Statement of Novelty

This study adopted a neural fuzzy model coupled with a genetic algorithm (GA) to conduct the waste plastic (WP) thermal pyrolysis analysis. The neural fuzzy model established mathematical expressions among the WP conversion and the pyrolysis rate, and the operating conditions (temperature and heating rate). Subsequently, GA was used to optimize the operating conditions for maximum WP conversions and pyrolysis rates in different temperature ranges.

Introduction

Waste plastic (WP) has caused large-scale environmental pollution and a health hazard to many organisms. Historically, a large amount of WP was disposed of via landfill or incineration [1]. Several methods have been proposed for treating WP in a more responsible way, namely, mechanical recycling, chemical recycling and energy recovery methods [2]. Among these methods, chemical recycling is a favorable method which can utilize the WP to produce fuels [3]. Moreover, WP thermal pyrolysis, which is performed in the absence of oxygen [4], is a most promising chemical recycling method. It can strongly reduce WP pollution while producing useful by-products such as biochar, bio-oil and syngas [5,6,7,8]. According to the literature [4], the temperature and heating rate are the determining factors in the WP pyrolysis process. Besides these, considering the economical aspect, the temperature, the conversion and the pyrolysis rate are also critical parameters for practical applications of WP pyrolysis [9,10,11].

Much research in thermogravimetric analysis (TG) has been conducted to try to obtain a better understanding about the WP pyrolysis process. Paraschiv et al. [12] adopted TG experimental results to determine the optimal operating parameters for hospital-based WP pyrolysis on different scales for a fixed bed reactor. Chen et al. [13] utilized TG analysis to investigate the WP co-pyrolysis process. Additionally, Navarro et al. [14] used TG analysis coupled with a distributed activation energy model to conduct a WP co-pyrolysis kinetic study. Chen et al. [15] investigating a waste phenolic fibre-reinforced plastic thermal pyrolysis process based on TG experiments with different heating rates. Singh et al. [16] adopted TG analysis to investigate the influence of the heating rate on the WP pyrolysis process. Moreover, Ippolito et al. [17] conducted TG experiments to determine the WP pyrolysis kinetic values. In conclusion, TG analysis is a promising method to investigate the WP pyrolysis process as it can provide important parameters—the WP relative weight over time and the temperature at different heating rates [18, 19]. However, TG experiments so-far could only provide the discrete mass fraction curves at disparate heating rates. This creates difficulties in determining the optimal conditions of the WP pyrolysis process. For the purpose of investigating the optimal conversion, Teng et al. [19] creatively adopted an artificial neural network (ANN) coupled with TG analysis and applied it to the Chlorella vulgaris pyrolysis process. In consequence, the C. vulgaris conversion turned out to be a continuous function of the temperature and the heating rate. Subsequently, a mathematical algorithm was utilized to obtain the optimal operating parameters over different temperature ranges. Therefore, the application of artificial intelligence coupled with TG analysis could, ideally, determine the optimal operating conditions of the WP pyrolysis process.

The neural fuzzy model, from artificial intelligence theory, is a promising method which could establish an arithmetic expression to describe the relationship between multiple independent variables and dependent variables [20]. Sadeghizadeh et al. [21] and Ronda et al. [22] investigated the effects of multiple operating conditions on the Pb (II) adsorption efficiency using a neural fuzzy model. Calero et al. [23] adopted a neural fuzzy model to determine the optimal copper biosorption capacity under the influence of three operational parameters. Iáñez-Rodríguez et al. [24] conducted research on the optimal temperature and residence time during a crop torrefaction process using a neural fuzzy model. Nevertheless, the values of the response variables predicted by the afore-mentioned researchers using neural fuzzy models were discrete. Arithmetic expressions, established by the neural fuzzy model between the multiple operating parameters and the response variables however, are continuous. Therefore, the robustness of predicted optimal operating conditions can be improved. Hence, it is necessary to adopt a mathematical calculation method for determining the optimal operating parameters in accordance with the arithmetic expression established using a neural fuzzy model.

