For the purpose of achieving more effective prediction of the absolute gas emission quantity, this paper puts forward a new model based on the hidden recurrent feedback Elman. The recursive part of classic Elman cannot be adjusted because it is fixed. To a certain extent, this drawback affects the approximation ability of the Elman, so this paper adds the correction factors in recursive part and uses the error feedback to determine the parameters. The stability of the recursive modified Elman neural network is proved in the sense of Lyapunov stability theory, and the optimal learning rate is given. With the historical data of mine actual monitoring to experiment and analysis, the results show that the recursive modified Elman neural network model can effectively predict the gas emission and improve the accuracy and efficiency of prediction compared with the classic Elman prediction model.
In the daily management of mine safety, an effective method of prevention and control of mine gas disasters is the scientific analysis of the gas emission data provided by the monitoring system [
In recent years, intelligent computing methods have been rapidly developed in dynamic system identification [
From the above observation, this paper proposes a novel strategy of adding correction factors in recursive part of ENN, resulting in a new model called recursive modified Elman neural network (RMENN). The stability and convergence of RMENN model are theoretically proved, and some meaningful results are obtained in this paper. In practice, through the analysis of the main factors affecting coal gas emission, this paper puts forward the gas emission prediction model based on recursive modified Elman neural network.
The rest of this paper is organized as follows. The establishment of RMENN model is described in Section
As discussed in Section
Topology of the RMENN.
With this feature, the new model called RMENN is able to improve update power of the classic ENN and exhibit rapid convergence and high prediction accuracy. The relationship between input and output of RMENN can be expressed as
The topology of the RMENN is shown in Figure
The main objective of learning algorithm is to minimize a predefined energy function by adaptively adjusting the vector of network parameters based on a given set of inputoutput pairs. The particular energy function used in the RMENN is as follows:
The weights of the RMENN are updated by the negative gradient of the energy function; those are
The appropriate learning rate can make the learning algorithm converge at a faster speed. According to the Lyapunov stability theory,
Let the weights of RMENN be updated by (
(1) If
(2) If
(3) If
(4) If
(1) Let the energy function be described by (
Since
Since
Proof (4) It is similar to the proof (1).
Since
Then
Hence,
The proof of
The proof of theorem is completed.
As explained before, we can get the optimal learning rate as follows.
Let
Let
The training algorithm procedures of RMENN are shown in Figure
Training algorithm procedures of RMENN.
China is the larger coal consumer among the developing countries. China’s secure producing situation of the coalmine is very grim, especially the accident of gas disasters, which would result in a large quantity of casualties and property losses, and has absorbed high attention of the government. The precise prediction of gas emission is important for the mineral production safety in China. Gas emission prediction model based on small sample has always been a significant subject in coal mine gas study field [
This paper selects Kailuan mining group money mining camp in May 2007 to December 2008 working face of absolute gas emission quantity [
The statistical data of coalface gas emission and influencing factors.
Number 















