Introduction
Material and Methods
Materials
Mix Composition
Cast and Curing
Testing
Modelling Methodology
GEP Methodology
ANN Methodology
Results and Discussions
Compressive Strength
Density
Result of GEP modeling
Result of ANN modeling
Comparison of GEP and ANN
Conclusions
^{} Introduction
Concrete, a fundamental construction material, is extensively utilized in civil engineering projects globally due to its inherent durability and strength. Comprising ingredients such as sand, cement, aggregates, and water in specific ratios, concrete serves as a composite mixture designed to achieve optimal performance. A notable avenue in concrete research involves the integration of waste materials, such as waste plastic, waste glass aggregates (WGA), recycled polyolefin waste, oil palm kernel shell, pumice and expanded perlite, and sawdust [1, 2, 3, 4, 5, 6], as a substitute for aggregates, introducing modifications to concrete properties. This substitution not only reduces the sand content but also imparts a lightweight characteristic to the concrete, deviating from traditional norms. Sawdust is a by-product or waste material that is generated from various woodworking processes, such as cutting, sanding, or sawing wood. When sawdust is burned, it releases a significant amount of carbon emissions that contribute to environmental pollution. However, if this waste material is utilized in the production of concrete, it can help reduce the emission of carbon dioxide into the environment [7]. In addressing the disposal challenges associated with sawdust, researchers have explored its potential as an aggregate in concrete mixes, especially for lightweight concrete applications. The physical and mechanical properties of sawdust concrete depend not only on the quantity of sawdust but also on its chemical and physical characteristics.
In the pursuit of sustainable construction practices, the use of waste materials in concrete mixes has gained recognition as an environmentally friendly approach to solid waste disposal. Examples such as palm oil fuel ash, volcanic ash, granulated blast-furnace slag, marble powder, silica fume, and waste glass powder (WGP) [8, 9, 10, 11, 12, 13, 14] have successfully replaced costly Portland cement, reducing environmental impact. Beyond cost reduction, these additions confer technical advantages, such as decreased heat of hydration, improved cohesiveness, chemical resistance, reduced bleeding, permeability, and continuous strength enhancement over time. The addition of waste glass powder to concrete is a strategy aimed at reducing the environmental and energy impacts of concrete production. Waste glass powder, available in abundance, is cost- effective and offers a desirable chemical composition for supplementary cementitious material [15]. However, the use of WGP in concrete has yielded varying results in previous studies, affecting both fresh and hardened concrete properties. Aliabdo et al. [16] employed WGP up to 25% as cement replacement. While incorporating WGP in mortar up to 10.0% improves the compressive strength of the mortar by 9%, quantities exceeding 15% lead to a reduction in the compressive strength of the concrete after 28 days. In addition, the inclusion of 10.0% WGP as a substitute for cement results in enhancements in the tensile strength, absorption, voids ratio, and density. Ibrahim [17] investigated the effect of adding WGP in different ratios of 0%, 5%, 10%, 15%, and 20% to ordinary concrete, and concrete containing silica fume and fly ash. This article identifies that the most effective amount of WGP substitution for ordinary concrete is determined to be 5%. The compressive and tensile strengths of silica fume and fly ash concrete decreased when substituting with WGP at all ratios. This reduction amounted to approximately 13% and 14% respectively, when using a 20% WGP ratio, in comparison to the control concretes. Baridjavan et al. [18] studied the mechanical properties of concrete due to the addition of WGP and PVC granules as a replacement for cement and aggregates, respectively. The findings of this research indicate that increasing WGP content leads to lower compressive strength, but it decreases the specific weight of the mixture as well, showing that WGP can be used for non-structure elements to make lightweight concrete.
Furthermore, many researchers have investigated the effect of adding sawdust as a proportion of aggregates. Previous studies have indicated challenges, including poor mechanical properties, especially when significant amounts of sawdust are used. Ganiron [6] evaluated the possibility of utilizing sawdust as a replacement for sand in concrete mixtures to produce lightweight concrete. The study provided evidence that sawdust can effectively substitute for sand, enabling the production of lightweight concrete. In the study conducted by Siddique et al. [19], they replaced fine aggregates in concrete with sawdust and observed that as the substitution of sawdust increased, there was a noticeable decrease in workability and hardened density. Ahmed et al. [20], Cheng et al. [21], Oyedepo et al. [22], and Osei and Jackson [23] also documented similar findings. Sawant et al. [7] utilized sawdust up to 25% instead of sand with metakaolin as an admixture, and investigated the influence of this substituting in compressive strength, and split tensile strength. They observed that 5% sawdust replacement by weight leads to satisfactory results for compressive and tensile strength, and with an increase in replacement percentage, the density of sawdust concrete decreases. Siddique [19] examined the properties of concrete with various percentages of water and sodium silicate treated sawdust as a replacement for sand. They noted that concrete containing 5% water or sodium silicate treated sawdust exhibited a similar level of compressive strength as the control concrete. However, when the replacement level was increased to 10%, both the compressive strength and split tensile strength decreased by approximately 30.30% and 32.19% respectively after 28 days. Olutoge et al. [24] conducted a study on the substitution of sawdust and palm kernel shells as aggregates. The findings indicated that replacing 25% of both components resulted in the production of a favorable lightweight material. Raheem et al. [25] considered the effect of sawdust ash (SDA) on compressive strength properties with proportions up to 25% instead of Ordinary Portland Cement (OPC). They stated that only 5% replacement is appropriate, and higher SDA causes a reduction in compressive strength. In another study, Marthong [26] investigated the possibility of using SDA as a construction material and used higher proportions of SDA (up to 40%). Increasing the amount of SDA constantly decreases the concrete strength. Olufemi and Sheriff [27] studied mixtures containing both WGP and SDA as substitutions for cement. They discovered that WGP has a better influence on 28-day strength compared to SDA. Additionally, there was a reduction in weight ranging from 14.5% to 17.9%. From many years ago, sawdust has been employed as a brick material. Turgut and Algin [28] studied the mechanical characteristics of brick samples containing sawdust. They demonstrated that the combination of sawdust and limestone powder provides lighter and more economical brick materials.
