Research on the Method of Gas Emission Prediction Using Improved Grey RBF Neural Network Model

Effectively avoiding gas accident is vital to the security of mineral manufacture, and the coal mine gas accident is often caused by gas concentration overrun. The prediction accuracy of gas emission quantity in coal mine is the key to solve this problem. To maintain concentration of gas in a secure range，grey theory and neural network model increasingly diffusely used in forecasting gas emission quantity in coal mine critically. Nevertheless, the limitation of the grey neural network model is that researchers merely bonded the conventional neural network and grey theory. To enhance accuracy of prediction, a modified grey GM(1,1) and RBF neural network model is proposed combined amended grey GM(1,1) model and RBF neural network model. Then the proposed model was put into simulation experiment which is built based on Matlab software. Ultimately, conclusion of the simulation experiment verified that the modified grey GM(1,1) and RBF neural network model not only boosts the precision of prediction, but also restricts relative error in a minimum range. This showed that the modified grey GM(1,1) and RBF neural network model achieves effectiveness in precision of prediction much better than grey GM(1,1) model and RBF neural network model.


Introduction
Through the years，coal mines have played a crucial role in energy resource around the world. Ranking the first in coal production, China is the largest consumer of coal all over the world which consumed roughly half of the world's coal consumption. Coal exploitation has made an important contribution to development economy in China covering providing employment opportunities and generating purchasing power. Coal still play a dominant role in the total primary energy even though the coal production declined in China [1,2]. Nevertheless, the production system in underground coal mine is a peculiarly complex disaster system ,which caused coal mine accidents occurring frequently [3].
Safe production of underground coal mines is threatened in the extreme by a wide variety of coal mine disaster. In China, high rate accident resulting from coal mine cause huge losses to Chinese economy and thousands of fatalities among coal miners, every year [4].Among various types of coal mine accident, gas accident is normally perceived as the hazardous one [5]. After 2 , methane is the second-biggest source of global greenhouse gas emission and a major source of methane emission is coal mine [6][7][8].
Studies have shown that methane emission relevant to coal-mine ventilation has an adverse impact of environment. And methane as a precious clean resources released into the atmosphere is a waste [9,10]. Methane emission from ventilation system is the primary source of coal mine methane emission. In China, there are approximately 85-90% of coal mine methane sourcing from underground coal mine [11].
In addition, methane is an explosive gas which has extremely energy [12]. Therefore, taking advantage of drained methane from coal mine will become critical in lessening methane emission in the atmosphere [13].
In China, coal and gas outburst is the severest cause which are leading to hazard of coal mines, which can let out plenty of coal gas as quick as thought and induce gas explosion. Intense and sudden release of coal and gas from coal mine has given rise to equipment damage and casualties [14][15][16]. Figure 1 is based on the web of state administration of coal mine safety, which publishes the number of accidents of Chinese situation of coal and gas outburst from 2006 to 2015 [17].
Since 1950, extremely serious gas explosion disasters are occurred in China frequently, till 2015 the happening of extremely serious gas explosion disasters having been reaching up to 126 [18]. Hence, it is imminently necessary to carry through an investigation which can accurately prophesy gas outburst, and furnish direction arrangement of tunnel support in coal mine. The energy contained in methane is in direct proportion to its risk degree. For this reason, it is becoming more popular in energy sector [19]. Indeed, abundant methane released during mining may create security problems, but coal mine enterprises can also obtain obvious economic benefits if they use coal mine methane rationally [20]. On account of low concentration of methane, some researchers focused on technologies of treating and recovering methane effectively [21].Meanwhile, in contrast to traditional fossil fuel energy, methane is a cleaner energy resource.
China as the largest coal producer all over the world, in excess of 95% the national coal production from underground coal mine. And comparing surface mines, underground coal mines have higher gas emissions. Enormous amount of methane is released during the mine process, especially from state-owned coal mines which have high-gas content. An estimated amount of 19 billion of cubic meters of methane discharged from China's coal mine every year, leading the world but a few pockets of methane was utilized [11,[22][23][24][25].
Methane is categorized as an important greenhouse gas. Extracting methane effectively is beneficial to protect the atmosphere [26]. But reality dictates that, in the process of mining, a considerable number of coal mine gas discharged into atmosphere through the ventilation system and a part of unused extracted methane is also released [9]. This may lead global warming and energy waste. Previous research has shown that gas concentration exceeding limit is commonly triggered by high gas emission. And gas concentration transfinite is associated with many serious conditions such as ignition and explosion [27]. Coal mine accidents arising from gas is extremely dangerous and with the increase of depth of the exploited seam, the content of gas increases. Gas emission prediction is crucial to impose restrictions on gas concentration transfinite [28].
In spite of methane consisting in nearly all coal mines in China, it is unrealistic to use other energy in lieu of coal mine in recent years. Mining excavations not only affect economic development, but is also inseparable from the people's livelihood. According to statistics, coal account for 70% of gross energy supply in China [29]. To guarantee the regular national economy, declining the gas emission and improving the utility ratio of extracted methane are appropriate. Gas emission is admittedly considered as a significant parameter of gas accidents, and has dramatically impacted mining process and the mine ventilation design [30].Hence, to achieve safety production, it is necessary to analysis data in terms of gas emission and forecast its change tendency in advance.
For the sake of processing complex and enormous data connected with gas emission, various forecasting approaches are proposed. The computational fluid dynamic(CFD) was used to simulate methane emission in underground coal mine [31].
As early as the 1996s, researchers have put forward methods to forecast gas emission associated with disturbed and undisturbed longwall faces [32].
With the rapid development of computer technology, in recent years, the numerical simulations were widely used to predict the gas emission.
In order to predicting gas emission quantity precisely, time series analysis on the strength of the Gaussian process regression model was used to gas emission prediction [33]. In study [34], directing at the steeply inclined and extremely thick coal seams, a new method which employed numerical simulation was applied to forecasting gas emission quantity. The issue related gas emission in multifarious geospatial context was analyzed by [35].
Some researchers used several kinds of mathematical models to predict and analyze gas emission simultaneously. Wei et al. focused on the gas emission prediction which based on grey prediction model, new information model as well as metabolism model and compared the results of the three prediction models [36]. Jing et al. used model GM(1,1) of grey and one element linear regression forecasting gas emission simultaneously and conclusions showed that the former has greater precision by contrast [30].
In this study, one improved RBF neutral network model of gas emissions from underground coal mine of China's Shanxi Province is applied to forecast. The analysis included six main affecting factors of gas emissions (coal seam thickness, coal seam spacing, coal seam depth, coal seam gas content, daily production, and daily progress). Processing these factors, a tool used in prediction which associate with gas emission model was built by the artificial neural network. Predictions of gas emission were appeared in this paper and the prediction accuracy was also discussed. Moreover, the paper compared predicted values with actual values.

