Leveraging Machine Learning (ML) to Enhance the Structural Properties of a Novel Alkali Activated Bio-Composite

Abstract

This study explored the use of Borassus fruit fiber as reinforcement for earthen matrices (BFRC). The experimental results of the testing carried out on the structural properties were used to generate a primary dataset for training and testing machine learning (ML) models. Linear regression (LR), Decision tree regressor (DTR), and gradient boosting regression (GBR) were used to build an ensemble learning (EL) model during the prediction of the hygroscopic properties, Young’s modulus, and compressive strength of the BFRC. Fiber content, activation concentration, curing days, dry weight, saturated weight, mass, flexural vibration, longitudinal vibration, correction factor, maximum load, and cross-sectional area were the various inputs considered in the structural properties prediction. The performance of both EL and single models (SMs) was appraised via three performance metrics—mean square error (MSE), root mean square (RMSE), and the coefficient of determination (R²)—to comparatively ascertain the model’s efficiency. Results showed that all models exhibited high accuracy in predicting Young’s modulus and compressive strength. Ensemble learning outperformed single models in predicting these properties, with MSE, RMSE, and R² of 0.01 MPa, 0.1 MPa, and 99% and 3,923,262.5 MPa, 1980.7 Pa, and 99% for compressive strength and Young’s modulus, respectively. However, for hygroscopic behavior, linear regression (LR) demonstrated superior performance compared to other models, with MSE, RMSE, and R² values of 0.13%, 0.36%, and 99%.

1. Introduction

In response to escalating environmental issues linked to the widespread production and utilization of cement and its byproducts, earthen materials, one of the most prevalent traditional building materials, have attracted significant interest in the construction industry in recent decades.

These concerns are mirrored in climate change and the depletion of raw material resources [1], ecological system instability, etc. Consequently, research has focused on identifying and generating “green” alternatives for the construction sector. Earthen materials constitute the best alternative because of their beneficial properties. They have a low thermal conductivity (0.5–1 W/mK) [2], robustness (defined from key factors such as strength and volumetric stability) [3], and low fabrication energy consumption (2856–17,136 GJ/tons) [4]. They also release no greenhouse gases during manufacturing or implementation [5], and they are readily available. These materials are attractive since they tackle the sustainability challenges posed by the extensive utilization of Portland cement, the production of which releases CO₂ and disrupts the environment [6]. Per contra, earthen materials have some drawbacks that hinder their widespread application [7]. Among these drawbacks, their properties are often lower than required for structural application [8]. Therefore, they are mixed with admixtures [9], additives [10], and fiber reinforcement [11], and treated by mechanical [12] or chemical activation [13], during their production. Among many other techniques for earthen matrix production, natural fiber reinforcement is the preferred strengthening technology. The most-utilized fibers are sisal [14], jute [15], and coconut fiber or coir [16].

The Borassus tree is a plant in the coconut tree plant family [17]. The fruit’s primary constituents are fiber and a jelly-like substance [18]. It is readily available in Asia and sub-Saharan Africa, where it remains underutilized and is therefore regarded as agro-waste. The use of agro-waste has garnered significant interest from the construction sector due to its renewability, reduction of dependence on less sustainable traditional materials, cost-effectiveness, and excellent performance. The palm oil business is one of the major producers of waste: from the entire number of fresh fruits, 20% is waste (nutshell waste), and 30% of fibers/empty bunches are produced [19], and coconut fibers, or coir, are utilized in the building and automotive industries [20]. Given their familiarity with coir, Borassus fruit fibers are an attractive option for fiber reinforcement in earthen composites for construction applications. To improve the mechanical properties of the earthen matrix, the fiber from the Borassus fruit has been utilized as reinforcement. A different strategy to increase the material’s toughness, ductility, and resistance to deformation is to add fibers to matrices that exhibit mechanical fragility. The fibers regulate crack growth throughout the matrix under various loading scenarios and when retracting takes place.

An area of computer science known as artificial intelligence (AI) aims to emulate human intelligence on tasks by training computers how to perceive and learn inputs for perception, knowledge representation, reasoning, problem-solving, and planning. There are many different types of innovative AI technologies that are all designed to replicate human cognitive abilities. Because of this, these systems can purposefully, intelligently, and adaptably deal with situations that are becoming more complicated and ambiguous [21]. AI is defined by Russell as “the study of how to make machines do things, which at the moment, people do better” [22]; it is a discipline that envelops everything that makes a machine intelligent [23]. Artificial intelligence is usually conceived of as combining data analytics and machine learning (ML). Without explicit programming, ML, a subfield of AI, enables computers to learn and perform better through data analysis. The primary goal of ML algorithms, which are used to create predictive models, is to identify and analyze patterns in datasets [24]. Among the ML techniques are the following: (i) Supervised ML: This field of research focuses on the method by which computers determine what to do after learning input and intended output pairs from labeled datasets. It is divided into classification and regression. (ii) Unsupervised Machine Learning: This field focuses on teaching machines the fundamental structures found in unlabeled datasets. It is categorized into clustering and dimension reduction techniques. (iii) Reinforcement Learning: This is a computational approach involving learning from the outcome of interactions with the environment. It can be defined as discovering an approach to maximize a scalar reward or reinforcement signal by mapping situations to actions. (iv) Deep Learning: This processes huge amounts of data and performs operations like speech translation and image recognition using intricate algorithms that mimic the structure of the human brain [25].

