Modeling the effect of extrusion parameters on density of biomass pellet using artificial neural network
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Abstract
Background
The relationships between the density of the biomass pellet and the related variables are very complicated and highly nonlinear, which make developing a single, general, and accurate mathematical model almost impossible. One of the most appropriate methods to solve these problems is the intelligent method. Shankar and Bandyopadhyay and Shankar et al. successfully used genetic algorithms and artificial neural networks to understand and optimize an extrusion process.
Results
The results showed that a four-layer perceptron network with training algorithm of back propagation, hyperbolic tangential activation function, and Delta training rule with ten neurons in the first hidden layer and four neurons in the second hidden layer had the best performance for the prediction of pellet density. The minimum root mean square error and coefficient of determination for the multilayer perceptron network were 0.01732 and 0.972, respectively. Also, the results of statistical analysis indicate that moisture content, speed of piston, and particle size significantly affected (P < 0.01) the density of pellets while the influence of die length was negligible (P > 0.05).
Conclusions
The results indicate that a properly trained neural network can be used to predict effect of input variable on pellet density. The ANN model was found to have higher predictive capability than the statistical model.
Keywords
Extrusion parameters Biomass pellet Density Artificial neural networkIntroduction
Municipal solid waste (MSW) is largely produced in Iran, and its management has become a challenge, both economically and environmentally. Composting MSW is considered as a method of transferring organic waste materials from landfills to a product, which is suitable for agricultural purposes at a relatively low cost (Eriksen et al. 1999; Wolkowski 2003). Composting MSW reduces the volume of the waste, kills pathogens that may be present, decreases germination of weeds in agricultural fields, and destroys malodorous compounds. Converting the municipal waste to compost is very important because useful materials as compost produced from waste has been widely used for agricultural and horticultural purposes (Mavaddati et al. 2010). Composting of MSW has the potential to become a beneficial recycling tool for waste management in Iran. The major barriers against the use of compost are their handling, application, and storage due to its low density. Therefore, these bulky residues can be densified into pellets by the extrusion process. Pelletizing is a method of increasing the bulk density of biomass with mechanical pressure (Erickson and Prior 1990). Pellets have low moisture content (about 12% wet basis (w.b)) and high bulk density (more than 1,000 kg/m^{3}). These characteristics make them easier to transport and store (Hamelink et al. 2005).
The process of forming biomass into pellets depends upon the physical properties of ground particles and the process variables during pelletizing. Modeling of the extrusion process focuses on understanding interactions between process parameters and product attributes (Moraru and Kokini 2003). This modeling approach helps to understand the behavior of the biomass grinds or particles during pelleting and to optimize the process conditions for obtaining a desirable pellet. The relationships between the density of the pellet and the related variables are very complicated and highly nonlinear, which make developing a single, general, and accurate mathematical model almost impossible. One of the most appropriate methods to solve these problems is the intelligent method. Shankar and Bandyopadhyay (2004) and Shankar et al. (2010) successfully used genetic algorithms (GA) and artificial neural networks (ANNs) to understand and optimize an extrusion process. In their studies, they used a combination of response surface methodology (RSM) and GA for better understanding of the extrusion pelletization process. Ganjyal et al. (2003) explained the relationship between extrudate properties and extrusion parameters through the neural network method. Numerical simulation and analysis have also been developed by researchers for the extrusion process (Dhanasekharan and Kokini 2003; Alves et al. 2009). The RSM has been a widely used approach for the modeling of the extrusion process (Munoz-Hernandez et al. 2006; Altan et al. 2008; Chakraborty et al. 2009). ANN is especially useful for the modeling of complex nonlinear and multidimensional functional relationships. One of the characteristics of ANN is its ability to learn the relationship between dependent and independent variables due to their ability to learn complex nonlinear and multivariable relationships between process parameters (Basheer and Hajmeer 2000).
In general, an ANN is made up of a large number of simple processing elements known as nodes or neurons, which are organized in layers. Each neuron is connected to other neurons by connections, each of which has an associate numerical value known as ‘weight’. These weights determine the nature and strength of the influence between the interconnected neurons. Information is stored in the interneuron connection. A node has many inputs but only one output.
Understanding the compaction mechanisms is important to design energy-efficient compaction equipment and to quantify the effects of various process variables on pellet density. In this research, ANN was used for the accurate modeling of the extrusion parameters' effect on density of composted MSW pellets which were produced by the laboratory method using an open-ended die.
