with untrained data. PSO-SVR exhibits a curve that is closer to the RF curve in training, although less steep in testing; however, it does not collapse as sharply as GA-ANN [42]. Table 2 shows the Performance Comparison of AUC.

Figure 13: ROC analysis of all models and averages in the training and testing phases.
Figure 13:

ROC analysis of all models and averages in the training and testing phases.

Table 2:

Performance comparison of AUC.

Model AUC (train) AUC (test) % Drop in AUC Performance notes
GA-ANN 0.97 0.91 ▼ 6.19 % Noticeable overfitting; weaker generalization.
RF 1.00 0.99 ▼ 1.00 % Very strong and stable performance overall.
PSO-SVR 0.97 0.93 ▼ 4.12 % Balanced performance with acceptable generalization.

3.2 K-fold cross validation

Figure 14a shows the AUC values for each model for each fold (training/test). The values are progressively colored from yellow (poorer performance) to dark red (stronger performance). We observed that the GA-ANN model achieved the highest values in training, with an AUC of 0.9983 in fold 5, reflecting a strong learning ability [43]. However, the values dropped significantly on the test set, reaching 0.9385, which is lower than that of the other models, confirming poor generalization and overfitting. For the PSO-SVR model, we observed a strong and balanced performance. The values in training were consistently close to 0.99, and in testing, they ranged between 0.9485 and 0.9515, indicating stable performance and high prediction confidence [44]. The RF model is the most balanced in terms of the difference in performance between training and testing, with AUCs ranging from 0.9863 to 0.9881 in training and from 0.9585 to 0.9615 in testing. This consistency reflects the strong ability to generalize without sacrificing the accuracy [45]. The dark color in the training rows indicates that all models were able to learn from the data, but the variance in the test rows reflected how well the models were generalized. Figure 14b shows the percentage drop in the model performance for each fold compared with its best performance. It is an important tool for measuring the stability and volatility of a model. The closer the values were to zero, the more stable they were. For GA-ANN, we noticed that the highest percentage drop in testing was on Fold 1 (0.32), which was almost equal to the highest percentage drop in PSO-SVR and RF. However, GA-ANN maintained a very low percentage drop in training, indicating that it preserved the data well, but did not generalize it as well. PSO-SVR exhibits moderate volatility in some folds (Fold 3 and Fold 4) but maintains a zero percentage drop in Fold 2, a good indicator of stability in that fold. Overall, it outperformed GA-ANN in terms of the convergence of performance across folds. RF exhibited the best balance of percentage drops [46]. The variances of the training and test folds are close and relatively low (ranging from 0.02 to 0.31), indicating that the model is stable and not significantly affected by different data splits [47].

Figure 14: The R2 for each fold for all models in training and testing phases.
Figure 14:

The R2 for each fold for all models in training and testing phases.

3.3 Performance of machine learning for compressive strength

Figure 15 shows a scientifically accurate comparison between the actual and predicted compressive strength (C.S.) values using three different models: Random Forest (RF), GA-ANN, and PSO-SVR, on the training and test datasets. Each graph represents the performance of a particular model, with blue data points used for training data, orange for test data, and dotted red lines representing the ideal relationship (y = x), indicating perfect predictions without error. In the first graph, the Random Forest model demonstrates a very accurate performance, with most points evenly distributed on both sides of (y = x), demonstrating the model’s ability to generalize the relationship between variables well [48]. The predicted values closely matched the actual values, particularly in the medium and high ranges of compressive strength, with slight deviations at lower values. The GA-ANN model appears to be relatively weak in its accurate prediction, especially at low and medium C.S. values. The points are further dispersed away from the (y = x) line, indicating that the model suffers from a generalization problem and may be overfitted or not well tuned to the input data. In contrast, the PSO-SVR model shows a robust and consistent performance similar to that of RF, with points distributed around the (y = x) line with apparent efficiency [49].

Figure 15: Actual, predicted results of compressive strength.
Figure 15:

Actual, predicted results of compressive strength.

