Product prediction of fixed-bed coal pyrolysis using a fusion model

2.1 Data selection

In this study, 29 types of coal were considered, including 6 kinds of lignite, 19 kinds of bituminous coal, and 4 kinds of anthracite coal. The ultimate and proximate analyses of the samples are shown in Tables 1 and 2. Sixty sets of experimental data on coal pyrolysis were obtained from the literature (Wu et al., 2022; Qian et al., 2019; Zhao et al., 2011; Zhang et al., 2014; Ban et al., 2022; Chen et al., 2021a, 2021b; Qiang et al., 2021), all of which were carried out in a fixed bed at various pyrolysis temperatures, and the yields of water, tar, syngas, and char in the pyrolysis products were measured.

2.2 Data analysis and pretreatment

Considering the ultimate and proximate analysis of the coal samples, and the different pyrolysis temperatures, nine characteristic parameters were selected as the inputs, namely moisture (M), ash (A), volatile matter (V), carbon (C), hydrogen (H), nitrogen (N), sulphur (S), oxygen (O), and temperatue (T). Detailed information on the dataset is provided in the Supplementary data.

The Pearson correlation coefficient (PCC), denoted as r, is used to describe the linear correlation between two variables, and its value ranges between − 1 and 1, and is calculated as follows (Abnisa and Daud, 2014):

2.3 Base models

This study uses suitable regression algorithms for MLR, SVM, and RF. Adequate testing and training were implemented to build the three base models via the scikit-learn library of the Python programming language. All inputs were normalized in advance using the equation (Fletcher et al., 2012):

The RF model is an integrated learning method based on decision trees, and can deal with high-dimensional feature samples with high degree of accuracy (Leng et al., 2021). The importance of features can be calculated and ranked using the average impurity removal method (Tang et al., 2020). Every partition makes a local optimal choice during the generation of the decision tree. Hence, the result cannot ensure that each choice is globally optimal, which can easily lead to overfitting.

The SVM model is a supervised learning model that uses classification and regression analysis to analyze data. It is adept at the cross validation of selection parameters, weighting of unbalanced samples, and probability estimation of class problems (Bai et al., 2017). Nevertheless, the use of larger datasets commonly lowers its predictive accuracy. For the resolution of nonlinear problems with no general standard for the selection of the kernel function, the predictive accuracy of the base model depends largely on the effectiveness of the kernel function, which for SVM is defined as follows:

The MLR model is a kind of subsection method, which converges more stably with the structural priors of pre-training and the optimization training of full-space parameter. However, the calculation and storage complexity of the model is high, and it is difficult to set the hyperparameters. The multiple linear regression equation is as follows (Xing et al., 2019):

2.4 Fusion models

The limited algorithms of base models limit their predictive performance in finding the optimal solution. However, integrating multiple machine learning models can improve overall predictive ability. Fig. 1 illustrates the structure of the FM. The 60 sets of coal pyrolysis data were randomly divided into training sets and test sets in a ratio of 2:1. Nine parameters were selected as inputs based on the results of Pearson correlation analysis. The training data were imported into the Python scikit-learn library to build the SVM and MLR models, while the RF model was established using the NumPy library. The predicted outputs of the base models were further optimized using the test data. Moreover, the predicted performance of the base models was quantified using a learning weight algorithm with 5-fold cross-validation. The quantified performance ulteriorly regulated the weights of the base models in the output of the FM. The better the base model performs, the higher its weighting in the FM. The FM was then trained and evaluated using the training data until its predictive performance reached the presupposed accuracy level.

Close

Fig. 1

Structure of the fusion model.

Export to PPT

2.5 Performance evaluation

The quality of a linear regression model may be evaluated using a variety of measures. In this study, the determination coefficient ( ${\mathrm{R}}^2$ ) and the root mean square error ( $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ ) were used, which are calculated as follows (Xue et al., 2020):

In the Eqs. (6) and (7), ${\mathrm{Y}}_{\mathrm{i}}^{\mathrm{e}\mathrm{x}\mathrm{p}}$ , ${\mathrm{Y}}_{\mathrm{i}}^{\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{d}}$ , and ${\overline{\mathrm{Y}}}^{\mathrm{e}\mathrm{x}\mathrm{p}}$ are the experimental, predicted, and average experimental values, respectively, and N is the total quantity of data in the test set. ${\mathrm{R}}^2$ varies between 0 and 1 and represents the goodness of fit of the model, while $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ is the mean of the square root of the error between the predicted and experimental values. Hence, having ${\mathrm{R}}^2$ close to 1 and $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}$ close to 0 means that the model achieved the expected results.