Recently, scientists have employed various computational techniques to minimize the need for building materials and experimental expenses. They have conducted a numerical study on the different characteristics of concrete, utilizing a range of software applications. Optimization approaches depend on Artificial Intelligence, like Neural Networks [29, 30, 31, 32, 33, 34, 35, 36], Feed Forward Neural Networks [37, 38, 39], Convolutional Neural Networks [40, 41], and Multi-layer Perceptron Neural Networks [42, 43, 44, 45], have been earning considerable concentration in the study. Furthermore, certain researchers have employed regression techniques including Support Vector Regression [46, 47, 48, 49], Principal Component Regression [50, 51, 52, 53], and Weibull [54, 55, 56, 57] to establish a mathematical equation linking the dependent variable with the independent variables. Asteris and Mokos employed Artificial Neural Networks to forecast the compressive strength of concrete that their models could anticipate with the accuracy of the R-square value exceeding 0.9 [58]. They used non-destructive testing outcomes, such as ultrasonic pulse velocity and Schmidt rebound hammer, as the basis for their inputs. Khademi et al. conducted a research on anticipating the 28-day compressive strength of recycled concrete aggregate (RCA) utilizing Artificial Neural Networks, Adaptive Neuro-Fuzzy Inference Systems (ANFIS), and Multiple Linear Regression approaches [59]. The findings revealed that the artificial neural networks approach yielded superior models compared to the ANFIS approach, while the MLR method proved ineffective with an R^{2} equal to 0.6. This indicates that linear regressions were inadequate for forecasting study results thanks to the presence of non-linear correlations between inputs and outputs, which the MLR method failed to capture. In another research focusing on prognosticating the SFR-lightweight concrete compressive strength, the findings’ of Altun et al. showed that the neural network approach exhibited better consistency with laboratory outcomes variables than the multiple linear regression method [60].
Artificial neural networks (ANNs) are computational systems that emulate biological neural networks through simulation-based processing. In this study, data sourced from various outlets is utilized to construct an ANN model for predicting the uniaxial compressive strength of sawdust concrete with the inclusion of waste glass powder. The ANN model, denoted as ANN5, examines four distinct parameters: the percentage of sawdust (%S), the percentage of waste glass powder (%WGP), the water-to-cement ratio (WC), and the seven-day compressive strength of the concrete samples $\mathrm{f}{\text{'}}_{\mathrm{c}(7-\mathrm{days})}$. The results reveal that ANNs offer dependable predictions for mechanical properties, substantiated by successful training, testing, and validation outcomes. These predictions of mechanical properties will prove valuable in anticipating the mechanical characteristics of sawdust concrete when incorporating waste glass powder under similar parameter conditions. As indicated previously, specific researchers have utilized the multi-layer perceptron [61, 62, 63]. Abbas et al. [62] employed an Artificial Neural Network (ANN) model to predict the residual strength of high-strength concrete post exposure to elevated temperatures. The network architecture incorporated three neuron models, namely, tan-sigmoid, log-sigmoid, and purelin activation functions, implemented through the backpropagation algorithm. Within the backpropagation algorithm, three network types were considered: feed-forward (FFBP), cascade-forward (CFBP), and Elman backpropagation (EBP). Three distinct ANN models were developed for calcareous, siliceous aggregates, and the entire dataset, all exhibiting R-square values surpassing 0.8.
However, traditional optimization approaches have a limitation in that they are not always able to generate explicit application formulas directly from laboratory results. To overcome this, scientists in the intelligence research area have turned to advanced methods, including non-gradient techniques and meta-heuristic algorithms [64]. The approach of Meta-heuristic Algorithms like Evolutionary Computation [65, 66], Ant Colony Optimization Algorithms [67, 68], and Artificial Bees Colony Algorithm [69, 70], have gained popularity among IR researchers. The selection of technique depends on the data sort and the specific issue being addressed. Gene expression programming, which is a subset of evolutionary computing, has been widely utilized due to its ability to generate highly accurate formulas [71]. GEP has been utilized in various studies to predict the behavior of different materials. For instance, Gandomi et al. [72] used GEP to formulate the viscoelastic behavior of modified asphalt binder, while Algaifi et al. [73] employed it to predict the compressive strength of bacterial concrete. Similarly, Alabduljabbar et al. [74] utilized GEP to model the compressive strength of high-performance concrete (HPC) and achieved robust and reliable results. In addition, GEP has been applied to predict elasticity modulus, shear strength, tensile strength, compressive strength, and flexural strength in different concretes [75, 76, 77]. Broadly, GEP is a program that can be devoted to solving real-world problems in fields such as engineering, finance, medicine, and biology.
This research aims to fill existing gaps in understanding the impact of sawdust and waste glass powder (WGP) as a replacement of sand and cement respectively on the properties of concrete. Sawdust concrete with higher ratios of sawdust and WGP compared to other studies have been employed to provide a lightweight and sustainable mixture for non-structures elements. There is a maximum 25% sawdust and 30% WGP substitution in this research which not only reduces the amount of cement and solve the environmental issues of sawdust, but also offer a significant lightweight concrete. Tests were carried out on various samples in accordance with ASTM standards, using curing periods of 7, 14, and 28 days. Prediction results of the 28-day compressive strength found by ANN and GEP models (based on the dataset reported in this research) had satisfactory compliance with experimental results; most of the R^{2} values of the models for the prediction of the compressive strength were above 0.96.