Methods
Sample preparation
Compost samples were ground using a hammer mill with three different screen sizes (0.3, 0.9, and 1.5 mm) in order to understand the influence of particle size on density. The ground feedstocks were stored at room temperature (25°C ± 2°C). The moisture content of the ground samples was determined following the procedure given in ASAE Standard S 269.4 (1998). The samples of compost were placed in an oven at 105°C ± 3°C for 48 h. To evaluate the effect of moisture content on density, the moisture content of ground feedstocks were adjusted to 35%, 40%, and 45% (w.b) by adding water and were equilibrated overnight.
Pellet production
Pellet density
The density of each pellet was calculated by measuring its length and diameter using an electronic caliper, and an electronic balance with 0.01-g precision was used for mass measurements. To have uniform length, the edges of the pellets were smoothened. Pellet density was calculated by dividing the mass of individual pellets by their volume calculated from the length and diameter (Shankar et al. 2007). The diameter of the pellet was 6 mm which is equal to the die diameter hole, and the length of the pellets varied between 15 and 25 mm. The reported values for pellet density are an average of five measurements.
Statistical analysis
where ρ is the predicted response (density); b_{0} is the interception coefficient; b_{ i }, b_{ ii }, and b_{ ij } are the linear, quadratic, and interaction terms, respectively; ϵ is the random error; and X_{ i } is the independent variable studied. The Design Expert 8.0.7.1 software (Stat-Ease Inc., Minnesota, USA) was used for the regression and graphical analysis of the data obtained. The significance of the RSM model was evaluated by the F test analysis of variation (ANOVA).
Artificial neural network model development
ANN modeling was performed using commercial software NeuroSolutions 5 (NeuroSolutions, Gainesville, FL, USA). Using the experimental data, a feedforward artificial neural network model was developed for modeling correlations between density and input variables. The multilayer perceptron (MLP) ANN, trained by backpropagation, was selected to develop density prediction models. The best ANN model and optimum values of network parameters were obtained by trial and error. All of the 81 patterns had five components (X_{1}, X_{2}, X_{3}, X_{4}, Y), where X_{ i }s were input variables, and Y was the output variable. The data were divided into three groups of 49, 15, and 17 patterns for the training, verification, and testing of ANN, respectively.
Results and discussion
Analysis of Variation (ANOVA) of fitted model
Source | Sum of squares | df | Mean square | F value | Probability > F |
---|---|---|---|---|---|
Model | 20,141.11 | 14 | 1,438.62 | 13.144 | <0.0001 |
Residual | 965.68 | 14 | 68.97 | ||
Lack of fit | 555.96 | 10 | 55.60 | 4.30689 | 0.8025 |
Pure error | 402.62 | 4 | 102.40 | ||
Cor total | 21,106.68 | 28 | |||
R^{2} = 0.95; | Adjusted R^{2} = 0.91 |
Coefficient values of the fitted model
Factor | Coefficient | Mean square | F value | P value probability > F |
---|---|---|---|---|
Moisture, X_{1} | 126.22 | 1,060.13 | 15.37 | 0.0015 |
Speed of piston, X_{2} | 46.58 | 8,472.19 | 122.84 | <0.0001 |
Die length, X_{3} | 16.64 | 94.71 | 1.37 | 0.2608 |
Particle size, X_{4} | -1.57 | 5,699.97 | 82.64 | <0.0001 |
X _{1} X _{2} | -0.18 | 53.67 | 0.78 | 0.3926 |
X _{1} X _{3} | 0.29 | 34.52 | 0.50 | 0.4909 |
X _{1} X _{4} | 1.27 | 57.99 | 0.84 | 0.3747 |
X _{2} X _{3} | -1.17 | 353.24 | 5.12 | 0.0401 |
X _{2} X _{4} | -2.79 | 178.81 | 2.59 | 0.1297 |
X _{3} X _{4} | 1.10 | 6.92 | 0.10 | 0.7560 |
X _{1} ^{2} | -0.6 | 1,440.37 | 20.88 | 0.0004 |
X _{2} ^{2} | -0.14 | 33.31 | 0.48 | 0.4985 |
X _{3} ^{2} | -0.14 | 1.91 | 0.03 | 0.8701 |
X _{4} ^{2} | -60.7 | 3,097.58 | 44.91 | <0.0001 |
Effect of independent variable
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.
