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.


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 adopted machine learning methods  and response surface methodology based on experimental results to predict 3D printed material properties and interfacial properties . 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 NaHCO 3 treatment solution to produce environmentally friendly and economical biocomposites.

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 NaHCO 3 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% NaHCO 3 /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).

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).

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.

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 NaHCO 3 , labeled A and B, respectively, as shown in Table 1.

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 NaHCO 3 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, R 2 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 (R 2 ) and root mean square error (RMSE) values provided by Equations 1 and 2 (Adewale George, Ighalo, and Marques 2021).
ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi yi; p À yi; e ð Þ 2 n s (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)). Another endothermic peak was detected in the range 600-800°C around T = 700°C, attributed to the decomposition of calcite (see Eq. (4)). In addition, an exothermic peak was detected around T = 355°C, and attributed to the polymorphic transition.
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).

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 NaHCO 3 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 NaHCO 3 treatment is obviously noticeable and provides a significant improvement in the mechanical properties of all treated specimens. However, the increase is dependent on the NaHCO 3 concentration and treatment period. The cracks are less accentuated in the specimens reinforced with 20% NaHCO 3 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 R 2 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 R 2 , 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 NaHCO 3 ), 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 R 2 , 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.
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 NaHCO 3 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 NaHCO 3 concentration levels (NaHCO 3 = 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.

ANN and RSM analysis of experimental results
An optimization of variables such as NaHCO 3 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 (R 2 ) 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 R 2 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 ) 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.

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 NaHCO 3 -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% NaHCO 3 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 (R 2 ), 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.