Skip to main content
NCBI home page
ACS Omega logoLink to ACS Omega
. 2021 Apr 21;6(17):11307–11318. doi: 10.1021/acsomega.1c00169

Prediction Model for Coal Spontaneous Combustion Based on SA-SVM

Jun Deng †,‡, Weile Chen †,‡,*, Caiping Wang †,‡, Weifeng Wang †,‡
PMCID: PMC8153949  PMID: 34056286

Abstract

graphic file with name ao1c00169_0016.jpg

Accurate predictions of the coal temperature in coal spontaneous combustion (CSC) are important for ensuring coal mine safety. Gas coal (the Zhaolou coal mine in Shandong Province, China) was used in this paper. A large CSC experimental device was adopted to obtain its characteristic temperatures from the macroscopic characteristics of gas production. A simulated annealing-support vector machine (SA-SVM) prediction model was proposed to reflect the complex nonlinear mapping between characteristic gases and the coal temperature. The risk degree of CSC was estimated in the time domain, and the model was verified by using in situ data from an actual working face. Furthermore, back-propagation neural network (BPNN) and single SVM methods were adopted for comparison. The results showed that the BPNN could not adapt to the small-sample problem due to overfitting and the output of a single SVM was unstable due to its strong dependence on the setting of hyperparameters. Through the SA global optimization process, the optimal combination of hyperparameters was obtained. Therefore, SA-SVM had higher prediction accuracy, robustness, and error tolerance rate and better environmental adaptability. These findings have certain practical significances for eliminating the hidden danger of CSC in the gob and providing timely warnings about potential danger.

1. Introduction

Coal spontaneous combustion (CSC) can cause the loss of coal resources and lead to gas explosions in mines, thereby threatening the safety of personnel and equipment and seriously damaging the environment. However, due to the hidden characteristics of residual CSC in the gob area, which are not easily detected by humans, and the limited methods for estimating and analyzing the risk degree of CSC, the disaster detection time has an inherent lag, causing considerable safety risks.1,2 Therefore, it is important in disaster prevention and control to analyze the characteristics of CSC and establish an early warning model of the risk degree so that spontaneous combustion can be effectively monitored and early warnings can be established. Based on the coal-oxygen adsorption theory, it is easy to generate heat via the physical and chemical adsorption of oxygen in the air and redox reactions under normal pressure and temperature conditions.3 If the heat generation rate between coal seams is greater than the heat dissipation rate, as heat accumulates and the characteristic temperature of CSC is reached, oxygen consumption will intensify and the reaction rate will accelerate.4−6 Finally, the ignition point of coal will be reached, and spontaneous combustion will occur.7

The critical and dryness temperatures of the CSC are the first and second acceleration points of the coal oxidation reaction process, respectively.8,9 With the continuous increase in the coal chemical adsorption degree, when the heat released by oxidation causes the temperature to exceed the gas desorption temperature and the dynamic equilibrium temperature of CO2 desorption, the critical self-ignition temperature (CSIT), which is characterized by increases in the CO and CO2 concentrations and a decline in the O2 concentration, is reached.10,11 Small molecular hydrocarbons such as C2H4 and C2H6 begin to appear when spontaneous combustion temperature reaches the dryness temperature.12,13 Due to the increase in oxygen consumption in the air, the oxidation of coal is not sufficient. From a macroperspective, the O2 concentration drops sharply, CO and CO2 concentrations increase sharply, and the temperature alteration ratio increases.14

Many scholars have conducted in-depth research on the factors that affect CSC. Wen et al. mainly considered changes in the CO concentration during the CSC process.15 Ma et al. studied the effect of the air humidity on CSC and concluded that the concentration of coal oxidation products increases with increasing humidity.16 Chen et al. studied the changes in the characteristic parameters, such as the temperature, gas concentration ratio, oxygen consumption rate, thermal intensity, and limit parameters, in the early stage of CSC from a macroscopic perspective.17 Ma et al. studied the effect of gas on the oxidation characteristics of coal, and the results showed that the CO/CO2 production and oxygen consumption of coal samples in methane-containing air flows were higher than those in methane-free air flows.18 Yi et al. studied the temperature, thermal product, and gas product evolution trends in the spontaneous combustion period of coal; they found that at a low heating rate, the characteristic temperature point slowly decreased, which made CSC more possible to occur.10,19 These studies provide a theoretical basis for an early identification model of CSC, and this paper is based on these studies.

CSC is a pretty complex chemical and physical process. Because the relationship between the degree of spontaneous combustion and the multi-index gases of spontaneous combustion is difficult to be determined, the chemical and physical mode has not been established by academic circles. Adopting mathematics prediction methods could reveal the nonlinear process of CSC. However, from global research, the main problems in the prediction of CSC in the gob are as follows:

  • 1.

    The existing models do not effectively describe complex nonlinear processes. CSC is an extremely complicated physical and chemical process, and no intuitive physical and chemical model has been established in academia because it is difficult to determine the corresponding relationship between the degree of spontaneous combustion and the multicomponent-index gases of CSC.

  • 2.

    Few data-mining studies have focused on CSC. Currently, most prediction methods are used to simulate the entire spontaneous combustion cycle of coal and obtain the critical values of the component gases and related indexes through statistical analysis, and these methods lack further data mining.

  • 3.

    The accuracy (ACC) of the existing prediction regression models, most of which are lag models, is low. These models cannot estimate the risk degree of CSC and have a low fault tolerance and poor noise resistance.

In this paper, macroscopic predictions of the risk degree of CSC are made by constructing natural combustion laboratory equipment with different coal thicknesses, air supply rates, fully mechanized caving face parameters, and other internal and external conditions; this approach creates an environment similar to the actual environment to simulate the cycle of spontaneous coal combustion at low temperatures. Additionally, the characteristics of CSC are determined, and the characteristic temperature of CSC is obtained based on a coal-oxygen multistage chemical reaction mechanism. Combined with the above conditions, a regression prediction model of the risk degree of CSC is established, and the performance of this model is tested. Finally, the model is verified using in situ data recorded at an actual working face. The accuracy and robustness of the model are determined through a comprehensive analysis of the related evaluation indexes.