Supervised ML techniques have gained attention in civil engineering applications, mainly for prediction of the mechanical properties of concrete and other composites. Supervised machine learning is a type of ML that trains on data that has already been labeled with the desired output [26]. This data is then used to build a model that can predict the output for new, unseen data. Many studies have been undertaken using ML approaches to forecast the strength properties of concrete and its structural elements as well [27]. Nguyen et al. [28] employed a machine learning approach to assess the compressive characteristics of geo-polymer concrete [28]. The thermo-mechanical properties of a waste-based composite was predicted through ML approaches. In that investigation the authors found that LR regression displayed the highest performance, followed by random forest (RF) and gradient boosting (GB) [29].

An ML technique called ensemble learning (EL) generates a single forecast that is more accurate than the predictions of many models by combining their predictions. EL is divided into three primary categories: stacking, boosting, and bagging. By choosing a subset of the provided dataset at random and replacing it, the bagging approach trains several models on various subsets of the data. Boosting is a method that trains the models sequentially, with each model trying to correct the errors of the previous model. Random forest is a variant of bagging algorithms [30], and adaptive boosting (AdaBoost) is one of the most popular boosting algorithms [31]. The stacking method trains a separate model (called a meta-learner) to combine the predictions from the other models [32]. An ensemble learning (EL) model has been used by Shatnawi et al. [33] to predict the shear capacity of slender steel fiber-reinforced concrete (SFRC) beams with high accuracy. The model displayed R² values of 0.963 and 0.972 for the testing and training sets, respectively. In addition, both the training and testing sets of the gradient boosting regression tree (GBRT) model had low RMSE and MAE values, indicating that the prediction capability of the EL model can be trusted with high confidence [33]. Gradient boosting (GBoost) was utilized by Munir et al. [34] to forecast the compressive strength of concrete with recycled and natural aggregate. According to their findings, GBoost outperformed the other models they employed to forecast the recycled aggregate concrete’s compressive strength [34]. Random forest, another EL model, outperformed Artificial Neural Network (ANN) models in terms of prediction accuracy during the forecast of geopolymer concrete’s strength [35]. An EL model was developed using the experimental data to forecast the structural characteristics of earthen composites.

The EL developed in this study is derived from gradient boosting regression (GBR), decision tree regression (DTR), and linear regression (LR). An ML model called linear regression (LR) fits a linear equation to the observed data in order to model the connection between a dependent variable and one or more independent variables [36]. The objective is to develop a mathematical formula that, given the values of the independent variables, reliably forecasts the value of the dependent variable. Linear regression is particularly effective when the relationship between variables is linear and can be easily interpreted [37]. Numerous disciplines, notably civil engineering, make extensive use of it. It is important to remember that linear regression assumes that there is a linear relationship, which may restrict its use when the data shows non-linear patterns. In contrast to decision trees, linear regression frequently necessitates meticulous data preprocessing, including managing outliers and missing values, to ensure accurate outcomes [29]. Additionally, while decision trees can handle both categorical and numerical data without extensive preprocessing, linear regression typically requires converting categorical data into numerical representations.

The decision tree regression (DTR) algorithm builds a model in the form of a tree using training data, with each internal node representing a test, the branches representing the test’s outcomes, and the leaves representing the decisions [38]. Tree creation and tree trimming are the two procedures in this form of modeling. The training dataset zone is separated into precisely defined sections as part of the first stage, also known as the tree-building phase. A tree with many branches could be the outcome of this stage. In order to reduce the size of the non-essential or unnecessary decision tree components, the second stage, known as tree pruning, is deciding which branches of the built tree to remove. The decision tree model is a graphical method that directly applies probability analysis; it depicts a mapping relationship between object characteristics and object outcomes [39]. Decision tree models were trained to categorize high-strength concrete mix design techniques based on concrete mix proportions with great accuracy. It was demonstrated that the model could correctly determine the mixing method by which the high-strength concrete mix was designed simply by providing the fundamental proportions of the basic elements [40]. A DTR with ensemble algorithms such as bagging was developed to predict the compressive strength of concrete with waste material. The results demonstrated that the DTR with bagging gives more precise performance than an individual one because DTR with bagging enhances the model accuracy by giving fewer errors [41]. The algorithm for DTR is comparatively straightforward and simple to comprehend. Additionally, it does not require any additional preprocessing to handle continuous and categorical information.

On the other hand, gradient boosting (GBR) is an efficient supervised machine learning technique that constructs an ensemble of weak learners (usually decision trees) one after the other until it produces a single, stronger prediction model. Every weak learner in the series concentrates on fixing the mistakes committed by the ones before it, creating a final model with higher precision [42]. Gradient boosting can provide state-of-the-art performance on a variety of tasks, such as regression, classification, and ranking, by iteratively improving predictions. It may operate with a variety of data formats, including mixed, continuous, and categorical features. It can be easier to comprehend how the model makes predictions by looking at the decision tree structure of weak learners, which can offer some insights into the model’s reasoning [33].

