# Artificial Neural Network as a Tool for Estimation of the Higher Heating Value of Miscanthus Based on Ultimate Analysis

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}= 0.77). The paper proves the possibility of using ANN models in practical application in determining fuel properties of biomass energy crops and greater accuracy in predicting HHV than the regression models offered in the literature.

## 1. Introduction

^{2}values with existing regression models.

## 2. Materials and Methods

#### 2.1. Crop Establishment and Data Collection

#### 2.2. Statistical Analysis

^{2}) (Equation (1)), root mean square error (RMSE) (Equation (2)), coefficient of determination (R

^{2}), mean bias error (MBE) (Equation (3)), mean percentage error (MPE) (Equation (4)), and sum of squared estimate of errors (SSE) (Equation (5)). The RMSE shows the efficiency of the model by comparing the predicted values with the already measured values. The value obtained by the MBE is used as an indicator of the standard deviation of the predicted values from the measured values [19]. The listed parameters are given by the following formula [20].

_{exp,i}stands for the experimental values and x

_{pre,i}is the predicted values calculated by the model, N and n are the number of observations and constants, respectively.

#### 2.3. ANN Modeling

_{1}and B

_{1}and W

_{2}and B

_{2}, respectively [26]. The neural network model can be represented in matrix notation: Equation for calculating the output data (Equation (7)) of the neural network [27]:

_{1}and f

_{2}represent the transfer function in the hidden and output layer, X represents the matrix of the input layer [28].

#### 2.4. Regression Models

## 3. Results

## 4. Discussion

#### 4.1. Prediction of HHV Using Developed Regression Models

^{2}) was used as the most important statistical parameter to evaluate the suitability of the mathematical models, which was lowest for model 1, 8 and model 10 (R

^{2}= 0.00) and highest for model 9 (R

^{2}= 0.47) in the calculations for 10 different models. The reliability of the regression models and ANN is ensured by the parameters MPE, SSE and R

^{2}, but other parameters (for most models) also show good performance. The calculated statistical parameter x

^{2}shows good performance in models 2,5,7 (0.19) and in model 9 (0.17). For the above-mentioned reason, it is necessary to consider several statistical parameters when evaluating performance of the model.

#### 4.2. ANN Model

^{2}value (0.77 overall) and an overall low sum of squares value (SOS) were achieved during the training cycle (Table 4).

^{2}(0.07), RMSE (0.27), MBE (−0.03), MPE (1.10), SSE (13.74), and R

^{2}(0.77). The residual analysis also yielded the parameters skewness (0.534), kurtosis (2.293), standard deviation (0.269), and variance (0.072). Conducted analysis shows that the model has good predictive accuracy.

## 5. Conclusions

^{2}value. The calculations performed according to the proposed non-linear mathematical models are not suitable enough to predict the HHV biomass of miscanthus (R

^{2}≤ 0.47). Incorporating available data from the ultimate analysis of miscanthus the developed neural network model showed high accuracy in predicting the higher heating value (overall R

^{2}= 0.77). The factors N, C, S, H, and O influence the value of HHV. In the developed model, the increase in HHV is mainly influenced by the increase in the values of the parameter S. Although these models are not yet widely used as mathematical models for prediction (especially for variables that have nonlinear relationships), they offer the possibility of obtaining the desired result with less time, lower cost, and satisfactory accuracy, which can replace existing empirical methods. The developed model will be able to make more accurate predictions as more input data is collected. Future plans are to expand the database (literature sources and experimental data) and the development of new models such as Random Forest Regression and Support Vector Machine.

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Sr.no. | Proposed Equations from the Literature | References |
---|---|---|

1 | HHV = a + b · C | [31] |

2 | HHV − a + b · H | [31] |

3 | HHV − a + b · O | [31] |

4 | $HHV=a+b\cdot \frac{O}{C}$ | [31] |

5 | $HHV=a+b\cdot \frac{H}{C}$ | [31] |

6 | HHV = a + b · C + c · H + d · C^{2} + e · H^{2} | [31] |

7 | $HHV=a+b\cdot \frac{O}{C}+c\cdot \frac{H}{C}+d\cdot {\left(\frac{O}{C}\right)}^{2}+e\cdot {\left(\frac{H}{C}\right)}^{2}$ | [31] |

8 | HHV = a · C − b | [5] |

9 | HHV = a + b · C^{2} + c · C + d · H + e · C · H + g · N | [30] |

10 | $HHV=a+b\cdot {\left(C\right)}^{2}$ | [31] |

**Table 2.**Average values of nitrogen, carbon, sulfur, hydrogen, and oxygen of investigated biomass of miscanthus.

Sample | N | C | S | H | O | HHV |
---|---|---|---|---|---|---|

MxG1 | 0.24 ± 0.15 ^{a} | 51.49 ± 0.58 ^{a} | 0.11 ± 0.04 ^{a} | 5.82 ± 0.32 ^{a} | 42.33 ± 0.74 ^{a} | 18.21 ± 0.54 ^{a} |

