Combination weighting prediction model and application of rock burst disaster based on game theory

doi:10.16265/j.cnki.issn1003-3033.2022.07.0620

Abstract

Abstract:

In order to solve the problems of poor rationality of combination weighting and poor applicability of maximum membership degree principle in rock burst classification prediction, a set pair analysis and prediction model based on game theory combination weighting is proposed. Firstly, the stress coefficient σ_θ/σ_c, brittleness coefficientσ_c/σ_t and elastic energy index W_et were selected as prediction indicators to establish the rock burst classification prediction index system. Secondly, game theory was used to optimize the combination weights obtained by the Delphi method and entropy weight method. Combined with the set pair analysis theory, the combination weights set pair analysis model of rock burst classification prediction is established. Then, the maximum membership principle and the confidence criterion were used to determine the level of rock burst disaster. Finally, the reliability of the model was verified with 15 sets of rock burst samples, and the rock burst intensity in deep mining of Jinchuan No.2 mine was predicted. The results show that the model improves the scientific rationality of combination weighting and grade determination. The prediction accuracy rate is 87%. The rock burst intensity grade of the 850 m horizontal middle section of Jinchuan No.2 mine is mild to moderate, consistent with the actual situation.

Key words: rock burst prediction, game theory, combination weight, set pair analysis, maximum membership principle, confidence criterion

ZHOU Yinghao, WANG Wenjie, LU Xizhou, WANG Kangwei. Combination weighting prediction model and application of rock burst disaster based on game theory[J]. China Safety Science Journal, 2022, 32(7): 105-112.

Figures/Tables 5

Tab.1

Tab.2

Rock burst grade and standard threshold

岩爆等级	标准阈值
Ⅰ级	$< s 1$	$≥ s 1$
Ⅱ级	$[s 1, s 2)$	$[s 2, s 1)$
Ⅲ级	$[s 2, s 3)$	$[s 3, s 2)$
Ⅳ级	$≥ s 3$	$< s 3$

Tab.2

Tab.3

Tab.4

Tab.5

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岩爆等级	σ_θ/σ_c	σ_c/σ_t	W_et
Ⅰ级	<0.3	≥40.0	<2.0
Ⅱ级	[0.3,0.5)	[26.7,40.0)	[2.0,3.5)
Ⅲ级	[0.5,0.7)	[14.5,26.7)	[3.5,5.0)
Ⅳ级	≥0.7	<14.5	≥5.0

样本编号	σ_θ/σ_c	σ_c/σ_t	W_et	实际等级
1	0.41	29.70	7.30	Ⅱ
2	0.11	31.20	7.40	Ⅰ
3	0.53	15.00	9.00	Ⅲ~Ⅳ
4	0.35	20.50	5.00	Ⅲ
5	0.55	11.10	3.97	Ⅲ
6	0.35	22.70	3.31	Ⅱ
7	0.72	13.90	9.05	Ⅳ
8	0.64	14.40	7.74	Ⅳ
9	0.44	26.90	5.50	Ⅱ
10	0.52	18.60	4.16	Ⅲ
11	0.27	21.70	5.00	Ⅲ
12	0.77	17.50	5.50	Ⅲ~Ⅳ
13	0.32	21.70	5.00	Ⅲ
14	0.82	18.50	3.80	Ⅲ~Ⅳ
15	0.42	21.70	5.00	Ⅲ

工程样本	f₁	f₂	f₃	f₄	α	本文方法	改进云模型^[8]	改进的灰评估模型^[6]	功效系数法^[7]	RBF-AR 模型^[15]	实际等级
1	0.000 0	0.563 5	0.106 4	0.330 1	0.63	Ⅱ	—	Ⅱ	Ⅲ	Ⅱ	Ⅱ
2	0.361 5	0.256 4	0.052 0	0.330 1	0.23	Ⅱ	—	Ⅰ	Ⅰ	Ⅰ	Ⅰ
3	0.000 0	0.126 5	0.260 3	0.613 2	0.93	Ⅳ	Ⅳ	Ⅲ~Ⅳ	Ⅲ	Ⅲ	Ⅲ~Ⅳ
4	0.180 8	0.180 8	0.303 3	0.335 2	0.19	Ⅲ	Ⅲ	Ⅱ	Ⅲ	Ⅱ	Ⅲ
5	0.000 0	0.152 0	0.539 6	0.308 4	0.63	Ⅲ	Ⅲ	—	—	—	Ⅲ
6	0.180 8	0.438 4	0.380 8	0.000 0	0.33	Ⅱ	—	—	—	Ⅱ	Ⅱ
7	0.000 0	0.000 0	0.000 0	1.000 0	—	Ⅳ	—	—	—	Ⅳ	Ⅳ
8	0.000 0	0.000 0	0.216 9	0.783 1	1.64	Ⅳ	—	—	—	Ⅳ	Ⅳ
9	0.000 0	0.441 6	0.228 3	0.330 1	0.40	Ⅲ	—	Ⅱ	Ⅱ	Ⅱ	Ⅱ
10	0.000 0	0.164 4	0.734 5	0.101 1	1.96	Ⅲ	—	—	—	Ⅲ	Ⅲ
工程样本	f₁	f₂	f₃	f₄	α	本文方法	改进云模型^[8]	改进的灰评估模型^[6]	功效系数法^[7]	RBF-AR 模型^[15]	实际等级
11	0.361 5	0.026 6	0.281 8	0.330 1	0.23	Ⅲ	Ⅲ	Ⅲ	Ⅱ	Ⅲ	Ⅲ
12	0.000 0	0.000 0	0.151 7	0.848 3	2.63	Ⅳ	Ⅳ	Ⅳ	Ⅲ	Ⅳ	Ⅲ~Ⅳ
13	0.289 2	0.098 9	0.281 8	0.330 1	0.18	Ⅲ	Ⅲ	Ⅲ	Ⅲ	Ⅲ	Ⅲ
14	0.000 0	0.099 0	0.433 3	0.467 7	0.33	Ⅳ	Ⅲ	Ⅲ~Ⅳ	Ⅳ	Ⅱ	Ⅲ~Ⅳ
15	0.000 0	0.357 4	0.312 5	0.330 1	0.22	Ⅲ	Ⅲ	Ⅲ	Ⅱ	Ⅲ	Ⅲ

岩性	σ_θ/MPa	σ_c/MPa	σ_t/MPa	σ_θ/σ_c	σ_c/σ_t	W_et	预测等级
大理岩	63.22	104.00	11.00	0.61	9.50	2.29	Ⅲ
二辉橄榄岩	63.22	114.70	7.00	0.55	16.40	3.47	Ⅲ
贫矿	63.22	133.90	11.90	0.47	11.30	2.55	Ⅱ
富矿	63.22	151.50	6.85	0.42	22.10	4.90	Ⅲ