This study intends to develop an ensemble learning (EL) model from linear regression (LR), decision tree regression (DTR), and gradient boosting regressor (GBR) models to compare with these individual models during the prediction of the hygroscopic and mechanical behavior of the Borassus fiber-reinforced composite (BFRC). The prediction of the hygroscopic and mechanical behavior is carried out to assess the structural property of the novel composite. The aim of building the EL model is to improve the prediction’s performance of the single model (SM).

Developed primary datasets were used for EL and SM data training, testing, and validation. The experimental results from the analyses of water absorption, Young’s modulus, and compressive strength were used to create our primary datasets. The main dataset was created in order to build models that can effectively handle modest amounts of data. The importance and originality of this study are as follows: (i) Conducting experimental work for Young’s modulus, compressive strength, and water absorption for BFRC to generate a primary dataset from the experimental results. (ii) Developing EL models and SMs that will efficiently perform on a small-sized dataset. (iii) Pioneering the comparative evaluation of EL vs. SM during the prediction of the structural properties of BFRC using primary dataset. This study develops and evaluates ensemble learning models specifically designed to perform effectively with limited primary data by providing a rigorous comparison to determine the effectiveness of the ensemble learning approach in predicting structural properties of BFRC. The importance of this research is to understand the role of input parameters such as fiber content, activator concentration, curing days, maximum loads on compression, torsion, and flexion on the accuracy of the output from the EL model and SM. Then a comparison of the models’ efficiency (EL and SM) in the case of this primary dataset is performed. Each model’s performance was appraised using the evaluation metrics. The outcome will enable supporting local economies through the valorisation of the Borassus fruit fiber into a sustainable reinforcement for construction applications.

2. Materials and Methods

2.1. Materials

2.1.1. Soil Excavation and Processing

The vegetal soil was provided from a construction field; thus, it is an excavated soil. The granulometry of the soil was obtained using sieve analysis. The coarse aggregates were crushed before removal of unwanted elements, mechanical grinding, and dry sieving were performed according to the British standard BS 1377:2 code [43]. Moisture content analysis was also carried out on the soil in accordance with the BS 1377:2 to facilitate the evaluation of the optimum moisture content, which guides the amount of water needed during sample production. Other soil’s characteristics such as specific gravity, dry density, and Atterberg limit were carried out in accordance with the ASTM D854—14 [44], D7263-21 [45,46], and D4318-17e1 [46], respectively.

2.1.2. Natural Fiber Extraction

The fiber used as reinforcement to the earthen matrix in this investigation was obtained naturally from Borassus fruit. The extraction was achieved manually and chemical-free on fully ripe Borassus fruit. The fruit was segmented vertically into smaller pieces to separate the mesocarp from the seed. Then it was washed under running tap water for 30 min [18]. The extracted fibers were oven-dried, and two types of fibers were extracted: coarse and fine, both used during this investigation. The natural fiber was used during this investigation without undergoing any chemical treatment, with a uniform length of 3 cm. The details of the Borassus tree, fruit, and extracted fibers are shown in Figure 1.

2.1.3. Composite Production

The processed earthen matrix was mixed with 0.5 wt% of natural Borassus fruit fiber (BF). The alkaline activator or KCO₃ was added to the dry mixture before mixing in a laboratory mixer for 5 min at a concentration level of 0.3 wt%. Distilled water at room temperature (27 °C) was added to the dry mixture gradually until reaching the required amount. The paste was allowed to cool for a few minutes because of the exothermic reaction before being placed into metallic moulds of 10 mm × 10 mm × 10 mm [47] and 40 mm × 40 mm × 160 mm [18] for compression and Young’s modulus testing, respectively. The sample underwent mechanical compression to attain denser and stronger bricks before being demoulded; the samples were oven dried for 24 h at 60 °C and left in an oven to cure for the curing periods of 14 and 90 days [18]. Figure 2 summarizes the steps undertaken during this investigation.

2.2. Experimental Program

2.2.1. Mechanical Behavior Experiment

Compressive strength defines the behavior of a material to deform under compression forces. It defines the structural integrity and ability of building materials to be used properly for load-bearing or non-bearing purposes, making it a significant property. It was carried out by placing the BFRC at a loading rate of 1.2 kN/s monotonically into an electromechanical testing machine, UTM7001 Model 4002, in accordance with ASTM C109/C109M-20 [48].

The elastic modulus, or Young’s modulus, is an essential property of construction materials. For the BFRC, the Young’s modulus testing was carried out via the impulse excitation technique (IET) using GrindoSonic equipment [49]. The method was selected because it was more cost-effective than a uniaxial compression test, safe, non-destructive, and quick to perform. While both methods yield precise measurements, destructive testing offers the most reliable results. According to ASTM C 1548–02 [50], its basic method is to measure the resonance frequencies by impulse in three separate vibrational modes: flexural, torsional, and longitudinal, as seen in Figure 3. It was determined according to the following equation [49]:

$$\mathrm{E}=0.9465\left(m{ \times f_f}^2/b \right)\left(L^3/t^3\right)T_1$$

(1)

where E is the Young’s modulus (Pa), m is the mass of the specimen (g), $f_f$ is the fundamental resonant frequency of the specimen during flexural vibration (Hz), b is the width of the specimen (mm), L is the length of the specimen (mm), t is the thickness of the specimen (mm), and T₁ is the correction factor that accounts for the finite thickness of specimen, Poisson’s ratio, and so forth [49].