^{} Material and Methods
Materials
The research incorporates several materials that will be described below, including natural aggregates, cement, sawdust, and waste glass powder (WGP).
Aggregates
In this research, locally sourced crushed natural river sand and gravel were obtained from mines around Mashhad City, Iran. The coarse aggregates typically have angular shapes. The coarse aggregates (CA) had a maximum size of 12.5 mm, while the fine aggregates (FA) had a maximum size of 4.75 mm. Figure 1 illustrates particle size distribution curves of fine and coarse aggregates.
Cement and Water
The experiments conducted in this study utilized Portland cement, specifically type 325-1, with a specific weight of 3150 kg/m3. This particular cement was produced by the Zaveh cement company by the ASTM-C150 standard [78]. The chemical composition of the cement, as outlined in Table 1, and its physical properties, as presented in Table 2, were considered. In the preparation of the concrete mixes, tap water was employed due to its crucial role in the chemical reaction with cement.
Table 1.
Material | Chemical composition (%) | ||||||||
SiO_{2} | Al_{2}O_{3} | Fe_{2}O_{3} | CaO | MgO | SO_{3} | K_{2}O | Na_{2}O | C_{3}S | |
Portland Cement | 21 | 4.6 | 3.9 | 63.5 | 2.9 | 2 | 0.45 | 0.5 | 1.15 |
Table 2.
Material | Setting Time | Compressive Strength (kg/cm^{2}) | |||
Initial (min) | Final (min) | 3 days | 7 days | 28 days | |
Portland Cement | 200 | 240 | 195 | 310 | 495 |
Sawdust
Sawdust is generated as small, discontinuous chips or fragments of wood when logs or timber are cut into various sizes using a saw. These chips are expelled from the cutting edges of the saw blade and fall to the floor during the sawing process. Sawdust, also referred to as wood dust, is the residual material produced when wood is cut or drilled using a saw or other tools. The sawdust as shown in Figure 2 utilized in this investigation was acquired from a local wood factory in Mashhad, Iran. Table 3 shows the chemical composition of the sawdust. Once the sawdust was thoroughly dried, it was sieved using an eighth-grade sieve to eliminate any remaining wood fragments. It is worth noting that researchers suggest that the ideal particle size range for sawdust in concrete is between the 0.25-inch sieve and the 16-grade sieve.
Table 3.
Material | Chemical composition (%) | |||||
SiO_{2} | Al_{2}O_{3} | Fe_{2}O_{3} | CaO | MgO | LOI | |
Sawdust | 87 | 2.5 | 2 | 3.5 | 0.24 | 4.76 |
Waste Glass Powder (WGP)
Waste glass powder (WGP), rich in silica, reacts pozzolanically to create strong, cost-effective, and eco-friendly concrete. WGP used in this article, as shown in Figure 3, was obtained from glass factories around Mashhad City, Iran. This glass powder, named Diamond, was obtained from cutting and polishing large glasses, which were collected from under the machines. The physical properties and chemical compositions of WGP illustrated in Table 4 and Table 5, respectively.
Table 4.
Material | Waste Glass Powder |
Maximum particle size (µm) | 75 |
Bulk density (kg/m^{3}) | 2573 |
Fineness modulus (%) | 0.89 |
Specific gravity | 2.55 |
Water absorption (%) | 0.68 |
Color | White |
Table 5.
Material | Chemical composition (%) | ||||||||
SiO_{2} | Al_{2}O_{3} | Fe_{2}O_{3} | CaO | MgO | Na_{2}O | K_{2}O | LOI | TiO_{2} | |
Waste Glass Powder | 72 | 0.58 | 0.76 | 7.96 | 3.27 | 11.36 | 0.19 | 2.97 | 1.15 |
Mix Composition
Based on the ACI-211-09, the concrete mixing plan was created by selecting a design compressive strength of 30 MPa. The detailed concrete mixing plan can be found in Table 6. The experimental project seeks to explore and evaluate how different ratios (0%, 15%, 20%, and 30%) of waste glass powder (WGP) affect the mechanical properties of sawdust concrete. In the laboratory procedure, five different mixing designs were created, resulting in a total of 45 samples for curing periods of 7, 14, and 28 days.
Table 6.
Cast and Curing
To prevent any issues with the hydration process, the sawdust was briefly soaked in water before being incorporated into the mixture of materials. During the mixing process, the sawdust was substituted for a specific volume percentage of sand. In order to prepare the concrete mixes, the specified quantity of sand was sieved, weighed, and placed into buckets. Additionally, the required amounts of cement and water were measured and added to the bucket, as depicted in Figure 4 The sawdust used in the experiment was also moistened by adding water once it was poured into the container, ensuring it was ready for mixing. Furthermore, glass powder was weighed for various volume percentages as a replacement for cement. Subsequently, the sand, cement, sawdust, and glass powder were all placed into the mixer and dry-mixed by activating the mixer. To facilitate a gradual mixing and reaction with the cement, the intended quantity of water for the experiment was added in three separate portions to the rotating mixture in the mixer. Once each mold was filled with concrete, measures were taken to eliminate air bubbles and enhance the workability of the concrete. This was achieved by tapping the concrete and utilizing vibrations to ensure the expulsion of any trapped air. Cube concrete specimens (150*150*150 mm) were cast in plastic molds and placed in a humidity chamber for 24 hours with a relative humidity of 90% and a temperature of 22 degrees Celsius. After 24 hours, the samples were de-molded and stored for 7, 14, and 28 days in water, as shown in Figure 5.
Testing
After completion of the curing period, the specimens were taken out from the curing tank and cleaned thoroughly. Then the weight of the specimens was noted down with accuracy. The compressive strength test is the most commonly conducted examination to assess the strength of hardened concrete [79, 80]. In this study, the test was conducted to measure the cube samples’ ability to withstand failure when subjected to compressive force after 7, 14, and 28 days of curing following the standards outlined in BS EN 12390-3 [81]. The compressive strength of each concrete mixture was determined by taking the average of the compressive strength values obtained from 3 specimens.