MxG2 | 0.19 ± 0.13 ^{a} | 51.3 ± 0.53 ^{a} | 0.14 ± 0.06 ^{a} | 5.85 ± 0.2 ^{a} | 42.53 ± 0.42 ^{a} | 18.16 ± 0.37 ^{a} |

MxG3 | 0.23 ± 0.15 ^{a} | 50.9 ± 0.96 ^{a} | 0.14 ± 0.06 ^{a} | 5.82 ± 0.2 ^{a} | 42.91 ± 0.89 ^{a} | 18.22 ± 0.58 ^{a} |

MxG4 | 0.22 ± 0.13 ^{a} | 51.75 ± 0.73 ^{a} | 0.21 ± 0.3 ^{a} | 5.83 ± 0.33 ^{a} | 41.99 ± 0.69 ^{a} | 18.24 ± 0.64 ^{a} |

MxG5 | 0.2 ± 0.09 ^{a} | 51.38 ± 0.8 ^{a} | 0.14 ± 0.08 ^{a} | 5.84 ± 0.33 ^{a} | 42.44 ± 0.82 ^{a} | 18.37 ± 0.48 ^{a} |

MxG6 | 0.31 ± 0.21 ^{a} | 51.53 ± 0.86 ^{a} | 0.21 ± 0.2 ^{a} | 5.89 ± 0.23 ^{a} | 42.06 ± 0.88 ^{a} | 18.45 ± 0.61 ^{a} |

MxG7 | 0.2 ± 0.13 ^{a} | 51.33 ± 0.93 ^{a} | 0.12 ± 0.09 ^{a} | 5.82 ± 0.33 ^{a} | 42.54 ± 0.92 ^{a} | 17.97 ± 0.73 ^{a} |

MxG8 | 0.2 ± 0.11 ^{a} | 51.65 ± 1.33 ^{a} | 0.11 ± 0.06 ^{a} | 5.88 ± 0.27 ^{a} | 42.16 ± 1.18 ^{a} | 18.23 ± 0.64 ^{a} |

MxG9 | 0.21 ± 0.12 ^{a} | 51.76 ± 0.77 ^{a} | 0.13 ± 0.05 ^{a} | 5.85 ± 0.35 ^{a} | 42.05 ± 0.86 ^{a} | 18.35 ± 0.32 ^{a} |

MxG10 | 0.18 ± 0.1 ^{a} | 51.48 ± 0.97 ^{a} | 0.11 ± 0.05 ^{a} | 5.83 ± 0.33 ^{a} | 42.4 ± 0.85 ^{a} | 18.1 ± 0.61 ^{a} |

MxG11 | 0.22 ± 0.16 ^{a} | 51.09 ± 1.14 ^{a} | 0.11 ± 0.05 ^{a} | 5.85 ± 0.27 ^{a} | 42.74 ± 1.12 ^{a} | 18.06 ± 0.33 ^{a} |

MxG12 | 0.19 ± 0.11 ^{a} | 51.6 ± 0.82 ^{a} | 0.12 ± 0.06 ^{a} | 5.86 ± 0.35 ^{a} | 42.24 ± 0.97 ^{a} | 18.51 ± 0.5 ^{a} |

MxG13 | 0.27 ± 0.22 ^{a} | 51.15 ± 0.8 ^{a} | 0.15 ± 0.09 ^{a} | 5.79 ± 0.36 ^{a} | 42.64 ± 0.86 ^{a} | 18.24 ± 0.6 ^{a} |

MxG14 | 0.2 ± 0.14 ^{a} | 51.53 ± 0.82 ^{a} | 0.09 ± 0.03 ^{a} | 5.31 ± 1.71 ^{a} | 42.86 ± 2.12 ^{a} | 17.83 ± 0.81 ^{a} |

MxG15 | 0.25 ± 0.15 ^{a} | 51.73 ± 0.99 ^{a} | 0.12 ± 0.05 ^{a} | 5.83 ± 0.38 ^{a} | 42.08 ± 1.19 ^{a} | 18.09 ± 0.4 ^{a} |

MxG16 | 0.18 ± 0.12 ^{a} | 51.11 ± 1.12 ^{a} | 0.11 ± 0.05 ^{a} | 5.83 ± 0.33 ^{a} | 42.77 ± 1.15 ^{a} | 18.02 ± 0.43 ^{a} |

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

Model 1 | 0.31 | 0.01 | 0.01 | 854.24 | 59.66 | 0.00 | −0.63 | 1.47 | 0.56 | 0.31 |