Regarding the global extremum calculation, the genetic algorithm (GA) is a promising method to find the optimal operating parameters based on the existing mathematical models. Javed et al. [25] utilized the GA for optimization of a hybrid energy storage system. Tuchler et al. [26] optimized the radial compressor of an automobile by evaluating the isentropic efficiency with the GA. Ascione et al. [27] conducted an optimization design of an envelope enclosure with the GA with multiple objective functional assessments. Rezaie et al. [28] adopted multiple objective functions to evaluate heat recovery in a steam generator. Subsequently, the GA was used to optimize the thermal design.

As there has been little research into the optimal WP conversion and pyrolysis rates with different temperatures and heating rates, this work aims to fully investigate the WP pyrolysis process, to provide guidance for industrial and commercial applications. This study investigated the optimal operating parameters—the temperature and the heating rate of the WP thermal pyrolysis conversions and the pyrolysis rates over different temperature ranges. Four TG experiments with different heating rates were conducted to obtain the experimental WP mass fraction during the pyrolysis process. Subsequently, the experimental WP conversion (calculated as WP conversion = 1−WP relative weight) and the pyrolysis rate (by derivation) were obtained. As previously discussed, the neural fuzzy model was adopted to establish arithmetic expressions to describe the relationships between the independent and dependent variables. The neural fuzzy model predicted WP mass fraction, conversion, and pyrolysis rate were highly accurate. Finally, the optimal operating conditions were determined using the GA.

Experiments and Methods

TG Experiments

The WP used for pyrolysis experiments, illustrated in Fig. 1a, was provided by Wanbei Plastic Recycling Development Base (Anhui-China). The WP is mainly composed of polyethylene (PE). In order to ensure the uniform composition of the WP, the WP was heated and melted and made into 3 mm pellets. As shown in Fig. 1b, the WP’s main functional groups are –CH2–, –CH, –CH3, and –OH [29]. The TG experiments were conducted at temperatures ranging from 25 °C to 600 °C at five representative heating rates—5, 10, 12, 15 and 20 °C/min [15, 19, 30,31,32]. Consequently, the WP mass fraction m variation with time was obtained for different heating rates. Hence, the conversion α and the pyrolysis rate rp were determined by the following equations.

$$\alpha = 1 - m$$
(1)
$$r_{p} = \left( {m_{i + 1} - m_{i} } \right)/\left( {t_{i + 1} - t_{i} } \right)$$
(2)

where mi and ti represent the ith mass fraction (wt%) and time (min) and mi+1 and ti+1 represent the (i + 1)th mass fraction (wt%) and time (min).

Fig. 1
figure 1

WP used for pyrolysis experiments in this study: a WP pellets; b FTIR spectrum

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Methods

Neural Fuzzy Model

The neural fuzzy model is inspired by the humanoid reasoning and the neural network’ structure. The neural fuzzy model was adopted for predicting the mass fractions and the WP conversion and pyrolysis rates based on the TG experimental data previously described. In the present study, there were two independent variables, i.e., the temperature and the heating rate. The certain dependent variable could be predicted by the following equation [20, 21]:

$$y_{{pre}} = {{\sum\nolimits_{{i = 1}}^{n} {\left( {a_{i} \cdot FR_{i} } \right)} } \mathord{\left/ {\vphantom {{\sum\nolimits_{{i = 1}}^{n} {\left( {a_{i} \cdot FR_{i} } \right)} } {\sum\nolimits_{{i = 1}}^{n} {FR_{i} } }}} \right. \kern-\nulldelimiterspace} {\sum\nolimits_{{i = 1}}^{n} {FR_{i} } }}$$
(3)

where ypre, n, ai and FRi represent the predicted value, the number of rules, the constant of each rule and the fuzzy rule, respectively.

The fuzzy rule can be expressed with the following equation:

$$FR_{i} = \prod\nolimits_{{i = 1}}^{m} {\mu _{i} \left( {x_{i} ,x_{i} \left( \Theta \right)} \right)}$$
(4)

where m, xi, xi(Θ) and μi(xi(Θ)) represent the number of independent values, the evaluation value of the level of the independent variable, the value of independent variable and the membership function, respectively.