Back-propagation neural networks (BPNNs) have notable advantages in processing high-dimensional data and performing nonlinear mapping.20 However, the empirical risk cannot converge to the expected risk based on the full probability when dealing with small-sample problems such as CSC prediction; additionally, overfitting can occur for the test set, and the gradient descent method makes parameter convergence slow.21−23

A support vector machine model can be used as a regression prediction model in various fields with effective adaptation for small-sample problems.24−27 However, due to the existence of a single support vector machine, the model accuracy is strongly dependent on the hyperparameters, and the model has no global optimization ability in the hyperparameter space, so the model fitting results are usually unstable.28 In recent years, many scholars have improved the inherent defects of single support vector machines. Zhang et al. used a support vector machine optimized with the K-fold cross-validation algorithm to predict the ash content of crude coal and used a genetic algorithm for feature selection.29 Li et al. used a genetic algorithm to optimize the punishment parameters, insensitive loss function, and kernel function parameters in a support vector machine, and a short-term prediction model of power generation energy was established.30 Wei et al. adopted improved gray wolf optimization (IGWO) and obtained the global optimal values of punishment parameters based on the information exchange and sharing among artificial wolves with different responsibilities, where each individual behavior decision of the collaborative group was used to search for the best path.31 Nieto et al. used particle swarm optimization (PSO) to predict the remaining service life of aircraft engines; in the paper, PSO was used to find the global minimum points of kernel parameters in a hyperparametric space.32 Chen et al. adopted the time-varying PSO (TVPSO) algorithm to optimize parameters and select features simultaneously, and a weighting function was considered; the TVPSO-SVM model performed well based on the accuracy (ACC) classification index.33 Chen et al. proposed an improved artificial swarm algorithm to optimize the weight of the penalty function, which improved the recognition accuracy and convergence performance of the model for fault diagnosis from images.34

The improvements to the inherent defects of SVMs not only increased the ability to minimize structural risk for small-sample problems but also effectively solved the subjectivity and instability issues caused by blindly setting hyperparameters. This paper presents a prediction method for the risk degree of CSC based on an SA-SVM model. Kirkpatrick et al. first put forward an annealing simulation algorithm, and it has been proved to meet the optimal requirement in partial. This method structure is simple and can solve complex nonlinear optimization problems. In the study, we have contrasted the prediction results between BPNN, SVM, and SA-SVM, and the least-square error evaluation index was employed to determine the accuracy and stability of the models. The results show that the SA-SVM model has a higher prediction accuracy and higher stability than a BPNN and single support vector machine. It has important practical significance for early prediction, early warning of coal spontaneous combustion and environmental safety judgment, scientific relief decision-making, and safety disaster relief of the fire zone.

2. Results and Discussion

2.1. Data and Model Settings

2.1.1. Experimental Results and Samples

According to the analysis of the CSC samples from the Zhaolou coal mine, the maximum CH4 concentration appeared when the temperature was 25–35 °C. As the temperature increased and the gas desorption speed accelerated, when the temperature was 35–45 °C, the concentrations of CO2 and CO reached minimum levels, and the concentration of CO2 remained largely unchanged during this period. The characteristic temperature was estimated based on the above macroscopic observation indexes and the results of this experiment. The results showed that the critical temperature appeared in the range of 50–65 °C and the dryness temperature appeared in the range of 95–105 °C. The highest temperatures in the furnace were selected as the reference values, and the temperature changes in the furnace over time are shown in Figure 1. Because the data was splashes, the linear fitting is the most appropriate for variation. The data was fitted by a Gaussian function. Compared with polynomial fitting, the Gaussian fitting has the advantage of simplicity in calculating the integral and cannot overfit, so we adopt Gaussian to fit temperature vs time.

Figure 1.

Figure 1

Open in a new tab

Gaussian curve fitting based on the experiment.

The concentrations of O2, N2, CO, CO2, CH4, C2H4, and C2H6 and the gas concentration ratios of CO2/CO and C2H6/C2H4 were selected as the input indexes of the SVM model.35,36 The coal temperature corresponding to each measurement index was taken as the output expectation of the model. The paper used the traversed spatial data of the CSC state to obtain samples that satisfied the independent, identically distributed conditions. After experimental determination, 75% of the samples were selected as training samples, and the remaining 25% were selected as test samples. The measured partial gas concentration, gas concentration ratios, and coal temperature were considered as a sample point, as listed in Table 1. The first column was the serial number of the sample point, the data corresponding to {3x} (x = 1–11) was the test set, and the data of the remaining points was the training set.

Table 1. Sample Composition.
sample O2 N2 CO CO2 CH4 C2H4 C2H6 CO2/CO C2H6/C2H4 coal temperature
1 20.4 78.89 281 1400 0.25 12 27 4.98 2.25 33.4
2 19.8 79.75 228 1800 0.21 30 52 7.89 1.73 37.5
3 19.6 79.88 509 2300 0.23 28 78 4.52 2.79 42
4 20 79.43 507 2400 0.27 16 68 4.73 4.25 40.2
5 20.16 79.34 594 2100 0.18 23 79 3.54 3.43 41.4
6 20.7 79.01 222 1400 0.13 12 29 6.31 2.42 43.3
‴       ‴   ‴     ‴ ‴
35 0.01 98.66 28 2500 1.08 8 50 89.29 6.25 36.1
Open in a new tab

The characteristic gas concentrations of the CSC components change with the coal temperature, as shown in Figure 2; we know that as the temperature rises, the concentration of gases CO, CH4, C2H4, C2H6, and CO2 had upward trends, the concentration of O2 had a downward trend, and the concentration of N2 was basically constant. The gas ratio changes with the coal temperature, as shown in Figure 3. We know that C2H6/C2H4 appeared later than C2H4, and as the temperature rose rapidly, it reached its maximum in the critical temperature range and then decreased rapidly. At the beginning of the experiment, CO2/CO first decreased and then increased with the increase of coal temperature, and as the temperature continued to rise, the CO2/CO showed a trend of rapid decline.

