**Coupling kinetic modeling with artificial neural networks to predict the kinetic parameters of pine needle pyrolysis**,"

*BioResources*19(4), 7513–7529.

#### Abstract

The pyrolysis behavior of biomass is critical for industrial process design, yet the complexity of pyrolysis models makes this task challenging. This paper introduces an innovative hybrid model to quantify the pyrolysis potential of pine needles, predicting the entire process of their pyrolysis behavior. Through experimental analyses and kinetic parameter calculations of pine needle pyrolysis, the study employs a kinetic model with a chemical reaction mechanism. Additionally, it introduces an improved dung beetle optimization algorithm to accurately capture the primary trends in pine needle pyrolysis. The developed artificial neural network model incorporates meta-heuristic algorithms to address process error factors. Validation is based on experimental data from TG at three different heating rates. The results demonstrate that the hybrid model exhibits strong predictive performance compared to the standalone model, with coefficients of determination (R²) of 0.9999 and 0.999 for predicting the conversion degree and conversion rate of untrained data, respectively. Additionally, the standard errors of prediction (SEP) are 0.249% and 0.449% for predicting the conversion degree and conversion rate of untrained data, respectively.

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**Coupling Kinetic Modeling with Artificial Neural Networks to Predict the Kinetic Parameters of Pine Needle Pyrolysis**

Langui Xu,^{a} Lin Zhang,^{a} Xiangjun He,^{a} Wenbin He,^{b} Ziyong Wang,^{c} Weihua Niu,^{d }Dong Wei,^{d} Yi Ran,^{e} Wendan Wu,^{f} Mingjun Cheng,^{f} Jundou Liu,^{g} and Ruyi Huang ^{a,e,}*

The pyrolysis behavior of biomass is critical for industrial process design, yet the complexity of pyrolysis models makes this task challenging. This paper introduces an innovative hybrid model to quantify the pyrolysis potential of pine needles, predicting the entire process of their pyrolysis behavior. Through experimental analyses and kinetic parameter calculations of pine needle pyrolysis, the study employs a kinetic model with a chemical reaction mechanism. Additionally, it introduces an improved dung beetle optimization algorithm to accurately capture the primary trends in pine needle pyrolysis. The developed artificial neural network model incorporates meta-heuristic algorithms to address process error factors. Validation is based on experimental data from TG at three different heating rates. The results demonstrate that the hybrid model exhibits strong predictive performance compared to the standalone model, with coefficients of determination (R²) of 0.9999 and 0.999 for predicting the conversion degree and conversion rate of untrained data, respectively. Additionally, the standard errors of prediction (SEP) are 0.249% and 0.449% for predicting the conversion degree and conversion rate of untrained data, respectively.

*DOI: 10.15376/biores.19.4.7513-7529*

*Keywords: Pine needle pyrolysis; Kinetic model; Artificial neural networks; Prediction*

*Contact information: a: School of Mechanical Engineering, North China University of Water Resources and Electric Power, Zhengzhou 450011, China; b: School of Mechanical Engineering, Zhengzhou University of Light Industry, Zhengzhou, China; c: Henan ALST New Energy Technology Co. LTD, Zhengzhou 450001, China; d: Zhengzhou Yuzhong Energy Co., LTD, Zhengzhou, China; e: Biogas Institute of Ministry of Agriculture and Rural Affairs, Key Laboratory of Development and Application of Rural Renewable Energy, Ministry of Agriculture and Rural Affairs, Chengdu 610041, China; f: Sichuan Pratacultural Technology Research and Extension Center Chengdu 610041, China; g: Sichuan Agricultural Planning and Construction Service Center, Chengdu 610041, China;*