2.2.2. Hygroscopic Analysis

The hygroscopic behavior was assessed through a water absorption experiment. The samples were immersed into distilled water at room temperature (27 °C) for 24 h. This was performed to assess the dimensional integrity of the samples when exposed to moisture resulting in their swelling. The testing procedure was replicated from the author’s previous work [51] using the following equation:

$$W_a={\displaystyle \frac{{(m}_{wet}-m_{dry})}{m_{dry}}}\times 100$$

(2)

where Wa is the water absorption in (%), m_wet the specimen’s wet mass in (g) and m_dry the specimen’s dry mass (g).

2.2.3. Scanning Electron Microscopy (SEM)/Electron Dispersive X-Ray (EDX)

After mechanical failure of the specimens, microstructural analysis was performed. Scanning electron microscopy (SEM) was carried out to determine the morphology of the Borassus fruit-reinforced composite (BFRC). Meanwhile, energy-dispersive X-ray spectroscopy (EDX) was used to detect the semi-quantitative estimates of the chemical compositions. This was done using a Carl Zeiss scanning electron microscope that was instrumented with a Model EVO LS10 EDX system.

2.2.4. Machine Learning Models

Using an ML technique called EL, several weak learners were combined to produce a single, stronger learner. Henceforth, during this investigation LR, GBR, and DTR were used to build up an EL as described in Figure 4. The mathematical formulation of the models used are detailed in

Table 1. Mathematical formulas of LR, GBRs and DTR.

LR	GBR	DTR
$\mathrm{Y} = {\mathrm{\beta }}_0 + {\mathrm{\beta }}_1 x$ + ε	$Y={\sum }_{m=1}^M{\gamma }_m{h}_m\left(x\right)$	Non-parametric, henceforth complex to represent mathematically

where Y represents the dependent variable, x is the independent variable, β₀ is the intercept (the value of y when x is 0), β₁ is the slope (the change in Y for a one-unit change in x), ε is the error term (the difference between the observed value of Y and the predicted value), h_m(x) are the basis functions; ${\gamma }_m$ are the shrinkage parameters.

.

The results obtained from the water absorption experiment were used to build a primary dataset composed of 72 observations with 5 input variables (fiber content, activator concentration, curing days, dry weight, and saturated weight) and the water absorption as the output variable, as seen in

Table 2. Details of input variables obtained from experiments during the prediction of the water absorption.

Fiber Content (%)	Activator (%)	Curing Days	Dry Weight (g)	Saturated Weight (g)	Water Absorption (%)
0.5	0.03	14	479.1	541.5	13.02
0.5	0.03	14	442.2	489.1	10.60
0.5	0.03	14	482.4	535.4	10.99
0.5	0.03	14	501.6	596.5	18.92
0.5	0.03	14	496.9	607.6	22.28
0.5	0.03	14	489.2	605.4	23.75
0.5	0.03	14	488.4	610.7	25.04
0.5	0.03	14	538.6	670.9	24.57
0.5	0.03	14	478.4	640.3	33.83
0.5	0.03	14	489.1	531.5	8.67
0.5	0.03	14	452.2	499.1	10.37
…	…	…	…	…	…
…	…	…	…	…	…
…	…	…	…	…	…
0.5	0.03	90	499.3	615.8	23.33
0.5	0.03	90	452.2	605.7	33.94
0.5	0.03	90	492.2	640.6	30.16

. Meanwhile, for the mechanical properties’ evaluation, an experimental test was performed for the compressive strength and Young’s modulus of the BFRC. The experimental results from the mechanical testing were used to generate a primary dataset on the compressive strength and Young’s modulus containing 72 observations for each property. The input variables for the compressive strength and Young’s modulus were 5 (fiber content, activator concentration, curing days, maximum load, and cross-sectional area) and 7 (fiber content, activator concentration, curing days, mass, flexural vibration, longitudinal vibration, and correction factor), as shown in

Table 3. Details of input variables used during the prediction of compressive strength obtained from experiments.

Fiber Content (%)	Activator (%)	Curing Days	Cross Sectional Area (mm2)	Maximum Load (kN)	Compressive Strength (MPa)
0.5	0.03	14	1000	1290	1.29
0.5	0.03	14	1000	1290	1.29
0.5	0.03	14	1000	1290	1.29
0.5	0.03	14	1000	2290	2.29
0.5	0.03	14	1000	2345	2.35
0.5	0.03	14	970	1234	1.27
0.5	0.03	14	970	1580	1.63
0.5	0.03	14	970	1305	1.35
0.5	0.03	14	970	1495	1.54
0.5	0.03	14	900	1495	1.66
0.5	0.03	14	900	1890	2.10
…	…	…	…	…	…
…	…	…	…	…	…
…	…	…	…	…	…
0.5	0.03	90	800	19,475	24.34
0.5	0.03	90	800	18,543	23.18
0.5	0.03	90	800	17,456	21.82

and

Table 4. Details of input variables obtained from experiments during the prediction of Young’s modulus.