Figure 2.

Figure 2

Open in a new tab

Effective samples and trends based on the experimental data.

Figure 3.

Figure 3

Open in a new tab

Gas concentration ratio and trends based on the experimental data.

2.1.2. In Situ Data

After determining the occurrence of spontaneous combustion near the gob open-off cut, relatively accurate in situ data were obtained with a beam tube monitoring system and chromatographic analysis. Additionally, corresponding disaster control measures were taken to effectively restrain the further expansion of the fire zone. Therefore, actual gob data could be divided into three stages: normal circumstances, spontaneous combustion and a governance stage, and return to normal. After analysis, several sets of data for the working face under crossheading were selected as the field data sample set. Effective samples and trends based on in situ data are shown in Figure 4. Additionally, the gas concentration ratios and corresponding trends based on in situ data are shown in Figure 5, and the coal temperature trend based on in situ data is shown in Figure 6. Under normal circumstances, the temperature of coal increased slowly with the increase of temperature, and its highest temperature reached 43 °C. In the case of inhibition after spontaneous combustion, the coal temperature increased rapidly at first and then decreased slowly, and its highest temperature reached 80 °C. After returning to normal, the coal temperature showed a trend of gradual decline. The concentration variation of gases CO, CH4, C2H4, C2H6, and CO2 was consistent with coal temperature. The concentration of O2 was basically consistent under normal conditions and rapidly decreased when coal began to spontaneously combust.

Figure 4.

Figure 4

Open in a new tab

Effective samples and trends based on the in situ data.

Figure 5.

Figure 5

Open in a new tab

Gas concentration ratio and trends based on the in situ data.

Figure 6.

Figure 6

Open in a new tab

Coal temperature trend based on the in situ data.

2.2. Modeling Process

The kernel function parameters and insensitive loss function of the SVM were optimized with a simulated annealing algorithm, and its mathematical expression process is in the Supporting Information. Thereinto, the penalty coefficient C is the parameter of the kernel function through supportive SVM, which means tolerance for error. The higher the C, the more prone it is to the overfitting phenomenon; the smaller the C is, the more likely the underfitting phenomenon is to occur. ε is the insensitive loss function parameter, ensuring the existence of the global minimum solution and the optimization of the reliable generalization bound. Through an iterative process, the optimal parameter combination was obtained as the output. The iterative cost function trend in simulated annealing optimization is shown in Figure 7. Moreover, the variations in the parameters based on experimental data are shown in Figure 8, and those based on in situ data are shown in Figure 9.

Figure 7.

Figure 7

Open in a new tab

Iterative cost function trend.

Figure 8.

Figure 8

Open in a new tab

Variations in parameters based on the experimental data.

Figure 9.

Figure 9

Open in a new tab

Variations in parameters based on the in situ data.

The cost function of structural risk minimization iteratively converged, and the system reached the global minimum state and froze. The parameters in this system state were determined to be the optimal parameters.

2.3. Prediction Results of SA-SVM

The algorithm combined with the least-squares SVM was compiled on the MATLAB platform. A radial basis function (RBF) was selected as the kernel function of the SVM.37 The simulated annealing algorithm provides a nonconvex optimization method that can avoid the local minima of the cost function and obtain the global minimum point. After the energy system was optimized by the algorithm, the kernel function parameter and insensitive loss value were found to be 959.968 and 5.7, respectively. The kernel function parameter and insensitive loss value of the model for the actual ignition working face were 112.618 and 190.8, respectively. Then, nine-dimensional training samples representing the risk degree of CSC were input into the SA-SVM model for training.

A regression model analysis of a single SVM and a BPNN38,39 was also performed. The BPNN model adopted a single hidden layer. To increase the fitting accuracy of the model, 10 neurons were used for feature extraction in the hidden layer. The single SVM method did not use an optimization algorithm to optimize relevant parameters. A scatter plot of the predicted and target coal temperatures based on the three aforementioned models is shown in Figure 10. For training samples, the results of the BPNN mode are uniformly distributed along the zero-error line y = x and are superior to those of the other two modes. For test samples, the results of the SA-SVM mode are uniformly distributed along the zero-error line y = x and are superior to those of the BPNN mode, which means that the BPNN mode shows a serious overfitting phenomenon. The box plot of the absolute error for the aforementioned models in the training and testing stages is shown in Figure 11. For both training samples and test samples, the box of the SA-SVM model is relatively flat and the data distribution is concentrated, indicating that the SA-SVM model has good stability. A summary of the prediction results based on the three aforementioned evaluation indicators is shown in Table 2.

Figure 10.

Figure 10

Open in a new tab

Scatter plot of predicted and target coal temperatures based on the three aforementioned models.

Figure 11.

Figure 11

Open in a new tab

Box plot of the absolute error for the aforementioned models in the training and testing samples based on the (a), (b) oxidation experiment data and (c), (d) in situ data.

Table 2. Summary of the Prediction Results Based on the Three Aforementioned Evaluation Indicators.

    MAE MAPE (%) RMSE R2 (%)
experimental data BP 0.48a 1.45a 0.69a 99.9446a
3.7b 7.4b 5.13b 96.6541b
SVM 1.42a 4.17a 1.73a 99.6573a
2.57b 6.4b 3.61b 98.3419b
SA-SVM 0.82a 2.56a 1.13a 99.8548a
2.13b 5.74b 2.47b 99.2224b
in situ data BP 2.39a 4.42a 4.65a 90.4574a
9.18b 15.33b 9.85b 37.5141b
SVM 8.58a 14.76a 9.61a 59.2487a
8.65b 14.09b 10.14b 33.8152b
SA-SVM 2.53a 5.13a 3.48a 94.6728a
3.56b 6.36b 4.6b 86.3676b
Open in a new tab
a

Represent the training samples.

b

Represent the testing samples.

The results show that the BPNN method performs better than the other two methods for the training set, with MAE = 0.48 and RMSE = 0.69 based on the experimental data and MAE = 2.39 and RMSE = 4.65 based on the in situ data. These findings indicate that the BPNN performs better than the other two methods based on both the training accuracy and stability. However, the error indexes for the test set are significantly higher than those of the other two methods. In this case, although the BPNN achieves the best performance for the training set, a serious overfitting phenomenon occurs for the test set, which leads to high error for the test set.

