Application of the artificial neural network (ANN) approach for prediction of the kinetic parameters of lignocellulosic fibers

Lignocellulosic fibers are widely applied as composite reinforcement due to their properties. The thermal degradation behavior determines the maximum temperature in which the fiber can be applied without significant mass loss. It is possible to determine these temperatures using Thermogravimetric Analysis (TG). In particular, when curves are obtained at different heating rates, kinetic parameters can be determined and more detailed characteristics of the material are obtained. However, every curve obtained at a distinct heating rate demands material, cost, and time. Methods to predict thermogravimetric curves can be very useful in the materials science field and in this sense mathematical approaches are powerful tools if well employed. For this reason, in the present study, curaua TG curves were obtained at three different heating rates (5, 10, 20, and 40 °C.min-1) and Vyazovkin kinetic parameters were obtained. After, the experimental curves were fitted using an artificial neural network (ANN) approach followed by a Surface Response Methodology (SRM). Curves at any heating rate between the minimum and maximum experimental heating rates were obtained with high reliability. Finally, Vyazovkin kinetic parameters were tested again with the new curves showing similar kinetic parameters from 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.


Introduction
Lignocellulosic fibers are versatile materials used in different applications. Their use englobes the entire fiber for reinforcement in composite materials [1,2], or the use of their derivatives (cellulose, hemicellulose, or lignin) in different uses as shape memory of lignin-rubber composites [3], to obtain nanocellulose [4], to reinforce expanded composites [5] or cellulose biomedical applications [6], for example. This potential of application can be attributed to the wide variety of chemical components (cellulose, hemicellulose, lignin, waxes, low molecular weight components, oil, etc.) presented in the lignocellulosic fibers [7,8]. Also, the same fiber can have different properties depending on the plant age, climate, soil among others [9].
Yao et al. [10] studied the thermal degradation behavior of ten different lignocellulosic fibers, focusing on the Arrhenius kinetic parameters. The activation energy in the function of the conversion degree presented similar values, independently of the chemical content of the fiber. A linear dependency in the conversion range α = 0.2-0.8 was observed for all fibers with an apparent activation energy of 160-170 kJ.mol -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 plays 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 mechanisms involved in the thermal degradation of lignocellulosic fibers based on the chemical composition. The main results indicate 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 the optimal training data for ANN application using thermogravimetric analysis. The results indicated 50-60 as the optimal number of training datasets for all fibers. Also, a reliable prediction of TG curves was obtained at different heating rates did not obtained experimentally.
Most of the fibers found in the literature follow a similar curve format, independently of the amount of the chemical components, indicating that the degradation process may follow certain degradation rules. For example, a mass loss of about 5-10% is obtained at 100 °C due to moisture evaporation and from 300 °C from the degradation of cellulose. In some cases, a shoulder is observed at DTG (derivative thermogravimetric analysis) due to the higher amount of hemicellulose in a small range before cellulose degradation [13,14]. Hence, the prediction of the thermogravimetric curves of a particular lignocellulosic fiber can be extended to most of the fibers due to these similarities.
The main objective of this study is to perform the thermal degradation kinetic behavior of curaua fiber using the Vyazovkin kinetic method and ANN approach. The experimental curves were kinetically tested, and curves do not tested experimentally were predicted, and new kinetic tests were done. The results presented reliable and robust data without the necessity of further experimental curves.

Materials and Methods
Curaua fiber received from CEAPAC (support center for community action projects) was used in this study. More details about the fiber characteristics can be found on [15,16].
Thermogravimetric analysis was carried out using a TA instrument model TGA-50 Shimadzu under nitrogen atmosphere from 25 to 900 °C. It was used ~10 mg of each sample at three distinct heating rates (5, 10, 20, and 40 °C.min -1 ). The curves were used to calculate the kinetic parameters according to the Vyazovkin method. The theoretical and ANN predicted curves were used to calculate the kinetic parameters. It was used in the previous study of Monticeli et al. [12] as a base for the obtaining of the new ANN curves at distinct heating rates. The predicted curves were used to calculate again the kinetic parameters.

Kinetic approach
The thermal degradation kinetic of lignocellulosic fibers follows the kinetics of the reaction of solids: where ⁄ is the degradation rate, ( ) is the rate constant, and ( ) is a function of the conversion. The degradation kinetic follows Arrhenius (Equation 2) and the heating rate changes linearly with temperature (Equation 3): where is the pre-exponential factor, is the activation energy, is the gas constant, is the temperature, is the heating rate, and ⁄ is the temperature in function of time.
The reaction model follows equation (4): where , , and p are constants.
In combining Equations (1) (2) (3) and (4) we obtain equation (5): Vyazovkin equation is proposed according to Equations (6) (corrected heating rate) and (7): , , where is the number of files for the corresponding heating rate, is the number of rows in the i-file, is a value of the temperature in the i-file in the j-row, and is the value of the time in the i-file in the j-row measurements. and are unknown parameters of the equation. ( , ) if found by numerical integration.
The kinetic calculation was performed with the help of the Software developed by Drozin et al. [17] with the experimental and predicted curves.

