Improved Prediction of the Higher Heating Value of Biomass Using an Artificial Neural Network Model Based on the Selection of Input Parameters
Abstract
:1. Introduction
2. Materials and Methods
3. Results
3.1. Dataset
3.2. Linear Regression
3.3. Multivariate Adaptive Regression Spline
−1.54⋅h(4.17−H) − 0.86⋅h(H-4.17) + 17.47⋅h(S−0.12),
3.4. ANN Simulation
4. Discussion
Model | RMSE | MAE | R2 | References |
---|---|---|---|---|
A correlation for calculating HHV from proximate analysis | 1.043 | 0.502 | 0.359 | Parikh et al. (2005) [46] |
A correlation for calculating HHV from proximate analysis | 1.431 | 0.679 | 0.456 | Nhuchhen and Salam (2012) [47] |
Genetic programming | 0.808 | 0.485 | 0.934 | Ghugare et al. (2014) [45] |
Support Vector Machines (SVR) model | 3.962 | 6.172 | 0.912 | Ghugare et al. (2014) [45] |
Our model with 2 inputs | 0.6223 | 0.3577 | 0.968 | This study |
Our model with 3 inputs | 0.5398 | 0.3794 | 0.976 | This study |
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
A | Ash content |
ANN | Artificial neural network |
BR | Bayesian regularization algorithm |
C | Carbon |
FC | Combustible solid content |
H | Hydrogen |
HHV | Heating value |
L-M | Levenberg-Marquardt |
LR | Linear regression |
M | Moisture |
MAE | Mean absolute error |
MAPE | Mean absolute percentage error |
MARS | Multivariate adaptive regression spline |
Max () | Maximum function |
MLP | Multilayer perception |
MLR | Multiple linear regression |
MSE | Mean squared error |
N | Nitrogen |
O | Oxygen |
R | Regression value |
R2 | Coefficient of determination |
RMSE | Root Mean Square Error |
S | Sulfur |
SCG | Scaled conjugate gradient algorithm |
V | Volatile matter |
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Determined Parameters | Device | Standard |
---|---|---|
Moisture M (%) | Laboratory dryer | ISO 18134 (2017) [26] |
Volatile matter V (%), ash content A (%) | FCF 2,5S electric muffle furnace made by Czylok with SM-946 electronic controller and temperature display (Warsaw, Poland) | ISO 18122 (2016) [27] |
Determination of total carbon, hydrogen and nitrogen (%) | CHNS Flash EA 1112 Series Elemental Analyzer (Thermo Finnigan, Walthman, MA, USA) | ISO 16948 (2015) [28] |
Higher heating value (HHV) (kJ/kg) | Mikado Calorimeter (Warsaw, Poland) | ISO 18125 (2015) [29] |
The content of other combustible solid fractions FC (%) | FC was determined from the difference FC = 100-A-W-V | [30] |
Quality Indicator | Formula | Meaning of Symbols |
---|---|---|
Regression value R | σy′—standard deviation of reference values of HHV, σy*—standard deviation of predicted values HHV, yi is the actual value of HVV, denotes the value of the HVV for the i-th observation obtained from the model | |
Mean Squared Error (MSE) | ||