Model 2 | 0.19 | 0.01 | 0.01 | 578.45 | 35.56 | 0.40 | −1.32 | 9.26 | 0.43 | 0.19 |

Model 3 | 0.30 | 0.01 | 0.01 | 810.35 | 57.95 | 0.03 | −0.67 | 2.10 | 0.55 | 0.30 |

Model 4 | 0.31 | 0.01 | 0.01 | 830.08 | 58.92 | 0.02 | −0.65 | 1.81 | 0.56 | 0.31 |

Model 5 | 0.19 | 0.01 | 0.01 | 623.98 | 36.77 | 0.38 | −1.19 | 6.78 | 0.44 | 0.19 |

Model 6 | 0.22 | 0.01 | 0.01 | 582.07 | 42.91 | 0.36 | −1.53 | 12.54 | 0.47 | 0.22 |

Model 7 | 0.19 | 0.01 | 0.01 | 585.55 | 35.77 | 0.40 | −1.28 | 8.67 | 0.43 | 0.19 |

Model 8 | 0.31 | 0.01 | 0.01 | 854.24 | 59.66 | 0.00 | −0.63 | 1.47 | 0.56 | 0.31 |

Model 9 | 0.17 | 0.01 | 0.01 | 526.96 | 31.57 | 0.47 | −1.79 | 13.09 | 0.41 | 0.17 |

Model 10 | 0.31 | 0.01 | 0.01 | 853.32 | 59.64 | 0.00 | −0.63 | 1.49 | 0.56 | 0.31 |

ANN | 0.07 | 0.27 | -0.03 | 1.10 | 13.74 | 0.77 | 0.53 | 2.29 | 0.27 | 0.07 |

^{2}—reduced chi-square, RMSE—root mean square error, R

^{2}—coefficient of determination, MBE—mean bias error and MPE—mean percentage error, ANN—artificial neural network.

Input Layer | Output Layer | ||||||
---|---|---|---|---|---|---|---|

Weight | Bias | Weight | Bias | ||||

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

−1.74 | 10.34 | −30.08 | −7.41 | 1.90 | 1.62 | −1.76 | 2.06 |

−0.28 | 3.37 | 1.69 | 2.99 | −4.61 | −0.37 | 1.18 | |

2.58 | −0.83 | −5.02 | −0.40 | −0.37 | −1.56 | 0.20 | |

4.23 | −0.73 | −6.78 | −0.79 | 0.10 | −1.40 | −0.31 | |

10.55 | −3.52 | −15.48 | 12.93 | −0.96 | −2.58 | −1.91 | |

1.08 | 1.54 | 1.49 | −2.03 | −3.48 | −1.57 | −0.44 | |

3.56 | −2.75 | −8.74 | 1.54 | 1.03 | −2.09 | −1.30 | |

−3.67 | 1.30 | 2.92 | 2.02 | −2.74 | −0.87 | 0.48 | |

−2.72 | −0.49 | 6.47 | −0.49 | 0.34 | 0.75 | −0.60 | |

2.25 | 2.01 | 6.90 | −5.15 | 1.20 | 3.20 | 0.47 | |

−1.14 | 1.93 | 2.53 | 0.98 | −1.49 | 0.71 | −1.56 |

Net. Name | Train. Perf. | Test Perf. | Valid. Perf. | Train. Error | Test Error | Valid. Error | Train. Algorithm | Error Function | Hidden Activation | Output Activation |
---|---|---|---|---|---|---|---|---|---|---|

MLP 5-11-1 | 0.861 | 0.902 | 0.951 | 0.042 | 0.026 | 0.021 | BFGS 71 | SOS | Tanh | Logistic |

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**MDPI and ACS Style**

Brandić, I.; Pezo, L.; Bilandžija, N.; Peter, A.; Šurić, J.; Voća, N. Artificial Neural Network as a Tool for Estimation of the Higher Heating Value of Miscanthus Based on Ultimate Analysis. *Mathematics* **2022**, *10*, 3732.
https://doi.org/10.3390/math10203732

**AMA Style**

Brandić I, Pezo L, Bilandžija N, Peter A, Šurić J, Voća N. Artificial Neural Network as a Tool for Estimation of the Higher Heating Value of Miscanthus Based on Ultimate Analysis. *Mathematics*. 2022; 10(20):3732.
https://doi.org/10.3390/math10203732

**Chicago/Turabian Style**

Brandić, Ivan, Lato Pezo, Nikola Bilandžija, Anamarija Peter, Jona Šurić, and Neven Voća. 2022. "Artificial Neural Network as a Tool for Estimation of the Higher Heating Value of Miscanthus Based on Ultimate Analysis" *Mathematics* 10, no. 20: 3732.
https://doi.org/10.3390/math10203732