**Corresponding author: huangruyi1983@qq.com*

**INTRODUCTION**

Biomass is globally acknowledged as a “zero carbon” renewable energy source (Huang *et al*. 2021), and its pyrolysis products hold vast potential for green economy applications, including biofuels and chemicals. Pyrolysis plays a crucial role in the formation and evolution of biomass fuels during the combustion process, exerting a direct impact on subsequent processes. Therefore, studying the pyrolytic properties of biomass is crucial for enhancing energy use efficiency (Gbolahan *et al*. 2022; Ke *et al*. 2022; Zhong *et al*. 2023). Due to the increasing demand for biomass fuels in science and industry, the study of the laws governing the pyrolysis and combustion behaviour of biomass is key to the effective use of biomass fuels (Ragauskas *et al*. 2006; Zhu *et al*. 2021; Vo *et al*. 2022). The main components of biomass are hemicellulose, cellulose, and lignin; based on such a composition, chemical kinetics provides a theoretical basis for the quantitative description of pyrolysis reaction processes (Kersten *et al*. 2005; Ka *et al*. 2012; Ding *et al*. 2020; Ding *et al*. 2023). Biomass pyrolysis kinetics are used to characterize the effects of parameters such as reaction temperature and reaction time on the conversion of reaction products during thermal decomposition reactions of biomass (Xu *et al*. 2020). Many scholars have conducted extensive research on the kinetic parameters of biomass pyrolysis processes (White *et al*. 2011), providing important data for the design of pyrolysis reactors and subsequent combustion equipment. While the prediction results of the kinetic model agree to some extent with the experimental data, there are still significant discrepancies between them (Ding *et al*. 2019; Liborio *et al*. 2024). Machine learning models show exceptional accuracy in predicting highly non-linear processes and can automatically learn from data without the need for real operating and chemical conditions, greatly reducing the need for human intervention (Breiman 1996; Sunphorka *et al*. 2017; Naqvi *et al.* 2018; Hu *et al*. 2022). These models have been used extensively to simulate thermal processes involving biomass pyrolysis, gasification, and combustion (Dubdub and Al-Yaari 2020; Bi *et al*. 2021; Yang *et al*. 2022). However, machine learning models have certain drawbacks: Machine learning models typically depend on significant amounts of high-quality data. Insufficient data or poor data quality can negatively affect model performance. Many machine learning algorithms are described as black-box models, meaning that their inner workings are complicated and difficult to elucidate, making it challenging to understand and characterize the model’s predictions (Dubdub and Al-Yaari 2020; Bi *et al*. 2021). In addition, machine learning models can accurately predict outcomes within the training domain, but they often perform poorly in domains outside the training data (Xing *et al*. 2019; Zhang* et al*. 2022). For example, forty-nine tobacco samples were used to study pyrolysis kinetics through machine learning approaches (Wei *et al.* 2023). A comprehensive artificial intelligence model without considering the chemical reaction mechanism窗体顶端窗体底端 was presented to predictive the thermal decomposition of rice husk (Alaba *et al. *2019). A large amount of laboratory data poses significant challenges to predictive work. Moreover, non-mechanistic models lack interpretability and are highly dependent on data.

To enhance predictive capability, an innovative framework has been developed to improve the generalization of predictive models. In the framework, kinetic models based on chemical reaction mechanisms were integrated with data-driven machine learning models. Kinetic models based on chemical reaction mechanisms were used to predict optimize initial values of the kinetic parameters (Kaczor *et al*. 2020; Dubdub and AlYaari 2021; Marchese *et al*. 2024). The BP-ANN model was used to predict the error distribution of the kinetic parameters. A combination of kinetic and artificial neural network models was used to provide a comprehensive prediction of pyrolysis in the training and non-training zones.

Pine needles are abundant in resins and oils, known for their high calorific value, flammability, low ash content, and minimal emissions of nitrogen and sulfur pollutants, making them an effective biomass fuel source (Martín-Lara *et al*. 2016). In this study, pine needles were chosen as the research subject to explore a method that combines chemical kinetics-based models with data-driven models for predicting the pyrolysis process. The objectives of this study were to (1) Conduct pyrolysis experiments to investigate the relationship between pine needle conversion degree and temperature at various heating rates (10, 20, and 40 K/min). (2) Optimize the kinetic parameters of three components using a kinetic model integrated with the mantis algorithm, and analyze the errors. (3) Utilize a BP-ANN model in conjunction with a genetic algorithm to predict errors in kinetic parameters and compare them with parameters obtained from a standalone kinetic model.

**EXPERIMENTAL**

**Thermal Analysis Experiments**

Pine needles were selected as samples for thermogravimetric (TG) experiments. The samples were initially ground in a grinder, and the resulting particles were then sieved through an 80-mesh sieve to achieve uniform particle size. The samples were baked at 423 K to ensure the evaporation of free and bound water (Zha *et al*. 2022). The pyrolysis process was conducted using a TA instruments (SDT Q600 Thermal Analyzer). Samples weighing 9.0 ± 0.5 mg were placed in an aluminum crucible and heated from 298 to 1173 K at heating rates of 10, 20, or 40 K/min. Nitrogen was circulated at a rate of 100 mL/min to maintain an ambient gas environment during pyrolysis.

