Improving the Mechanical Performance of Biocomposite Plaster/ Washingtonia filifera: Optimization Comparison Between ANN and RSM Approaches

ABSTRACT

The present research is an extension of a previous paper published by the authors. In the first part of the research, the flexural properties of Washingtonia filifera (WF) fiber-reinforced plaster composite treated with sodium bicarbonate were explored using response surface method statistics. In the current study, the data was analyzed using artificial neural network tool. The main objective of the current research is to model the flexural properties of an environmentally friendly gypsum biocomposite reinforced with treated and untreated WF fibers using response surface method and artificial neural networks. For this purpose, the study reports a comparative approach between models predicted by response surface methodology (RSM) and artificial neural networks (ANNs). The statistical results as root mean square error and coefficient of determination reveal that ANN and RSM are effective techniques for bending properties prediction of plaster/WF biocomposites. In addition, ANN and RSM models correlate highly with the experimental data. However, artificial neural network model displayed more accuracy.

摘要

本研究是作者先前发表的论文的延伸. 在研究的第一部分中，使用响应面法统计研究了碳酸氢钠处理的Washingtonia filifera（WF）纤维增强石膏复合材料的弯曲性能. 在当前的研究中，使用人工神经网络工具分析数据. 当前研究的主要目的是使用响应面方法和人工神经网络来模拟由经处理和未经处理的WF纤维增强的环保石膏生物复合材料的弯曲性能. 为此，该研究报告了响应面方法（RSM）和人工神经网络（ANN）预测模型之间的比较方法. 均方根误差和确定系数的统计结果表明，ANN和RSM是预测石膏/WF生物复合材料弯曲性能的有效技术. 此外，ANN和RSM模型与实验数据高度相关. 然而，人工神经网络模型显示出更高的准确性.

KEYWORDS:

• Washingtonia filifera
• plaster-gypsum
• TG/DSC
• prediction
• artificial neural networks
• response surface methodology

关键词:

• 石膏
• 预言
• 人工神经网络
• 响应面方法

1. Introduction

Mineral-bonded panels offer many applications in flooring, interior wall coverings, partitions, and ceilings. Compared to other composite wood materials, these boards (such as fiberboard bonded to gypsum) are more durable and display greater strength when subjected to fire exposure. However, the addition of certain quantity of natural fibers provides a reinforcement effect, whereas above that quantity, they can have a negative effect. Gypsum is moderately important in the construction field relative to other aggregates, despite its many benefits such as abundant product availability, reduced cost, rapid setting, and lighter weight. Its principal limitation is its brittleness and poor tensile strength, which reduce its potential applications. Currently, there is a tendency to investigate sustainable materials for building construction, using natural fibers as a reinforcement material for lime plasters (Le Bella et al. 2014; Troëdec et al. 2011; Di). The use of natural fibers in construction materials is attractive in general due to their high accessibility worldwide, and their low cost, density, thermal conductivity, and recyclability (Boumaaza, Belaadi, and Bourchak 2022b; Cheng et al. 2023a, 2023b; Iucolano et al. 2015), making them a good alternative to synthetic fibers.

Different researchers have investigated the influence of incorporating various types of natural fibers in the plaster matrix, concrete, or cement mortar on the mechanical properties of the composite material. Some fibers used as reinforcement in the plaster matrix were sisal fiber (Di Bella et al. 2014), ramie (Cheng et al. 2021), kenaf fibers, jute (Adda et al. 2021; Tabet et al. 2021), hemp, olive fibers, flax (Iucolano et al. 2018; Makhlouf et al. 2020) and date palm fiber (Belakroum et al. 2018; Lekrine et al. 2022).