According to previous studies [20, 23], the Gaussian membership function μi(xi(Θ)) can predict the dependent variables most accurately. Therefore, in the present study, the Gaussian membership function μi(x) was adopted. It can be expressed using the following equation:

$$\mu_{i} \left( {x_{i} ,x_{i} \left( \Theta \right)} \right) = \exp \left( { - 0.5 \cdot \left( {\left( {x_{i} - x_{i} \left( \Theta \right)} \right)/L} \right)^{2} } \right)$$
(5)

where L represents the Gaussian distribution width.

GA

When the experimental data was processed with the neural fuzzy model, the constant of each rule ai and the Gaussian distribution width L could be obtained. Accordingly, the GA was adopted to determine the optimal operating conditions of the WP pyrolysis process. The GA is literally developed according to evolution theory and is designed to obtain an optimal condition containing multiple chosen parameters [15, 33,34,35,36,37].

The WP conversion, for example, was determined by two parameters, i.e., the temperature and the heating rate. Hence, a single value for the WP conversion was considered to be an individual. It contained two “genes”, the temperature and the heating rate. A population was studied, composed of N individuals. In the first generation, these N individuals were treated as “parents”. N children were reproduced after N sets of parents underwent mutation and crossover processes. The next step was to calculate the fitness values of these N children. Children with worse fitness were replaced by children with better fitness to complete the first generation. In the next generation, these N children would be treated as the “parents” and follow the same processes as mentioned before. Therefore, the GA optimization procedure could be described using the following equations:

The mutation is expressed according to the following equation:

$$child_{i}^{j} = \nu_{mut} \cdot \left( {1 - t/iter} \right)^{2} \cdot parent_{i}^{j}$$
(6)

where i, j, νmut, t, and iter represent the number of individuals, the number of genes, the probability of mutation, the number of the generation and the number of total generations, respectively.

The crossover is expressed using the following equation:

$$if r_{i,cro} < \nu_{cro} , child_{i}^{j} = child_{n}^{j}$$
(7)

where ri,cro, νcro, and n represent a random number value between 0 and 1, the probability of a crossover and the random number iteration between 1 and N, respectively.

The fitness of an individual and the highest fitness could be expressed using the following equations:

$$fitness_{i} = {{\sum\nolimits_{{i = 1}}^{n} {\left( {a_{i} \cdot FR_{i} } \right)} } \mathord{\left/ {\vphantom {{\sum\nolimits_{{i = 1}}^{n} {\left( {a_{i} \cdot FR_{i} } \right)} } {\sum\nolimits_{{i = 1}}^{n} {FR_{i} } }}} \right. \kern-\nulldelimiterspace} {\sum\nolimits_{{i = 1}}^{n} {FR_{i} } }}$$
(8)
$$fitness_{best} = \max \left( {fitness_{i} } \right)$$
(9)

where fitnessi and fitnessbest represent the fitness of the i-th individual and the maximum value of fitness, respectively. The best child is the one with the maximum fitness value.

The replacement can be expressed with the following equation:

$$If~fitness_{i} < 0.2 \cdot \left( {\max \left( {fitness_{i} } \right) - \min \left( {fitness_{i} } \right)} \right) + \min \left( {fitness_{i} } \right),~$$
$$child_{i}^{j} = child_{i,best}^{j}$$
(10)

where \(child_{i,best}^{j}\) represents the best child.

In the present study, the number of individuals N and generations iter are 1000 and 1000. The probabilities of mutation νmut and crossover νcro are 0.2 and 0.2. Moreover, the neural fuzzy model used in the present study is from the Matlab software toolbox. The GA was also coded in Matlab.

