Predictive Models for Modulus of Rupture and Modulus of Elasticity of Particleboard Manufactured in Different Pressing Conditions

Multiple linear regression

The MLR method is widely employed to analyze a variety of problems regarding engineering applications [28]. It is a statistical tool that intends to learn more about the linear relationship between one dependent variable and several independent variables [29, 30, 31]. The dependent variable is called the predictand, whereas the independent variables are called the predictors [32]. The MLR analysis is based on least squares: The model is fit such that the sum of squares of differences of actual and predicted values is minimized. In the current study, the analysis was conducted to predict the MOR and MOE of particleboard using Statistical Package for The Social Science 11.5 software. Eq. (1) presents a general example of a MLR model.

where Y is the dependent variable, X_i is independent variables, β_i is predicted parameters, and ε is the error term [33].

Artificial neural networks

ANN is an intelligent modeling approach that tries to simulate some important functions of the human brain [34]. It is employed as a modeling tool for solving various problems in many engineering applications [35, 36]. A specific ANN model comprises an input layer, an output layer and one or more hidden layers that allow the network to uncover complex and nonlinear relationships between inputs and outputs [37, 38].

The layers of the network include many processing elements called neurons. Figure 1 depicts general function of a neuron. The neurons of the network are connected from a layer to the next one by weight factors Wij. A neuron (j) in a given layer receives information Xi from the neurons of the antecedent layer. It then gathers information netj weighted by factors corresponding to the connection and the bias of the layerθj and transmits output valuesyj calculated by applying a mathematical function [f(.)] to netj, to all neurons of the next layer. This procedure is formulated in eqs. (2) and (3) and is shown in Figure 1 [20, 39].

Figure 1:

General functioning of an artificial neuron.

The number of neurons in the ANN layers plays a key role on the network performance. The number of input neurons corresponds to the number of input variables, and the number of output neurons is equal to the number of output variables [40]. However, there is no specific rule concerning the number of the hidden layers and their neurons. Complexity level of the problem is decisive to detect the number of them [34]. It was also reported that few number of hidden neurons is not enough to capture complex relationship between inputs and outputs, whereas excessive number of them causes a loss of time to learn the relationship [41]. Hence, a trial and error process is generally performed to decide the optimum number. In this context, various approaches are advised in the literature [42, 43, 44, 45].

ANNs should be also trained by modifying connection weights among the neurons in order to obtain a minimum difference between actual and predicted values of output variables [46]. The back-propagation algorithm is the most frequently used training algorithm [34] and has been successfully used in solving many engineering problems [47, 48].

Particleboard manufacturing process

Pine (Pinus pinea L.) wood was used in the manufacture of particleboards. Pine logs were provided from the forest area of Karadeniz Technical University in Trabzon, Turkey. Wood samples were chipped using a hacker, and then the chips were reduced into smaller particles using a laboratory-scale knife ring Pallmann flakers. They were classified with a horizontal screen shaker. The particles remaining between 3 and 1.5 mm sieves and between 1.5 and 0.5 mm sieves were used in the core and surface layers of particleboards, respectively. It is also important to state that the wood particles were dried at 110 °C in a temperature-controlled oven to reach the target moisture content (2–3 %). The particles then were blended with urea formaldehyde (UF) resin with a solid content of 62 % and melamine formaldehyde (MF) resin with a solid content of 50 %. The UF and MF resins were used at 11 % and 9 % adhesive levels for the outer and core layers based on oven-dry weight, respectively. Ammonium chloride was also used in the manufacture of the particleboards as a hardener in 1 %, and its solid content was 18 %. The boards were formed using fine and coarse particles for the outer and core layers, respectively. The weight ratio of the outer/core/outer layers was 1:3:1, respectively. Hand-formed mats were next pressed at varying temperatures (120, 135 and 150 °C) and pressures (21 and 25 kg/cm²) for varying durations (5, 6 and 7 min). Thus, a total of 36 particleboards under different conditions were manufactured. The target density of particleboards manufactured with lengths of 420 mm, widths of 420 mm and thicknesses of 10 mm was 0.65 g/cm³.

Determination of mechanical properties

Prior to the experiments, the boards were conditioned to constant mass at a temperature of 20±2 °C and a relative humidity of 65 ± 5 % for 30 days. Then, a total of 360 (36×10) experimental samples by preparing ten samples from each type of the boards were cut from 36 particleboards manufactured using two different resin types, two different pressing pressures, three different pressing times and three different pressing temperatures as process variables. The dimensions of experimental samples of the MOR and MOE were 250×50×10 mm. The MOR and MOE values of the particleboard samples were detected according to the procedure of EN 310 standards [49].

Data preparation

Prediction of MOR and MOE of particleboard by the ANN and MLR was achieved using the data provided from the experimental study. The average values of MOR and MOE were used in the models, namely a total of 36 data. Each data represents to the average of ten measurements of MOR and MOE. In developing the ANN models, a total of 36 experimental data for each of MOR and MOE were randomly divided into three subsets because a neural network is mostly created in three phases known as training, validation and testing. Training, validation and testing sets include 26 data (70 % of all data), 5 data (15 % of all data) and 5 data (15 % of all data), respectively. On the other hand, all existing data (36 data) were used for the MLR models.