The model demonstrates remarkable accuracy in predicting both the training and test data, especially in the higher ranges of compressive strength, reflecting the success of the PSO algorithm in optimizing the SVR parameters and tuning the model optimally [50]. Based on this analysis, it can be concluded that both Random Forest and PSO-SVR provide robust and accurate predictive performance, with PSO-SVR having a comparative advantage in terms of consistency and reduced dispersion [51]. In contrast, GA-ANN performs less accurately and requires re-parameterization or an improved model architecture to obtain more reliable results. Figure 16 shows three comparison plots of the actual and predicted compressive strength (C.S.) values using three different allometric fit models: Random Forest (RF), Genetic Algorithm-Adapted Neural Networks (GA-ANN), and PSO-SVR. Each plot contained two curves representing the relationship between the predicted and actual C.S. values for both the training and test data. In the first plot (RF Allometric Fit), the relationship between the actual and predicted C.S. values followed an exponential curve with constant values of (a = 1.14, b = 0.96) for training and (a = 1.39, b = 0.91) for testing. The convergence of the curves indicates that the model achieves good consistency between training and testing, with a slight tendency for over-predictions in the testing phase compared to training, as evidenced by the higher value of (a) in testing. In the middle plot (GA-ANN Allometric Fit), the regression coefficient for training (a = 2.08) is higher than that for testing (a = 1.89), whereas the value of b is lower for training (0.78) than for testing (0.81), indicating that the model learns a steeper pattern on the training data, but exhibits more moderate behavior on the testing data [52]. The curves are convergent, but this model exhibits greater variability in the coefficient, which may indicate a higher sensitivity to the training data. In the third plot (PSO-SVR Allometric Fit), the training and testing curves are more convergent than those of the previous two models, with a = 1.38 for training and a = 1.17 for testing, with similar b values (0.90 and 0.96). This suggests that the model exhibits a more balanced performance between the training and testing phases, demonstrating a good generalization ability and the absence of overfitting. In general, all models showed a good fit to the actual data, but the PSO-SVR model had the best balance between the training and testing phases, while the GA-ANN model showed a clearer variance in the coefficients, which may be interpreted as being more sensitive to the training data [53].

Figure 16: Allometric fit analysis of compressive strength for training and testing.
Figure 16:

Allometric fit analysis of compressive strength for training and testing.

3.4 Statistical analysis

Figure 17 shows an extensive evaluation of the predictive model performance comparison of RF, GA-ANN, and PSO-SVR along with MAE, MSE, RMSE, R2, MAPE, and Max Error. The performance of each model was evaluated during training and testing. Based on the graph, the Random Forest model outperformed the other models in terms of accuracy in both phases, recording the lowest mean absolute error (MAE) of approximately 1.0 in training and 2.0 in testing. It also recorded the lowest MSE value in training, at approximately 2.0, and the lowest RMSE value, at approximately 1.4. This is reflected in the R2 value, which approached 1.0, in both phases, indicating that the model can explain most of the variance in the data [54]. In contrast, the GA-ANN model demonstrated relatively poor performance, with the highest values recorded for most metrics [55]. For example, the MAPE value was approximately 41.0 in training and 31.0 in testing, which is a relatively high error rate indicating that the model suffers from generalization problems. The MSE values were also very high, reaching 33.0 in training and 32.0 in testing, indicating a large discrepancy between the actual and predicted values [56].

Figure 17: Comparative evaluation of the statistical performance metrics of the RF, GA-ANN and PSO-SVR.
Figure 17:

Comparative evaluation of the statistical performance metrics of the RF, GA-ANN and PSO-SVR.

The PSO-SVR model achieved an average performance between those of the other two models. The MAE value was approximately 1.5 in training and 2.8 in testing, whereas the RMSE value was in the range of 4.5–5.0. The MAPE value was 20.0 in training and 25.0 in testing, which is lower than that of GA-ANN, but still higher than RF, indicating acceptable accuracy, but not the best [57]. The R2 value was close to 0.95, reflecting good predictive quality but lower than that achieved by the RF model. In terms of maximum error, the RF model showed the lowest maximum prediction error at approximately 10.8, compared to 31.0 for GA-ANN and over 32.0 for PSO-SVR, further strengthening the Random Forest model’s superiority in minimizing worst-case errors. Therefore, it can be concluded that the Random Forest model is the most reliable and accurate of the three models, followed by PSO-SVR, whereas GA-ANN showed less consistent and generalizable performance in predicting the compressive strength [58].