Ravikumar et al. examined the impact of eco-friendly sodium bicarbonate treatment using response surface methodology on the delamination and surface roughness of jute fiber reinforced polyester composites (Ravikumar et al. 2022). Sumesh et al. focused on the impact of bio-waste loading from banana, pineapple, and coconut plants in epoxy-based composites for mechanical applications (Sumesh et al. 2021). Recently, Cheng et al. investigated the penetration behaviors of 3D printed continuous ramie yarns woven and non-woven polylactic acid (PLA) biocomposites reinforced. To evaluate the effect of the 3D printed architecture according to a novel interlaced print path and a conventional (unidirectional and orthogonal) print path, the authors performed quasi-static penetration tests (Cheng et al. 2023a, 2023b).

The hydrophilic properties of natural fibers and their inadequate adherence to the matrix is a drawback (Belaadi et al. 2020; Zuber et al. 2012), resulting in a limited ability to transfer the matrix stresses to the fiber. The dimensional changes in the fibers can cause micro-cracking of the biocomposite, decreasing its performance and properties (Belaadi et al. 2022; Dembri et al. 2022). In order to enhance fiber adhesion to the matrix and increase the biocomposite strength, fiber surface modification is usually effected by chemical treatments that modify the fiber surface. The most commonly adopted chemical approach is alkali treatment, in which the fibers are treated with alkaline solution (NaOH) to obtain better properties. Many studies have been conducted on the effects of this treatment on the properties of biocomposites, such as solution concentration, temperature, and immersion time (Cai et al. 2015; Saaidia, Belaadi, and Haddad 2022).

According to some experimental results, a variety of parameters, such as fiber type, treatment type, and concentration percentage significantly influence flexural properties. It is, thus, necessary to search for the best fabrication conditions, guaranteeing a compromise between production cost and product characteristics. Evaluating the contribution of different parameters to flexural property improvement takes time and money. Therefore, the focus of most recent studies about biocomposite materials engineering is to predict the biocomposite properties through numerical models with reduced experimentation. Modeling and predicting the mechanical properties of engineering materials requires considerable effort. The natural fiber composites have been tried with ANN, GRA, Taguchi approaches for optimization. Sumesh and Kanthavel applied the Taguchi method and gray relational analysis to find the optimized process parameter for the impact hammer test on the damping behavior of epoxy-based sisal/black/alumina nanocomposites (Sumesh and Kanthavel 2020). In addition recently, the authors investigated the factors contributing to the mechanical stability of epoxy-based composites reinforced with sisal and banana natural fibers using Taguchi optimization based on the gray relational approach for the compression molding technique (Sumesh and Kanthavel 2022).

RSM and ANN are widely used to develop approximation models to optimize the response (output variable), which is affected by many independent parameters (input variables). ANN and RSM were applied in civil engineering to model the behavior of materials, optimize construction structures, and predict mixing proportions of concrete composition based on experimental investigations. Cai et al. adopted machine learning methods (Cai et al. 2022) and response surface methodology based on experimental results to predict 3D printed material properties and interfacial properties (Cai et al. 2022). Nazerian et al. (2018) used ANN and RSM to model the bending strength of gypsum board reinforced with fibers; others researchers (Nambiar and Ramamurthy 2006) suggested models correlating the mixture proportion with concrete strength and density using RSM. Recently, Boumaaza et al. examined the performance of gypsum mortar biocomposites reinforced with three natural fibers, specifically sisal, flax, and jute, treated chemically with NaOH by changing the fiber length (5, 10, 20 mm) and NaOH concentrations (0%, 1.5%, 2%, and 4%) (Boumaaza, Belaadi, and Bourchak 2022a). A variety of parameters affecting the mechanical properties of gypsum biocomposites were examined in the literature, but limited information has been reported concerning fiber effect on the bending properties of biocomposite materials based on gypsum.

To the best of our knowledge, this is the first report proposing RSM and ANN models in predicting the flexural properties of untreated and sodium bicarbonate treated WF-reinforced gypsum biocomposites. To this end, the study reports a comparative approach between the models predicted by RSM and ANN as a function of immersion time fiber and percentage of NaHCO₃ treatment solution to produce environmentally friendly and economical biocomposites.