Fiber Content (%)	Activator (%)	Curing Days	Mass (g)	Flexural Vibration (Hz)	Torsional Vibration (Hz)	Correction Factor	Young’s Modulus (Pa)
0.5	0.03	14	465.17	3.15	4.41	1.4115625	462,555.777
0.5	0.03	14	500.12	3.12	4.48	1.4115625	534,674.114
0.5	0.03	14	520.09	2.94	2.71	1.4115625	578,226.139
0.5	0.03	14	421.16	2.74	4.07	1.4115625	379,170.854
0.5	0.03	14	469.08	2.73	4.41	1.4115625	470,364.51
0.5	0.03	14	532.77	3.11	4.35	1.4115625	606,764.603
0.5	0.03	14	487.53	3.13	3.9	1.4115625	508,093.224
0.5	0.03	14	469.46	3.03	3.87	1.4115625	471,126.9
0.5	0.03	14	476.57	3.1	3.18	1.4115625	485,505.454
0.5	0.03	14	520.6	2.59	3.16	1.4115625	579,360.711
0.5	0.03	14	451.6	2	2.63	1.4115625	435,961.943
…	…	…	…	…	…	…	…
…	…	…	…	…	…	…	…
…	…	…	…	…	…	…	…
0.5	0.03	90	425.16	3.02	3.16	1.4115625	386,407.467
0.5	0.03	90	468	2.97	2.63	1.4115625	468,201.089
0.5	0.03	90	512	2.82	3.37	1.4115625	560,377.43

, respectively. To identify the most effective model between EL and SM for this composite, the prediction outcomes of the models were assessed comparatively based on their performance metrics.

Feature preprocessing: All numerical features were normalized using min–max scaling to ensure comparability and to improve convergence during training. No categorical variables were involved.

Feature selection: Correlation analysis was performed to identify and eliminate redundant features. Only variables with significant contributions to prediction accuracy were retained.

• Performance metrics

A model’s efficiency can be appraised by the combination of performance metrics because each performance metric estimates the error differently. The testing and training metrics used during this investigation are mean square error (MSE), root mean square error (RMSE), and the coefficient of determination (R²). MSE measures the average of the squares of the errors; it is a key metric because it emphasizes larger errors more than smaller ones due to squaring each error [52]. RMSE is the square root of MSE; it provides a measure of the model’s accuracy during the output prediction. R² is a measure of the way the regression of the predicted output fits the experimental data [24]. The various metrics can be described in Equations (3), (4) and (5) respectively, where $y_{exp}$ is the experimental data values, $y_{pred}$ is the predicted value, and n is the total number of data value.

$$MSE=1/n{\sum }_{i=1}^n{(y_{exp}-y_{pred})}^2$$

(3)

$$R^2=1-{\displaystyle \frac{\sum _{i=1}^n{(y_{exp}-y_{pred})}^2}{\sum _{i=1}^n{\left(y_{pred}-(1/n\sum _{i=1}^n{y}_{exp}\right))}^2}}$$

(4)

$$RMSE=\sqrt{MSE}$$

(5)

b.

Framework to establish the machine learning models

Python 2.7.12 was utilized to implement the tests. Figure 5 depicts the various steps from the composite manufacturing until the comparative analysis of the EL and SM models’ performance. During the training and validation of DTR, optimal values were determined through grid search were max_depth = 5, min_samples_split = 2, and min_samples_leaf = 1. The following features of the experimental protocol are included to enhance its reproducibility [53]:

Data: X (matrix), y (vector)

Split: X_train, y_train, X_test, y_test

Tree: T = DecisionTree()

• T.build(X_train, y_train)

  ○

  Recursively split nodes:

  ■

  Find best feature f using a splitting criterion (e.g., Gini impurity, information gain)

  ■

  Split node into child nodes based on f

  ○

  Stop splitting when criteria met

Prediction:

• ŷ = T.predict(x)

Evaluation:

• Metrics on X_test

For GBR, the best parameters obtained via grid search were n_estimators = 300, max_depth = 3, and learning_rate = 0.1. Meanwhile, its experimental protocol is outlined below [53]:

Initialization:

• ŷ₀ = initial model prediction (e.g., average target value)
• M = ensemble of weak learners

Boosting iterations:

• For m = 1 to M:

  ○

  Calculate residuals: r_i = y_i − ŷ_i−1

  ○

  Train weak learner hₘ(x) on (X, r)

  ○

  Update ensemble: ŷ_i = ŷ_i−1 + α ∗ hₘ(x_i)

Prediction:

• ŷ = Σ[αₘ ∗ hₘ(x)]

Evaluation:

• Metrics on X_test

For LR, default settings were used with no hyperparameters required. The following experimental procedure was used during the prediction of the LR model:

Initialization:

• ŷ₀ = initial model prediction
• y = model parameters: β = 0

Training:

• For each training (x_i, y_i):

  ○

  Calculate the residual: r_i = y_i − ŷ_i

  ○

  Update the model parameters: β = β + α ∗ x_i ∗ r_i

  ○

  Update the prediction: ŷ_i = β ∗ x_i

Prediction:

• For a new input x:

  ○

  Calculate the predicted value: ŷ = β ∗ x

Evaluation:

• Calculate metrics on X_test

For the EL strategy, a weighted averaging method was employed, where weights were assigned to each model based on its validation performance. This allowed the EL model to leverage the strengths of individual algorithms while minimizing weaknesses. These additions clarify the methodological rigor adopted in the study and ensure reproducibility of the proposed framework.