Compared with the BPNN method, the single SVM displays better performance for small-sample problems. However, because hyperparameters are difficult to determine, the regression results are strongly dependent on human factors, leading to inferior accuracy and stability for the test set compared to the results of the SA-SVM method for the test set. Because there is more noise in the in situ data than in the experimental data, the stability of the single SVM method further decreases. Based on comprehensive analysis, there are two main reasons for the weak generalization ability of the model that lead to overfitting:

  • 1.

    The inherent structure of a network. We cannot accurately estimate the nonlinear complexity of the physical processes, such as the CSC process, and the matching degree of the network structure. Specifically, at the beginning of network design, the number of free network parameters (weight and bias, kernel function parameters, and insensitive loss function) cannot correspond to the number of existing training sets based on actual CSC data.40

  • 2.

    There is noise in the actual data. The network loads the learned CSC characteristics as the synaptic weights and biases of the BPNN and SVM parameters. When the network yields unexpected results due to noise in the input samples, the corresponding characteristics will be stored in the parameter histories. The poor noise-filtering ability of the model will lead to high error for the test set and a reduction in the generalization ability.

According to the output results of the SA-SVM model, the mean absolute error (MAE), mean absolute percentage error (MAPE), and root-mean-square error (RMSE) of the prediction based on experimental data are 2.13 °C, 5.74%, and 2.47, respectively. No matter what types of data, eq 7, R2 of SA-SVM is minimal, which shows that the model has high degree of linearization and strong antinoise ability. Compared with that of the single support vector machine method, the accuracy of the proposed method is improved, and this approach has obvious advantages over the BPNN method. Notably, the maximum absolute error predicted by the BPNN method is 14.163 °C, and the variance is 200.59. The maximum absolute error predicted by the ordinary SVM method is 8.54 °C, and the variance is 72.93. The maximum absolute error predicted by the SA-SVM method is 4.685 °C, and the variance is 21.95 °C. Additionally, the maximum MAE of the test samples predicted by the SA-SVM method is much smaller than that of other methods, suggesting that the SA-SVM model has good robustness to the problem. Moreover, the MAE, MAPE, and RMSE based on the data from the ignition working face are 3.56 °C, 6.36%, and 4.6, respectively, which are the lowest error values among all of the methods. Thus, the SA-SVM method is most suitable for data with certain levels of noise.

3. Conclusions

This paper presents an SA-SVM regression model for CSC prediction. The model can estimate the CSC risk degree in the time domain based on the relevant CSC characteristics. A large CSC experimental device is used to simulate an actual ignition situation. Additionally, the characteristic temperature points of CSC were identified by simulating the CSC process. Using the SA-SVM model to extract the characteristics of CSC, the complex nonlinear relationships associated with CSC were well fitted. Finally, the SA-SVM model was verified using in situ data from an actual ignition working face, and the model effectively and dynamically tracked different ignition stages and responded quickly to determine the risk degree of CSC. This work has certain practical significances for ensuring safe production and reducing the cost of manual monitoring. Because the coal composition, ventilation, and surroundings are quite different in each coal mine, there are differences in the nonlinear relationship between gases and CSC degree. Hence, the mode set up in the manuscript is only used in the Zhaolou coal mine, and when establishing the prediction model of CSC in other coal mines, the coal sample data of corresponding coal mines should be used. The detailed conclusions are as follows:

  • 1.

    The BPNN method performs better than the other two methods for the training set. However, when facing small-sample problems and with some noise in the samples, a serious overfitting phenomenon occurs, which results in poor performance for the test set.

  • 2.

    The single support vector machine model displays better performance than the BPNN in small-sample problems and has obvious advantages. However, the model relies on the setting of hyperparameters, which is highly subjective.

  • 3.

    Compared with other machine learning methods, the SA-SVM model yields higher regression accuracy and robustness. The penalty function parameters and insensitive loss function are globally optimized, and the SVM is based on a simulated annealing method. This approach ensures that the optimal parameter combination is obtained for the SVM model to avoid the issues associated with single SVM modeling.

4. Experiments and Methods

4.1. Oxidation Experiment for Coal

CSC is an extremely complicated process that releases characteristic gases with different concentrations according to the degree of spontaneous combustion, such as CO, CO2, CH4, C2H4, C2H6, and other gases.35 With increasing coal temperature, the gas concentration of each component will change. In this paper, the coupled relationship between characteristic gases and the coal temperature in the process of CSC is used to predict the risk degree of CSC. In fact, CO, alkanes, and alkenes change significantly near the characteristic temperature point. Therefore, according to the experiment conducted in this paper, the characteristic temperature point of CSC is estimated.41

First, coal was collected from the Zhaolou coal mine (Shandong) and crushed using a jaw crusher. The pulverized coal sample was weighed and packaged in XK—III equipment to simulate different coal thicknesses, air leakage rates, oxygen supply rates, heat storage levels, and other conditions. Thus, the CSC cycle was simulated, and the low-temperature spontaneous combustion characteristics of coal were determined. Next, the gases collected at different coal temperatures were quantitatively analyzed.42 Finally, machine learning training and test samples were obtained, and the SA-SVM model was used to extract the features of the samples and make predictions in the time domain. Conceptual illustrations of the experimental device and CSC prediction method are shown in Figure 12.

Figure 12.

Figure 12

Open in a new tab

Experimental device and prediction method for coal spontaneous combustion.

The laboratory equipment consisted of a furnace body, a control system, and a test system. The furnace body was cylindrical with an outer diameter of 1.8 m, an inner diameter of 1.2 m, and a height of 2.2 m. The effective coal storage space was 1.63 m3, and the total experimental coal mass was approximately 1791 kg. The furnace wall was composed of an insulation layer and a temperature control layer. Additionally, several thermistor probes were arranged to detect the temperature in the furnace in real time. The center shaft of the furnace was provided with a gas sampling pipe for gas sampling and testing.