Root Mean Square Error (RMSE) | ||
Mean Absolute Percentage Error (MAPE) | ||
Mean Absolute Error (MAE) |
Fuel Type | Industrial Analysis (%) | Elemental Analysis (%) | HHV MJ/kg | ||||||
---|---|---|---|---|---|---|---|---|---|
M | A | V | FC | C | H | N | S | ||
Oak Bark | 7.93 | 1.57 | 71.50 | 19 | 41.20 | 3.73 | 0.84 | 7.93 | 16.08 |
Pine | 6.88 | 1.46 | 64.10 | 27.56 | 36.41 | 3.51 | 0.17 | 6.88 | 14.98 |
Hornbeam | 5.88 | 1.14 | 41.10 | 51.88 | 31.47 | 2.89 | 0.23 | 5.88 | 10.13 |
Alder | 10.39 | 1.97 | 79.10 | 18.54 | 44.86 | 4.17 | 0.39 | 10.39 | 19.39 |
Oat Straw | 6.03 | 4.32 | 43.20 | 46.45 | 42.20 | 3.80 | 0.51 | 6.03 | 16.45 |
Wheat Straw | 6.16 | 3.15 | 71.34 | 19.35 | 43.26 | 4.03 | 0.64 | 6.16 | 18.47 |
Maize Straw | 7.02 | 4.20 | 81.80 | 16.98 | 46.00 | 6.00 | 0.56 | 7.02 | 16.43 |
Rape Straw | 9.05 | 5.50 | 76.54 | 18.91 | 45.00 | 2.80 | 0.47 | 9.05 | 15.02 |
Douglas Fir Bark | 6.6 | 3.0 | 68.65 | 21.75 | 66.45 | 7.26 | 1.31 | 6.6 | 26.70 |
Spruce | 5.9 | 1.37 | 73.10 | 19.63 | 54.00 | 5.70 | 0.5 | 5.9 | 20.84 |
Larch | 7.2 | 0.5 | 52.10 | 40.2 | 51.60 | 5.60 | 0.8 | 0.16 | 20.61 |
Rye Straw | 5.9 | 4.0 | 76.4 | 13.7 | 46.60 | 0.6 | 0.6 | 0.09 | 13 |
Triticale Straw | 6.1 | 2.1 | 75.2 | 16.6 | 43.90 | 0.59 | 0.4 | 0.11 | 13.42 |
Barley Straw | 5.8 | 4.0 | 77.3 | 12.9 | 47.50 | 0.59 | 0.5 | 0.15 | 13.32 |
Reed Pulp | 5.8 | 11.4 | 70.78 | 12.02 | 43.50 | 5.93 | 3.42 | 0.01 | 16.5 |
Roegrass Haughty | 7.8 | 2.7 | 69.66 | 19.84 | 38.38 | 8.84 | 0.44 | 0.03 | 16.8 |
Wooly Spikelet | 6.2 | 9.1 | 79.65 | 17.05 | 44.98 | 5.66 | 1.86 | 0.01 | 14.8 |
Reed Fescue | 6.5 | 9.2 | 77.56 | 16.74 | 39.47 | 5.07 | 1.2 | 0.02 | 15.3 |
Gigant Miscanthus | 7.6 | 9.2 | 79.78 | 13.42 | 42.86 | 4.81 | 3.62 | 0.12 | 17.7 |
Hay | 6.9 | 8.9 | 85.36 | 16.4 | 46.58 | 5.87 | 0.47 | 0.12 | 18 |
No. of Network | 1 | 2 | 3 |
---|---|---|---|
Training algorithm | Levenberg-Marquardt | Scaled Conjugate Gradient | Bayesian Regularization |
Epoch | 13 | 27 | 76 |
Performance | 1.15*10−21 | 0.573 | 1.81 |
Best training performance | 1.4215 at epoch 8 | 1.1868 at epoch 21 | 1.8125 at apoch 73 |
Gradient | 9.19*10−10 | 0.993 | 1.02 |
Levenberg-Marquardt | Scaled Conjugate Gradient | Bayesian Regularization | |
---|---|---|---|
R (all data) | 0.98453 | 0.96794 | 0.91375 |
MSE | 0.3873 | 0.7789 | 2.0084 |
RMSE | 0.6223 | 0.8826 | 1.4172 |
MAPE | 0.0210 | 0.0428 | 0.0768 |
MAE | 0.3577 | 0.6894 | 1.1896 |
No. of Network | 1 | 2 | 3 |
---|---|---|---|
Training algorithm | Levenberg-Marquardt | Scaled Conjugate Gradient | Bayesian Regularization |
Epoch | 11 | 26 | 904 |
Performance | 0.118 | 0.624 | 1.25 |
Best training performance | 0.61523 at epoch 5 | 1.0617 at epoch 20 | 1.2438 at epoch 159 |
Gradient | 0.296 | 1.18 | 0.617 |