3. Results and Discussion

3.1. Physico-Morphological Observations of Borassus Fruit-Reinforced Composite (BFRC)

Using mechanical sieving in compliance with BS 1377:2, the excavated soil’s particle size distribution was ascertained; it showed that about 75% of the soil’s particles were smaller than 80 µm (Figure 6).

This particle size distribution is similar to the one displayed by the soil obtained from the termite hill in a previous work carried out by the authors [54]. The degree to which soil particles pack together depends on their size and arrangement. The fact that about 75% of our soil particles are below 80 µm enables the obtention of a denser earthen matrix, as seen in the micrograph (Figure 7a). On the other hand, from the micrograph, it can be noticed that the soil’s particles depict curved, flaky, and annular morphologies. The curved, flaky, and annular shapes observed in this matrix enable it to pack easily with fewer voids. Thus, the packing and density behavior of the earthen matrix is significantly affected by the soil particles’ shapes. They also affect the water retention and stability of the matrix because the curved and flaky particles create more friction and smaller channels for water to flow through the matrix [55].

The plasticity index and liquid limit—the points above which soil transitions from a solid to a plastic and from a plastic to a liquid state—were evaluated by looking at the excavated soil’s Atterberg limit. This makes it easy to comprehend how the soil behaves during stress and moisture changes, avoiding potential issues with dimensional stability brought on by matrix swelling or shrinking [56]. The strength and dimensional stability of the earthen matrix are significantly impacted by the moisture content, which is found to be 3.55%. It was shown that measuring the matrix’s level of compaction guarantees that the soil particles would bond together efficiently during compaction, increasing stability and strength. By supplying the proper amount of moisture required during the composite construction process, it permits the removal of voids and inhibits erosion. As the moisture content increases, the soil lubricates itself, making it easier to compact and have a higher density [57].

The dry density and specific gravity of the excavated soil were 0.56 g/cm³ and 2.5 respectively; they influence the compaction behavior of the earthen matrix and the void ratio. The results of the physical characterization are shown in

Table 5. Raw material characteristics.

Soil’s Physical Characteristics		BNF Properties: Fine Fibers
Particle size distribution	75% > 80 μm	Length/diameter	5 cm/50 µm
Specific gravity	2.50	Elongation	25%
Dry density	0.56 g/cm3	Modulus	7.5 GPa
Moisture content	3.55%	BNF Properties: Coarse Fibers
Liquid limit	33.50%	Length/diameter	10 cm/170 µm
Plastic limit	20.30%	Elongation	30%
Plasticity index	13.20%	Modulus	8.5 GPa

. A higher dry density typically leads to improved strength, stiffness, and bearing capacity. However, excessive dry density can reduce workability and increase susceptibility to cracking. The optimal balance between specific gravity and dry density is crucial for achieving desired mechanical performance in various applications [58].

The morphology of both the earthen matrix and the BNF are very important to understand the bonding mechanism between the reinforcement and the matrix. The results of the morphological characterization performed on the BNF indicated a length variation of 5 cm to 10 cm for both fine and coarse fiber. These results are within the range of the results obtained in a previous work on the Borassus fiber [59]. However, the diameter greatly varied from 50 µm to 170 µm, with an elongation of 25–30%, as illustrated in Figure 7b. The presence of superficial pores in the fibers with minimal depths is also noticed from the micrograph (Figure 7a). These pores cannot trap significant moisture due to their depth, but these pores can create less friction resulting in a better adhesion to the earthen matrix [60]. Figure 7c shows the detachment line of the fiber during the mechanical failure.

3.2. Young’s Modulus Prediction

During the prediction of the Young’s modulus of BFRC, all models exhibited high accuracy: single models and the ensemble model with a high R² value of 99%, indicating a strong relationship between the selected input variables (fiber content, activator concentration, curing days, mass, flexural vibration, longitudinal vibration, and correction factor) and the output (Young’s modulus). Linear regression exhibited a strong linear relationship between predicted and experimental values and achieved excellent performance, with MSE = 0.46, RMSE = 0.67, and R² = 99% (Figure 8a). A lower value of MSE and RMSE indicates higher accuracy of the model; meanwhile, high metric values mean low performance. In terms of MSE and RMSE, all the models displayed high values; however, linear regression exhibited lesser values compared to the other models. Ensemble learning demonstrated an ideal fit with minimal deviation, achieving superior performance, with MSE = 3.98, RMSE = 1.99, and R² = 99% (Figure 8d). Linear regression and ensemble learning performed well: they demonstrated the best performance, with LR showing an almost linear fit and EL achieving the lowest MSE and RMSE values. Higher values of MSE and RMSE indicate lower performance of the model. LR might be suitable for linear relationships, while EL can handle more complex patterns. The gradient roosting regressor showed a less perfect fit (Figure 8b), especially for higher Young’s modulus values (after 550,000 Pa). Performance metrics for GBR were MSE = 13.6, RMSE = 3.68, and R² = 99%.