The control system consisted of two parts: a temperature control system and an air supply control system, which were automatically adjusted by the industrial control machine according to the experimental process. The temperature control system maintained the balance between heat storage and heat release, which ensured the accuracy of the experimental results. The air supply control system was used to adjust the air supply volume at a relatively constant level and adjust the temperature and humidity of the air before entering the furnace to the same temperature and humidity as the air inside the furnace.43

The experimental coal samples were placed in the furnace, and the relevant parameters are shown in Table 3. The initial temperature of the experiment was 20.7 °C, which was the same as that of the gob area in the Zhaolou coal mine. The coal samples underwent a natural warming process when the temperature and air supply control systems were started. The temperature and the characteristic gas changes during the CSC experiment were continuously tracked. A certain sample mixture of gases was extracted from the sampling tube by a manual sampling method each day and sent to an SP3430 gas chromatograph for gas composition and concentration analyses. The characteristic gas samples were O2, N2, CO, CO2, CH4, C2H4, and C2H6.36,44

Table 3. Coal-Related Parameters.

coal sample origin void content average particle size (d50) air supply (m3 h–1) initial temperature (°C)
Zhaolou coal mine 0.404 4.765 0.10–1.60 6.8592
Open in a new tab

4.2. In Situ Observation Data

In this paper, to verify the application of the SA-SVM prediction model for an actual ignition working face with considerable environmental disturbances, the CSC characteristics for an actual ignited working face were used as inputs to further verify the accuracy and robustness of the model. The source of ignition of the working face is shown in Figure 13.

Figure 13.

Figure 13

Open in a new tab

Schematic diagram of the fire source location.

The elevation of the working face is −432.0 to −352.0 m, the working face area is approximately 452118.2 m2, and the average thickness of the coal seam is 8.45 m, which is a stable extrathick coal seam. Due to equipment debugging issues and other reasons, the advance speed of the working face was slow.45 When the working face was pushed to 30 m, spontaneous combustion smoke was detected in the return airway, and a fire location was found in the coal body at the top of the open-off cut. The occurrence of a CSC event was confirmed.

Compared with the experimental data, the in situ data have more noise interference and are influenced by uncontrollable environmental factors; therefore, the prediction model must have a high generalization adaptability. This paper adopts the in situ data in the following case. The characteristic gas concentrations of all components in CSC, encompassing the whole process from normal operation to spontaneous combustion and the governance stage and finally then back to normal after disaster management, are used as the inputs of the SA-SVM model. Model comparisons are performed to determine whether this model provides higher prediction accuracy and robustness in practical applications compared to other models.

4.3. SA-SVM Model

Before using the support vector regression (SVR) method, kernel function parameters and the insensitive loss function should be determined.37,46−48 A simulated annealing algorithm was used to optimize the above two parameters and search for the optimal combination of SVM parameters within a certain range to improve model performance.

The simulated annealing algorithm was first proposed by Kirkpatrick et al.49 and has been widely used in the optimization of structures due to its advantage of avoiding local minimum points.50−55 The simulated annealing algorithm optimizes the loss function for a physical system with multiple degrees of freedom in thermal equilibrium and at different finite temperatures. The annealing process was based on the Monte Carlo method adopted by Metropolis et al.56 Given a low-energy state describing a computational system, at the lowest temperature, the system molecules are rearranged in a certain structure. The statistical dynamics characteristics indicate that the energy associated with the temperature T and molecules remaining in state r satisfies the Boltzmann probability distribution

4.3. 1

where E(r) is the energy of the state r, kB is the Boltzmann constant, E̅ is a random variable related to the molecular energy, and Z(T) is the partition function. Equation 1 means that the higher the temperature is, the greater the cooling probability of the primary energy difference is and the lower the temperature, the less probability there is to be a cooling. As the temperature slowly decreases, the above rearrangement process is repeated until the system state converges to the minimum value. The solution at the minimum value is saved as the global optimal solution. When seeking the most optimal solution by the annealing simulation algorithm, it is necessary to introduce the natural mechanism of a physical system annealing process to prevent the local optimal solution. The state of physical annealing corresponds to the solution of the optimization problem. The energy function corresponds to the objective function of the optimization problem. The lowest energy state corresponds to the optimal solution of the optimization problem. In this paper, samples correspond to problem instances, energy corresponds to the structural risk minimization cost function of support vector machines, and the temperature is the control parameter.

To satisfy the finite time approximation property and accelerate the convergence rate of the algorithm, the temperature parameter T must be discretized. The annealing schedule of the cooling rate was determined, and the cooling schedule of parameter T was defined as follows.49

4.3. 2

In this paper, the temperature drop coefficient α is 0.9, and the partition function is constant at 1. Because the system perturbations produce energy fluctuations that result in E1 < E2, the probability of molecules remaining in a state of low energy is greater than the probability of molecules remaining in a state of high energy. When there are two different energies in the state space, the Boltzmann probability associated with the lowest energy state is greater than 1/2, and the new solution in the low-energy state is considered acceptable according to this probability. Additionally, because the acceptance probability is not 1 in the nonlimiting state, that is, the system has a certain probability of accepting the deteriorating solution in the high-energy state, the algorithm can avoid local optima to some extent.

4.3. 3

For the nonminimum energy state, the distribution probability of molecules in the increasing energy state is monotonically reduced by the above equation. The lower the temperature is, the higher the probability of achieving a low-energy state is. In the limit state, only the probability of the lowest energy is not equal to zero. When the system solution no longer avoids local optima with high probabilities, the state is considered stable, and the system freezes. In turn, the annealing process stops, and the optimized parameters are the global optimal parameters. The implementation steps of the SA-SVM algorithm are shown in Figure 14. The steps in simulated annealing optimization are shown in the Supporting Information algorithm pseudocode. The main steps are as follows:

Figure 14.

Figure 14

Open in a new tab

Algorithm flow chart.

Step 1: The initial temperature T = T0, the initial state r = r0, and the initial energy E(r) = E(r0).