RBF neural network
RBF neural network is a model based on Cover which can use primary function approximating arbitrary function.
where X = ( 1 , 2 , … , ) ∈ , and represent input vector, output vector and NO. i node, respectively. is the centre and express NO. i primary function.
represent weight between hidden layer and output layer and i as well as j express NO. i of hidden layer and NO. j node of output layer.‖•‖ is Euclidean norm. N is the number of centers and hidden layer node. (•) is primary function of hidden layer.
To solve output vector , parameters in the Eq. (1) should be confirmed which are , and (•) .
The center of RBF neural network can be determined by means of K-means algorithm. It is considering that elect center can simplify network. Thus, the data which is selected as RBF neural network center should reduce number of element in hidden layer immensely.
Confirming radius should guarantee the space of training sample that can be contained by the set of acceptance region of RBF unit. The general method for determining and is employing K-means algorithm, as shown in Eq. (2).
Then using linear least square method adjust weight between the hidden layer and output layer through Eq. (3)(4).
It is a common practice to consider Gaussian function as (•) , as shown in Eq. (5).
where X = ( 1 , 2 , … , ) represent input vector and is NO. i perceptive variate which defines width. In this equation express center and subscript i represent NO.i primary function. N is the number of nodes in hidden layer.
Eventually, the output vector can be ciphered out though Eq. (6)

Grey prediction model
The grey prediction model is to process the seemingly irregular data column into a regular data column through a certain method. Therefore, the grey prediction model is to generate a new sequence and also to generate a sequence model. Modified grey forecasting model GM(1,1) is a valid model of bating randomness of sample data and enhancing accuracy in forecasting gas emission quantity. The first step is to acquire data of factors that can influence gas emission quantity.
By means of computing logarithmic [10] is an eminent way to make data more smoother, for improving accuracy of prediction. The algorithm is shown as below. There are x groups training samples and y groups predicted samples, compute logarithmic of these x+y groups of samples.
Take gas emission quantity (0) for example: Then obtaining x+y groups samples respectively are (0) (1), (0) (2), … (0) (6), (0) (7) . Among these samples, Secondly, a grey predicted model will be built. As the purpose for the model is dealing the stochastic data and making them regular. The most familiar method to establish grey system model is accumulation.

Modified RBF neural network
Improved RBF Neural Network Structure is shown in Fig.1.
(1) To determine δ the width of the Gaussian function, set a variable A(l), store the sum of heterogeneous outputs, and set a variable B(l) to count the heterogeneous samples, where l, the number of classes is represented.
(2) With ) , 1 1 y x ( as the first sequence, a network is established, and there is only one hidden neuron node in the network. Let 1 c is the center of the hidden layer node, and the weight of the hidden layer node to the output layer is: (3) For the second sequence ) , (x 2 2 y , calculate the distance between 2 x and 1 c : , then 1 c is the nearest neighbor clustering of 2 x , and let c is the hidden node center. A neuron node is added to the hidden layer of step (2), and the weight from the node to the output layer is Let the output of the i node of the hidden layer be: 2 2 ( ) exp( ) The network output is: The objective function is: Adjust the weights w ,  , and  to obtain the increment factor by the gradient descent method, where: The iteration formula to get weights and biases is:

Modeling and prediction of improved grey RBF neural network model
The modeling and prediction steps of the improved grey RBF neural network model are as follows: (1) Group x is the training sample and group y is the prediction sample.