^{} Modelling Methodology
GEP Methodology
In 1991, Ferreira developed the Gene Expression Programming (GEP) algorithm and formally introduced it in 2001. The genotype of the chromosome is coded as fixed-size linear strings. In contrast, the phenotype of the chromosome is represented by a tree structure called Expression Trees (ETs), which solves the chromosomes’ dual position limitation in Genetic Algorithms and Genetic Programming. GEP uses numerous operators of genetics to ensure the offspring’s chromosomes’ fitness, making it quicker than genetic programming.Ferreira asserted that GEP has surpassed the initial natural evolutionary thresholds. Each chromosome in GEP contains one or more genes with a head of functions and terminals and a tail of only terminals, all described using the Karva language. This language allows genes to terminate correctly as ETs, ensuring the robust performance of the algorithm. For instance, the linear GEP chromosome with two genes can be defined in the Karva language as shown below:
(1)
$*\phantom{\rule{.5em}{0ex}}-\phantom{\rule{.5em}{0ex}}\mathrm{a}\phantom{\rule{.5em}{0ex}}/\phantom{\rule{.5em}{0ex}}\mathrm{b}\phantom{\rule{.5em}{0ex}}\mathrm{a}\phantom{\rule{.5em}{0ex}}3\phantom{\rule{.5em}{0ex}}\mathrm{b}\phantom{\rule{.5em}{0ex}}\mathrm{b}\phantom{\rule{.5em}{0ex}}+\phantom{\rule{.5em}{0ex}}\mathrm{b}\phantom{\rule{.5em}{0ex}}\mathrm{a}\phantom{\rule{.5em}{0ex}}*\phantom{\rule{.5em}{0ex}}\mathrm{b}\phantom{\rule{.5em}{0ex}}\mathrm{b}\phantom{\rule{.5em}{0ex}}7\phantom{\rule{.5em}{0ex}}\mathrm{a}\phantom{\rule{.5em}{0ex}}\mathrm{b}$The phrase mentioned above belongs to the Karva language and is employed in Gene Expression Programming to represent genes as a compound of functions and terminals that contain input variables and numerical constants. This expression can be visualized as a tree structure, where each expression tree (ET) represents an uncomplicated mathematical relationship. Ferreira devised quadruple regulations to alter linear strings into tree structures in the Karva language. GEP’s chromosomes, each comprising subsets of ETs known as Sub-ETs, use multiplication as a linking function, as illustrated in Figure 6. These ETs are constructed from functions, not terminals, and include both active components (Open Reading Frames, ORFs) and inactive components (non-coding). This mimics biological gene structure, where understanding the roles of these components is crucial for comprehending gene expression and regulation. During GEP, ETs guide the selection phase based on fitness, while genetic operators modify chromosomes during reproduction, not their associated ETs. Figure 7. provides a general overview of the execution of the GEP algorithm.
The investigation involved the analysis of 15 laboratory samples from 5 distinct mixing designs, each representing three ages (7, 14, and 28 days). Modeling was carried out utilizing GenXpro Tools version 5.0 software. The aim was to anticipate the 28-d compressive strength of sawdust concrete (SC) by considering various parameters, and the precision of these predictions was confirmed using the laboratory data. Additionally, concrete characteristics are primarily influenced by numerous factors, including mix design, material type, and most significantly, the concrete constituents. The input parameters utilized to establish meaningful correlations concerning the compressive strength of the concrete mixture encompassed the percentage of sawdust (%S), the percentage of waste glass powder (%WGP), the water-to-cement ratio (WC), and the seven-day compressive strength of the concrete samples ($\mathrm{f}{\text{'}}_{\mathrm{c}(7-\mathrm{d})}$). It is important to acknowledge that predicting the compressive strength behavior of concrete poses a complex challenge due to the multitude of variables involved. Table 7 outlines the specified values for the input and output variables incorporated in this predictive model.
Table 7.
To conduct modeling using GEP-based and other numerical methods, it is crucial to partition the dataset into two distinct subsets: one for training and the other for testing. The training set is utilized to establish the model’s structure, while the testing set, which was not part of the model’s development process, is employed to assess the model’s effectiveness. This method ensures a dependable and systematic categorization of the data. For this study, 12 data values (80%) were allocated to training, while 3 data values (20%) were assigned to testing.
This study utilizes five models based on the Genetic Expression Programming (GEP) approach. The essential factors for constructing these models are presented in Table 8. Four statistical parameters, namely Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), R-square (R^{2}), Root Relative Square Error (RRSE), and Relative Absolute Error (RAE), are employed to evaluate the performance of the models. The error functions utilized in this research are provided in Equations (2), (3), (4), (5), (6) below.