Step 2: A new state r1 formed by random disturbance, and determine whether the temporary state satisfies e = E(r1) – E(r). If e ≤ 0, then a new state is accepted; if e > 0, look for a new solution by the Metropolis principle.

Step 3: Determine whether k is less than the preset number of iterations; if not, return to Step 2; if so, analyze whether T is the minimum value of the annealing schedule: if not, update parameter T according to the annealing schedule and return to Step 2, and if so, stop the calculation.

Step 4: The optimized parameters are taken as the optimal parameters of the SVM model, and the modeling and prediction are carried out.

4.4. Performance Indicators

To reflect the accuracy of the SA-SVM model in predicting the coal temperature in spontaneous combustion, this paper uses the average mean absolute error (MAE), mean absolute percentage error (MAPE), and root-mean-square error (RMSE) to describe the training set and testing set errors of the BPNN, SVM, and SA-SVM.57 The performance indicators are defined as shown in eqs 4–7

4.4. 4
4.4. 5
4.4. 6
4.4. 7

where yi is the predicted output of the model (°C), di is the average of the temperature value (°C), di is the average of the temperature value (°C), and n is the total number of samples. The smaller the value of eqs 4 and 5, the higher the accuracy and robustness. The closer eq 7 is to 1, the better the linearization of the model.

Acknowledgments

This work has been supported by the National Key Research and Development Program (Grant No. 2018-YFC-0807900), the Key Research and Development Program of Shaanxi Province (Grant No. 2017ZDCXL-GY-01-02-03), the National Natural Science Foundation of China (Grant No. 5197-4234), the Science and Technology Innovation Talent Promotion Plan of Shaanxi Province (Grant No. 2019KJXX-050), and the Excellent Youth Science and Technology Foundation of Xi’an University of Science and Technology (Grant No. 2019YQ2-03).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.1c00169.

  • SA-SVM algorithm pseudocode and steps for establishing a hyperplane based on a support vector machine (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao1c00169_si_001.pdf (107.3KB, pdf)