**Parallel Reaction Kinetic Modelling Predictions**

The concept of kinetic parallel reaction prediction aims to optimize kinetic parameters using a kinetic model combined with an improved dung beetle optimization algorithm with TG experimental data. The method aims to predict the pyrolysis process of pine needles by utilizing optimized parameters and comparing experimental results with predicted outcomes to derive prediction deviations.

*Kinetic modelling of parallel reactions*

The decomposition of pine needles is considered as the sum of parallel reactions of three components: hemicellulose, cellulose and lignin (Machmudah *et al*. 2020). The parallel kinetics scheme for the three components is given as Eq. 1,

^{ }(1)

where *v*_{i} represents the volatile yield of each component reaction. According to the Arrhenius equation, it is assumed that the reaction mechanisms of each component are all of one order. The reaction rates of these three components can be expressed as Eq. 2,

* * (2)

where denotes the degree of response of the i-th component. The conversion degree (a) can be defined as follows,

(3)

where and represent the initial and final sample masses, respectively.

The total conversion degree is defined as the sum of individual component conversions and was calculated as follows,

(4)

where represents the initial mass fraction of component i, and , the overall kinetic equation for the three-component can be expressed as Eq. 5,

(5)

In Eq. 5, eight unknown parameters must be determined to fit the experimental data. The objective of the optimization method is to minimize the difference between the experimental and simulated values. This is achieved by minimizing the sum of the squared differences between the experimental and simulated mass loss values at all heating rates, as shown in Eq. 6,

(6)

here the superscripts “exp” and “simu” represent the experimental and simulated values, respectively. The index “j” represents the number of heating rates, and “k” represents the number of data points in the experiment. In optimization computations, the parameters R² and SEP were used to assess the discrepancy between experimental and simulated values.

**Improved Dung Beetle Optimization Algorithm**

The Dung Beetle Optimization Algorithm (DBO) is a mathematical model inspired by the behavior of dung beetles, including rolling balls, dancing, foraging, stealing, and breeding. The algorithm performs an iterative update through the following steps: initializing the dung beetle population, evaluating the fitness of individual dung beetles, updating the position and orientation of the dung beetles, and finally outputting the optimal solution (Xue and Shen 2022; Zhu *et al*. 2024). However, the dung beetle optimization algorithm has limitations in global search and tends to converge slowly when dealing with complex optimization problems. Therefore, this study proposes an improved dung beetle optimization algorithm (Shen *et al*. 2023). The improved dung beetle optimization algorithm enhanced the convergence speed and accuracy of the search process by introducing an initialized logistic chaos mapping population and improving the position update mechanism of individuals in the population using the Sinusoidal Algorithm (MSA). In addition, an adaptive Gauss-Cauchy perturbation modification strategy was used to enhance the adaptability and robustness of the model for complex problems. Compared to the traditional dung beetle algorithm, the MSADBO algorithm demonstrates a significant improvement in search efficiency and solution quality (Guo *et al*. 2023).

**Artificial Neural Network (ANN) Model Predictions**

The deviations predicted by the kinetic model based on chemical reactions were used as training inputs for the neural network. A genetic algorithm was then introduced to construct a data-driven back-propagation neural network model to predict the errors calculated by the kinetic model.

*Back propagating artificial neutral net (BP-ANN) model*

BP-ANN, a multilayer neural network using an error backpropagation algorithm, is renowned for its powerful learning and nonlinear mapping capabilities, making it one of The BP-ANN consists of an input layer, hidden layers, and an output layer, where information is transferred between neurons across different layers. The number of neurons in the input and output layers is determined by the input parameters and output targets, respectively, while the number of neurons in the hidden layer can be adjusted as needed (Cheng *et al*. 2022).

**GA-BP-ANN Collaboration Model**

Genetic algorithms (GA) are widely used in artificial neural networks due to their robustness, stochastic nature, global perspective, and inherent parallel processing capabilities (Quan *et al*. 2016). The main objective of integrating genetic algorithms with artificial neural networks is to use genetic algorithms to optimize the weighting parameters of artificial neural networks, replacing traditional, inefficient, and less intelligent learning algorithms with more effective advanced methods based on genetic algorithms (Conn *et al*. 1991). The backpropagation mechanism in BP-ANN searches for the extrema of a nonlinear function using the gradient method, which can lead to the issue of getting trapped in local minima. In contrast, GA possesses a powerful macro search capability and demonstrates excellent global optimization performance. They continuously enhance the quality of candidate solutions by simulating natural selection and genetic variation processes, thereby approaching closer to the global optimal solution. Therefore, this study combined GA with BP-ANN to leverage their complementary strengths, effectively overcoming the local extremum problem inherent in the backpropagation algorithm. This integration improved the overall performance and accuracy of the neural network (Zhu *et al*. 2020).