2. Materials and methods

2.1. Materials used

The plaster used was a local Algerian product, commercially available for interior purposes. Washingtonia filifera (WF) is locally grown in the Guelma region (Algeria). The fibers were manually collected, immediately placed in distilled water to clean the surface, and then dried at room temperature in air to avoid moisture. Thereafter, the fibers were chemically treated using NaHCO₃ sodium bicarbonate to generate high-performance fibers with a reduced diameter, which improved matrix/fiber adhesion and mechanical properties. In this process, the WF fibers were tempered in a 5%, 10%, and 20% NaHCO₃/water solution for 24, 72, 168, and 240 h. The treated WF fibers were cleaned with distilled water to eliminate the sodium impurities and then cured at 50°C for 24 h in an air oven, before being cooled and stored (Benzannache et al. 2021).

2.2. Characterization of the raw materials

The binder chemical composition was performed by thermal simultaneous analysis (DSC-TGA), by means of a NETZSCH STA 449 F3 Jupiter brand. The weighted specimens were specifically heated on alumina plates between 25 and 1000°C with a 10°C/min heating rate in an azote environment.

The binder mineralogical composition was analyzed by X-ray diffraction (XRD), with a Bruker D8 ECO type instrument equipped with a copper anticathode tube with a wavelength Kα1 = 0.15406 nm. The WF fiber density was estimated using a helium pycnometer (MultiVolume Pycnometer 1305, Micromeritics).

2.3. Fabrication process of samples

The biocomposite, consisting of powdered plaster and short WF fibers, was initially homogenized and mixed with water for about 60 s. The 2% fibers incorporated into the gypsum matrix were cut into lengths ranging from 20 mm to 40 mm. The W/P ratio of water to plaster was 0.7. The compound was poured into 4 × 4 × 16 cm open molds and compacted for 40 s using a traditional vibrator. The samples were demolded after 5 h of plaster setting, dried for 72 h at T = 45°C and then stocked at 23–25°C and RH = 48–50% in a chamber until testing. For each sample type, three specimens were tested. The parameters of the developed biocomposites are shown in Table 1. The 3-point bending test was performed according to ASTM C348 standard using a 5kN universal testing machine with an axial displacement speed of 1 mm/min at 140 mm span. The displacements at mid-span and the load were controlled with a data acquired system.

Table 1. Experimental results for stress, displacement, and flexural modulus.

Number of experiment	Input variables		Output variables
			σf (MPa)			y (mm)			Ef (MPa)
	NaHCO3 (%)	Time (h)	EXP	RSM	ANN	EXP	RSM	ANN	EXP	RSM	ANN
1	20	24	5.583	5.552	5.499	5.606	5.273	5.606	1361.62	1346.06	1360.80
2	20	240	3.383	3.361	3.383	3.387	4.305	3.387	1249.31	1261.92	1271.69
3	20	168	6.103	6.125	6.100	8.425	7.604	8.425	1625.84	1596.00	1625.45
4	20	72	6.269	6.300	6.268	6.923	7.373	6.923	1415.77	1448.57	1416.99
5	0	0	2.527	2.527	2.518	1.783	1.143	1.783	720.01	720.01	720.24
6	5	24	3.009	3.005	3.010	2.433	3.054	2.433	889.59	905.16	894.43
7	5	72	3.411	3.360	3.380	5.230	5.579	5.230	1020.95	996.50	997.12
8	5	168	3.726	3.857	3.815	6.613	6.661	6.634	1157.59	1167.93	1157.94
9	5	240	2.949	2.873	2.951	3.310	4.000	3.705	893.83	892.37	893.73
10	10	24	4.408	4.443	4.405	3.410	3.464	3.484	1217.43	1217.42	1217.86
11	10	240	3.543	3.641	3.540	4.936	3.773	3.566	1155.65	1144.50	1114.28
12	10	168	5.367	5.213	5.382	6.962	6.646	6.962	1432.18	1451.68	1431.78
13	10	72	4.913	4.933	5.070	5.704	5.848	5.745	1312.76	1304.41	1290.68

2.4. Experimental design approach of plaster biocomposite

The studied orthogonal design outputs were chosen to predict the bending properties of biocomposites through the artificial neural networks and response surface methodology for analysis the influence of input factors on reinforced plaster bending properties. Mix ratios in the investigations were generated by applying a statistical experimental design technique in plaster biocomposites. Three responses were determined: flexural strength (σ_f), displacement (y), and flexural modulus (E_f). This experimental design included 13 experiments. In this study, two control variables were considered: (1) fiber immersion time and (2) percent concentration of NaHCO₃, labeled A and B, respectively, as shown in Table 1.