DTR generated results that were almost exactly the same as the GBR results, with the ideal line matching the best fitting line and the prediction line occasionally deviating slightly from the two lines that came before it (Figure 8c). The MSE, RMSE, and R² performance scores for DTR were 7.62, 2.76, and 99%, respectively. The DTR and GBR performed similarly, with just tiny departures from the optimum fit, particularly at higher Young’s modulus values. When gradient boosting was used to predict the Young’s modulus of compositionally complex alloys alongside extreme gradient boosting (XGboost), support vector machine (SVM), LASSO regression, random forest (RF), etc., it displayed the highest accuracy with lower performance metric values (R² and MAE) [53]. This similarity with our present investigation can be attributed to the fact that when using a boosting technique, weak learners may change into strong ones. Though this is not always the case, decision trees are typically employed as a base for weak learners. Many boosting techniques construct models step-by-step and then generalize them by optimizing any differentiable loss function. Boosting techniques also partially mitigate the issue of over-fitting, assist in addressing collinearity among features, and resolve non-linear relations between target properties and inputs [61].

The highest error values were showcased by GBR as an SM. The R² of 99% obtained using LR during this study is completely different from the one obtained when the mechanical properties of fly-ash/slag-based geopolymer concrete were predicted. During the prediction of the fly-ash/slag-based geopolymer, LR presented a value of 63.7% for R², showing that LR may be used to anticipate non-linear analysis results to a limited extent [62]. However, in that same investigation, DTR as an SM showcased an R² of 76%, which is less performant that the value obtained by DTR in the present investigation.

3.3. Compressive Strength Prediction

The results presented in Figure 9a–d demonstrate the performance of different ML models used in predicting the compressive strength of the BFRC. While all models exhibited high accuracy, as evidenced by the R² values approaching 1, the specific performance metrics and the visual representation of the predicted versus experimental values revealed distinct characteristics. LR demonstrated a strong linear relationship between predicted and experimental values, as indicated by the almost linear fitting line. It achieved reasonable performance as an SM, with MSE, RMSE, and R² values of 0.073, 0.27, and 99%, respectively. However, its accuracy decreased for higher compressive strength values (11.5 MPa), suggesting potential limitations in capturing non-linear relationships. With a near-perfect R² value of 99% and lower MSE and RMSE values of 0.01 and 0.1, respectively, GBR showed a more accurate fitting line than LR. The smallest difference between the predicted and actual value fitting lines showed that the GBR model was robust in capturing both linear and non-linear interactions. DTR showed intermediate performance, with MSE, RMSE, and R² values of 0.04, 0.2, and 99%, respectively. DTR’s performance was consistent across different compressive strength ranges, suggesting its potential for generalizability, even though the predicted vs. experimental fitting line was completely vertical, which is completely different from the fitting lines displayed by the other models and indicates a nonsensical relationship between the input and output variables. EL exhibited excellent accuracy in predicting the compressive strength of BFRC, with performance metrics MSE, RMSE, and R² of 0.01, 0.1, and 99% respectively, comparable to GBR performance. In a study where DT, LR, RF, and other models were used to predict the compressive strength of fly-ash-based concrete; DT and GB models have demonstrated high efficiency (R² = 99%), achieving minor errors as compared to other ML models [63]. This result is like the findings of the present study. An EL model built from random forest (RF), regression tree (RT), and gradient boosting (GB) was used for the estimation of unconfined compressive strength of cemented paste backfill, where the EL model displayed higher performance than the SM, similarly to our present findings [64]. A comparison of four (4) EL models—AdaBoost, GBDT, XGBoost, and RF—was carried out during the prediction of high-performance concrete strength. The study resulted in the GBDT model outperforming other models, with higher efficiency, like the present study [65].