(2)
$\mathrm{RMSE}=\sqrt{\frac{{\sum}_{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{h}}_{\mathrm{i}}-{\mathrm{p}}_{\mathrm{i}}{)}^{2}}{\mathrm{n}}}$(3)
$\mathrm{MAE}=\frac{{\sum}_{\mathrm{i}=1}^{\mathrm{n}}|{\mathrm{h}}_{\mathrm{i}}-{\mathrm{p}}_{\mathrm{i}}|}{\mathrm{n}}$(4)
${\mathrm{R}}^{2}=\frac{(\mathrm{n}\phantom{\rule{.5em}{0ex}}\sum {\mathrm{h}}_{\mathrm{i}}{\mathrm{p}}_{\mathrm{i}}-\sum {\mathrm{h}}_{\mathrm{i}}\sum {\mathrm{p}}_{\mathrm{i}}{)}^{2}}{(\mathrm{n}\phantom{\rule{.5em}{0ex}}\sum {\mathrm{h}}_{\mathrm{i}}^{2}-(\sum {\mathrm{h}}_{\mathrm{i}}{)}^{2}\left)\right(\mathrm{n}\phantom{\rule{.5em}{0ex}}\sum {\mathrm{p}}_{\mathrm{i}}^{2}-(\sum {\mathrm{p}}_{\mathrm{i}}{)}^{2})}$(5)
$\mathrm{RRSE}=\sqrt{\frac{{\sum}_{\mathrm{i}}({\mathrm{h}}_{\mathrm{i}}-{\mathrm{p}}_{\mathrm{i}}{)}^{2}}{{\sum}_{\mathrm{i}}({\mathrm{h}}_{\mathrm{i}}-(\frac{{\sum}_{\mathrm{i}}{\mathrm{h}}_{\mathrm{i}}}{\mathrm{n}}){)}^{2}}}$(6)
$\mathrm{RAE}=\frac{{\sum}_{\mathrm{i}}|{\mathrm{h}}_{\mathrm{i}}-{\mathrm{p}}_{\mathrm{i}}|}{{\sum}_{\mathrm{i}}\left|{\mathrm{h}}_{\mathrm{i}}-\left(\frac{{\sum}_{\mathrm{i}}{\mathrm{h}}_{\mathrm{i}}}{\mathrm{n}}\right)\right|}$In relation to the aforementioned statistical calculations, “hi” represents the number of laboratory specimens, “pi” represents the forecasted outcomes value of specimens, and “n” represents the whole value of data. Moreover, a machine learning model with R^{2} values greater than 0.8 and lower statistical error values such as RMSE, MAE, RRSE, and RAE is considered reliable and efficient.
Table 8.
ANN Methodology
Inspired by Ramón y Cajal’s 1899 work on neural networks in the pigeon brain, Artificial Neural Networks (ANNs) have emerged as computational models designed to emulate the human brain’s remarkable information processing capabilities. In this study, Multi-Layer Perceptrons (MLPs) are employed for discerning more intricate patterns, featuring an input layer, one or more hidden layers, and an output layer. This fundamental neural network architecture emulates the transfer function observed in the human brain, comprehensively incorporating various aspects of brain behavior and signal propagation, earning it the designation of a feed-forward neural network (FFNN). As depicted in Figure 8, the presented MLP model comprises three hidden layers, with a fixed number of neurons in the input and output layers. The input layer serves as the initial layer, receiving the input data, while the output layer represents the final layer, yielding the computed results. Each of these layers contains a specific number of neurons, with the input and output layer neurons corresponding to the number of input features and output variables, respectively. The intermediate hidden layers can vary in number and typically encompass numerous neurons. To ensure the precision and generalization of the training outcomes, these hidden layers must undergo a rigorous training process, involving training, validation, and testing with an extensive dataset.
The accuracy of the network’s predictions is directly influenced by the number of neurons in the hidden layer, a parameter typically determined by an empirical formula [82]. The empirical formula for determining the number of neurons in the hidden layer is represented by Equation (7):
where N represents the number of neurons in the hidden layer, I and O denote the quantities of neurons in the input layer and output layer, respectively, and C signifies a constant, typically assumed to fall within the range of 1–10 [82].
Similar to the response of nerve cells in the biological system, necessitating a specific threshold of input signals to generate movement or, more broadly, an output signal, artificial neural networks also employ a concept known as the activation function or transfer function. This function dictates that when the input surpasses a predefined value or falls within a specified range, the neuron produces an output. Nonlinear activation functions are predominantly employed in neural networks. In the hidden layer, the sigmoid function, comprising the log-sigmoid and tan-sigmoid functions, is a commonly utilized nonlinear activation function. The accompanying Figure 9 illustrates the log-sigmoid and tan-sigmoid functions along with their mathematical formulations:
Within a MLP neural network, every layer’s input undergoes weighting with corresponding weights. The summation of these weighted inputs, along with the bias, constitutes the input to the transfer function. Figure 10 illustrates a simplified model of the output generation process in FFNN neurons. Subsequently, the neurons employ specific transfer functions (expressed by Equations (8), (9), (10), (11)) to generate their respective outputs (${y}_{j}$) [62]:
(8)
${y}_{j}={f}_{1}\left({Z}_{j}\right)=\frac{1}{1+{e}^{-{z}_{j}}}\phantom{\rule{.5em}{0ex}}\mathrm{for}\phantom{\rule{.5em}{0ex}}\mathrm{log}-\mathrm{sigmoid}\phantom{\rule{0ex}{0ex}}\mathrm{transfer}\phantom{\rule{.5em}{0ex}}\mathrm{function}$(9)
${y}_{j}={f}_{2}\left({Z}_{j}\right)=\frac{2}{1+{e}^{-z*{z}_{j}}}-1=\mathrm{tanh}\left({Z}_{j}\right)\phantom{\rule{0ex}{0ex}}\mathrm{for}\phantom{\rule{.5em}{0ex}}\mathrm{tan}-\mathrm{sigmoid}\phantom{\rule{.5em}{0ex}}\mathrm{transfer}\phantom{\rule{.5em}{0ex}}\mathrm{function}$(10)
${y}_{j}={f}_{3}\left({Z}_{j}\right)={Z}_{j}\phantom{\rule{.5em}{0ex}}\mathrm{for}\phantom{\rule{.5em}{0ex}}\mathrm{linear}\phantom{\rule{.5em}{0ex}}\left(\mathrm{purelin}\right)\phantom{\rule{0ex}{0ex}}\mathrm{transfer}\phantom{\rule{.5em}{0ex}}\mathrm{function}$Where,
In the provided equations, (${W}_{ij}$) represents the weight associated with each connection, and (${b}_{j}$) denotes the bias. The determination of weights and biases is carried out with the objective of minimizing the loss function. It is noteworthy that activation functions exhibit efficacy within specific ranges. The outcomes of the sigmoid function fall within the range of 0 to 1 (for log-sigmoid) or -1 to 1 (for tan-sigmoid). In cases where the final layer of a multi-layer perceptron (MLP) employs a sigmoid transfer function, the output is constrained within the limits of 0 to 1 or -1 to 1. However, it should be noted that the output value can extend to the range of -ꝏ to ꝏ [83].