3. Statistical analysis

In previous study, the Analysis of Variance (ANOVA) to validate the resulting experimental data was applied to determine the appropriate model at α = 0.05 level of significance (i.e., for 95% probability). In addition, parameters such as fiber immersion time and NaHCO₃ concentration were optimized using RSM to obtain the optimal values of the bending properties. In this study, ANNs inspired by biological neural systems were used to model the nonlinear processes. This approach is based on the weighted sum of inputs obtained by the neuron through (usually nonlinear) activation functions producing outputs (Altun, Kişi, and Aydin 2008; Kewalramani and Gupta 2006; Yilmaz and Yuksek 2009). ANNs typically consist of multiple layers, an input layer, hidden layers, and an output layer. Neurons in the input layer acquire feedback from the outside environment to be transferred to neurons in the hidden layer that are fully weight-connected among themselves (Mansour et al. 2004; Qu, Cai, and Chang 2018). These neurons may comprise many hidden computing units as represented in the ANN architecture (Sarıdemir 2009).

To achieve the ultimate model, R² was chosen to serve as the primary criterion for choosing which network can generate the best model. Training the neural network was considered a major procedure to acquire accurate results; insufficient training renders ANNs inefficient and can yield imprecise predictions. These experimental inputs were therefore divided into three subsets: 70% were used to train the network, 15% to validate it, and the last 15% for testing purposes. The input numbers determine the neurons in the input layer, and the output numbers determine the neurons in the output layer. The number of neurons in the hidden layer was determined by running multiple neural network tests until the output value (MSE) was at a minimum. For this investigation, the Levenberg-Marquardt algorithm was selected to train the ANN model for predicting the WF reinforced gypsum biocomposite flexural properties.

The accuracy of the generated ANN model was checked through the correlation coefficient (R²) and root mean square error (RMSE) values provided by Equations 1(1) $\mathit{RMSE}={\sum }_1^n\sqrt{\frac{{\left(\mathit{yi},\mathit{p}-\mathit{yi},\mathit{e}\right)}^2}{\mathit{n}}}$(1) and 2(2) $R^2=1-\frac{{\sum }_{i=1}^n{\left({\mathit{Y}}_{\mathit{Predicted}}-Y_{\mathit{Experiment}}\right)}^2}{{\sum }_{i=1}^n{\left({\mathit{Y}}_{\mathit{Predicted}}-Y_{\mathit{Mean}}\right)}^2}$(2) (Adewale George, Ighalo, and Marques 2021).

(1) $\mathit{RMSE}={\sum }_1^n\sqrt{\frac{{\left(\mathit{yi},\mathit{p}-\mathit{yi},\mathit{e}\right)}^2}{\mathit{n}}}$(1)

(2) $R^2=1-\frac{{\sum }_{i=1}^n{\left({\mathit{Y}}_{\mathit{Predicted}}-Y_{\mathit{Experiment}}\right)}^2}{{\sum }_{i=1}^n{\left({\mathit{Y}}_{\mathit{Predicted}}-Y_{\mathit{Mean}}\right)}^2}$(2)

