Based on the experimental data, the developed quadratic models in terms of actual variables are given in Equation 6. This equation predicted the density well with high R2 and low probability.
The value of ‘Probability < F’ less than 0.0001 revealed that the quadratic model of response variables is a reliable model. The model had a high determination coefficient (R2 = 0.92) and low lack of fit (Table 1). All the independent variables included in this study except die length had a significant effect on the density of the pellet (Table 2). The feedstock particle size and speed of piston showed a negative relationship with the density. The increase of die length had a negligible effect on the increase of the density. With increasing moisture, initially, the density increases and then decreases.
Effect of independent variable
Moisture content increment initially increased and then decreased density (Figure 4A). In the densification process, water acts as a film-type binder by strengthening and promoting the bonding via van der Waals forces and increasing the contact area of the particles (Mani et al. 2003). As a general rule, the higher the moisture content, the lower the density of the pellet. According to a previous research, the optimum level of moisture content for the densification process is different depending on the type of biomass and process conditions. The increase of moisture content from an optimal range reduces the intermolecular forces, and a much higher moisture content causes a biphasic mixture (liquid phase and solid phase) and disappears intermolecular forces entirely (Zafari and Kianmehr 2012).
Feedstock particle size had a negative influence on pellet density (Figure 4B). Density decreased with increasing particle size, which was in agreement with the results from the study by Zhou et al. (2008) which showed that corn stover density decreased with an increase in particle size. Similar results were also observed for wheat straw and switchgrass samples studied by Lam et al. (2008). Carone et al. (2011) reported that to produce high-density pellets, the raw material should have a moisture content lower than 10% w.b and a reduced particle size.
The use of a thicker die was found to enhance the density of the pellet (Figure 4C). This result followed the same trend as the experimental result from the study by Theerarattananoon et al. (2011). Results from the study by Behnke (unpublished data) showed that the use of a thicker die significantly increases pellet durability. Kaliyan and Morey (2009) reported that the factors which increase pellet durability could also increase the density; although, the relationship between the durability and the density of the biomass pellets was still unknown. The speed of piston will influence the flow rate and holding time of feedstock in the die. The results showed that the low speed of piston had significant effect on increasing the pellet density (Figure 4D). The increase in shear force which is resulting from increased friction between feedstock and die may be the reason of increasing density. The results of this study were in agreement with those reported by Li and Liu (2000) for the processing of oak sawdust. In order to visualize the effect of interaction of the two factors on pellet density, interaction response surfaces are shown in Figure 5.
Artificial neural network model
ANNs were developed and tested for the prediction of density of the MSW pellet based on the four input variables namely moisture content, piston speed, die length, and particle size. Among the various ANN structures, model of good performance was produced by a four-layer ANN structure, 4-10-4-1, with hyperbolic tangent transfer function. Experimental testing data of the artificial neural network is shown in Table 3. This model showed a good capacity to learn the relationship between the input and output parameters without overtraining. The model produced the smallest RMSE in training, 0.01732, and testing, 0.0548. The final ANN parameters used for density prediction are shown in Table 4. Before arriving at this optimum, the range of ANN parameter values tried were the number of hidden layers: 1 and 2; neurons hidden layer: from 3 to 60; activation function: sigmoid, linear, and tanh; learning rate: 0.1 to 0.9; momentum: 0.1 to 0.9; and epoch size: 1,000 to 30,000.
An analysis with other ANN constructions indicated that two hidden-layer networks produced better results than a one-hidden layer. Figure 6 shows that the RMSE is represented as a function of number of epochs for the final structure, 4-10-4-1. The error on the training data generally decreases with increasing number of epochs, with an initial large drop in error that slows down as the network begins to learn the patterns representing the training data set (Figure 6).
In this study, the number of epochs was limited to 10 × 103. However, for the epochs in the range of 5 × 103 to 30 × 103, the errors on both training and verification sets were in the acceptable range (Figure 6). Figures 7 and 8 show the predicted density data versus the same set of measured data for the final network trained with 10 × 103 epochs. It was observed that the predictive capability was good.
The resulting correlation coefficient was 0.972 for the regression between measured and predicted values (Figure 7), indicating that the ANN provided satisfactory results over the whole set of values for the dependent variable. The low value of RMSE between the predicted and measured data indicates that there is no difference between the predicted and measured values. Finally, these results confirm that a properly trained neural network was capable to produce a mapping between density and four input variables.
To prove the fact that the ANN model successfully learned the relationship between the four input variables and the density as the output, one within the whole range of the data, the distribution pattern of the relative errors was reported in Figure 9. It is evident that the residuals were well distributed at either sides of the horizontal band centered on zero and displayed no systematic tendencies towards any clear pattern.
Comparison of RSM and ANN models
In this study, RSM and ANN methods were applied for the modeling and optimization of the density of the biomass pellet from compost. In order to test the validity of RSM and ANN results, experiments were conducted for 16 new trials, consisting of combinations of experimental factors, which do not belong to the training data set. The actual and predicted values, together with the residuals (the difference between predicted and actual values), for both approaches are shown in Table 5. Figure 10 shows the distribution of residuals of two approaches to compare them. The fluctuations of the residuals are relatively small and regular for ANN compared to RSM model-based statistical analysis. The RSM model shows greater deviation than the ANN model. The performances of the constructed ANN and RSM models were also measured by the R2 and RMSE (Equations 4 and 5). Table 6 presents the statistical comparison of RSM and ANN models. Both RSM and ANN models provided good quality predictions in this study, yet the ANN showed a clear superiority over the RSM for both data fitting and estimation capabilities.