To address this complexity, the initial processing in the network training process involved normalizing the input and output data frames. This normalization procedure entails setting the mean of the data to zero and standardizing the data’s standard deviation to unity [58], as delineated in Equations (12), (13), (14). The selection of the number of neurons in the hidden layers follows the prescription outlined in Equation (1), while the number of neurons in the input and output layers remains constant.
The dataset utilized in the Artificial Neural Network (ANN) model corresponds precisely to the data employed in the Gene Expression Programming (GEP) model, ensuring the establishment of an effective and dependable model. Statistical analysis of the data was conducted to compute quartiles, mean, standard deviation (SD), coefficient of variation (CV), skewness, kurtosis, and the Anderson Darling normality test. The numerical values of these statistical parameters are presented in Table 9. Additionally, to assess the interrelationships among variables, the Pearson correlation coefficient for the data presented in Table 10 has been computed.
Table 9.
Table 10.
Skewness serves as a statistical metric utilized for characterizing the asymmetry or absence of symmetry in a data distribution. It aids in evaluating the form of the distribution curve and offers insights into the concentration of data points on either side of the mean. A positive skewness indicates a distribution with a longer or fatter tail on the right side, while negative skewness signifies a distribution with a longer or fatter tail on the left side. Kurtosis, on the other hand, is a statistical measure that quantifies the shape and “tailedness” of a probability distribution. It provides information about the distribution’s tails and the extent to which it deviates from a normal distribution.
The p-value holds significance as a statistical measure in hypothesis testing, aiding in the determination of evidence against a null hypothesis. It represents the probability of obtaining observed data or more extreme results under the assumption that the null hypothesis is true. In the context of the Anderson Darling normality test, the A-square statistic serves as a measure to assess whether a sample originates from a specific theoretical distribution, commonly the normal distribution. The Anderson-Darling test is employed to test the null hypothesis that a sample is drawn from a population conforming to a particular distribution, such as the normal distribution.
The deductions derived from the statistical analysis include:
ⅰ)Standard deviation (SD) is a measure indicating the extent of fluctuations in data. In this study, the low value of 0.021 for the data deviation of the WC variable signifies a narrow range of observations. However, WGP (%), S (%), $\mathrm{f}{\text{'}}_{\mathrm{c}(28-\mathrm{d})}$, $\mathrm{f}{\text{'}}_{\mathrm{c}(7-\mathrm{d})}$ exhibit higher fluctuation ranges, respectively.
ⅱ)The Coefficient of Variation (CV) reveals the ratio of the standard deviation to the mean for each variable. The CV for the WC variable is the lowest, indicating a narrower range of changes. This criterion also highlights that WGP (%), $\mathrm{f}{\text{'}}_{\mathrm{c}(28-\mathrm{d})}$, $\mathrm{f}{\text{'}}_{\mathrm{c}(7-\mathrm{d})}$ S (%) have undergone changes in a broader range, respectively.
ⅲ)The Anderson-Darling normality test, including P-value and A-square, is a statistical examination of the normal distribution of each dataset. Under the null hypothesis assuming normal distribution, if the P-value exceeds 5%, the distribution is considered normal; otherwise, it is not. Consequently, WC follows a normal distribution, other variables deviate from normal distribution.
ⅳ)The correlation coefficient evaluates the relationship between variables, ranging from 1 to -1. Proximity to 0 signifies lower correlation, while values nearing 1 and -1 indicate higher positive and negative correlations, respectively. Although the Pearson correlation coefficient is calculated in Table 3 assuming normal distribution, the non-normal distribution revealed by the Anderson-Darling test questions the statistical validity of correlation types. Spearman’s rank correlation coefficient (Table 11) is employed for correlation analysis.
ⅴ)According to this correlation coefficient, WC and S (%) variables, as well as WPG (%), exhibit a strong negative correlation. This implies that an increase in the quantity of WPG (%), WC, or S (%) results in a decrease in the uniaxial compressive strength of sawdust concrete in both 7-day and 28-day samples.
Table 11.
The specific ANN model employed to elucidate a causal relationship between uniaxial compressive strength and independent variables utilizes inputs such as the percentage of sawdust (%S), the percentage of waste glass powder (%WGP), the water-to-cement ratio (WC), and the seven-day compressive strength of concrete samples ($\mathrm{f}{\text{'}}_{\mathrm{c}(7-\mathrm{d})}$) in MPa. This model produces an output representing the 28-day compressive strength of sawdust concrete in MPa.
As previously noted, for optimal modeling, it is imperative to divide the dataset into two separate subsets: one designated for training and the other for testing purposes. The training set is utilized to formulate the model’s structure, whereas the testing set, which remains independent of the model’s development, is employed to evaluate the model’s efficacy. Consistent with the approach employed in other modeling instances, 80% of the data values (12 instances) were allocated to the training subset, while the remaining 20% (3 instances) were assigned to the testing subset.
This investigation employs five models utilizing the Artificial Neural Network methodology, with the crucial factors for constructing these models outlined in Table 12. The assessment of the models’ performance relies on four statistical parameters: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), R-square (R^{2}), Root Relative Square Error (RRSE), and Relative Absolute Error (RAE). The error functions utilized in this study are defined in Equations (2), (3), (4), (5), (6) above. The determination of the number of neurons in the hidden layer is based on the application of Equation (7).
Table 12.