4. Results and discussion

4.1. DSC and XRD analysis

The results of the thermal analysis, reported in Figure 1(a), revealed the presence of three distinct endothermic and one exothermic peak. The first endothermic peak, around 25–100°C was attributed to moisture, 2nd peak in the range 100–200°C around T = 135°C, attributed to dehydration of the hemihydrate (see Eq. (3)(3) $\mathrm{CaS}{\mathrm{O}}_4\mathit{\hspace{0.17em}}.\frac{1}{2}{\mathrm{H}}_2\mathrm{O}\to \mathrm{CaS}{\mathrm{O}}_4\mathit{\hspace{0.17em}}+\mathit{\hspace{0.17em}}\frac{1}{2}{\mathrm{H}}_2\mathrm{O}$(3) ). Another endothermic peak was detected in the range 600–800°C around T = 700°C, attributed to the decomposition of calcite (see Eq. (4)(4) $\mathrm{CaC}{\mathrm{O}}_3\to \mathrm{CaO}+\mathrm{C}{\mathrm{O}}_2\mathit{\hspace{0.17em}}$(4) ). In addition, an exothermic peak was detected around T = 355°C, and attributed to the polymorphic transition.

(3) $\mathrm{CaS}{\mathrm{O}}_4\mathit{\hspace{0.17em}}.\frac{1}{2}{\mathrm{H}}_2\mathrm{O}\to \mathrm{CaS}{\mathrm{O}}_4\mathit{\hspace{0.17em}}+\mathit{\hspace{0.17em}}\frac{1}{2}{\mathrm{H}}_2\mathrm{O}$(3)

(4) $\mathrm{CaC}{\mathrm{O}}_3\to \mathrm{CaO}+\mathrm{C}{\mathrm{O}}_2\mathit{\hspace{0.17em}}$(4)

Figure 1. (a) XRD of the WF fiber and plaster matrix (H = CaSO₄_0.5 H₂O; H/A = CaSO₄; C = CaCO₃) and (b) TG/DSC of the plaster matrix.

The mineralogical composition performed by XRD confirmed the previous results. In fact, the scheme reported in Figure 1(b) showed a large peak for anhydrite, seven peaks to hemihydrate, and three to calcite corresponding to the two-theta diffraction. The peak attributed to anhydrite is around (26), for calcite is around (42–29), and for hemihydrate is around (29–54).

4.2. Results of ANN modeling methods

More information on the RSM was discussed in Benzannache et al. (2021), in which the resulting data were explored on the basis of RSM statistics. There was a significant effect of NaHCO₃ concentration (A) for σf and E_f (Prob ≤0.05) although it was less significant for y. For the time of treatment (B), it was not significant for σ_f but more significant for E_f. Their interaction (AB), however, showed a significant effect for σ_f and less significant for y and E_f. An effect of the NaHCO₃ treatment is obviously noticeable and provides a significant improvement in the mechanical properties of all treated specimens. However, the increase is dependent on the NaHCO₃ concentration and treatment period. The cracks are less accentuated in the specimens reinforced with 20% NaHCO₃ treated fiber for 168 h compared to the other specimens, which obviously explains the improvement of its mechanical properties in bending (Benzannache et al. 2021).

The treatment of Doum fiber with 1% NaOH (Figure 5(b)) causes the removal of amorphous materials from the fiber surface leading to a cleaner surface, rough and to the formation of irregular scratches on the surface of the fiber, which increases the fiber-matrix adhesion.

In the current work, the data will be analyzed using ANN statistics. The ANN architecture used in this work is shown in Figure 2. Table 2 shows the correlation coefficient during training, validation, testing and all predicted values (output) to actual values (target) (98.98%, 99.44%, and 99.56%) corresponding to all predicted values for σ_f, y, and E_f, respectively. A well correlation of the experimental response and measured R² values with the predicted ANN response was observed; therefore, the developed ANN model results based on the experimental data perfectly predicted the tested responses (σ_f, y, and E_f) among the various models. As a result of having the high value of R², 2-8-1, 2-7-1, and 2-6-1 were adopted as appropriate architectures to model σ_f, y, and E_f. Two input nodes (fiber immersion time and percentage of NaHCO₃), 8, 7, and 6 nodes to the hidden layer, and 1 node for the output were considered for (σ_f, y, and E_f), respectively, and the model architectures are shown in Table 3 and Figure 2. To evaluate the adequacy of the model, experimental (“real”) values of σ_f, y, and E_f were compared to the predicted ANN model values represented by the perfect y = x fit line with the predicted and experimental data presenting a high correlation. The majority of the intersection points were clearly observed to be close to the midline. A plot of the ANN outputs from the modeling process is provided in Figure 3 in comparison to the actual data for the gypsum/WF biocomposite across the training, validation, and testing steps. The experiment data variability of the model was reported by the coefficient of determination R², which showed the model’s prediction accuracy (Macedo et al. 2015). The correlation precision for training, testing, and total is (0.9999, 1, 0.9944), (1, 1, 0.9956), and (0.9977, 1, 0.9798) for σ_f, y, and E_f, respectively, leading to a high level of confidence regarding the output model. The ANN predicted values approached parity level and fit nicely with the experimentally determined ones. Consequently, a confident prediction of the bending properties of gypsum/WF biocomposites can be performed via the ANN approach.

