岩爆灾害博弈论组合赋权预测模型及应用

doi:10.16265/j.cnki.issn1003-3033.2022.07.0620

摘要/Abstract

摘要：

为解决岩爆分级预测中组合赋权合理性以及最大隶属度评判原则适用性较差的问题,提出基于博弈论组合赋权的集对分析预测模型。首先,选取应力系数σ_θ/σ_c、脆性系数σ_c/σ_t、弹性能量指数W_et作为预测指标,建立岩爆分级预测指标体系;其次,应用博弈论对德尔菲法和熵权法得到的指标权重进行组合赋权优化,结合集对分析理论,建立岩爆分级预测的组合赋权集对分析模型;然后,综合使用最大隶属度原则和置信度准则判定岩爆等级;最后,以15组岩爆样本数据验证该模型的有效性,并预测金川二矿深部开采中的岩爆烈度。结果表明:该模型可提高组合赋权及等级判定的科学合理性,预测准确率为87%;金川二矿850 m水平中段岩爆烈度等级为轻微~中等,与实际情况相符。

关键词: 岩爆预测, 博弈论, 组合赋权, 集对分析, 最大隶属度原则, 置信度准则

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

周英豪, 王文杰, 卢西洲, 王康伟. 岩爆灾害博弈论组合赋权预测模型及应用[J]. 中国安全科学学报, 2022, 32(7): 105-112.

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.

图/表 5

表1

表2

岩爆等级与标准阈值

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	$≥ s 3$	$< s 3$

表2

表3

表4

表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