(1)  1.92  408  2.0  10  2.0  4.42  155  96  2.02  1.50  20  1  5.03  3.34 
(2)  2.14  421  1.8  11  1.8  4.13  145  95  2.64  1.62  19  1  4.75  3.56 
(3)  2.58  450  2.3  10  2.3  4.67  150  95  2.41  1.48  18  2  4.91  3.67 
(4)  2.40  456  2.2  15  2.2  4.51  160  94  2.55  1.75  20  2  4.63  4.17 
(5)  3.22  516  2.8  13  2.8  3.45  180  93  2.21  1.72  12  2  4.78  4.60 
(6)  2.80  527  2.5  17  2.5  3.28  180  94  2.81  1.81  11  1  4.51  4.92 
(7)  3.23  517  2.8  13  2.8  3.46  180  93  2.23  1.71  12  2  4.76  4.61 
(8)  3.35  531  2.9  9  2.9  3.68  165  93  1.88  1.42  13  2  1.82  4.78 
(9)  3.61  550  2.9  12  2.9  4.02  155  92  2.12  1.60  14  2  4.83  5.23 
(10)  3.71  573  3.2  11  3.2  2.92  175  91  3.11  1.46  13  2  4.63  5.62 
(11)  4.21  590  5.9  8  5.9  2.85  170  79  3.40  1.50  18  3  4.77  7.24 
(12)  4.03  604  6.2  9  6.2  2.64  180  81  3.15  1.80  16  3  4.70  7.80 
(13)  4.80  630  6.5  9  6.16  2.77  165  78  3.02  1.74  17  3  4.62  7.68 
(14)  4.67  640  6.3  11  .3  2.75  175  80  2.56  1.75  15  3  4.60  7.95 
(15)  2.43  450  2.7  11  2.7  4.32  165  93  2.35  1.85  16  2  4.58  5.06 
(16)  3.16  544  2.7  17  2.7  3.81  165  93  2.81  1.79  13  2  4.90  4.93 
(17)  4.62  629  6.4  13  6.4  2.80  170  80  3.35  1.61  19  3  4.63  8.04 
(18)  4.53  635  6.2  9  6.2  2.73  160  72  2.94  1.73  17  3  4.61  7.56 
(19)  3.87  580  3.9  11  3.9  2.85  170  92  3.02  1.39  14  2  4.72  5.82 
(20)  3.24  509  2.5  14  2.5  4.40  160  93  2.79  1.72  13  2  4.65  4.36 
In order to reduce the influence of the different dimension, the experimental data are conducted by generating a value between lower and upper limits of each factor by using the formula
After 50 times independent simulations, we compare the training effects of the two models. From the point of view of training error traces, Figures
Comparison of convergence from the classic ENN and the RMENN.
The best training error traces
The average training error traces in 50 independent simulations
The worst training error traces
From the point of view learning speed, the RMENN has superior convergence speed than the classic ENN. When it averagely reach 348 epochs, the training error of the RMENN meets the requirement, but the classic ENN do not meet the requirements in the best training error traces as shown in Figure
Figure
Comparison of the relative error from the classic ENN and the RMENN.
Figure
The contrast of gas emission average prediction in 50 times independent simulations.
The mean squared error (MSE), median absolute error (MAE), and mean absolute percentage error (MAPE) are used as the indicators to measure the prediction precision. These indicators are defined as follows:
Table
Results of the error analysis based on MSE, MAE, and MAPE.
Number  Actual data  ENN  RMENN  

Output results  Relative error/%  Output results  Relative error/%  
(17)  8.04  7.5926  5.56  7.7611  3.47 
(18)  7.56  7.9246  4.82  7.8958  4.44 
(19)  5.82  5.6757  2.48  5.8015  0.32 
(20)  4.36  4.7576  9.12  4.5990  5.48 


MSE (m^{3}⋅min^{−1})  0.1280  0.0620  


MAE (m^{3}⋅min^{−1})  0.3385  0.2181  


MAPE (%)  5.50  3.43 
To comprehensively evaluate the performance and differences significant of the two prediction models, DieboldMariano (DM) test and three loss functions are adopted, including MSE, MAE, and MAPE. DM test is a comparison test that focuses on the predictive accuracy and can be used to evaluate the prediction performance of the proposed hybrid model and other comparing models. The details of DM test are given as follows:
Table
DM values based on MSE, MAE, and MAPE.
MSE  MAE  MAPE  

DM  2.1383 
3.2718 
2.6912 
In order to further verify the validity of the RMENN model, four sets of sample data are randomly selected for validation and other data are selected for training. Table
Results of the error analysis based on MSE, MAE, and MAPE.
Number  Actual data  ENN  RMENN  

Output results  Relative error/%  Output results  Relative error/%  
(2)  3.56  3.6555  2.68  3.6006  1.14 
(3)  3.67  3.8832  5.81  3.7566  2.36 
(10)  5.62  5.4835  2.43  5.4687  2.69 
(13)  7.68  7.9757  3.85  7.7862  1.38 


MSE (m^{3}⋅min^{−1})  0.0402  0.0108  


MAE (m^{3}⋅min^{−1})  0.1852  0.0962  


MAPE (%)  0.0369  0.0189 
DM values based on MSE, MAE, and MAPE.
MSE  MAE  MAPE  

DM  1.4139  1.7445 
1.9719 
In this paper, we analyze the drawback of the classic ENN. A novel type of network architecture called RMENN has been proposed for gas emission prediction. In theory, the convergence and stability of learning algorithm of RMENN are proved, and the approximate optimal learning rate is given. In practice, experiment analysis results on the gas emission prediction have demonstrated that RMENN has better performance in convergence rate and prediction accuracy than the class ENN, at the cost of slightly heavier structure (correction factors). Therefore, the RMENN has certain application value and the prospect.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This research was supported by Foundation of Liaoning Educational Committee (Grant no. LJ2017QL021) and the National Natural Science Foundation of China (Grant no. 61304173).