Figure 2. ANN architecture used in this study for experimental (a) strength and (b) displacement and (c) Young modulus data.

Figure 3. ANN modeling results for biocomposites WF/Plaster (a-c) strength (d-f) displacement and (g-i) Young modulus data.

Table 2. ANN tested architectures MSE and R-values for training, validation, and testing of Plaster/WF.

Model	Network structure		Percentage	Samples	RMSE	R value
Strength	2-8-1	Training	70	8	9.05209E–3	9.97974E–1
		Test	15	3	4.39864E–2	9.98630E–1
		All	15	2	6.27221E–1	1.00000E–0
Displacement	2-7-1	Training	70	9	7.97625E–4	9.99895E–1
		Test	15	2	2.40900E–1	1.00000E–0
		All	15	2	8.13889E–2	9.99999E–1
Young modulus	2-6-1	Training	70	9	5.98877E–20	1.00000E–0
		Test	15	2	3500.32E–0	1.00000E–0
		All	15	2	401.116E–0	9.95674E–1

Table 3. Mathematical models obtained with ANN method for different biocomposites.

ANN response
Strength	$3.6725\times H_1+0.1712\times H_2-2.7032\times H_3-1.0002\times H_4+2.6884\times H_5+3.0322\times H_6+0.8562\times H_7+2.5553\times H_8+0.4286$ $\left\{\begin{array}{c}{H}_1=tanh(0.5\times (0.1666\times \mathrm{NaHC}{\mathrm{O}}_3+0.0158\times \mathit{Time}-3.9858))\\ H_2=tanh(0.5\times (0.0383\times \mathrm{NaHC}{\mathrm{O}}_3-0.0010\times \mathit{Time}+0.0238))\\ H_3=tanh(0.5\times (-0.3343\times \mathrm{NaHC}{\mathrm{O}}_3-0.0091\times \mathit{Time}+2.9180))\\ H_4=tanh(0.5\times (0.0287\times \mathrm{NaHC}{\mathrm{O}}_3-0.0027\times \mathit{Time}+0.3854))\\ H_5=tanh(0.5\times (-0.2927\times \mathrm{NaHC}{\mathrm{O}}_3-0.0051\times \mathit{Time}+3.7651))\\ H_6=tanh(0.5\times (-0.0102\times \mathrm{NaHC}{\mathrm{O}}_3-0.0181\times \mathit{Time}+4.3881))\\ H_7=tanh(0.5\times (0.0081\times \mathrm{NaHC}{\mathrm{O}}_3-0.0008\times \mathit{Time}-0.1787))\\ H_8=tanh(0.5\times (0.0470\times \mathrm{NaHC}{\mathrm{O}}_3-0.0181\times \mathit{Time}+3.2435))\end{array}\right.$
Displacement	$-158.88\times H_1+\mathit{\hspace{0.17em}}844.12\times H_2+\mathit{\hspace{0.17em}}3.4546\times H_3-36.459\times H_4+-96.306\times H_5+16.091\times H_6+\mathit{\hspace{0.17em}}57.521\times H_7-610.61$ $\left\{\begin{array}{c}{H}_1=tanh(0.5\times (0.0262\times \mathrm{NaHC}{\mathrm{O}}_3-0.0087\times \mathit{Time}+2.5708))\\ H_2=tanh(0.5\times (0.0166\times \mathrm{NaHC}{\mathrm{O}}_3+-0.0031\times \mathit{Time}+3.2253))\\ H_3=tanh(0.5\times (0.1151\times \mathrm{NaHC}{\mathrm{O}}_3-0.0185\times \mathit{Time}+0.5553))\\ H_4=tanh(0.5\times (-0.0118\times \mathrm{NaHC}{\mathrm{O}}_3+0.0184\times \mathit{Time}-3.1275))\\ H_5=tanh(0.5\times (0.0057\times \mathrm{NaHC}{\mathrm{O}}_3+0.0065\times \mathit{Time}+0.5592))\\ H_6=tanh(0.5\times (0.0510\times \mathrm{NaHC}{\mathrm{O}}_3-0.0079\times \mathit{Time}-1.5253))\\ H_7=tanh(0.5\times (-0.0187\times \mathrm{NaHC}{\mathrm{O}}_3+0.0169\times \mathit{Time}-1.0927))\end{array}\right.$
