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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

mathematical problems in engineering

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