3.5 Sensitivity analysis of ML models

Figure 18 presents a sensitivity analysis of the prediction output across different input feature ranges, including plastic waste, water-to-cement ratio (w/c), foam content, sand content, and cement content. These insights are crucial for identifying the most influential variables across various value intervals. Starting with plastic waste, the sensitivity is entirely concentrated in the highest interval (0.0–360.0), with a sensitivity value exceeding 12, whereas other bins show zero contribution [59]. This implies that only the presence of significant plastic waste had a noticeable influence on the prediction. For the w/c ratio, the interval (0.4–0.5) yielded the highest prediction sensitivity (∼15), followed by moderate sensitivity (∼10) in the intervals (0.3–0.3) and (0.5–0.8). This shows that w/c within the range of 0.4–0.5 is the most critical for the model response. In the case of foam content, sensitivity was highest in the middle ranges (0.2–0.3 and 0.2–0.2) with values around 8.5, whereas the highest foam bin (0.3–22.0) results in the lowest sensitivity (∼5). This suggests that moderate foam content has a greater influence on the predicted compressive strength [60]. As for sand content, the sensitivity gradually increases with the sand quantity, peaking at the interval (826.0–1,355.0) with a value near 15, indicating that larger sand volumes strongly influence the prediction results. The lower ranges had notably less of an impact. Finally, the cement content exhibits relatively consistent sensitivity across all bins, with the highest sensitivity observed in mid-to-high cement ranges (699.7–992.8), where the sensitivity reaches 8 [61]. This indicates that a higher cement content marginally improves the prediction sensitivity, although the influence is distributed more uniformly compared with other features [62]. Figure 20 depicts the five most influential input features for the prediction of the compressive strength of the machine learning model. The importance score of a feature measure its importance with respect to the model’s input decision features. Of all the features, cement clearly has the most prevailing factor, with an importance score of 0.621, indicating that over 62 % of the predictive capacity of the model is explained by cement content alone [63]. This aligns with engineering understanding, as cement is the primary binding agent and strength contributor to concrete. Following cement, sand had the second-highest influence, with a score of 0.201, representing a substantial yet secondary contribution. The foam content ranks third at 0.137, reflecting its role in altering the density and pore structure, which can influence the compressive strength of foamed or lightweight concretes. Conversely, the water-to-cement (w/c) ratio showed minimal influence, with a score of 0.032, and plastic waste had the lowest impact at 0.009. This suggests that although the w/c ratio is traditionally critical in conventional mix designs, its impact may be overshadowed by other variables in this specific dataset or model context. Similarly, plastic waste appears to play a negligible role in determining the compressive strength.

Figure 18: Sensitivity analysis of prediction output across different input feature ranges.
Figure 18:

Sensitivity analysis of prediction output across different input feature ranges.

The set of partial dependence plots illustrates the marginal effect of five key input features–cement, sand, water-to-cement ratio (w/c), foam content, and plastic waste-on the predicted compressive strength (C.S), as shown in Figures 19 and 20. These plots are instrumental in understanding how changes in a single input variable, while keeping the others constant, influence the model’s prediction. Cement shows a strong positive correlation with compressive strength [64]. As the cement content increased from approximately 350 to 900 kg/m3, the predicted C.S increased nonlinearly from approximately 10 MPa to > 35 MPa. This emphasizes the dominant role of cement in strength development. Sand also demonstrates a positive effect, though with a slightly more gradual slope. As sand increases from 200 to 1,000 kg/m3, C.S increases from approximately 14 MPa to nearly 29 MPa, reflecting its significant contribution to concrete density and compactness [65]. In contrast, the w/c ratio exhibited a clear negative relationship. As w/c increases from 0.3 to 0.8, the C.S steadily drops from 25 MPa to approximately 22 MPa. This aligns with the known behavior, where excess water leads to porosity and weakens the hardened matrix [66]. For foam content, the partial dependence plot exhibits a sharp decline in C.S with increasing foam content. Starting at a foam ratio of 0.1, the C.S is above 28 MPa, but drops below 21 MPa as the foam content increases to 0.6. This indicates that a high foam content reduces material density and strength. The plastic waste exhibited a non-monotonic effect. Initially, as the plastic waste increased to ∼150 kg/m3, the compressive strength improved slightly to above 25 MPa. However, further increases lead to a plateau or slight decline, suggesting that plastic inclusions have an optimal threshold beyond which structural integrity diminishes.

Figure 19: Feature importance score of all inputs.
Figure 19:

Feature importance score of all inputs.