References

  1. Song J. J.; Deng J.; Zhao J. Y.; Zhang Y. N.; Shu C. M. Comparative analysis of exothermic behaviour of fresh and weathered coal during low-temperature oxidation. Fuel 2021, 289, 119942 10.1016/j.fuel.2020.119942. [DOI] [Google Scholar]
  2. Qin Y.; Liu W.; Yang C.; Fan Z.; Wang L.; Jia G. Experimental study on oxygen consumption rate of residual coal in goaf. Saf. Sci. 2012, 50, 787–791. 10.1016/j.ssci.2011.08.033. [DOI] [Google Scholar]
  3. Deng J.; Song J. J.; Zhao J. Y.; Zhang Y. N.; Ren S. J.; Shu C. M. Macrocharacteristics of gaseous indicator products and exothermicity during low-temperature oxidation of samples from different regions of the same coal seam from Huainan, Anhui, China. J. Therm. Anal. Calorim. 2021, 143, 781–794. 10.1007/s10973-019-09239-9. [DOI] [Google Scholar]
  4. Zhao J. Y.; Wang T.; Deng J.; Shu C. M.; Zeng Q.; Guo T.; Zhang Y. Microcharacteristic analysis of CH4 emissions under different conditions during coal spontaneous combustion with high-temperature oxidation and in situ FTIR. Energy 2020, 209, 118494 10.1016/j.energy.2020.118494. [DOI] [Google Scholar]
  5. Song J. J.; Deng J.; Zhao J. Y.; Zhang Y. N.; Wang C. P.; Shu C. M. Critical particle size analysis of gas emission under high-temperature oxidation of weathered coal. Energy 2021, 214, 118995 10.1016/j.energy.2020.118995. [DOI] [Google Scholar]
  6. Wang C. P.; Yang N. N.; Xiao Y.; Bai Z. J. Effects of Moisture and Associated Pyrite on the Microstructure of Anthracite Coal for Spontaneous Combustion. ACS Omega 2020, 5, 27607–27617. 10.1021/acsomega.0c04161. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Wang H.; Dlugogorski B. Z.; Kennedy E. M. Coal oxidation at low temperatures: oxygen consumption, oxidation products, reaction mechanism and kinetic modelling. Prog. Energy Combust. Sci. 2003, 29, 487–513. 10.1016/S0360-1285(03)00042-X. [DOI] [Google Scholar]
  8. Deng J.; Zhang Y.. Microcosmic Mechanism of Coal Spontaneous Combustion; China University of Ming and Technology Press, 2015. [Google Scholar]
  9. Tang Y. B. Experimental investigation of applying MgCl2 and phosphates to synergistically inhibit the spontaneous combustion of coal. Energy 2018, 91, 639–645. 10.1016/j.joei.2017.06.006. [DOI] [Google Scholar]
  10. Xiao Y.; Li Q. W.; Deng J.; Shu C. M.; Wang W. Experimental study on the corresponding relationship between the index gases and critical temperature for coal spontaneous combustion. J. Therm. Anal. Calorim. 2017, 127, 1009–1017. 10.1007/s10973-016-5770-6. [DOI] [Google Scholar]
  11. Wojtacha-Rychter K.; Smoliński A. The interaction between coal and multi-component gas mixtures in the process of coal heating at various temperatures: An experimental study. Fuel 2018, 213, 150–157. 10.1016/j.fuel.2017.10.115. [DOI] [Google Scholar]
  12. Wang H.; Dlugogorski B. Z.; Kennedy E. M. Pathways for production of CO2 and CO in low-temperature oxidation of coal. Energy Fuels 2003, 17, 150–158. 10.1021/ef020095l. [DOI] [Google Scholar]
  13. Lu W.; Hu Q. Relation between the change rules of coal structures when being oxidized and spontaneous combustion process of coal. J. China Coal Soc. 2007, 32, 939–944. [Google Scholar]
  14. Xu Q.; Yang S.; Tang Z.; Cai J.; Zhong Y.; Zhou B. Free radical and functional group reaction and index gas CO emission during coal spontaneous combustion. Combust. Sci. Technol. 2018, 190, 834–848. 10.1080/00102202.2017.1414203. [DOI] [Google Scholar]
  15. Wen H.; Yu Z.; Fan S.; Zhai X.; Liu W. Prediction of spontaneous combustion potential of coal in the gob area using CO extreme concentration: A case study. Combust. Sci. Technol. 2017, 189, 1713–1727. 10.1080/00102202.2017.1327430. [DOI] [Google Scholar]
  16. Ma D.; Qin B.; Song S.; Liang H.; Gao A. An experimental study on the effects of air humidity on the spontaneous combustion characteristics of coal. Combust. Sci. Technol. 2017, 189, 2209–2219. 10.1080/00102202.2017.1368500. [DOI] [Google Scholar]
  17. Chen X.; Li H.; Wang Q.; Zhang Y. Experimental investigation on the macroscopic characteristic parameters of coal spontaneous combustion under adiabatic oxidation conditions with a mini combustion furnace. Combust. Sci. Technol. 2018, 190, 1075–1095. 10.1080/00102202.2018.1428570. [DOI] [Google Scholar]
  18. Ma L.; Guo R.; Gao Y.; Ren L.; Wei G.; Li C. Study on coal spontaneous combustion characteristics under methane-containing atmosphere. Combust. Sci. Technol. 2019, 191, 1456–1472. 10.1080/00102202.2018.1531286. [DOI] [Google Scholar]
  19. Yi X.; Xiao Y.; Lü H. F.; Shu C. M.; Deng J. Thermokinetic behavior and microcharacterization during the spontaneous combustion of 1/3 coking coal. Combust. Sci. Technol. 2018, 1769–1788. 10.1080/00102202.2018.1534839. [DOI] [Google Scholar]
  20. Hecht-Nielsen R.Theory of the Backpropagation Neural Network. In Neural Networks for Perception; Academic Press, 1992; pp 65–93. [Google Scholar]
  21. Hagiwara K.; Fukumizu K. Relation between weight size and degree of over-fitting in neural network regression. Neural Networks 2008, 21, 48–58. 10.1016/j.neunet.2007.11.001. [DOI] [PubMed] [Google Scholar]
  22. Kachar O.; Boltnev A.; Kalitkin N. In Speeding up the Convergence of Simple Gradient Methods, Proceedings of the 10th International Conference MMA2005 & CMAM2; Trakai, Lithuania, 2005; pp 349–354.
  23. Feng Q.; Zhang J.; Zhang X.; Wen S. Proximate analysis based prediction of gross calorific value of coals: a comparison of support vector machine, alternating conditional expectation and artificial neural network. Fuel Process. Technol. 2015, 129, 120–129. 10.1016/j.fuproc.2014.09.001. [DOI] [Google Scholar]
  24. Wang L.; Liu Z.; Zhao Z.; Zhang Y. Support-vector-machines learning controller based on small sample sizes for biped robots. Control Theory Appl. 2011, 28, 1133–1139. 10.7641/j.issn.1000-8152.2011.8.CCTA100777. [DOI] [Google Scholar]
  25. Zhou T.; Lu H.; Wang W.; Wang H. A new model for hospitalization expenses of gastric cancer based on clustering and support vector machine. Control Theory Appl. 2017, 34, 803–810. 10.7641/CTA.2017.60545. [DOI] [Google Scholar]
  26. Shao Y. E.; Lu C. J.; Wang Y. C. A hybrid ICA-SVM approach for determining the quality variables at fault in a multivariate process. Math. Probl. Eng. 2012, 2012, 284910 10.1155/2012/284910. [DOI] [Google Scholar]
  27. Zhang X.; Pan F. Parameters optimization and application to glutamate fermentation model using SVM. Math. Probl. Eng. 2015, 2015, 320130 10.1155/2015/320130. [DOI] [Google Scholar]
  28. Cherkassky V.; Ma Y. Practical selection of SVM parameters and noise estimation for SVM regression. Neural Networks 2004, 17, 113–126. 10.1016/S0893-6080(03)00169-2. [DOI] [PubMed] [Google Scholar]