**Coupled Kinetic Model and GA-BP-ANN Model Predictions**

The kinetic model, enhanced by the dung beetle optimization algorithm, predicted the kinetic parameters of each component. These optimal parameters were then utilized to predict the pyrolysis of pine needles. The model predictions were compared with experimental (TG) data to calculate differences. These differences served as input data for training the GA-BP-ANN model to predict the error values generated by the kinetic model. The prediction results from the kinetic model were combined with the error predictions from the GA-BP-ANN model to generate the overall prediction data. Figure 1 illustrates the framework of this integrated approach.

**Fig. 1.** Structure of coupled schematic diagram of the GA-BP-ANN

**RESULTS AND DISCUSSION**

**Thermogravimetric Analysis**

Figure 2 displays the conversion degree () and conversion rate () curves for three heating rates. The pyrolysis process of pine needles occurred between 420 K and 800 K, with a peak occurring between 600 K and 650 K. Additionally, distinct shoulder regions appeared on either side of the peak. As the heating rate increased, both the shoulder and the peak shifted to higher temperatures, which is consistent with Chang *et al*. (2008). The increasing prominence of the shoulder region indicates an increase in the complexity of the reaction, implying the presence of multiple overlapping reactions. This complexity makes it challenging to construct an accurate kinetic model to predict pyrolysis behavior.

**Kinetic Modelling Predictions**

In this study, a kinetic model and the MSADBO algorithm were introduced to predict the kinetic parameters of hemicellulose, cellulose and lignin from TG data. The optimized initial values of the kinetic parameters (*A* and *E*_{a}) for hemicellulose, cellulose,

and lignin were calculated using the iso-conversion method of the Kissinger-Kai method (Xu* et al*. 2023), as shown in Table 1.

**Table 1. **Optimal Parameters by MSADBO on Two Heating Rates

The parameters of the pine needle pyrolysis model to be optimized consisted of three aspects (9 parameters in total): the initial mass fraction (*r*_{i}) and the chemical kinetic parameters (*A*_{i}, *E*_{i}) for hemicellulose, cellulose, and lignin. Since the sum of the mass fractions of the three main components is 1, only eight parameters need to be optimized. Table 1 shows the initial values and search ranges for these optimization parameters. Note that the optimization process did not include TG data at a heating rate of 40 K/min. The optimal kinetic parameters derived from the optimization were then used to predict the biomass conversion degree () and conversion rate (), in the trained regions (10 and 20 K/min) and the untrained region (40 K/min), as shown in Fig. 3.

In Fig. 3 (a-c), the model’s trend in predicting the conversion degree at the three heating rates was generally accurate, but there were some notable differences, mainly from 400 to 600 K, and 650 to 900 K. In Fig. 3 (d-f), the model predictions for the conversion rate showed significant errors in the shoulder regions on both sides of the peak, corresponding to the error regions in the conversion degree. These results indicate that the prediction model needed improvement and should be the focus of future research.

Table 2 shows that the R² values for the kinetic modeling of conversion degree were all above 0.98, while the predicted R² values for conversion rate were all below 0.75. Additionally, the standard error of prediction (SEP) for conversion degree and conversion rate in untrained zones were 3.570% and 9.409%, respectively. Although the model performed well in predicting conversion, it still needs to be improved in predicting the conversion rate. This suggests that further optimization and refinement are needed for the prediction model to improve its overall predictive performance.

**Table 2. **R^{2} and SEP from the Kinetic Model

**GA-BP-ANN Model Predictions**

The GA-BP-ANN model was trained using experimental data collected at heating rates of 10 and 20 K/min. The trained model was used to predict the conversion degree () and the conversion rate () at the trained heating rates (10 and 20 K/min), as well as at an untrained heating rate (40 K/min). Figure 4 compares the experimental values with the predicted values at three heating rates.

In Fig. 4 (a-f), the predictions for the conversion degree () and conversion rate () in the training temperature ranges (10 and 20 K/min) were in general agreement with the experimental data. However, around the peak temperature (about 630 K) for all three heating rates, there was a noticeable underestimation and leftward shift between the predicted and experimental values of , particularly evident in the untrained range. This observation is supported by the R^{2} and SEP values in Table 3: within the trained range, the R^{2} values for predicted conversion degree () were all above 0.995 and for they were all above 0.97. Conversely, in the untrained range (40 K/min), the R^{2} value dropped to 0.994, and for it dropped to approximately 0.95.