Figure 20: Sensitivity analysis for RF model for partial dependence plots (PDPs).
Figure 20:

Sensitivity analysis for RF model for partial dependence plots (PDPs).

3.6 Taylor diagram of ML models

Figure 21 shows a Taylor diagram, which was used to compare the performance of different prediction models across three key metrics: standard deviation, correlation coefficient, and root mean square error (RMSE). The black star-shaped dot represents the actual values, which served as the ideal reference for the models. The Random Forest (RF) model performed the best among the three models. The dot representing the training data (dark red) was very close to the reference, showing a correlation coefficient of R2 = 0.988 and a standard deviation very close to the reference (approximately 16.8), reflecting very high accuracy and excellent consistency. On the test data, the model also performed well, with R2 = 0.923 and an acceptable standard deviation, indicating high generalization ability and no overlearning [67].

Figure 21: Taylor diagram comparison of ML models for compressive strength predictions.
Figure 21:

Taylor diagram comparison of ML models for compressive strength predictions.

In contrast, GA-ANN performs less accurately. For the training data, the correlation coefficient R2 was 0.816, whereas for the test data, it was 0.813. Although the values were close between the two runs, their standard deviation was significantly lower than that of the reference, indicating a poor ability to represent the true dispersion of the data and a possible tendency to underfit the model. The PSO-SVR model performed on an average better than the other two models. It achieved R2 = 0.882 in the training data and R2 = 0.857 in the test data, which are good results and indicate the relative stability between the two runs [68]. However, the positions of its points on the graph show a lower standard deviation than the reference data, reflecting some bias in representing the variance of the data [69]. Based on the Figure ure, it can be concluded that the RF model performed best and was closest to the reference data in both the training and test data, followed by the PSO-SVR model, which performed well but fell short of RF accuracy. The GA-ANN model ranked last in terms of both closeness to the reference values and statistical accuracy [70].

3.7 Environmental impact

Using waste plastic as a partial substitute for fine aggregates in foamed concrete can reduce the embodied carbon of the mixture. The upstream impacts associated with diverting, processing, and reusing plastic waste are typically lower than those from extracting and transporting natural sand, so CO2 emissions tend to decline as the plastic fraction increases within a practical range. Beyond a certain point, however, the environmental gains may level off or reverse due to added processing needs or performance trade-offs. Overall, this strategy supports circularity diverting plastic from landfills, reducing reliance on virgin aggregates, and aligning with sustainability objectives for lower-carbon construction [15].

4 Discussion and limitations

  1. This study focused on compressive strength as the primary mechanical indicator, establishing a baseline for the feasibility of incorporating plastic waste and foundry sand. However, durability-critical properties such as water absorption/sorptivity, drying shrinkage, and resistance to chemical (e.g., sulfate/chloride) attack were beyond the present scope and remain decisive for long-term serviceability. Future work will implement a structured durability test matrix under representative exposures (e.g., wet-dry and freeze-thaw cycling, chloride/sulfate ingress, and elevated-temperature conditioning), complemented by microstructural diagnostics (porosity and pore-size distribution) to link mechanisms with performance. The machine learning models were trained on a dataset of 191 experimental samples, which is relatively small and may affect statistical robustness. This limitation is primarily due to the resource- and time-intensive nature of preparing and testing experimental mixtures. To mitigate this, techniques such as cross-validation, hyperparameter tuning, and sensitivity analysis were employed. Nevertheless, future research will focus on expanding the dataset through additional laboratory work and integration of data from literature sources, thereby improving the generalizability of the predictive models. The very high R2 values reported, particularly for GA-ANN (0.9979), may raise concerns about overfitting. While safeguards such as K-fold cross-validation, train–test data splitting, and rigorous hyperparameter optimization were applied, the possibility of overfitting cannot be entirely ruled out. To address this, future work will explore ensemble approaches and external validation with independent datasets to further ensure the robustness of the predictive models. Although the study highlights the environmental advantages of valorizing plastic waste and foundry sand, these benefits were discussed qualitatively rather than quantified. Indicators such as carbon footprint reduction, energy savings, and waste diversion rates would provide stronger evidence of sustainability. Accordingly, future studies will incorporate life cycle assessment (LCA) and quantitative analyses of environmental impacts to strengthen the sustainability argument. The surface modification of recycled plastics through polyester resin immersion followed by foundry sand coating offers a novel dual-action approach that combines chemical adhesion with mechanical interlocking. The proposed composite shows promise for applications in low-cost housing, lightweight infill panels, and other non-structural elements, where sustainability, cost-effectiveness, and adequate mechanical performance are prioritized over high load-bearing capacity.