Results and Discussion

TG Analysis

Figure 2 illustrates the experimental WP mass fractions and pyrolysis rates (which vary with the pyrolysis temperature) for heating rates of 5, 10, 12, 15 and 20 °C/min. The pyrolysis onset temperature To, the end pyrolysis temperature Te and the maximum pyrolysis temperature Tm are also shown. To, Te and Tm were proposed to describe the pyrolysis process more precisely [38,39,40]. The onset pyrolysis temperature To occurs at the intersection of the tangent to the pyrolysis rate rise curve and the temperature-axis; The end pyrolysis temperature Tm occurs at the intersection of the tangent to the falling part of the pyrolysis rate curve and the temperature-axis; The maximum pyrolysis temperature Tm is the temperature coordinate value at the pyrolysis rate curve’s peak. As shown in Fig. 2a, the WP mass fraction curves have the same trend regardless of the different heating rates. The WP mass fraction curve decreases slowly at the initial pyrolysis stage and the WP decomposed at a relatively high speed over a narrow temperature range. Finally, at high temperatures, the WP mass fraction curve flattened out again. Besides that, the WP mass fraction curve shifted laterally to a higher temperature when the heating rate was increased from 5 to 20 °C/min.

Fig. 2
figure 2

Experimental WP mass fractions (a) and pyrolysis rates (b) at different heating rates

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In terms of the pyrolysis rate, the WP had one peak at all heating rates. The single peak only represents the overall conversion rate, which does not indicate the WP is pyrolyzed in a one-step mechanism [41, 42]. The WP is decomposed into short-chain hydrocarbons via random and Beta scission reactions [43, 44]. The peak of WP pyrolysis rate curves shifted laterally to a higher temperature when the heating rate was increased from 5 to 20 °C/min, which had the same trend as the WP mass fraction curves. Higher heating rates resulted in the thermal hysteresis from the TG instrument to WP, thereby extending the time to reach the WP’s initial pyrolysis heat [45]. On the other hand, higher heating rates could accelerate the WP pyrolysis process by providing sufficient heat [45, 46]. Therefore, the maximum pyrolysis rate increased with the increasing heating rate. The WP pyrolysis rate curves were more complex compared to those for the individual plastic types [13, 14], e.g., PE, PS, PET, etc. This is because that the pyrolysis mechanism transformations are caused by the co-pyrolysis effects from the different individual plastics [13, 15, 16].

To, Te, Tm and the maximum pyrolysis rates of the WP at different heating rates are listed in Table 1. The values of To, Te and Tm increased with the heating rate, which is consistent with the literature results [13, 14, 17, 40, 47, 48]. While it was noticeable that the difference between To and Te was quite constant, at the different heating rates, they shifted by up to 50 °C. Moreover, the WP was undergoing pyrolysis at a relatively high-speed considering the maximum pyrolysis rate values. For instance, the maximum WP pyrolysis rate could reach up to 59.82 wt%/min at a heating rate of 20 °C/min. Additionally, the pyrolysis rate also increased with the heating rate.

Table 1 To, Te, Tm and the WP maximum pyrolysis rates for different heating rates
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Neural Fuzzy Model Predicted Results

In Fig. 3, the WP mass fraction and the pyrolysis rate were determined as functions of the temperature and the heating rate using the neural fuzzy model. Experimental data obtained for different heating rates—5, 10, 15 to 20 °C/min was used. In order to reduce the calculation time, the data set used by the neural fuzzy model to predict the WP mass fraction and pyrolysis rate was sampled to be one fifth the size of the experimental data. The experimental data was chosen with equal time intervals. As depicted in Fig. 3a, the WP mass fraction predicted by the neural fuzzy model followed the same trend as the experimental data. The slope of the predicted WP mass fraction surface was small in the temperature range of 300–400 °C. Subsequently, the slope became very steep at the temperature range of 400–500 °C. However, the predicted WP mass fraction surface became flat again after a pyrolysis temperature of 500 °C. Regarding the effect of the heating rate on the WP mass fraction during the pyrolysis process, the surface becomes bumpy when the heating rate is close to 10 °C/min. In addition, the WP mass fraction decreased faster at a higher heating rate, which was consistent with the results obtained experimentally for the WP mass fraction, as depicted in Fig. 2.