Artificial neural network
An ANN is conventionally constructed with three layers, i.e. an input, an output, and a hidden layer. Each layer has different numbers of neuronal elements. In the present case, we use as input vectors a set of iTG curves at different heating rates. In this sense, the network will modify the weight of the interconnections between neurons in order to reproduce the given parameters. Figure 1 shows the scheme of the calculation process. The main issues necessary to be defined before using the networks are the quality and number of the initial TG curves, the training algorithm, and the number of neurons in the hidden layer. The number of initial TG curves used for the training should not be excessively large in order to avoid the over-training of the network, and it has to be distributed correctly, in the sense that normally it is a good idea to avoid sets of input vectors with the same output vectors. These kinds of orthogonal combinations produce better results than using random sets of parameters [18].
The following conditions (Table 1) were used to training the ANN network: Table 1 -Parameters used to perform the ANN fit.
With the training of the network, we can feed the network with different curves and predicted new curves. The main drawback is that the curves outside the lower and higher heating rate cannot be created due to the accumulation of errors [18,19]

Surface Response Methodology (SRM)
The SRM is a statistical approach for modeling and analyzing a process in which the response of interest is affected by various variables [12,20,21]. Equation 8 describes the degradation curve interaction among the combination of temperature and heating rate. In using this method, the statistical relevance is kept and the number of experiments can be reduced.
where Y represents the predicted response (i.e., degradation curve -(%)), xi and xj are variations parameter, in which i represents the -axis (temperature T (ºC)) and j is the -axis (heating rate HR (ºC.min -1 )). β0 is the constant coefficient; βi is the linear coefficient; and βij is the interaction coefficient. Figure 2 a-b) shows the experimental thermogravimetric curves and the respective derivatives of curaua fiber at different heating rates. The curves maintain the same format independently of the heating rate used only shifting the curve to higher temperature due to the thermal lag. Three visible main loss stages are visualized: i) at around 100 °C a mass loss of 5% can be mainly attributed to the evaporation of intrinsic moisture, ii) at around 300 °C a more abrupt mass loss attributed mainly to hemicellulose that extends up to 350 °C and, iii) from 350 °C to 400 °C the degradation of cellulose (the main component) in a narrower range, representing the main degradation stage. Lignin degrades overall extension range [7,22,23].  All the curves above were used to calculate the kinetic parameters using the Vyazovkin kinetic model in the temperature range from 100 to 435 °C (main degradation stage). The corrected heating rates (provided by the Software) using the Vyazovkin method were 10.09, 20.1, and 39.79 °C.min -1 . Figure 3a   Based on experimental degradation curves, the ANN fit was constructed with parameters variation, in which temperature and heating rate as the input parameters and the loss of mass (kinetic behavior) as output. The experimental dots were used to training the ANN. The number of training data influences the predictive curve, which was thoroughly investigated in previous work to optimize the ANN method [12]. Figure  4a presents the trained curves with the experimental ones, and Figure 4b exhibits the enlargement of initial degradation. An excellent fit was obtained for all heating rates tested. The coefficient of determination was R 2 > 0.99 for all curves.  [12], and b) enlargement of initial degradation Only 1/10 of the experimental dataset has been used for training the ANN, resulting in a perfect fitting, resulting in an appropriate predictive result. Regarding the ANN application, new degradation behavior could be predicted with no need for long experiments [24].

Results and discussion
From the ANN predicted curves, intermediate heating rates were predicted using the surface response methodology (SRM), resulting in a 3D Surface response to predict mass loss as a function of temperature and heating rate variation. Dot curves give the experimental data. The coefficient of determination R 2 = 0.96, indicating high reliability of predicted results. For the lowest heating rate (i.e., 5 ºC/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 ºC. With the increased heating rate, more abrupt degradation occurs, increasing the onset and endset temperature.
A well-trained ANN could develop a degradation mechanistic understanding of the natural fiber considered, considering that the ANN method is a purely phenomenological approach. For a better approximation of the theoretical and experimental results, the equation of the three-dimensional curve in Figure 5 was divided into three, presented in Eq. (9) -for the temperature range of 25 -250 ºC, Eq. (10) -for the temperature range of 250 -410 ºC, and Eq. (11) -for the temperature range of 410 -810 ºC.
Following Figure 5 and Eqs. (9) -(10), Figure 5 exhibits the predicted values of curaua fiber degradation using the heating rates of 7, 15, 30, and 50 ºC.min -1 . Through the ANN and RSM combination, it is possible to predict other degradation curves with different analysis parameters not accessed experimentally, which decreases costs and time related to tests repetitions with high reliability The values obtained, mainly the activation energy is close to the experimental curves. Also, the extrapolated curve (at 50 °C.min -1 ) used in condition b) seems to be satisfactory in the present study. 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.

Conclusions
The present study proposed obtaining new thermogravimetric curves for curaua fiber at any heating rate situated between the minimum and maximum heating rates experimentally tested. For this, an Artificial Neural Network (ANN) followed by the Surface Response Methodology (SRM) was used to obtain new TG curves. Vyazovkin kinetic method was used in the experimental curves and in the newly obtained curves. The kinetic results presented similar values for the experimental and predicted curves. This approach can be extended to any material to obtain properties, parameters or to optimize processes.