Mathematical Problems in Engineering

Volume 2017 (2017), Article ID 7189803, 11 pages

https://doi.org/10.1155/2017/7189803

## A Fisher’s Criterion-Based Linear Discriminant Analysis for Predicting the Critical Values of Coal and Gas Outbursts Using the Initial Gas Flow in a Borehole

^{1}Key Laboratory of Coal Methane and Fire Control, Ministry of Education, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China^{2}School of Safety Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China

Correspondence should be addressed to Xiaowei Li; nc.ude.tmuc@iewoaixil

Received 28 May 2016; Revised 18 August 2016; Accepted 10 October 2016; Published 11 May 2017

Academic Editor: Luis M. López-Ochoa

Copyright © 2017 Xiaowei Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The risk of coal and gas outbursts can be predicted using a method that is linear and continuous and based on the initial gas flow in the borehole (IGFB); this method is significantly superior to the traditional point prediction method. Acquiring accurate critical values is the key to ensuring accurate predictions. Based on ideal rock cross-cut coal uncovering model, the IGFB measurement device was developed. The present study measured the data of the initial gas flow over 3 min in a 1 m long borehole with a diameter of 42 mm in the laboratory. A total of 48 sets of data were obtained. These data were fuzzy and chaotic. Fisher’s discrimination method was able to transform these spatial data, which were multidimensional due to the factors influencing the IGFB, into a one-dimensional function and determine its critical value. Then, by processing the data into a normal distribution, the critical values of the outbursts were analyzed using linear discriminant analysis with Fisher’s criterion. The weak and strong outbursts had critical values of 36.63 L and 80.85 L, respectively, and the accuracy of the back-discriminant analysis for the weak and strong outbursts was 94.74% and 92.86%, respectively. Eight outburst tests were simulated in the laboratory, the reverse verification accuracy was 100%, and the accuracy of the critical value was verified.

#### 1. Introduction

Coal is the main nonrenewable energy resource consumed in China. Due to the advancement of coal mining in recent years, mining depths have reached 1,300 m and are estimated to reach 1,500 m within the next 20 years [1, 2]. As mining depth increases, ground stress as well as the pressure and content of gas in coal seams will increase, causing a corresponding increase in the outburst risk in coal seams. Outburst prediction is an important aspect of outburst coal seam mining to prevent accidents. For example, a serious accident occurred in 2011 in Sizhuang coal mine of Yunnan in China; the accident resulted in 43 deaths. Therefore, seam-mining countries around the world have all conducted extensive studies on outburst prediction. Outburst prediction methods can be divided into two categories: a single or comprehensive index and applying a statistical mathematical model.

In terms of the single or comprehensive index, the former Soviet Union proposed a -based comprehensive index method and a -based comprehensive index method [3] that were applied successively. Later, the Chinese researcher Wang [4] proposed a four-factor comprehensive index method involving the value. Based on this method, the Fushun Institute of Coal Science [5, 6] of China proposed a comprehensive [6] index method involving the and values. Subsequently, the coal research and development institutes in China proposed a method involving the drill cutting desorption indexes and . Jiang [7, 8] proposed a method based on the initial gas expansion energy released (IGEER). In addition, other countries have used index methods involving [9] and [10]. All of the aforementioned methods measure the outburst risk at a certain point and use one point to represent the whole coal mass; in other words, they assume that the outburst risk in the predicted area is consistent with the outburst risk at the measured point. However, a coal mass is not a homogeneous body, making point prediction greatly limited.

Many factors can influence outburst prediction. Some researchers have used mathematical models to improve the accuracy of outburst prediction. Hao and Yuan [11], Tian and Zhou [12], and Qu et al. [13] studied the neural network model of outburst prediction. These methods are trained to capture the correlation between the outburst factors and the prominent outburst. To improve the accuracy of outburst prediction, Zhu et al. [14] combined principal component analysis (PCA) with the neural network. Zhang and Li [15] studied pattern recognition and the possibility prediction of coal and gas outbursts. With eight factors as the main discriminant, the pattern recognition method was used to perform possibility prediction of coal outbursts. Wang [16] studied the coal and gas outburst prediction based on fuzzy matter-element analysis. Guo et al. [17] studied the prediction method of coal and gas outbursts using the analytic hierarchy process and fuzzy comprehensive evaluation. The prediction of coal and gas outbursts was also studied using the analytic hierarchy process (AHP) and fuzzy comprehensive evaluation. In the prediction method, AHP was used to confirm the weights of the coal and gas outburst factors; the judgment matrix of each factor was constructed by membership functions; and the prediction model of coal and gas outbursts was established using the fuzzy comprehensive evaluation method. Zhao and Tan [18] studied the premonitory time series prediction of coal and gas outbursts based on chaos theory. According to the chaos characteristic of outburst prediction data, the outburst prediction model was established using the method of chaotic prediction. In addition, Peng and Wang [19] studied the improved analytic hierarchy process for coal and gas outburst prediction. Because the initial gas flow in the borehole (IGFB) is affected by many factors, and some of these factors are connected with each other while others are relatively independent, the IGFB are fuzzy and chaotic. These studies can be used as valuable references. However, the critical value of an outburst is usually measured under the simplest conditions. In the same way, research on the IGFB has discarded some minor factors. The fuzziness and chaos are relatively less. In addition, these methods are based on the results of point predictions and share the same disadvantages. Therefore, there are differences between research into the IGFB and the references.

The method established in the present study, which is based on the IGFB, is a linear prediction method. The mechanism of this method is as follows: during drilling, the volume of gas released from the borehole is continuously measured. Through data processing, the measured volume is converted to the total volume of gas released from a 1 m long borehole with a diameter of 42 mm within 3 min. The larger this flow is, the higher the outburst risk of the coal seam is. This method can continuously predict the outburst risk of coal seams passed during the drilling process. Therefore, this is a neoteric prediction method.

Wang and Yu [20–22] first analyzed such indexes in terms of the volume of drill cuttings and the volume of gas emitted from the borehole and found that the measured volume of gas emitted from the borehole exhibited fractal dimension characteristics. Based on Wang and Yu’s study, Han [23], Qin et al. [24], Nie [25, 26], and Yuan [27] studied the borehole wall and the emission pattern of coal cuttings and gas during the drilling process. Based on the aforementioned studies, Wu [28] completed comprehensive laboratory and field application studies on the outburst risk prediction during the tunneling of soft coal seams and roadways using the continuous flow method; however, because of the complexity of field studies on outbursts, Wu obtained only the safety value of IGFB (32.30 L).

These studies show that IGFB is influenced by many factors, such as the degree of coal deformation, the gas permeability coefficient, the borehole diameter, the gas pressure, and the radius in front of the drill bit. Therefore, IGFB also has the characteristics of fuzziness and chaos. However, in studying the critical value of IGFB, we can change some influencing factors to build a research model under the most dangerous conditions. This model is an ideal rock cross-cut coal uncovering model. The effect of coal weight is neglected in this model. If the barrier layer is assumed to be dense and hard rock, then the amount of gas in the soft coal that leaks through the barrier into the tunnel is approximately zero. Then, the gas pressure in various locations in the soft coal remains at the initial pressure. Thus, regardless of the length of the driving cycle footage, the surface gas pressure in the exposed coal body after uncovering is equal to the initial gas pressure, and the outburst risk is at its highest level. Ideal rock cross-cut coal uncovering occurs under this condition, as shown in Figure 1. This condition also has the highest probability of outburst; using this outburst risk as the basis for prediction, the conditions are more stringent, thus achieving a higher safety margin. All of the tests in this study were conducted with this condition.