5 Conclusions

This research evaluated the effectiveness of Random Forest (RF), Regression Error Characteristic (PSO-SVR), and a Genetic Algorithm-optimized Artificial Neural Network (GA-ANN) in predicting the compressive strength of foam concrete incorporating plastic waste. The main findings and conclusions are as follows.

  1. Both the RF and GA-ANN models demonstrated great accuracy in predicting the compressive strength, achieving R2 values of 0.9872 and 0.9979 for training and 0.9005 and 0.8853 for testing, respectively.

  2. The PSO-SVR model achieved an average performance between those of the other two models. The MAE value was approximately 1.5 in training and 2.8 in testing, whereas the RMSE value was in the range of 4.5–5.0.

  3. In the RF model, sensitivity analysis showed that the input parameters cement (0.39), foam (0.34), sand (0.17), water-cement ratio (0.11), and plastic waste (0.39) had the greatest impact on compressive strength. The strongest contributors to the GA-ANN model were cement (0.41), sand (0.31), water-cement ratio (0.13), foam (0.11), and plastic waste (0.05).

  4. The PSO-SVR model maintained a good balance (AUC = 0.97 in training and AUC = 0.93) in testing.

  5. Partial dependence plots suggested that higher cement quantities generally improve the compressive strength, but higher water-cement ratios weaken it. The effects of foam, sand, and plastic ash are complex, multifaceted, and non-linear.

  6. The models effectively explained the complex relationships between the mix design parameters and the compressive strength in foam concrete with plastic waste.

  7. The use of AI-based RF and GA-ANN models proved successful in optimizing mix designs and predicting the performance of sustainable foamed concrete containing recovered plastic waste.

  8. By incorporating waste materials into concrete mixtures, these models assisted in accurately predicting strength, thus enabling the formulation of more sustainable concrete mixtures.

  9. This study demonstrated the importance and accuracy of machine-learning methods for the design of sustainable foam concrete. The knowledge gained from this study can be applied to improve mix design and promote the use of recycled materials in concrete production.

Corresponding author: Zhixiong Yang, Gansu Province Transportation Planning Survey & Design Institute Co, Ltd., Lanzhou 730030, Gansu, China, E-mail:

Acknowledgments

The research team thanks the Deanship of Graduate Studies and Scientific Research at Najran University for supporting the research project through the Nama’a program, with the project code (NU/GP/SERC/13/698-1).

  1. Funding information: Graduate Studies and Scientific Research at Najran University for supporting the research project through the Nama’a program, with the project code (NU/GP/SERC/13/698-1).

  2. Author contributions: H. T: conceptualization, methodology, formal analysis, writing-original draft. Z. Y: supervision, resources, writing, reviewing, and editing. A. H. A.: data acquisition, validation, writing, reviewing, and editing. R. S. A: software, formal analysis, writing, reviewing, and editing. M. A.: software, visualization, formal analysis, validation. A. M. M.: conceptualization, supervision, resources, methodology. All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflicts of interest: The authors state no conflict of interest.

  4. Data availability statement: The dataset generated and/or analyzed during the current study are available from the corresponding author upon reasonable request.

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Received: 2025-07-28
Accepted: 2025-10-06
Published Online: 2025-11-24

© 2025 the author(s), published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/rams-2025-0172
Keywords for this article
lightweight foamed concrete; compressive strength; gene expression programming (GEP); sensitivity analyses; waste plastic
Creative Commons
BY 4.0

Articles in the same Issue

  1. Review Articles
  2. Utilization of steel slag in concrete: A review on durability and microstructure analysis
  3. Technical development of modified emulsion asphalt: A review on the preparation, performance, and applications
  4. Recent developments in ultrasonic welding of similar and dissimilar joints of carbon fiber reinforcement thermoplastics with and without interlayer: A state-of-the-art review
  5. Unveiling the crucial factors and coating mitigation of solid particle erosion in steam turbine blade failures: A review
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  8. A scientometric review on the utilization of copper slag as a substitute constituent of ordinary Portland cement concrete
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  10. Recent advance of MOFs in Fenton-like reaction
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