Parameter settings | Models | ||||
ANN1 | ANN2 | ANN3 | ANN4 | ANN5 | |
Number of epochs | 7000 | 7000 | 5000 | 5000 | 1400 |
Number of hidden layers | 1 | 1 | 2 | 2 | 3 |
Number of neurons* | 11 | 13 | 13 | 12 | 13 |
Activation function (1st layer) | log-sigmoid | Tan-sigmoid | Log-sigmoid | Tan-sigmoid | Tan-sigmoid |
Activation function (2nd layer) | - | - | Tan-sigmoid | Tan-sigmoid | Log-sigmoid |
Activation function (3rd layer) | - | - | - | - | Purelin |
Fitness function | MSE | MSE | MSE | MSE | MSE |
learning rate | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 |
Optimizer function | Adam | Adam | Adam | Adam | Adam |
^{} Results and Discussions
Compressive Strength
Figure 11 depicts the findings of the uniaxial compressive strength experiment carried out on cube specimens (measuring 150 x 150 mm) after 7, 14, and 28 days. It can be observed that the compressive strength of concrete decreased with the incorporation of sawdust and WGP. However, all mixtures exhibited increasing compressive strength with age. Samples containing no WGP and 15% WGP showed higher compressive strength values at 7, 14, and 28 days compared to samples containing 20% and 30% WGP. At the age of 7 days, the reference sample has a compressive strength of 26.5 MPa, while the other samples range from 5.1 to 10.5 MPa. It means mixtures replacing WGP by 15, 20, and 30% and sawdust by 25% are demonstrated only 25.2%, 24.1%, and 19.2% strength of control mixture in 7-day curing periods. The highest and lowest decrease in the compressive strength of concrete samples containing WGP at this age compared to the control sample was related to S25WGP0 and S25WGP30 samples, respectively.
The decrease in compressive strength observed in concrete samples incorporating glass waste powder can be attributed to several factors. It has a lower water absorption capacity and high smoothness [17]. Consequently, the bonding between WGP and other components is compromised, resulting in the formation of voids and microcracks at the interface between the paste and aggregates. These defects weaken the overall structure of the concrete. Furthermore, the decrease in the compressive strength of concrete mixtures when incorporating and increasing the content of sawdust can be attributed to the lower strength of sawdust particles. Sawdust particles are more porous and weaker than natural aggregates. Additionally, the high initial free water content in sawdust concrete may lead to bleeding and poor interfacial bonding between the cement paste and aggregates [20]. This finding aligns with previous studies conducted by Sawant et al. [7], Olutoge et al. [24], and Ahmed et al. [20], where they also observed a reduction in compressive strength with higher sawdust content as a partial replacement for natural aggregates.
As the curing time increased, the compressive strength of all samples, especially those containing WGP, improved in comparison to their strength after 7 days of curing. Figure 12 shows the influence of curing age on the compressive strength of different mixtures. The observed improvement in designs incorporating waste glass powder (WGP) compared to their 7-day strength can be attributed to the minimal water absorption capacity of glass and the existence of free water within the mixture. This reduces the drying shrinkage of concrete specimens and subsequently prolongs the progress of the cement hydration process. The 28-day compressive strength of the control design is 31.6 MPa, while the values for the other samples fall within the range of 6.4 to 12.5 MPa.
Density
In spite of the reduction in compressive strength, there has been a notable decline in the density of the samples that incorporate sawdust. The 7-day control sample has a particular density of 2363 Kg/m^{3}, whereas the other samples have densities ranging from 2010 to 2081 Kg/m^{3}. It means the WGP substitution ratios of 15, 20, and 30% were found to be lighter up to 14.2% and 14.8% in 7 and 28 days of curing, respectively. The decline in density is primarily caused by the sawdust particles having a lower specific gravity compared to the fine aggregates. Figure 13 illustrate the specific weight of various combinations during the 7, 14, and 28 days of the curing process. An average of 15% reduction in specific weight was seen in the samples compared to the reference sample.
Result of GEP modeling
Table 13 presents the outcomes of the statistical parameters used to evaluate the constructed models. After evaluating the criteria, it was found that model GEP3 had the least amount of error and made the most accurate predictions compared to other models. The statistical parameters of model GEP3, including RMSE, MAE, R^{2}, RRSE, and RAE, were calculated for both the training and test sets. For the training set, the values were 0.1093, 0.0929, 0.9999, 0.0122, and 0.0143 respectively, while for the testing set, they were 0.2859, 0.2196, 0.9999, 0.0244, and 0.0199 respectively. These findings show that model GEP3 is a reliable and effective predictor. Figure 14 demonstrates the ET of model GEP3.
Table 13.
According to the ET of the GEP3 model presented in Figure 14, the extracted formula is determined as follows:
(15)
$\mathrm{f}{\text{'}}_{\mathrm{c}(28-\mathrm{d})}=\left[\sqrt[54]{\sqrt{{\mathrm{d}}_{0}}+{\mathrm{d}}_{2}+{\mathrm{d}}_{1}}\right]\phantom{\rule{0ex}{0ex}}\times \left[{\mathrm{d}}_{3}-{\left(\frac{\sqrt[16]{{\mathrm{d}}_{2}}\times {\mathrm{d}}_{0}}{{\mathrm{d}}_{3}+{\mathrm{C}}_{2}}\right)}^{2}\right]\times \left[\sqrt[9]{\sqrt{{\mathrm{d}}_{3}}-{\mathrm{d}}_{0}^{2}+{\mathrm{d}}_{0}^{16}}\right]$It should be noted that all the parameters defined in ET for the GEP3 model, which include d_{0}, d_{1}, d_{2} and d_{3}, refer to the percentage of sawdust (%S), the percentage of waste glass powder (%WGP), the water- to-cement ratio (WC), and the seven-day compressive strength of the concrete samples ($\mathrm{f}{\text{'}}_{\mathrm{c}(7-\mathrm{d})}$), respectively. For the GEP3 model approach, the constant quantities in the formula are equal to in Sub-ET2 C2 = -8.01.
