Game Theory and an Improved Maximum Entropy-Attribute Measure Interval Model for Predicting Rockburst Intensity

Abstract

To improve the accuracy of predicting rockburst intensity, game theory and an improved maximum entropy-attribute measure interval model were established. First, by studying the mechanism of rockburst and typical cases, rock uniaxial compressive strength σc, rock compression-tension ratio σc/σt, rock shear compression ratio σθ/σc, rock elastic deformation coefficient Wet, and rock integrity coefficient Kv were selected as indexes for predicting rockburst intensity. Second, by combining the maximum entropy principle with the attribute measure interval and using the minimum distance Di−k between sample and class as the guide, the entropy solution of the attribute measure was obtained, which eliminates the greyness and ambiguity of the rockburst indexes to the maximum extent. Third, using the compromise coefficient to integrate the comprehensive attribute measure, which avoids the ambiguity about the number of attribute measure intervals. Fourth, from the essence of measurement theory, the Euclidean distance formula was used to improve the attribute identification mode, which overcomes the effect of the confidence coefficient taking on the results. Moreover, in order to balance the shortcomings of the subjective weights of the Analytic Hierarchy Process and the objective weights of the CRITIC method, game theory was used for the combined weights, which balances experts’ experience and the amount of data information. Finally, 20 sets of typical cases for rockburst in the world were selected as samples. On the one hand, the reasonableness of the combined weights of indexes was analyzed; on the other hand, the results of this paper’s model were compared with the three analytical models for predicting rockburst, and this paper’s model had the lowest number of misjudged samples and an accuracy rate of 80%, which was better than other models, verifying the accuracy and applicability.