Compared to the traditional dynamics prediction model, the GA-BP-ANN model showed significant advantages with significantly lower SEP values and higher prediction accuracy. Specifically, the SEP value of the conversion degree in the training region was only 0.554% and 0.508%, and the SEP value of the conversion rate was 2.323% and 2.171%. This result indicates that the GA-BP-ANN model was able to fit the training data well and provide relatively accurate predictions. However, when the model was applied to untrained regions, there was a significant drop in prediction performance. In these untrained regions, the SEP value for the degree of conversion increased to 0.774%, while the SEP value for the conversion rate increased to 4.615%. This change indicates that although the GA-BP-ANN model performed well in the trained regions, its predictive ability was relatively weak in the untrained regions. Overall, as a data-driven approach, the GA-BP-ANN model demonstrated excellent performance within the training domain but exhibited significant deterioration in performance outside the trained conditions, highlighting the model’s limitations in extrapolating to untrained scenarios.

**Table 3. **R^{2} and SEP from the GA-BP-ANN Model

**Kinetic-ANN Coupled Model Predictions**

A kinetic model was used to predict the main trends in pyrolysis, and a GA-BP-ANN model was used to predict process deviations. Together, these two parts made the complete prediction. Figure 5 parts (a-f) depict the complete predictions of conversion degree () and conversion rate () by the coupled model for heating rates of 10, 20 (trained region) and 40 K/min (untrained region). These figures show that the predictions of the coupled model closely matched the experimental data. The coupled kinetic-ANN model exhibited significant improvement over separate models, particularly in regions not explicitly trained. This indicates that coupled models were more effective in capturing and predicting trends in experimental data, especially when dealing with complex datasets.

Table 4 presents the R^{2} and SEP for the conversion degree () and conversion rate (*da/dT*). The R^{2 }values for the conversion degree () were all above 0.9999, while those for *da/dT* were above 0.999. The SEP for the conversion degree () was below 0.25%, and for* da/dT*, it was below 0.45%, particularly in the untrained range (40 K/min), where the performance significantly exceeded that of a single model. This indicates that the coupled model performed well across the temperature range, offering substantial predictive advantages. However, at 40 K/min, there was a slight increase in the SEP, but it remained within acceptable limits. This could be attributed to unknown factors affecting the predictions of the coupled model in this range or insufficient training data. Nonetheless, the coupled model demonstrated high accuracy and robustness, significantly outperforming a single model in prediction.

**Table 4. **R^{2} and SEP from the Coupled Kinetic-ANN Model

**Accuracy of Kinetic, GA-BP-ANN and Coupled Kinetic-ANN Models**

This section compares the predictive effectiveness of the kinetic model, the GA-BP-ANN model, and the coupled model (Fig. 6). Figure 6 (a-c) compares the prediction results of the conversion degree for three different heating rates among the three models with the experimental results. Figure 6 (d-f) compares the prediction results of the conversion rate for three different heating rates among the three models with the experimental results. The prediction curves of the coupled model were the most consistent with the experimental curves, followed by GA-BP-ANN, with the kinetic model performing the worst. Figure 7(a) compares the predictive effectiveness of the three models for conversion degree based on R² values. Although the kinetic model’s predictions were poor, its results were still higher than 0.98. The other models performed well in predicting conversion degree, with R² values above 0.99. In particular, the coupled kinetic-ANN model had an R² value of more than 0.9999, which was better than both the kinetic model and the GA-BP-ANN model. However, Fig. 7(b) shows that the kinetic model performed extremely poorly in predicting conversion rate () at the untrained heating rate of 40 K/min (R^{2}: 0.74119), whereas the coupled model maintained a high level of accuracy with an R^{2} value of 0.99944. However, whether in the trained or untrained regions, it was found that the R² value of the conversion degree was consistently higher than that of the conversion rate. This difference may be due to the fact that the conversion rate is derived from the derivative of the conversion degree, making it more susceptible to noise.

Figure 7 (a, c) compares the predictive effectiveness of three models for conversion degree based on R² and SEP. Although the kinetic model’s predictions were poor, the R² results were still higher than 0.98. The other models performed excellently in predicting the conversion degree, with R² values above 0.99. In particular, the coupled kinetic-ANN model achieved an R² value of more than 0.9999, outperforming both the kinetic model and the GA-BP-ANN model. This is consistent with the SEP trend, which was below 0.25% for the coupled model, compensating for the lack of predictive power of a single model in untrained regions.