  29. Zhang Z.; Yang J.; Wang Y.; Dou D.; Xia W. Ash content prediction of coarse coal by image analysis and GA-SVM. Powder Technol. 2014, 268, 429–435. 10.1016/j.powtec.2014.08.044. [DOI] [Google Scholar]
  30. Li G.; Sun Y.; He Y.; Li X.; Tu Q. Short-term power generation energy forecasting model for small hydropower stations using GA-SVM. Math. Probl. Eng. 2014, 2, 381387 10.1155/2014/381387. [DOI] [Google Scholar]
  31. Wei Y.; Ni N.; Liu D.; Chen H.; Wang M.; Li Q.; Cui X.; Ye H. An improved grey wolf optimization strategy enhanced SVM and its application in predicting the second major. Math. Probl. Eng. 2017, 6, 9316713 10.1155/2017/9316713. [DOI] [Google Scholar]
  32. Nieto P. J. G.; Garcia-Gonzalo E.; Lasheras F. S.; Juez F. J. D. C. Hybrid PSO-SVM-based method for forecasting of the remaining useful life for aircraft engines and evaluation of its reliability. Reliab. Eng. Syst. Saf. 2015, 138, 219–231. 10.1016/j.ress.2015.02.001. [DOI] [Google Scholar]
  33. Ling Chen H.; Yang B.; Jing W. S.; Wang G.; Liu D.; Li H.; Liu W. Towards an optimal support vector machine classifier using a parallel particle swarm optimization strategy. Appl. Math. Comput. 2014, 239, 180–197. 10.1016/j.amc.2014.04.039. [DOI] [Google Scholar]
  34. Chen G.; Zhang X.; Wang Z. J.; Li F. An enhanced artificial bee colony-based support vector machine for image-based fault detection. Math. Probl. Eng. 2015, 2015, 638926 10.1155/2015/638926. [DOI] [Google Scholar]
  35. Adamus A.; Šancer J.; Guřanová P.; Zubicek V. An investigation of the factors associated with interpretation of mine atmosphere for spontaneous combustion in coal mines. Fuel Process. Technol. 2011, 92, 663–670. 10.1016/j.fuproc.2010.11.025. [DOI] [Google Scholar]
  36. Deng J.; Xiao Y.; Li Q.; Lu J.; Wen H. Experimental studies of spontaneous combustion and anaerobic cooling of coal. Fuel 2015, 157, 261–269. 10.1016/j.fuel.2015.04.063. [DOI] [Google Scholar]
  37. Keerthi S. S.; Lin C. J. Asymptotic behaviors of support vector machines with gaussian kernel. Neural Comput. 2003, 15, 1667–1689. 10.1162/089976603321891855. [DOI] [PubMed] [Google Scholar]
  38. Li Y.; Tian Y. J.; Qin Z. J.; Yan A. Classification of HIV-1 Protease Inhibitors by Machine Learning Methods. ACS Omega 2018, 3, 15837–15849. 10.1021/acsomega.8b01843. [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. Niu H. T. Smart safety early warning model of landslide geological hazard based on BP neural network. Saf. Sci. 2020, 123, 104572 10.1016/j.ssci.2019.104572. [DOI] [Google Scholar]
  40. Hagiwara K.; Fukumizu K. Relation between weight size and degree of over-fitting in neural network regression. Neural Networks 2008, 21, 48–58. 10.1016/j.neunet.2007.11.001. [DOI] [PubMed] [Google Scholar]
  41. Lin Q.; Wang S.; Liang Y.; Song S.; Ren T. Analytical prediction of coal spontaneous combustion tendency: Velocity range with high possibility of self-ignition. Fuel Process. Technol. 2017, 159, 38–47. 10.1016/j.fuproc.2016.09.027. [DOI] [Google Scholar]
  42. Zhao H.; Yu J.; Liu J.; Tahmasebi A. Experimental study on the self-heating characteristics of Indonesian lignite during low temperature oxidation. Fuel 2015, 150, 55–63. 10.1016/j.fuel.2015.01.108. [DOI] [Google Scholar]
  43. Su H.; Zhou F.; Li J.; Qi H. Effects of oxygen supply on low-temperature oxidation of coal: A case study of Jurassic coal in Yima, China. Fuel 2017, 202, 446–454. 10.1016/j.fuel.2017.04.055. [DOI] [Google Scholar]
  44. Wen H.; Zhang F.; Jin Y.; Liu W. Experiment research on effect of sulfur on characteristic parameters of coal spontaneous combustion. Saf. Coal Mines 2011, 42, 5–7. 10.13347/j.cnki.mkaq.2011.10.034. [DOI] [Google Scholar]
  45. Xia T.; Zhou F.; Wang X.; Zhang Y.; Li Y.; Kang J.; Liu J. Controlling factors of symbiotic disaster between coal gas and spontaneous combustion in longwall mining gobs. Fuel 2016, 182, 886–896. 10.1016/j.fuel.2016.05.090. [DOI] [Google Scholar]
  46. Liu M. S.; Cao Z. M.; Zhang J.; Wang L.; Huang C.; Luo X. Short-term wind speed forecasting based on the Jaya-SVM model. Int. J. Electr. Power Energy Syst. 2020, 121, 106056 10.1016/j.ijepes.2020.106056. [DOI] [Google Scholar]
  47. Cherkassky V.; Ma Y. Practical selection of SVM parameters and noise estimation for SVM regression. Neural Networks 2004, 17, 113–126. 10.1016/S0893-6080(03)00169-2. [DOI] [PubMed] [Google Scholar]
  48. Prada J.; Dorronsoro J. R. In SVRs and Uncertainty Estimates in Wind Energy Prediction, International Work-Conference on Artificial Neural Networks; Springer: Cham, 2015; pp 564–577.
  49. Kirkpatrick S.; Gelatt C. D.; Vecchi M. P. Optimization by simulated annealing. Science 1983, 220, 671–680. 10.1126/science.220.4598.671. [DOI] [PubMed] [Google Scholar]
  50. Dupanloup I.; Schneider S.; Excoffier L. A simulated annealing approach to define the genetic structure of populations. Mol. Ecol. 2002, 11, 2571–2581. 10.1046/j.1365-294X.2002.01650.x. [DOI] [PubMed] [Google Scholar]
  51. Bandyopadhyay S.; Saha S.; Maulik U.; Deb K. A simulated annealing-based multiobjective optimization algorithm: AMOSA. IEEE Trans. Evol. Comput. 2008, 12, 269–283. 10.1109/TEVC.2007.900837. [DOI] [Google Scholar]
  52. Ekren O.; Ekren B. Y. Size optimization of a PV/wind hybrid energy conversion system with battery storage using simulated annealing. Appl. Energy 2010, 87, 592–598. 10.1016/j.apenergy.2009.05.022. [DOI] [Google Scholar]
  53. Kuo Y. Using simulated annealing to minimize fuel consumption for the time-dependent vehicle routing problem. Comput. Ind. Eng. 2010, 59, 157–165. 10.1016/j.cie.2010.03.012. [DOI] [Google Scholar]
  54. Lyden S.; Haque M. E. A simulated annealing global maximum power point tracking approach for PV modules under partial shading conditions. IEEE Trans. Power Electron. 2016, 31, 4171–4181. 10.1109/TPEL.2015.2468592. [DOI] [Google Scholar]
  55. Haznedar B.; Kalinli A. Training ANFIS structure using simulated annealing algorithm for dynamic systems identification. Neurocomputing 2018, 302, 66–74. 10.1016/j.neucom.2018.04.006. [DOI] [Google Scholar]
  56. Metropolis N.; Rosenbluth A. W.; Rosenbluth M. N.; Augusta H. T. Equation of state calculations by fast computing machines. J. Chem. Phys. 1953, 21, 1087–1092. 10.1063/1.1699114. [DOI] [Google Scholar]
  57. Huber P. J.Robust Statistics. In International Encyclopedia of Statistical Science; Springer: Berlin, Heidelberg, 2011; pp 1248–1251. [Google Scholar]

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

ao1c00169_si_001.pdf (107.3KB, pdf)

Articles from ACS Omega are provided here courtesy of American Chemical Society

RESOURCES