Results and Discussion
In order to test the prediction effect of the model, this paper uses 300 sets of gas data from a coal mine in Shanxi as shown in Table 1. Among them, , respectively, represent the coal seam depth, coal seam thickness, coal seam gas content, coal seam spacing, daily progress, daily output, and gas emission. As mentioned in the previous chapters, these six factors are the main influencing factors based on the research results of previous researchers. Therefore, this article will no longer find the main factors through some methods.
The first 275 groups of 1 to 275 groups are taken as training samples, and the last 25 groups of 276 to 300 groups are used as prediction samples to check the prediction accuracy. Using MATLAB 7.8, write programs to build RBF neural network models, grey RBF neural network models, and improved grey RBF neural network models. These three models are used to make predictions respectively. The predicted values are compared with the actual values, and the relative errors of the three models are calculated for analysis and comparison.

RBF neural network model prediction
The input vector of the RBF neural network model is the six main factors affecting the gas emission amount, and the output vector is the gas emission amount. The modeling and prediction steps are as follows: (1) Take the first 275 sets of training samples x as the target vector; (2) Input the input vector and the target vector into the RBF neural network model to learn and train; (3 ) The last 25 sets of prediction samples   6  5  4  3  2  1   ,  ,  ,  ,  , x x x x x x are input into the trained RBF neural network model, and the prediction value is calculated; (4) Finally, we can calculate the relative error. Figure 4 is the comparison between the predicted and actual values of the model, and Figure 5 is the relative error of the model.

Grey RBF neural network model prediction
The grey RBF neural network model combines the GM (1,1) model with the RBF neural network model. The input layer and the output layer are six and two neuron nodes, respectively. The modeling and prediction steps are as follows: (1) The first 275 sets of training samples , which is used as the input vector of the RBF neural network model; (2) The first 275 sets of training samples (6) Subtraction: x is the final predicted value; (7) Find the relative error. Figure 6 is the comparison between the predicted value and the actual value of the grey RBF neural network model, and Figure 7 is the relative error of the model.

3 Improved grey RBF neural network model prediction
Follow the steps to build an improved grey RBF neural network model and make predictions. The modeling and prediction steps are as follows: (1) The first 275 groups of training samples 7  6  5  4  3  2  1   ,  ,  ,  ,  , , are log processed to obtain the corresponding number series . Logarithmic processing of the last 25 groups of prediction samples 7 x of the last 25 groups does not perform logarithmic processing; (2) The sequence obtained by the first 275 logarithmic processing in (1) is used to accumulate a generated sequence (1) (1) (1) (1), (2), , , which is used as the input vector of the improved RBF neural network model; (3) Then we can bring ,which is Obtained by logarithmic processing before 275 groups in step (1), into GM(1,1) and calculate ) 7 ( ), 6 ( is the target vector of the improved RBF neural network model; (4) A cumulative operation is performed on the ) 6 ( ),..., 2 ( ), 1 ( obtained by the last 25 groups of logarithmic processing to obtain a generated sequence (1) (1) (1) (1), (2), , (1), (2), , () x Q t e = , (0) () Qt is the final predicted value; (8) Finding the relative error.

Analysis and comparison of prediction results of three models
Compare the relative errors of the above three models, as shown in Figure 8.
As can be seen from Figure 8, the relative errors of the RBF neural network model, the grey RBF neural network model, and the improved grey RBF neural network model become smaller in order, and the model's prediction accuracy improves in turn, indicating the grey GM (1,1) model The introduction of the method weakens the randomness of the sample, which improves the prediction accuracy of the grey RBF neural network model. It also shows that after introducing the improved GM (1,1) model and the improved RBF neural network model, compared with the grey RBF neural network model, On the one hand, the sample data becomes smoother, which further weakens the sample randomness. On the other hand, the RBF neural network model has been improved, and the model performance has been improved. Therefore, the improved grey RBF neural network model further improves the prediction accuracy. Among the three models, the improved grey RBF neural network model has the highest prediction accuracy. Besides, the relative errors of the improved grey RBF neural network model are mostly within 5%, and the other few are also basically within 10%.
As can be seen from Figure 6 and 7, the relative errors of the RBF neural network model, the grey RBF neural network model, and the improved grey RBF neural network model become smaller in order, and the model's prediction accuracy improves in turn, indicating the grey GM (1,1) model The introduction of the method weakens the randomness of the sample, which improves the prediction accuracy of the grey RBF neural network model. It also shows that after introducing the improved GM (1,1) model and the improved RBF neural network model, compared with the grey RBF neural network model, On the one hand, the sample data becomes smoother, which further weakens the sample randomness. On the other hand, the RBF neural network model has been improved, and the model performance has been improved. Therefore, the improved grey RBF neural network model further improves the prediction accuracy. Among the three models, the improved grey RBF neural network model has the highest prediction accuracy. Besides, the relative errors of the improved grey RBF neural network model are mostly within 5%, and the other few are also basically within 10%.