Network architectures

To obtain the optimal network architectures, the networks were trained by making attempts to try different network parameters and configurations. The trained networks were then tested using the test data in order to ensure the desired generalization ability. As a consequence, the models that yield the closest outputs to the experimental results of MOR and MOE were selected to make predictions. Figure 2 depicts the architectures of the selected optimal ANNs.

Figure 2:

The optimal network architectures proposed for predicting MOR and MOE.

The selected models include four neurons in the input layer and one neuron in the output layer for each of MOR and MOE. In the models, resin type, pressing temperature, pressing time and pressing pressure were the input parameters, whereas the MOR and MOE were output parameters.

One of the most crucial tasks in developing an ANN model is to detect the optimal network architecture concerning the number of hidden layer and hidden neurons [50]. As mentioned before, there is no rigid rule to decide the number of the hidden layers and their neurons. In the current study, the optimal network architectures were therefore decided by trying different number of them. Finally, the network architectures including six hidden neurons for the MOR and five hidden neurons for the MOE revealed the optimum performance of the models in terms of the performance indicators.

Performance evaluation

The predictive abilities of the models for the current study were evaluated by the indicators such as the mean absolute error (MAE), the mean absolute percentage error (MAPE), the root mean square error (RMSE) and determination coefficient (R²). Especially, MAPE and R² are more important to evaluate the predictive capability of the established models. R² is a measure of the relationship or similarity between experimental and predicted values [51]. On the other hand, MAPE shows the average deviation from the targeted value as a percentage of the error [52]. Hence, it must be as small as possible [51]. The performance indicators were calculated using the following equations:

where t_i is the experimental output, td_i is the predicted output, N is the total number of samples, and tˉ is the average of predicted outputs.

Effects of process variables on MOR and MOE of particleboard

The MOR and MOE values of particleboards were determined as a result of the carrying out experiments. Table 1 presents the MOR and MOE values of the experimental samples and the data sets used in the prediction models.

Moreover, the effects of pressing temperature, pressing time, pressing pressure and resin type on the MOR and MOE were evaluated by analysis of variance (ANOVA). The results of the ANOVA revealed that the effects of all variables on the MOR and MOE of particleboards were statistically significant. A comparison of the means values of the MOR and MOE was performed using the Duncan test. Thus, it was detected, which groups were significantly different from others. The results of Duncan’s grouping are shown in Figure 3 by letters.

Figure 3:

The results of Duncan’s multiple mean comparison test (letters define homogeneity groups).

When Table 1 and Figure 3 are examined together, it is understood that particleboards bonded with MF showed higher strength values compared to those with UF. For example, the average values of the MOR and MOE were found as 13.90 and 1,515.80 N/mm² for MF, respectively, whereas the MOR and MOE for UF were 10.97 and 1,326.81 N/mm², respectively (Figure 3). The poor performance of UF resin may be because of hydrolysis that occurs during the hot pressing process [53, 54]. It was reported that UF includes the amino-methylene link, and it therefore is susceptible to hydrolysis at higher temperatures especially [55].

Pressing temperature and time significantly affect MOR and MOE of particleboard. It was reported that the pressing temperature and its duration are important factors for particleboard because they provide the heat and time required for the curing of the resin and create more cross-linking [56, 57]. In the present study, an increase in the pressing temperature generally exhibited a positive influence on MOR and MOE of particleboards. In other words, the MOR and MOE generally increased with the increase in the pressing temperature. The highest average values of the MOR and MOE were found as 13.41 and 1,505.95 N/mm², respectively, in the samples pressed at 150 °C. On the other hand, the lowest values were obtained in the samples pressed at 120 °C. The findings of the current study on pressing temperature were similar to those reported by earlier researchers who investigated the mechanical properties of particleboard in different pressing temperature. Hashim et al. [10] observed an increase in the MOR values of particleboard with increasing pressing temperature. Similar results were also reported by several researchers [9, 58]. In addition to the pressing temperature, pressing time noticeably affected the MOR and MOE of particleboards. It was observed that the MOR and MOE increased from 5 min of pressing time to 6 min considerably and then decreased for 7 min of pressing time slightly. In other words, the highest values of MOR and MOE were obtained in the samples pressed for 6 min. Therefore, it can be said that 6 min of pressing time is sufficient to transfer heat to the core section of the mat for ensuring enough curing. Similar findings were also noted in the literature [2, 9].

Pressing pressure is another important parameter influencing the mechanical behavior of particleboard. In the present study, the particleboards pressed under higher pressure (25 kg/cm²) generally yielded higher MOR and MOE values than particleboards pressed under lower pressure (21 kg/cm²). In other words, the MOR and MOE improved when the pressing pressure was increased from 21 to 25 kg/cm². The highest average values of MOR and MOE for pressing pressure were determined as 12.67 and 1,444.49 N/mm² (Figure 3), respectively. Rafighi and Tabarsa [11] reported similar results regarding the effect of pressing pressure on the MOR and MOE. The reason behind the enhanced strength of the samples at higher pressure is likely due to better contact between the fibers [10].