3.1 Statistical analysis of the dataset

Fig. 2 shows box and whisker plots of data obtained from the proximate and ultimate analyzes of the coal samples and the yields of pyrolysis products. The main parameters in the Fig. 2 include the coal characteristics of moisture (M), ash (A), volatile matter (V), and fixed carbon (FC) and the elemental content of carbon (C), hydrogen (H), oxygen (O), and nitrogen (N). The distribution of the experimental data shows that A has the largest spread, with a range of 3.29 wt% to 44.11 wt%, while N. has the smallest (0.40 wt% to 2.25 wt%). In addition, the contents of N and H obtained from ultimate analysis were lower than that of other elements, and were mainly concentrated from 1.00 wt% to 5.00 wt%. In terms of the yield of pyrolysis products, the values of water yield and tar yield have outliers above the upper limit, which reflects the fact that altering the pyrolysis conditions has a greater effect on the yields of these two products. In terms of the proximate analysis, the difference between the mean and median of A (3.10 wt%) is higher than that of M (1.28 wt%), V (2.25 wt%), and FC (2.25 wt%). Moreover, in terms of the ultimate analysis, the mean value of C is 76.42 wt% and its median is 78.08 wt%. In terms of the product distribution, the difference between the mean and median of the char yield is 2.18 wt%, which is close to that of syngas (2.18 wt%), while the yields of water and char ranged from 1.27 wt% to 19.67 wt% and 54.1 wt% to 83.4 wt%, respectively. These results show that the divergence of the data is in the order of proximate analysis > yields of pyrolysis products > ultimate analysis, suggesting that the thermochemical properties of coal have a more pronounced effect on the pyrolysis product distribution than the elemental compositions.

Close

Fig. 2

Distributions of proximate analysis, ultimate analysis, and yield of pyrolysis products.

Export to PPT

Fig. 3 illustrates the linear relationships between two arbitrary variables. As the figure shows, FC (p < 0.01) is perfectly negatively correlated with V (p < 0.01), with a correlation coefficient of − 1. Here, the p-value indicates the reliability of the linear correlation, which is associated with the equation FC = 100 – (V + A + M) for the estimation of fixed carbon. Moreover, Fig. 3 also shows that FC is significantly influenced by A, C, H, N, and O, and that the pyrolysis temperature is positively correlated with most of the variables. On the other hand, Fig. 3 reveals a less significant linear relationship between the proximate and ultimate analyses of the experimental data. Oppositely, there is a positive correlation between C and H with a correlation coefficient of 0.26, while that of C and V is negative, at − 0.45. S, however, is only positively correlated with A and V, with correlation coefficients of 0.31 and 0.15, respectively. In general, V and FC are moderately correlated with H and N and strongly correlated with O. There is also a clear correlation between FC and C, while M is unaffected by the elemental composition of coal. These results also indicate that the thermochemical properties of coal have a weak relationship with its S content.

Close

Fig. 3

Matrix of Pearson correlation coefficients between the different variables.

Export to PPT

3.2 Predictive performance of base models and FM

Table 3 shows the R² and RMSE values of the predicted results from the different models. It is evident that all models perform well for the prediction of tar, water, and syngas yields. But none of the models do well in predicting the char yield due to the moderate correlation between FC and the elemental composition of coal. When all models have poor prediction effect on Char, RF and FM model have relatively good prediction effect. Although the R² value of FM model is only higher than that of RF model 0.0198. Overall, the prediction effect of FM model is better than base models. Nevertheless, the FM has better predictive accuracy than the base models in forecasting the tar and syngas yield. Further, the water yield is also well predicted by the FM, which is only marginally behind the MLR model. However, the maximum R² of the base models for the prediction of the char yield is just 0.5017, which is far lower than those for the tar, water, and syngas yields, which suggests that the base models are less effective in predicting coke yield. It is also worth noting that the FM has the best predictive ability for the char yield of all the models, with the highest R² (0.5215) and the lowest RMSE (5.2134). As a result, the FM performs consistently well in predicting the pyrolysis yields of coal. This is because, even when the base models perform poorly, the FM is still able to proactively adjust the model output of the model via the learning weight method, resulting in greater predictive accuracy.

Fig. 4 shows a comparison between the experimental data and the predicted output of the different models, with the parity line indicated in blue. The results show that all the models achieve acceptable accuracy in predicting the tar, water, and syngas yields, with the predictive accuracy of the FM model being higher than the other base models. On the contrary, a noticeable deviation is observed between the predicted and experimental values of the char yield. The point-cloud distribution of all models is concentrated when the char yield is from 70 wt% to 80 wt%, and the prediction effect is acceptable. Within this range, as Fig. 4D shows, the point-cloud of char for the FM is more intensive and nearer the blue line than that of the base models, indicating that its a predictive performance is more reliable than the base models. The final result shows that the prediction performance of FM model is better than the base model.