Fig. 3
figure 3

The neural fuzzy model predicted WP mass fraction (a) and pyrolysis rate (b)

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As for the predicted pyrolysis rate of the WP, it was noteworthy that the peak value increased with the heating rate as illustrated in Fig. 3b. This was in good agreement with the experimental WP pyrolysis rate as shown in Fig. 2b. At first, the predicted pyrolysis rate increased with temperature, then at higher temperatures it decreased. The temperature of the maximum pyrolysis rate became higher when the heating rate increased.

The Accuracy of the Neural Fuzzy Model

In Figs. 4a–d the WP mass fraction and pyrolysis rate obtained experimentally were compared with the neural fuzzy model predictions at different heating rates of 5, 10, 15 and 20 °C/min, respectively. Additionally, we calculated the R-squared values between the experimental and the predicted WP mass fraction and pyrolysis rates to determine the accuracy of the neural fuzzy model. The R-squared values of the WP mass fraction and the pyrolysis rates at heating rates of 5, 10, 15 and 20 °C/min are depicted in Figs. 4e, f, respectively. In Figs. 4a–d, the predicted WP mass fraction and the pyrolysis rate are in good agreement with the experimental values regardless of the temperature and heating rate. The coincidence degrees between the experimental and the predicted WP mass fraction were very high at all heating rates. As demonstrated in Fig. 4e, the R-squared values of the WP mass fraction were 0.99999 at heating rates of 5, 10, 15 and 20 °C/min. The R-squared values were close to 1 for every heating rate which indicated that the neural fuzzy model predicted values were highly accurate [45].

Fig. 4
figure 4

Comparisons of the experimental WP mass fraction and the pyrolysis rate with the neural fuzzy model predicted values: a At 5 °C/min; b At 10 °C/min; c At 15 °C/min; d At 20 °C/min; e R-squared values of the WP mass fraction; f R-squared values of the WP pyrolysis rate

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As for the WP pyrolysis rate, the neural fuzzy model predicted results also coincided with the experimental results to a great extent. For a heating rate of 5 °C/min, as illustrated in Fig. 4a, the predicted and the experimental WP pyrolysis rates had the same trend. The maximum experimental WP pyrolysis rate was 17.18 wt%/min at 467.5 °C. The maximum predicted WP pyrolysis rate was 17.73 wt%/min at 472.5 °C. The agreement between the experimental and the predicted maximum pyrolysis rates was within 3.2%. For the heating rate of 10 °C/min, as depicted in Fig. 4b, the maximum experimental and the predicted WP pyrolysis rates were 33.80 wt%/min at 482.5 °C, and 32.59 wt%/min at 482.5 °C, respectively. The difference between the experimental and the predicted maximum pyrolysis rates was around 3.6%. As shown in Fig. 4c, the peak values of the experimental and the predicted WP pyrolysis rate curves at 15 °C/min were 47.81 wt%/min at 490.0 °C, and 47.59 wt%/min at 487.5 °C, respectively. The error of the peak values between the experimental and the predicted maximum pyrolysis rates was 0.46%. For a heating rate of 20 °C/min, as illustrated in Fig. 4d, the maximum experimental and the predicted WP pyrolysis rates were 59.51 wt%/min at 489.3 °C, and 60.63 wt%/min at 491.7 °C, respectively. The difference between the experimental and the predicted maximum pyrolysis rates was 1.9% at a rate of 20 °C/min. As described in Fig. 4f, the R-squared values of the WP pyrolysis rate were 0.99674, 0.99697, 0.99923 and 0.99934 at heating rates of 5, 10, 15 and 20 °C/min, respectively. In conclusion, the neural fuzzy model allowed for a high accuracy in predicting the WP mass fractions and pyrolysis rates.