Young modulus	$227\times H_1+2766\times H_2-687\times H_3+508\times H_4+2647\times H_5+588\times H_6+2431$ $\left\{\begin{array}{c}{H}_1=tanh(0.5\times (0.2060\times \mathrm{NaHC}{\mathrm{O}}_3-0.0082\times \mathit{Time}-1.4022))\\ H_2=tanh(0.5\times (0.0426\times \mathrm{NaHC}{\mathrm{O}}_3-0.0048\times \mathit{Time}+0.2094))\\ H_3=tanh(0.5\times (0.0283\times \mathrm{NaHC}{\mathrm{O}}_3-0.0304\times \mathit{Time}+2.3462))\\ H_4=tanh(0.5\times (0.2607\times \mathrm{NaHC}{\mathrm{O}}_3+0.0011\times \mathit{Time}-2.4684))\\ H_5=tanh(0.5\times (0.0599\times \mathrm{NaHC}{\mathrm{O}}_3+0.0015\times \mathit{Time}-1.2007))\\ H_6=tanh(0.5\times (-0.2157\times \mathrm{NaHC}{\mathrm{O}}_3-0.0005\times \mathit{Time}+3.6457))\end{array}\right.$

The histogram of the errors distributed over an interval of 20 bins generated was produced within the model network by means of the errors in the training, validation, and testing as shown in Figure 4, where the errors were clearly located around the zero line. The training and validation processes were stopped at the third and sixth iteration for σ_f, y, and E_f models, respectively (Figure 5(a-c)). After an optimal validation was registered at 1.4625E–12, 4.0393E–13, and 1.8433E–10 by the gradient at the 6th, 9th, and 7th iteration for σ_f, y, and E_f respectively, ANN evaluated the stop point to be an ideal one, beyond which the validation bias exceeded accepted tolerances (Figure 6(a-c)). The combined interactions of the effects among the inputs and response variables can also be examined with other plotted illustrations, such as the surface contour and 3D plots (Ositadinma, Tagbo, Boumaaza, Belaadi, and Bourchak 2021; Ositadinma, Chamberlain, and Elijah 2019). These graphs are presented in Figure 7 and applied to show the effect of varying parameters on the flexural properties. The surface graphics were obtained by varying two parameters in the experimental trial range in the model. An interactive effect of NaHCO₃ concentration level and fiber immersion time was exhibited. The bending stress, displacement, and Young’s modulus were found to increase to their optimum values with increasing NaHCO₃ concentration levels (NaHCO₃ = 20); however, these values increased to an optimum immersion time (t = 168 h) and then decreased. This is in good agreement with the results obtained by RSM. According to the surface contour and the 3D plot type, an interactive effect of fiber treatment concentration and immersion time was significant.

Figure 4. ANN distribution of errors results for (a) strength and (b) displacement and (c) Young modulus data.