3.4. Hygroscopic Properties Prediction

The prediction of hygroscopic behavior was assessed using three evaluation metrics: Mean squared error (MSE), root mean squared error (RMSE), and R-squared (R²). These metrics provide insights into the accuracy and reliability of the different models. LR demonstrated the best performance among the models (Figure 10a), with the lowest MSE (0.13) and RMSE (0.36) values and the highest R² (99%) value. This indicates a strong linear relationship between the predicted and experimental values, suggesting that LR effectively captures the hygroscopic behavior of the BFRC as a SM. GBR exhibited a scattered plot, as shown in Figure 10b, indicating some degree of variability in its predictions, while the R² value was still high (95%), and MSE was 4.07 and RMSE was 2.01. The R² was lower than that of LR, suggesting that GBR might not be as accurate in capturing the exact linear relationship (Figure 10c). A study using XGboost during the prediction of water absorption displayed an R² value of 94%, which is very close to the present finding, and a MAE of 0.036 [66]. The ensemble learning (EL) model showed improved performance compared to its individual components (Figure 10d). As demonstrated by the EL model’s reasonably accurate results, which include MSE, RMSE, and R² values of 2.04, 1.42, and 97%, respectively, integrating multiple models can increase the hygroscopic forecast accuracy. DTR produced a vertical line that showed the expected and actual values, indicating that there was little variability in its predictions. This suggests that DTR might not be suitable for capturing the hygroscopic behavior in this case, with MSE, RMSE, and R² values of 5.89, 2.43, and 93%, respectively. It is impossible to precisely evaluate the BFRC’s efficiency because the use of DTR provides insufficient information to predict its hygroscopic characteristics. However, when DTR was used as the EL model, better prediction was demonstrated. This aligns with the results of a previous work in which DT was used individually and with a bagging approach, which improved its R² from 72% to 92% [57]. LR appears to be the most effective model for predicting hygroscopic behavior in this context. However, its performance might be limited to scenarios with a strong linear relationship between the predictors and the target variable.

The analysis of the model’s performance during the prediction of Young’s modulus depicts the LR as a single model displaying the lowest metrics in terms of MSE, RMSE, and R², proving the linear relationship between the selected input and the predicted Young’s modulus. It is followed by the EL model, which exhibited lower errors than DTR and GBR.

3.5. Feature Importance Analysis

A feature importance analysis was performed using the decision tree and gradient boosting models, which provide built-in measures of feature contribution. The results indicate that fiber content (%) and curing days were the most influential predictors of Young’s modulus, followed by water absorption (%), while activator content (%) had a relatively smaller effect. This finding is consistent with the experimental observations and domain knowledge, thereby reinforcing the credibility of the predictive models (

Table 6. Feature importance.

Feature	Importance
	Young’s Modulus	Compressive Strength	Water Absorption
Fiber content (%)	0.5535	0.6218	0.4715
Activator (%)	0.2504	0.2227	0.2740
Curing days	0.1961	0.1555	0.2545

).

4. Limitations, Challenges, and Practical and Theoretical Implications with Examples to Enhance Decision-Making

In this section, some key limitations and challenges that must be carefully considered when applying model-based predictions in real-world scenarios are considered. By understanding these limitations, we can develop strategies to mitigate their impact and ensure the reliability and robustness of our predictions. These limitations arise from various factors, including the quality of the data used to train the models, the complexity of the underlying relationships, and the inherent uncertainty associated with predictions.

• The input used during training has a substantial impact on the model’s performance based on the expected attributes.
• EL models can often achieve higher accuracy; however, some SMs compete with EL models in terms of performance.
• Making rational choices requires quantifying the degree of uncertainty in the forecasts. Because of the amount and caliber of the dataset, the models were straightforward to comprehend.

The investigation’s implications center on the choice of model, which ought to be determined by the needs of the application. The models’ performance is also impacted by the amount and quality of the experimental data and the choice of predictive techniques.

4.1. Theoretical Implications

Various SMs were used, and the EL model was developed based on the application of the properties predicted. The EL model often lead to better predictions; however, the combination of the SMs needs to be carried out taking into consideration various parameters.

4.2. Practical Implications

Considering things like the type of data (e.g., linear vs. non-linear relationships) while choosing a model, integrating predictions from various base models by stacking or combining different GBR models, analyzing models utilizing both visual analysis and performance measures (such as R², MSE, and MAE) will assist in detecting potential biases, constraints, and areas in need of development.

5. Conclusions

The mechanical behavior and physical characteristics of Borassus fiber-reinforced earthen composite (BFRC) were examined in this work. The findings revealed that the excavated soil’s particle size distribution and morphology significantly influence the packing density and water retention of the earthen matrix. Some of the focal findings can be summarized as follows:

• The morphological characterization of the Borassus fibers showed an appropriate fiber length and diameter for reinforcement, with superficial pores that could improve adhesion to the matrix. The earthen matrix properties are influenced by its moisture content, Atterberg limits, dry density, and specific gravity.
• The prediction of the Young’s modulus and compressive strength of the BFRC using machine learning (ML) models demonstrated the superiority of ensemble learning (EL) and gradient boosting regression (GBR) over single models (SMs). These models exhibited high accuracy and robustness in capturing the complex relationships between the input variables and the output properties.
• Using ML models to predict the hygroscopic properties, it was shown that LR best captured the linear relationship between the experimental and predicted values. Even while the EL model performed better than its SM, in this instance, it was not superior to LR.

In summary, the models can be used to track material qualities and spot any deviations from planned requirements during production, and the findings can help design high-performance and sustainable earthen composites for a range of applications. This can help engineers and architects select the most suitable materials for specific applications, prevent the use of substandard materials, reduce the risk of structural failurem and ensure structural integrity and safety. The models can be used to optimize the mix design of novel construction materials by predicting the different properties based on the various proportions of the new mix components. To enhance predictive modeling of mechanical and hygroscopic properties, future studies need to (i) examine non-linear models for hygroscopic behavior and (ii) validate models in practical settings.