# Application of the Artificial Neural Network (ANN) Approach for Prediction of the Kinetic Parameters of Lignocellulosic Fibers

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## Abstract

**:**

^{−1}) and Vyazovkin kinetic parameters were obtained using free available software. After, the experimental curves were fitted using an artificial neural network (ANN) approach followed by a Surface Response Methodology (SRM) aiming to obtain curves at any heating rate between the minimum and maximum experimental heating rates. Finally, Vyazovkin kinetic parameters were tested again, with the new predicted curves at the heating rates of 7, 15, 30 and 50 °C·min

^{−1}. Similar values of the kinetic parameters were obtained compared to the experimental ones. In conclusion, due to the capability to learn from the own data, ANN combined with SRM seems to be an excellent alternative to predict TG curves that do not test experimentally, opening the range of applications.

## 1. Introduction

^{−1}for most of the fibers studied. Sunphorka et al. [11] studied an artificial neural network (ANN) model using 150 data from different lignocellulosic fibers in relation to Arrhenius kinetic parameters. The main results indicated that cellulose played a major role in the pre-exponential factor while the hemicellulose on the reaction order. According to the authors, all components affected the activation energy. Ornaghi Jr. et al. [7] studied the kinetic mechanisms involved in the thermal degradation of lignocellulosic fibers based on the chemical composition. The main results indicated that the activation energy of the fibers followed similar values to the cellulose component and that the thermogravimetric curves followed a similar pattern, independently of the chemical composition. Monticeli et al. [12] studied an ANN approach for lignocellulosic fibers using thermogravimetric analysis. The results indicated 50–60 as the optimal number of training datasets for all fibers. In addition, a reliable prediction of TG curves was obtained at different heating rates did not obtain experimentally.

## 2. Materials and Methods

^{−1}), from 25 to 900 °C, using ~10 mg of each sample at four distinct heating rates (5, 10, 20 and 40 °C·min

^{−1}). The theoretical and predicted curves were used to calculate the kinetic parameters according to the Vyazovkin method. The calculation was carried out using the software developed by Drozin et al. [17]. A previous study Monticeli et al. [12] was used as a base for the obtaining of the new ANN curves at distinct heating rates. The predicted curves were used to calculate the kinetic parameters again and compare the results.

#### 2.1. Kinetic Approach

#### 2.2. Artificial Neural Network (ANN)

#### 2.3. Surface Response Methodology (SRM)

_{i}and x

_{j}are variations parameter, in which i represents the $x$-axis (temperature T (°C)) and j is the $y$-axis (heating rate HR (°C·min

^{−1})). $\gamma $

_{0}is the constant coefficient; $\gamma $

_{i}is the linear coefficient; and $\gamma $

_{ij}is the interaction coefficient.

## 3. Results and Discussion

^{−1}. Figure 3a represents the activation energy in the conversion function and while Figure 3b the degradation rate in the function of conversion degree. An appropriate correlation between the theoretical and calculated degradation rate vs. alpha is obtained. The results presented the following values: E

_{a}= 192.02 KJ·mol

^{−1}, A = 10.6 × 10

^{15}, m = 0.9, n = 1.71 and p = 0.

^{2}> 0.99 for all curves.

^{2}= 0.96 indicates the high reliability of predicted results. For the lowest heating rate (i.e., 5 °C/min), the degradation curve initiates at the lowest temperature for onset and endset, resulting in the slowest degradation of the remaining residue (15%), between 375–810 °C. At higher heating rates, more abrupt degradation occurs, increasing the onset and endset temperatures.

_{onset}; T

_{onset}to T

_{endset}; and T

_{endset}to the final temperature, according to the procedure presented in reference [12].

^{−1}. Through the ANN and SRM combination, it is possible to predict other degradation curves with different analysis parameters not accessed experimentally, decreasing costs and time related to tests repetitions with high reliability.

^{−1}and (b) 7, 15, 30 and 50 °C·min

^{−1}. The results presented the following values for condition (a): E

_{a}= 228.74 KJ·mol

^{−1}, A = 3.59 × 10

^{19}, m = 0.1, n = 1.00 and p = 0 and for condition (b): E

_{a}= 226.92 KJ·mol

^{−1}, A = 6.92 × 10

^{18}, m = 0.1, n = 1.53 and p = 0.

^{−1}) used in condition b was also obtained. Of course, that the extrapolation of data using ANN is not well recommended due to the accumulation of errors. However, it can be used carefully and seems to work if the behavior did not change drastically from the previous behavior.

_{a}and A values, as shown in Table 2. The results confirmed that the E

_{a}and A are directly proportional to the heating rate fluctuation since in both cases F > F

_{critical}and p-value < 0.05, confirming that there is a significant difference between experimental and predicted values. In addition, the percentage of contribution (PC) shows that error presented less influence on degradation kinetics parameters. This means that even with a slight variation on activation energy and pre-exponential factor, the use of different heating rate values has a high level of contribution in the determination of kinetic degradation parameters.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**(

**a**) Thermogravimetric and (

**b**) derivative TG curves of curaua fiber at different heating rates. The heating rates of 10, 20 and 40 °C·min

^{−1}are represented by the red, blue and green lines. The vertical cyan lines represent the limit of calculation of the kinetic parameters.

**Figure 3.**Kinetic calculation of the experimental curves. (

**a**) Activation energy in function of conversion degree and (

**b**) degradation rate in function of conversion degree.

**Figure 4.**(

**a**) Thermogravimetric curves of curaua fiber at different heating rates trained using ANN approach according to Monticeli et al. [12], and (

**b**) enlargement of initial degradation.

Technique | Number of Layers | Number of Hidden Neurons in Each Layer | Training Repetitions | Neural Network Algorithm | Error Function | Threshold of Error Function | Activation Function |
---|---|---|---|---|---|---|---|

TGA | 1 | 12 | 3 | Resilient backpropagation with back tracking | Sum of squared errors | 0.01 | Tangent hyperbolicus |

F | p-Value | F_{critical} | PC (%) | |
---|---|---|---|---|

E_{a} | 255.88 | 8.93 × 10^{−5} | 7.71 | 99.80 |

error | 0.20 | |||

A | 16.64 | 0.015 | 5.14 | 94.15 |

error | - | - | - | 5.85 |

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**MDPI and ACS Style**

Ornaghi, H.L., Jr.; Neves, R.M.; Monticeli, F.M.
Application of the Artificial Neural Network (ANN) Approach for Prediction of the Kinetic Parameters of Lignocellulosic Fibers. *Textiles* **2021**, *1*, 258-267.
https://doi.org/10.3390/textiles1020013

**AMA Style**

Ornaghi HL Jr., Neves RM, Monticeli FM.
Application of the Artificial Neural Network (ANN) Approach for Prediction of the Kinetic Parameters of Lignocellulosic Fibers. *Textiles*. 2021; 1(2):258-267.
https://doi.org/10.3390/textiles1020013

**Chicago/Turabian Style**

Ornaghi, Heitor Luiz, Jr., Roberta Motta Neves, and Francisco M. Monticeli.
2021. "Application of the Artificial Neural Network (ANN) Approach for Prediction of the Kinetic Parameters of Lignocellulosic Fibers" *Textiles* 1, no. 2: 258-267.
https://doi.org/10.3390/textiles1020013