Levenberg-Marquardt | Scaled Conjugate Gradient | Bayesian Regularization | |
---|---|---|---|
R (all data) | 0.98827 | 0.96817 | 0.90396 |
MSE | 0.2914 | 0.7672 | 2.1978 |
RMSE | 0.5398 | 0.8759 | 1.4825 |
MAPE | 0.0226 | 0.0411 | 0.0694 |
MAE | 0.3794 | 0.6896 | 1.0359 |
Quality Indicators | Model with 2 Inputs (C, H) | Model with 3 Inputs (C, H, S) |
---|---|---|
Model 1 | Model 2 | |
R (all data) | 0.98453 | 0.98827 |
MSE | 0.3873 | 0.2914 |
RMSE | 0.6223 | 0.5398 |
MAPE | 0.0210 | 0.0226 |
MAE | 0.3577 | 0.3794 |
Input Variables | Type of ANN | ANN Architecture | R2 | Activation Functions | Authors |
---|---|---|---|---|---|
FC, V, M, A | Levenberg-Marquardt | 3-7-1 | 0.9852 | Sigmoid symmetry | [23] |
FC, V, M, A | Levenberg-Marquardt | 1-23-1-1 | 0.9591 | Hyperbolic tangent sigmoid and linear | [47] |
C, H, N, S, O, A, H2O | Radial basis function combined with Levenberg- Marquardt | 0.997 | Radial basis function | [48] | |
V, FC, A, M, C, H, N, S, and O | Levenberg- Marquardt | 9-10-1 | 0.985 | Tangent sigmoid | [49] |
C, H, N, S, O | Levenberg- Marquardt | 5-11-1 | 0.77 | Tangent sigmoid | [50] |
FC, V, A | Levenberg- Marquardt | 3-10-1 | 0.966 | Hyperbolic tangent sigmoid transfer function | [51] |
Temperature, Time, FC, V, A, C, O, H | Levenberg- Marquardt | 5-10-1 | 0.8321 | Tangent sigmoid | [52] |
V, FC, A, M, C, H, N, S, and O | Levenberg- Marquardt | 9-10-1 | 0.909 | Tangent sigmoid | [53] |
C, H, S | Levenberg-Marquardt | 3-9-1 | 0.976 | Hyperbolic tangent sigmoid transfer function | This study |
C, H | Levenberg-Marquardt | 2-8-1 | 0.968 | Hyperbolic tangent sigmoid transfer function | This study |
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Kujawska, J.; Kulisz, M.; Oleszczuk, P.; Cel, W. Improved Prediction of the Higher Heating Value of Biomass Using an Artificial Neural Network Model Based on the Selection of Input Parameters. Energies 2023, 16, 4162. https://doi.org/10.3390/en16104162
Kujawska J, Kulisz M, Oleszczuk P, Cel W. Improved Prediction of the Higher Heating Value of Biomass Using an Artificial Neural Network Model Based on the Selection of Input Parameters. Energies. 2023; 16(10):4162. https://doi.org/10.3390/en16104162
Chicago/Turabian StyleKujawska, Justyna, Monika Kulisz, Piotr Oleszczuk, and Wojciech Cel. 2023. "Improved Prediction of the Higher Heating Value of Biomass Using an Artificial Neural Network Model Based on the Selection of Input Parameters" Energies 16, no. 10: 4162. https://doi.org/10.3390/en16104162
APA StyleKujawska, J., Kulisz, M., Oleszczuk, P., & Cel, W. (2023). Improved Prediction of the Higher Heating Value of Biomass Using an Artificial Neural Network Model Based on the Selection of Input Parameters. Energies, 16(10), 4162. https://doi.org/10.3390/en16104162