# Energy Potentials of Agricultural Biomass and the Possibility of Modelling Using RFR and SVM Models

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## Abstract

**:**

^{2}= 0.79) and SVM (R

^{2}= 0.93) models. The developed models have shown promising results in accurately predicting the HHV of biomass from various sources. The use of these algorithms for biomass energy prediction has the potential for further development.

## 1. Introduction

^{2}= 0.97) was used as the main evaluation parameter. SVM models for estimating HHV are applicable to different types of biomass, thus providing a good solution to the problem of estimating HHV [15]. A machine learning (ML) model created to estimate HHV of biomass was based on the input parameters of proximate analysis data (percentage of fixed carbon, ash and volatile matter). An extreme learning machine (ELM) method proved to be very practical in estimating the HHV, as evidenced by the high coefficient of determination for the input parameters of fixed carbon (0.972), volatiles (0.989) and ash (0.968) [12]. Bychkov et al. [16] investigated developed models for predicting the HHV of plant biomass from ultimate analysis data. In the conducted study, authors used 150 models of which 8 were selected for model testing, with 3 showing good performance in estimating the HHV of biomass with small deviations from actual values.

## 2. Materials and Methods

#### 2.1. Data Collection

#### 2.2. Nonlinear Modelling

_{i}prior probability of each given class. In order to solve the nonlinear problem, the Kelner function is used to map the input vectors into a multidimensional vector proctor that is used to find the hyperplane [30]. The equation used to create the SVM model is shown in the following equation (Equation (2)) [31]:

#### 2.3. Models Verification

^{2}(reduced chi-square) from Equation (3), RMSE (root mean square error) from Equation (4), MBE (mean bias error) from Equation (5), MPE (mean percentage error) from Equation (6), and SSE (sum of squared estimate error) from Equation (7). “Goodness of fit” is calculated using the above statistical parameters to find the model with the lowest error, and they are represented by the following equations [32]:

## 3. Results

## 4. Discussion

#### 4.1. Support Vector Machine (SVM)

#### 4.2. Random Forest Regression (RFR)

#### 4.3. Goodness of Fit

^{2}(0.82), RMSE (0.90), MBE (−0.03), SSE (49.28), AARD (44.12) and R

^{2}(0.93), and the residual analysis skewness (−3.04), kurtosis (14.32), SD (0.91) and Var (0.82) show the low level of error of the SVM model. The values of x

^{2}(5.99), RMSE (2.43), MBE (−0.01), MPE (8.32), SSE (359.53), AARD (103.30), and R

^{2}(0.79) were calculated for the RFR model in the table. The skewness (0.94), kurtosis (2.08), SD (2.45) and variance (5.99) parameters were determined by the residual analysis. Both developed models showed satisfactory performance in modeling the HHV values. Considering that, R

^{2}is used as the main indicator of the model’s ability for estimation.

^{2}= 0.79 for the RFR model, while the overlap values in the SVM model have a higher coefficient of determination (R

^{2}= 0.93). In the study conducted by Xing et al. [38], machine learning models were built to estimate the HHV value of biomass based on the input parameters of ultimate and proximate analysis. The RFR model in the study shows a great fit for prediction (R

^{2}> 0.94), while the SVM model also shows good performance (R

^{2}~0.90). The RFR models give good results in terms of performance. The parameters R

^{2}, MAPE and RMSE are calculated at 0.94, 0.57 and 2.56, respectively, while for the SVM model the parameters R

^{2}, MAPE and RMSE are 0.90, 0.76 and 3.53, respectively. The study also showed the relative importance of the input parameters of ultimate analysis in the models for C (61.6%), H (20%), O (9.6%) and N (8.8%). Considering everything, it can be concluded that the developed models are suitable for estimating the HHV based on the input parameters of the ultimate analysis. Using the performed statistical test “Goodness of Fit”, the parameters showed a low level of error in estimating the HHV, while the SVM model shows a higher level of performance in modeling.