Predictive ability of ANN and MLR models

Table 2 shows the ANN-predicted values and percentage errors of experimental samples of MOR and MOE.

It is clear in Table 2 that the MOR and MOE prediction was achieved with low percentage errors by the ANN models. The maximum absolute percentage error did not exceed 4.81 % for MOR and 3.95 % for MOE. Because of high agreement between experimental and predicted values, it may be claimed that the proposed ANN models exhibited a good performance in predicting the MOR and MOE of particleboard samples.

In addition to the ANN models, the MLR models were developed to predict the MOR and MOE of particleboard. Consequently, the following equations (eqs. (8) and (9)) were obtained for MOR and MOE, respectively.

In eqs. (8) and (9), X_i represents independent variables (respectively, resin type, pressing temperature, time and pressure).

Evaluation results of the ANN and MLR models in terms of the performance indicators are presented in Table 3.

As emphasized previously, the MAPE and R² are generally adopted as the main criteria in making a decision on the performance of a model [51]. Therefore, in the present study, the predictive capability of the models was principally evaluated in terms of these performance criteria. As seen in Table 3, MAPE was determined as 0.438 %, 1.413 % and 2.937 % in the prediction of MOR, and 0.464 %, 1.554 % and 2.198 % in the prediction of MOE for training, validation and testing data sets, respectively. These low levels of the errors demonstrate that the ANN models effectively generate accurate results. In other words, these models provide an acceptable accuracy and reliability in predicting MOR and MOE of particleboard samples manufactured under given conditions. In addition, the MAPE values were found as 4.282 % and 3.373 % in predicting the MOR and MOE by MLR, respectively. As seen from the results, ANN models exhibited higher predictive capability than MLR models based on evaluation criteria. Several researchers reported that the prediction performance of a model is accepted as excellent when its MAPE is lower than 10 % [52, 59, 60]. Accordingly, the prediction ability of both techniques can be accepted as excellent since their MAPE values are lower from 10 %.

Figure 4 shows the relationship between the experimental and ANN-predicted values for all data sets, respectively.

Figure 4:

The relationship between the experimental results and the ANN predicted results of MOR and MOE for data sets.

It can be seen from Figure 4 that the R² values were found as 99.8 %, 99.7 % and 95.5 %, in the prediction of MOR, and 99.1 %, 99.0 % and 92.9 % in the prediction of MOE for training, validation and testing data sets, respectively. These results mean that the models designed are capable of explaining at least 95.5 % of the experimental data of MOR and 92.9 % of the experimental data of MOE in the testing phase. Hence, it is possible to say that the proposed networks have a high generalization capability.

Figure 5 shows the relationship between the experimental results and the predicted results by the regression models for all data of MOR and MOE.

Figure 5:

The relationship between the experimental results and predicted results of MOR and MOE by MLR models for all data.

The R² values were found as 85.2 % and 80.3 % in the prediction of MOR and MOE by means of MLR models, respectively. The results indicated that both modeling approach can be employed for accurate predictions because they have a high degree of explanatory. On the other hand, in a comparison between the results obtained by the MLR and ANN, the best fit was observed as the ANN method is employed. The results of higher R² when ANN is employed are consistent with the literature [13, 14, 61].

The limited information is available on predicting the MOR and MOE of particleboard. Fernandez et al. [13] predicted the MOR and MOE of particleboard by ANN and regression models. In another study, Eslah et al. [27] predicted the MOR and MOE of particleboard by regression models. On the other hand, some attempts have been made to model mechanical behaviors of wood and wood-based composites so far. Table 4 gives a summary of modeling results of some mechanical properties of wood and wood-based composite products by ANN and MLR techniques.

It is possible to see in Table 4 that the values of R² obtained from the present study are generally higher compared to the values obtained from previous modeling attempts for predicting the mechanical properties of wood and wood-based composites. In addition, Table 4 shows that the ANN approach yielded higher values of R² compared to the MLR approach, as obtained in the present study.

Figure 6 shows the comparison of experimental and ANN results for the training, validation and testing data in predicting the MOR and MOE. In addition, Figure 7 shows the comparison of the experimental results, the ANN results and the MLR results.

Figure 6:

Comparison of the experimental values and the ANN predicted values of MOR and MOE for data sets.

Figure 7:

Comparison of the experimental results, the ANN results and MLR results for all data.

By analyzing the comparison plots presented in Figures 6 and 7, it can be clearly seen that the ANN results are nearer to the experimental values compared to the MLR results in predicting MOR and MOE. The high degree of the similarity between the experimental and predicted outcomes increases the reliability of the proposed ANN models. Based on the results of the present study, it can be said that the models developed using ANN have been proved as a successful tool for predicting the MOR and MOE of particleboard manufactured in different pressing conditions without conducting the more experimental study requiring much time and high experimental costs.