Close

Fig. 4

Comparison between the experimental data and predicted outputs for different models: (A) SVM; (B) RF; (C) MLR; (D) FM.

Export to PPT

3.3 Relative error analysis of the models

Fig. 5 shows the relative error between the experimental data and the predicted results. The Y-axis on the left represents the relative error, while that on the right represents the experimental yield of the pyrolysis products. The X-axis represents the number of sample groups in the test set. A smaller relative error indicates a more accurate prediction result, meaning that the predictive performance of the model is better. Fig. 5A indicates that all models do well in predicting the tar yield, with the predictive performance of the RF model being better than the SVM and MLR models. The relative errors between the RF model and the experimental data range from − 0.083 % to 0.251 %, with the maximum relative error corresponding to the experimental dataset labelled as No. 1. Meanwhile, the maximum relative error of the FM was the lowest among all the models, at 0.247 %, indicating that the predictive performance of the FM model is superior to all the base models in predicting the tar yield.

Close

Fig. 5

Relative error between predicted outputs and experimental data: (A) tar yield; (B) water yield; (C) char yield; (D) syngas yield.

Export to PPT

Fig. 5B shows that, just as for the tar yield, the maximum relative errors of all models occurred for the experimental dataset No.1. The relative error of the FM was the lowest among all the models, at 0.370 %. When the water yield was in the range of 3.01 wt% to 6.80 wt%, the FM and SVM models showed the best predictive accuracy. Further, when the water yield is > 6.80 wt%, the FM still possesses excellent predictive accuracy, with a relative error range from − 0.136 % to 0.006 %. Hence, compared with the base models, the FM better predicts the water yield.

Fig. 5C shows the relative errors of the char yield. The MLR model has the largest relative error range. The maximum relative error of RF model is 0.193 %. It appears that the RF model exhibits the best predicted accuracy for char yield among the base models. When the char yield is < 70.25 wt%, however, all models show worse predicted performance than for the other pyrolysis products (water, tar, and syngas). On the other hand, when the char yield is > 70.25 wt%, the predictive results for the base models are lower than the experimental data values. Further, the predictive accuracy of the FM for the char yield is lower than that of the RF model due to the poor predictive performance of the MLR and SVM models. However, the predictive performance of FM model is still comparatively excellent in the same condition. The relative error range of FM was − 0.132 % to 0.244 %, which was very close to that of the RF model (−0.120 % to 0.193 %). As Fig. 5D shows, the maximum relative error for the syngas yield was 0.351 %, obtained from the RF model. The predictive accuracy of the SVM model was the best of the base models, ranging from − 0.065 %. to 0.251 %. Furthermore, the percentages of model outputs that were higher than the corresponding experimental data values are 80 %, 50 %, and 40 % for RF, MLR, and SVM, respectively. The relative error of the FM is in the range of − 0.132 % to 0.244 %, meaning it has better predictive accuracy than the base models. Moreover, two-thirds of the predicted outputs from the FM model are, higher than the corresponding experimental values. Since the FM is derived from a combination of the base models, this indicates that it actively regulates the base model by training the weighting algorithm, which results in better predictive performance.

These results demonstrate that the FM is superior to the base models in predicting the yields of tar, water, and syngas, while coming a close second to the RF model for the char yield. Further, a maximum relative error of only 0.244 % indicates that the FM effectively utilizes the learning weight algorithm to proactively improve the predicted outputs.

3.4 Feature importance

Fig. 6 illustrates feature importance of input variables among the FM and base models. The feature importance indicates the extent of influence of input characteristics on the predicted yield of pyrolysis products. Fig. 6A shows that the oxygen content has the greatest influence on predicting the tar yield for each model. Moreover, the FM significantly enlarges the feature importance of oxygen content and reduces that of carbon content during the modelling process. As Fig. 6B, the most feature important input in predicting the water yield for each model is also the oxygen content, with the feature importance of oxygen content from the FM being larger than that of the base model. Meanwhile, the FM significantly lowers the feature importance of carbon content and volatile matter. The feature importance of input variables for predicting syngas is quite different from those for predicting tar and water.

Close

Fig. 6

Feature importance of input variables via the FM and base models: (A) tar yield, (B) water yield, (C) syngas yield (D) char yield.

Export to PPT

Fig. 6C shows the inconsistency in the feature importance variation of moisture content. The feature importance of moisture content in the FM (41.45 %) is much lower than that of the base models (57.59 %). Fig. 6D shows that the FM significantly decreases the feature importance of moisture content, while that of oxygen content in the FM (22.07 %) is larger than that of the base models (12.40 %). In terms of the results From Figs. 5 and 6, it is evident that the FM proactively varies the feature importance of inputs to improve the predicted outputs.