## 5. Conclusions

^{2}= 0.93) and RFR models (R

^{2}= 0.79) in estimating HHV based on the input parameters of the ultimate analysis of observed agricultural biomass.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Sample | C (%) | H (%) | N (%) | S (%) | O (%) | HHV (MJ/kg) |
---|---|---|---|---|---|---|

Corn biomass | 48.45 ± 7.3 ^{a} | 5.29 ± 1.11 ^{b} | 0.70 ± 0.50 ^{a} | 0.08 ± 0.09 ^{a} | 38.11 ± 11.22 ^{a} | 19.42 ± 2.72 ^{a} |

Soybean biomass | 47.37 ± 3.48 ^{a} | 4.53 ± 0.73 ^{a} | 1.38 ± 2.32 ^{b} | 0.22 ± 0.3 ^{b} | 46.5 ± 6.83 ^{b} | 17.93 ± 1.04 ^{a} |

Sunflower biomass | 54.16 ± 8.9 ^{b} | 6.51 ± 0.9 ^{c} | 2.22 ± 1.64 ^{c} | 0.06 ± 0.13 ^{a} | 35.62 ± 9.25 ^{a} | 22.46 ± 4.41 ^{b} |

Significance | ** | * | * | ** | * | * |

Minimum | 47.37 | 4.53 | 0.70 | 0.06 | 35.62 | 17.93 |

Maximum | 54.16 | 6.51 | 2.22 | 0.22 | 46.50 | 22.46 |

Average | 49.99 | 5.44 | 1.44 | 0.12 | 40.08 | 19.94 |

Vector No. | Weights | Support Vector | Decision Constant | ||||
---|---|---|---|---|---|---|---|

C | H | N | S | O | |||

1 | 9.00 | 0.22 | 0.63 | 0.07 | 0.07 | 0.73 | −0.09 |

2 | −7.34 | 0.20 | 0.68 | 0.07 | 0.12 | 0.70 | |

3 | −0.21 | 0.95 | 0.00 | 0.21 | 0.02 | 0.00 | |

4 | −1.01 | 0.35 | 0.49 | 0.00 | 0.32 | 0.96 | |

5 | 0.34 | 0.25 | 0.71 | 0.11 | 0.47 | 0.83 | |

6 | −9.00 | 0.28 | 0.67 | 0.17 | 0.09 | 0.72 | |

7 | 6.14 | 0.51 | 0.70 | 0.16 | 0.00 | 0.64 | |

8 | −1.95 | 0.77 | 0.96 | 0.57 | 0.00 | 0.36 | |

9 | 4.02 | 1.00 | 0.97 | 0.59 | 0.00 | 0.20 |

Residual Analysis | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Model | x^{2} | RMSE | MBE | MPE | SSE | AARD | R^{2} | Skewness | Kurtosis | SD | Variance |

SVM model | 0.82 | 0.90 | −0.03 | 3.07 | 49.28 | 44.12 | 0.93 | −3.04 | 14.32 | 0.91 | 0.82 |

RFR model | 5.99 | 2.43 | −0.01 | 8.32 | 359.53 | 103.30 | 0.79 | 0.94 | 2.08 | 2.45 | 5.99 |

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**MDPI and ACS Style**

Brandić, I.; Antonović, A.; Pezo, L.; Matin, B.; Krička, T.; Jurišić, V.; Špelić, K.; Kontek, M.; Kukuruzović, J.; Grubor, M.;
et al. Energy Potentials of Agricultural Biomass and the Possibility of Modelling Using RFR and SVM Models. *Energies* **2023**, *16*, 690.
https://doi.org/10.3390/en16020690

**AMA Style**

Brandić I, Antonović A, Pezo L, Matin B, Krička T, Jurišić V, Špelić K, Kontek M, Kukuruzović J, Grubor M,
et al. Energy Potentials of Agricultural Biomass and the Possibility of Modelling Using RFR and SVM Models. *Energies*. 2023; 16(2):690.
https://doi.org/10.3390/en16020690

**Chicago/Turabian Style**

Brandić, Ivan, Alan Antonović, Lato Pezo, Božidar Matin, Tajana Krička, Vanja Jurišić, Karlo Špelić, Mislav Kontek, Juraj Kukuruzović, Mateja Grubor,
and et al. 2023. "Energy Potentials of Agricultural Biomass and the Possibility of Modelling Using RFR and SVM Models" *Energies* 16, no. 2: 690.
https://doi.org/10.3390/en16020690