Artificial neural network model
Experimental testing data of artificial neural network
Moisture (%) | Speed of piston (mm/s) | Die length (mm) | Particle size (mm) | Measured density (kg/m3) | Predicted density (kg/m3) |
---|---|---|---|---|---|
45 | 2 | 8 | 0.3 | 1,119.16 | 1,123.18 |
35 | 6 | 12 | 0.9 | 1,097.00 | 1,094.18 |
35 | 2 | 8 | 0.9 | 1,106.11 | 1,105.54 |
45 | 6 | 10 | 0.9 | 1,113.46 | 1,113.78 |
45 | 10 | 10 | 0.9 | 1,076.70 | 1,068.88 |
40 | 10 | 8 | 0.9 | 1,098.96 | 1,095.96 |
35 | 2 | 10 | 0.3 | 1,118.30 | 1,118.43 |
35 | 2 | 12 | 0.9 | 1,129.29 | 1,131.93 |
40 | 10 | 10 | 0.9 | 1,090.44 | 1,086.14 |
45 | 6 | 10 | 1.5 | 1,075.81 | 1,074.51 |
35 | 10 | 8 | 1.5 | 1,039.36 | 1,041.35 |
45 | 2 | 10 | 1.5 | 1,110.50 | 1,117.71 |
35 | 10 | 12 | 0.9 | 1,062.64 | 1,066.61 |
45 | 6 | 8 | 0.9 | 1,103.36 | 1,104.14 |
45 | 6 | 8 | 0.3 | 1,097.87 | 1,101.81 |
40 | 10 | 8 | 0.3 | 1,097.84 | 1,092.71 |
45 | 6 | 10 | 0.3 | 1,104.67 | 1,104.09 |
The optimum values of the ANN model used to predict the density of biomass pellet
Optimum | Transfer function | Mean value | ||||
---|---|---|---|---|---|---|
MLP structure | Learning rate | Momentum | RMSE train | RMSE test | Epoch | |
4-10-4-1 | 0.7 | 0.5 | Tanh | 0.01732 | 0.0548 | 10,000 |
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.
Comparison of RSM and ANN models
Validation data set
Moisture | Speed of piston | Die length | Particle size | Actual | Predicted | |
---|---|---|---|---|---|---|
(mm/s) | (mm) | (mm) | Quadratic model | ANN model | ||
50 | 5 | 6 | 0.6 | 1,053.74 | 1,008.10 | 1,043.80 |
30 | 5 | 6 | 0.6 | 1,072.02 | 1,030.12 | 1,065.76 |
50 | 5 | 6 | 2 | 984.21 | 826.24 | 937.40 |
30 | 5 | 6 | 2 | 918.24 | 848.26 | 928.93 |
50 | 5 | 15 | 0.6 | 1,141.28 | 955.24 | 1,132.00 |
30 | 5 | 15 | 0.6 | 1,051.02 | 977.26 | 1,039.04 |
50 | 5 | 15 | 2 | 1,062.02 | 773.38 | 1,058.90 |
30 | 5 | 15 | 2 | 923.50 | 795.40 | 931.00 |
50 | 15 | 6 | 0.6 | 1,003.47 | 1,103.98 | 993.60 |
30 | 15 | 6 | 0.6 | 1,096.75 | 1,126.01 | 1,088.09 |
50 | 15 | 6 | 2 | 897.95 | 922.12 | 904.90 |
30 | 15 | 6 | 2 | 942.96 | 944.14 | 930.93 |
50 | 15 | 15 | 0.6 | 949.30 | 945.40 | 961.96 |
30 | 15 | 15 | 0.6 | 934.03 | 967.42 | 942.94 |
50 | 15 | 15 | 2 | 870.04 | 763.54 | 861.78 |
30 | 15 | 15 | 2 | 806.51 | 785.56 | 809.00 |
Comparison of RSM and ANN models
Parameters | RSM | ANN |
---|---|---|
RMSE | 0.54 | 0.017 |
R ^{2} | 0.92 | 0.97 |
Conclusions
The present work examined the effects of moisture content, piston speed, die length, and particle size on the density of biomass pellets. In this research, artificial neural network was used for modeling the effect of independent variables on the density of the pellet and results compared with results of RSM method. The results indicate that a properly trained neural network can be used to predict effect of input variable on pellet density. The ANN model was found to have higher predictive capability than the RSM model. Statistical analyses confirmed that the moisture content, speed of piston, and particle size significantly affected the pellet density while the influence of die length was negligible. The result of present research can be useful for designing and constructing a suitable pelleting machine for producing biomass pellets.
Authors' information
AZ and RA are Graduate students, and MHK is Associate professor of the Department of Agrotechnology, College of Abouraihan, University of Tehran, Iran.
Notes
Acknowledgements
This research was supported by grants from the College of Abouraihan, University of Tehran.
Supplementary material
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