In accordance with the GEP3 formula, Figure 15 illustrates a robust correlation between the anticipated outcomes and the laboratory results for the GEP3 model, which covers both the training and testing sets. This indicates that the model’s prognoses are highly accurate and reliable.
Result of ANN modeling
Table 14 illustrates the results of the statistical parameters employed for the evaluation of the developed models. Following a comprehensive assessment of the criteria, it was discerned that model ANN5 exhibited the minimal error and achieved the highest precision in predictions compared to alternative models. Furthermore, model number five stands out as the most optimal model, considering the number of epochs and analysis time, crucial aspects for mitigating the risk of overfitting and ensuring the model’s reliability. The statistical parameters of model ANN5, encompassing RMSE, MAE, R^{2}, RRSE, and RAE, were computed for both the training and test sets. Specifically, for the training set, the values were 0.1827, 0.1334, 0.9996, 0.0205 and 0.0206, respectively. Correspondingly, for the testing set, these values were 0.3162, 0.2578, 0.9993, 0.0267 and 0.0231. These outcomes establish that model ANN5 is a dependable, optimal, and efficacious predictor. Figure 16 illustrates the loss per epoch diagram for ANN models.
Table 14.
These diagrams illustrate the graphical representation of the loss per epoch for the assessed models. The loss per epoch diagram, commonly depicted as a training and validation loss curve, offers valuable insights into the training dynamics and performance evaluation of a machine learning model. The significance of this aspect lies in the observation that the loss curve serves as a crucial tool for monitoring the model’s progress during training, indicating the speed at which the model is learning and its convergence to a solution. Overfitting occurs when a model excessively learns the intricacies of the training data, incorporating noise and outliers, resulting in poor generalization. On the contrary, underfitting transpires when a model is overly simplistic, failing to capture the inherent patterns in the data. Detection of overfitting can be identified when the training loss decreases while the validation loss rises or remains stagnant. Conversely, both elevated training and validation losses, with minimal reduction, suggest the occurrence of underfitting. Furthermore, the loss curve aids in determining the optimal number of training epochs, representing the stage where additional training fails to substantially enhance the model’s performance on the validation set and may potentially lead to overfitting. Any anomalies in the loss curve, such as sudden spikes or plateaus, may indicate challenges in the training process, including data preprocessing issues, suboptimal learning rate choices, or problems in the model architecture, prompting the need for debugging and troubleshooting procedures. Based on the depiction in Figure 16, it is evident that the ANN5 model exhibits the most superior performance, characterized by the steepest slope in the loss curve.
Comparison of GEP and ANN
In the realm of predictive modeling, selecting the most effective algorithm is crucial for achieving high accuracy and efficiency. Gene Expression Programming (GEP) and Artificial Neural Networks (ANN) are both powerful computational techniques widely used in various engineering and scientific applications due to their ability to model complex relationships. However, their performance can vary significantly depending on the nature of the dataset and the specific problem at hand.
To determine which method offers superior predictive capabilities, a detailed comparison of several statistical parameters was conducted: RMSE, MAE, R², Root RRSE, and RAE, as shown in Table 15. These metrics were calculated for both the training and testing datasets across multiple models within each method. By systematically comparing these performance indicators, the goal is to identify the model that demonstrates higher efficiency and accuracy in predicting the target variable, thereby providing valuable insights into the optimal choice of predictive modeling technique for this specific dataset.
Table 15.
Both GEP and ANN models exhibited commendable performance, but analysis revealed that the GEP method demonstrated superior performance over the ANN approach. The GEP3 model emerged as the most accurate predictor, exhibiting exceptional precision with an R² value of 0.9999 and remarkably low error rates (RMSE of 0.2859 and MAE of 0.2196) on the testing dataset, which serves as a more reliable real- world performance indicator. While the ANN5 model derived from the ANN method also exhibited robust predictive capabilities, the GEP method overall provided more accurate and efficient predictions.
^{} Conclusions
The findings of this research can be summarized as follows:
ㆍThe compressive strength of concrete decreased with the inclusion of sawdust and waste glass powder (WGP). Samples containing no WGP and 15% WGP showed higher compressive strength values compared to samples with 20% and 30% WGP. In the 7-day curing period, the reference sample had a compressive strength of 26.5 MPa, while the other samples ranged from 5.1 to 10.5 MPa. This means that mixtures replacing WGP by 15%, 20%, and 30% and sawdust by 25% exhibited only 25.2%, 24.1%, and 19.2% of the strength of the control mixture.
ㆍDespite the decrease in compressive strength, the samples containing sawdust exhibited a significant decrease in density. The samples showed an average reduction of 15% in density compared to the reference sample.
ㆍThe decrease in strength with higher sawdust content can be attributed to factors such as lower strength of sawdust aggregates and higher initial free water content in sawdust concrete that causes poor interfacial bonding between the cement paste and aggregates. Furthermore, as WGP has a lower water absorption capacity and high smoothness, therefore increase in WGP percentage leads to a reduction in the compressive strength of samples. The strength of all samples, especially those with WGP, improved with longer curing time due to reduced drying shrinkage and prolonged cement hydration.
ㆍThe statistical analysis revealed that the output results from the GEP and ANN models were extremely aligned with the experimental findings, exhibiting R^{2} values surpassing 0.99. Among all the models, the GEP3 model emerged as the most effective, showcasing R^{2} values of 0.9999 in both the training and testing datasets. The ANN5 model, which was developed using the ANN method, also demonstrated strong predictive abilities, with an R^{2} value of 0.9993 for the testing datasets. Overall, in this study, the GEP method exhibited superior performance over the ANN approach.