GA Optimization

GA is a promising optimization method to determine the multiple operating parameters needed to obtain the optimal objective results. In this study, GA is used to calculate the optimal WP conversions and pyrolysis rates in different pyrolysis temperature ranges, based on neural fuzzy model predicted data. From the experimental WP mass fractions described in Fig. 2, it could be concluded that the WP pyrolysis process started at about 300 °C and finished at around 550 °C. Simultaneously, the WP pyrolysis process proceeded relatively slowly before 400 °C. Hence, according to [19], 6 temperature ranges were chosen to investigate the optimal WP conversions: 300–400 °C, 400–430 °C, 430–460 °C, 460–490 °C, 490–520 °C, and 520–550 °C, in this sequence. The optimal WP conversions in different temperature ranges calculated using GA are shown in Figs. 5a–f. As depicted in Fig. 5a, generally a larger WP conversion was obtained for a higher pyrolysis temperature and lower heating rate. For instance, the WP conversion increased from 0.66% to 1.37% when the pyrolysis temperature increased from 300 °C to 400 °C at 20 °C/min. Furthermore, the WP conversions were enhanced from 1.37% to 1.64% when the heating rate decreased from 20 to 5 °C/min. Additionally, a hollow appeared at around 15 °C/min on the WP conversion surface, as seen in Fig. 5a. The same situation occurred for the temperature range of 400–430 °C shown in Fig. 5b. Subsequently, the optimal WP conversion determined using the GA was 1.64% at 5.00 °C/min and 400 °C. The optimal WP conversions were 2.35% at 5.00 °C/min and 430.00 °C, 20.31% at 5.00 °C/min and 460.00 °C, 96.24% at 5.00 °C/min and 490.00 °C, 97.68% at 5.00 °C/min and 497.89 °C, and 97.63% at 5.00 °C/min and 550 °C in the temperature ranges of 400–430 °C, 430–460 °C, 460–490 °C, 490–520 °C, and 520–550 °C, respectively. It is noteworthy that the predicted WP conversion slightly lowered from 97.68% to 97.63% when the temperature increased from 497.89 °C to 550 °C, which contradicted the other results of the experiment. However, the difference value was just − 0.05%, which is almost negligible.

Fig. 5
figure 5

Optimal WP conversions in different temperature ranges calculated using GA: a 300–400 °C; b 400–430 °C; c 430–460 °C; d 460–490 °C; e 490–520 °C; f 520–550 °C; g Experimental and predicted optimal conversions; h Relative errors between experimental and predicted optimal conversions

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Figures 5g, h depict the experimental and predicted optimal WP conversions for temperature ranges of 300–400 °C, 400–430 °C, 430–460 °C, 460–490 °C, 490–520 °C and 520–550 °C. These temperature intervals are denoted as 1 to 6, respectively in Figs. 5g, h. As shown in Fig. 5g, the experimental WP conversions were 1.59%, 2.43%, 20.11%, 96.39%, 97.51% and 97.63% at a heating rate of 5.00 °C/min, and at temperatures of 400.00 °C, 430.00 °C, 460.00 °C, 490.00 °C, 497.89 °C and 550.00 °C, respectively. Moreover, as demonstrated in Fig. 5h, the relative errors between the experimental and the predicted optimal WP conversions for different temperature ranges were 3.18%, − 3.25%, 0.96%, − 0.16%, 0.17% and 0.00%. The absolute values of the relative error were less than 3.50%. Moreover, the deviation percentage Dev% between the experimental and predicted WP conversions was 0.13, which satisfied the fitting acceptability Dev% < 4, according to [14, 49]. This also indicated a satisfactory accuracy for the WP conversions predicted by the neural fuzzy model.