Figure 5. ANN validation results for (a) strength and (b) displacement and (c) Young modulus data.

Figure 6. ANN training conditions results for (a) strength and (b) displacement and (c) Young modulus data.

Figure 7. 3D and contour plot for biocomposites WF/Plaster (a,b) strength (c,d) displacement and (e,f) Young modulus data.

4.3. ANN and RSM analysis of experimental results

An optimization of variables such as NaHCO₃ concentration and fiber immersion time with RSM was performed by Benzannache et al. (2021) to attain the optimum values of σ_f, y, and E_f for the plaster/WF biocomposite. To validate the accuracy of the mathematical models, the correlation between the actual and predicted values for σ_f, y, and E_f was verified. Figure 8(a-c) showed the comparison of the experimentally obtained results and those predicted by the RSM and ANN models for σ_f, y, and E_f, along with their absolute error percentages. It was found that the predicted results obtained for σ_f, y, and E_f using both models were in perfect correlation with the actual data. The well relationship between these outcomes verified that the mathematical models were successful in reflecting the predicted outcomes. Also, the performance of the developed RSM and ANN models is statistically measured and is shown in Table 2. The determination coefficient (R²) in ANN training, validation, and test for σ_f takes the value of 99.79, 99.86%, and 1.00%, respectively. The same thing was observed for y and E_f (Table 2). The R² calculated by ANN methods shows more accuracy than RSM models shown in the previous work (Benzannache et al. 2021).

Figures 8 (d-f) show the variations of the residuals of the two prediction approaches. Indeed, the residuals are quite low and regular for the ANN compared to the RSM. The latter model shows a larger deviation than the ANN model. These residuals confirm that the learning procedure, the validation, and the ANN test were performed satisfactorily, with a very low error level, and that the mathematical model is relevant. This is in good agreement with the results obtained by (Boumaaza et al. 2022) which indicated that the ANN models performed better than those obtained by the RSM models. However, it is important to mention that the ANN models efficaciously estimated the experimental findings.

Figure 8. (a-c) Comparison between experimental and predicted RSM and ANN models and (d-f) residuals data.

5. Conclusions

In the current investigation, the ANN and RSM statistics on the flexural property data of gypsum/WF were reported. The plaster reinforcement with untreated and NaHCO₃-treated fibers provided the plaster biocomposite with higher flexural strength, displacement, and elastic modulus than those obtained by raw fibers. The optimal condition for maximum flexural strength, displacement, and flexural modulus showed that treatment with 20% NaHCO₃ for a duration of 168 h provided the optimal composition of the gypsum/WF biocomposite. This is probably due to the improvement in the surface condition of chemically treated fibers by this formulation leading to good adhesion between the fibers and the matrix. The formulated ANN predictive models (2:8:1), (2:7:1) and (2:6:1) showed greater flexibility and the ability to exhibit a non-linear relationship for predicting flexural properties. The variations of the residuals are quite small and regular for ANN compared to RSM. This last model shows higher deviation than the ANN one. The comparison of the two RSM and ANN models revealed that the ones predicted by ANN are significantly more robust than those of RSM, as confirmed by their correlation coefficient (R²), close to 1 and their low MSE error. Therefore, the ANN method can be an effective strategy to anticipate values in experimental studies, saving time and cost when performing new experiments.

Biocomposites developed through this process have a significant role to offer new materials for the civil engineering industry. Such as for building walls and other construction elements, and for the production of reinforced gypsum boards.

Highlights

• WF fibers treated with NaHCO₃ had good adhesion to plaster matrix.

• The ANN was used to model and optimize the flexural properties of the plaster/WF biocomposite.

• The ANN model was more accurate in its predictive ability than RSM.

Acknowledgements

This research work was funded by Institutional Fund Projects under grant no. (IFPIP:1368-135-1443). The authors gratefully acknowledge technical and financial support provided by the Ministry of Education and King Abdulaziz University, DSR, Jeddah, Saudi Arabia.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Institutional Fund Projects under grant no. (IFPIP:1368-135-1443).