Figure 6 describes the optimal WP pyrolysis rates for the different temperature ranges calculated using the GA. Because of the low pyrolysis rate before 400 °C and after 550 °C, 5 temperature ranges were used to investigate the WP optimal pyrolysis rates, i.e., 400–430 °C, 430–460 °C, 460–490 °C, 490–520 °C, and 520–550 °C, in this sequence [19]. The GA determined optimal WP pyrolysis rates in different temperature ranges are depicted in Figs. 6a–e. As shown in Fig. 6a, the WP pyrolysis rate decreased with a heating rate of around 5–10 °C/min, while it increased with a heating rate of around 10–20 °C/min in a temperature range of around 400–405 °C. Moreover, in the temperature range of 405–425 °C, the WP pyrolysis rate decreased with a heating rate from around 5–10 °C/min, increased with a heating rate of around 10–15 °C/min, and decreased again with a heating rate of around 15–20 °C/min. Consequently, the optimal WP pyrolysis rate determined by the GA was 0.39 wt%/min at 20.00 °C/min and 430.00 °C in the temperature range of 400–430 °C. Furthermore, as depicted in 6b–e, the GA optimized WP pyrolysis rates were 9.78 wt%/min at 5.00 °C/min and 460.00 °C, 60.07 wt%/min at 20.00 °C/min and 490.00 °C, 60.66 wt%/min at 20.00 °C/min and 492.09 °C, and 0.84 wt%/min at 20.00 °C/min and 520.00 °C in the temperature ranges of 430–460 °C, 460–490 °C, 490–520 °C, and 520–550 °C, respectively. In conclusion, the optimal heating rate is 20 °C/min in the lower temperature range (400–430 °C) and the higher temperature range (460–550 °C), while the optimal heating rate is 5 °C/min in the medium temperature range (430–460 °C). Higher heating rates could accelerate the WP’s mass loss, thereby increasing the pyrolysis rate [4]. However, higher heating rates can also cause thermal hysteresis, which is not conducive to the thermal decomposition of WP [3]. The thermal hysteresis might have a stronger influence on the WP’s pyrolysis than the acceleration of WP’s mass loss in the medium temperature range, thus the lowest heating rate was most conducive to the reaction rate of WP’s pyrolysis. Moreover, the maximum WP pyrolysis rate was obtained at 492.09 °C and 20.00 °C/min.

Fig. 6
figure 6

Optimal WP pyrolysis rates in different temperature ranges calculated using GA: a 400–430 °C; b 430–460 °C; c 460–490 °C; d 490–520 °C; e 520–550 °C; f Experimental and predicted optimal pyrolysis rates; g Relative errors between experimental and predicted optimal pyrolysis rates

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Figures 6f, g illustrate the experimental and the GA optimized WP pyrolysis rates in the temperature ranges of 400–430 ℃, 430–460 ℃, 460–490 ℃, 490–520 ℃, and 520–550 °C, denoted 1 to 5 respectively in Figs. 6f, g. As demonstrated in Fig. 6f, the experimental WP pyrolysis rates were 0.39 wt%/min, 9.68 wt%/min, 59.25 wt%/min, 59.14 wt%/min, and 0.53 wt%/min in the temperature ranges of 400–430 °C, 430–460 °C, 460–490 °C, 490–520 °C, and 520–550 °C, respectively. Furthermore, as described in Fig. 6g, the relative errors between the experimental and the predicted optimal WP pyrolysis rates in the different temperature ranges were 0.57%, 1.04%, 1.39%, 2.57%, and 57.63%. Except for the temperature range of 520–550 °C, the absolute values of relative error between the experimental and the predicted optimal pyrolysis rates were less than 2.6%. The temperature range of 520–550 °C was approaching the end of the WP pyrolysis [43], in which the highest pyrolysis rate was merely 0.53 wt%/min. Although the relative error was high, the difference between predicted and the experimental optimal pyrolysis rates was only 0.31 wt%/min in the temperature range of 520–550 °C. Besides, the deviation percentage Dev% between the experimental and predicted WP pyrolysis rates was 1.33, which showed the high accuracy of the neural fuzzy model predicted results [14, 49].

Applicability of the Neural Fuzzy Model

For the purpose of certifying the applicability of the neural fuzzy model, one fifth of the experimental data for the WP conversion and the pyrolysis rate, different from that used for predicting by the neural fuzzy model, was sampled at equal interval for comparison with the neural fuzzy model predicted results. Figures 7a–e illustrate the comparison between the experimental and predicted WP mass fractions and pyrolysis rates at heating rates of 5–20 °C/min, respectively. Overall, the predicted WP mass fraction and the pyrolysis rate were consistent with the experimental data. Moreover, in order to determine the reliability of the neural fuzzy model predicted data, the R-squared values of the WP conversion and the pyrolysis rate were calculated, as depicted in Figs. 7f, g. It was noteworthy that the accuracy of the neural fuzzy model prediction of the WP mass fraction was lower at 12 °C/min compared to the predicted data at heating rates of 5, 10, 15 and 20 °C/min. As shown in Fig. 7e, the R-squared value of the WP conversion at 12 °C/min was 0.99996, while the R-squared values of the WP conversion were all 0.99999 at heating rates of 5, 10, 15 and 20 °C/min, respectively. The R-squared values of the WP mass fraction were all close to 1 at heating rates of 5–20 °C/min, exhibiting a high accuracy for the neural fuzzy model predicted values.

Fig. 7
figure 7

Applicability of the neural fuzzy model: a At 5 °C/min; b At 10 °C/min; c At 15 °C/min; d At 20 °C/min; e At 12 °C/min; f R-squared values of the WP mass fraction; g R-squared values of the WP pyrolysis rate

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In terms of the WP pyrolysis rate, the neural fuzzy model predicted results were in good agreement with the experimental data. As described in Fig. 7a, the predicted and experimental WP pyrolysis rate curves almost coincided with each other at 5 °C/min. Moreover, the predicted and the experimental maximum pyrolysis rates were 17.66 wt%/min at 473.8 °C, and 17.73 wt%/min at 468.8 °C, respectively. The relative error between the predicted and the experimental maximum pyrolysis rates was around 0.39%. As depicted in Fig. 7b, the predicted and the experimental maximum pyrolysis rates at 10 °C/min were 32.62 wt%/min at 483.7 °C, and 34.04 wt%/min at 481.2 °C, respectively. The agreement between the predicted and the experimental maximum pyrolysis rates was within 4.18%. As illustrated in Fig. 7c, the peak values of the predicted and experimental WP pyrolysis rate curves were 47.61 wt%/min and 48.02 wt%/min at 488.8 °C, respectively. The relative error of the peak values between the predicted and the experimental maximum pyrolysis rates was 0.84%. As shown in Fig. 7d, the predicted and the experimental maximum pyrolysis at 20 °C/min were 60.61 wt%/min at 492.7 °C, and 59.52 wt%/min at 488.0 °C, respectively. The relative error between the experimental and predicted maximum pyrolysis rates was around − 1.84%. Additionally, as demonstrated in Fig. 7f, the R-squared values of the WP pyrolysis rates were 0.99675, 0.99658, 0.99911 and 0.99926 at heating rates of 5, 10, 15 and 20 °C/min, respectively. Moreover, the R-squared value of the WP pyrolysis rate was 0.99449 at 12 °C/min, which indicated that the neural fuzzy model predicted values were highly precise.

Conclusion

This study investigated the WP thermal pyrolysis process to provide guidance for prospective industrial and commercial applications. The temperature, the conversion and the pyrolysis rate are the determining factors for industrial applications. Therefore, TG experiments were conducted at different heating rates of 5, 10, 12, 15 and 20 °C/min to obtain the WP mass fraction, the conversion and the pyrolysis rate, which varied with the temperature and heating rate. A neural fuzzy model was adopted to predict the WP conversion and the pyrolysis rate based on the experimental TG data. According to the experimental results, the WP conversion and the pyrolysis rate were investigated for the temperature ranges of 300–550 °C and 400–550 °C, respectively. Furthermore, the GA was adopted to determine the optimal operating conditions in the different temperature ranges. The neural fuzzy model was validated using the comparison of the experimental and predicted results. The accuracy of neural fuzzy model predicted results was investigated by determining the R-squared values of the mass fraction (~ 1) and the pyrolysis rate (> 0.994) compared with the available experimental observations. Subsequently, the GA optimized WP conversion and the pyrolysis rate were 97.68% at 5.00 °C/min and 497.89 °C, and 60.66 wt%/min at 20.00 °C/min and 492.09 °C, respectively. Additionally, the neural fuzzy model predicted results were consistent with the supplementary experimental data, which certified the applicability of the neural fuzzy model. The hybrid algorithm of the neural fuzzy model coupled with GA could be used to model and analyze the co-pyrolysis behavior of WP and other materials (biomass, waste paper, etc.).