基于SAA-GRNN优化模型的厚松散层条件下概率积分法参数求解

doi:10.16265/j.cnki.issn1003-3033.2026.05.0204

中国安全科学学报 ›› 2026, Vol. 36 ›› Issue (5): 18-26.doi: 10.16265/j.cnki.issn1003-3033.2026.05.0204

基于SAA-GRNN优化模型的厚松散层条件下概率积分法参数求解

张建国¹^,²^,³(), 王文唱¹^,^**(), 任连伟⁴, 邹友峰⁵, 顿志林⁴

¹ 河南理工大学安全科学与工程学院, 河南焦作 454003
² 炼焦煤资源绿色开发全国重点实验室, 河南平顶山 467002
³ 中国平煤神马控股集团有限公司, 河南平顶山 467002
⁴ 河南理工大学土木工程学院, 河南焦作 454003
⁵ 河南理工大学测绘与国土信息工程学院, 河南焦作 454003

收稿日期:2026-01-11 修回日期:2026-03-13 出版日期:2026-05-28
通信作者:
^** 王文唱(1996—),男,江苏徐州人,博士研究生,研究方向为采空区场地建设技术。E-mail:1269811881@qq.com。

作者简介:

张建国 (1963—),男,河南滑县人,博士,教授级高级工程师,博士生导师,主要从事煤矿灾害治理、瓦斯资源利用和煤矿智能化建设等方面的研究。E-mail:Zhangjg9681@163.com。

任连伟教授。

邹友峰教授。

顿志林教授。

基金资助:
国家自然科学基金联合基金重点项目资助(U23A20600); 河南省科技攻关项目(252102320335)

Parameter solution of probability integral method under condition of thick loose layer based on SAA-GRNN optimization model

Zhang Jianguo¹^,²^,³(), Wang Wenchang¹^,^**(), Ren Lianwei⁴, Zou Youfeng⁵, Dun Zhilin⁴

¹ College of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo Henan 454003, China
² State Key Laboratory of Coking Coal Resources Green Exploitation, Pingdingshan Henan 467002, China
³ China Pingmei Shenma Holding Group Co., Ltd., Pingdingshan Henan 467002, China
⁴ School of Civil Engineering, Henan Polytechnic University, Jiaozuo Henan 454003, China
⁵ School of Surveying and Land Information Engineering, Henan Polytechnic University, Jiaozuo Henan 454003, China

Received:2026-01-11 Revised:2026-03-13 Published:2026-05-28

摘要/Abstract

摘要：

为解决现有方法在求取厚松散层条件下采空区地表变形预测的概率积分法(PIM)参数时存在精度不高与适配性不足的问题,选取36组采煤工作面地表移动实测数据,通过系统聚类分析(HCA)、熵权法(EWM)及灰色关联度(GRD)分析,筛选采矿地质条件的核心指标,进而融合K折交叉验证和模拟退火算法(SAA)邻域扰动策略优化广义回归神经网络(GRNN)模型,构建SAA-GRNN优化模型,用于求取PIM参数,并以济宁地区45组厚松散层采煤工作面数据开展实例分析。结果表明:7项采矿地质条件指标可划分为3类,经筛选后得到开采厚度M、煤层倾角α、开采深度H、走向采动程度D₃/H和松散层厚度h共5项核心输入指标;SAA-GRNN优化模型的均方误差最大值不超过0.190 4,平均绝对误差最大值控制在0.133 9,平均绝对百分比误差最大值为0.153 6,R²值总体控制在0.8以上;同等条件下较误差反向传播(BP)神经网络模型和GRNN模型,求解误差均大幅度下降。

关键词: 模拟退火算法(SAA), 广义回归神经网络(GRNN), 厚松散层, 概率积分法(PIM), 参数求解

Abstract:

To address the problems of low accuracy and insufficient adaptability in existing methods for determining the parameters of PIM for predicting surface deformation prediction in goaf areas under thick unconsolidated layers, 36 sets of measured surface movement data from coal mining working faces were selected. The core indicators of mining-geological conditions were screened via Hierarchical Cluster Analysis (HCA), Entropy Weight Method(EWM) and Grey Relational Degree (GRD) analysis. Furthermore, the GRNN model was optimized by integrating K-fold cross-validation with the neighborhood perturbation strategy of SAA, and an SAA-GRNN optimization model was constructed for PIM parameter determination. A case study was conducted using 45 sets of data from coal mining working faces with thick unconsolidated layers in the Jining area. The results show that: seven mining-geological condition indicators can be classified into three categories, and five core input indicators were identified screening, namely mining thickness M, coal seam dip angle α, mining depth H, strike mining degree D₃/H, and unconsolidated layer thickness h. The maximum root-mean-squared error (RMSE) of SAA-GRNN model is no more than 0.190 4, the maximum mean absolute error (MAE) is controlled within 0.133 9, the maximum mean absolute percentage error (MAPE) is 0.153 6, and the overall coefficient of determination (R²) is generally above 0.8. Under the same conditions, the prediction errors are greatly reduced compared with those obtained using Back Propagation (BP) neural network and the conventional GRNN model.

Key words: simulated annealing algorithm (SAA), generalized regression neural network (GRNN), thick unconsolidated layer, probability integral method (PIM), parameter solution

中图分类号:

X936

张建国, 王文唱, 任连伟, 邹友峰, 顿志林. 基于SAA-GRNN优化模型的厚松散层条件下概率积分法参数求解[J]. 中国安全科学学报, 2026, 36(5): 18-26.

Zhang Jianguo, Wang Wenchang, Ren Lianwei, Zou Youfeng, Dun Zhilin. Parameter solution of probability integral method under condition of thick loose layer based on SAA-GRNN optimization model[J]. China Safety Science Journal, 2026, 36(5): 18-26.

图/表 10

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工作面序号	采矿地质条件							PIM参数
工作面序号	f	M/m	α/(°)	H/m	D₃/H	D₁/H	h/m	q	b	tanβ	θ/(°)
1	5.2	2.1	19	110	5.27	1.23	50	0.88	0.3	2	80
2	6	2.4	12	280	2.46	0.46	17.4	0.655	0.282	1.99	86
3	3.2	2.1	30	60.5	6.58	1.98	10	0.66	0.2	1.55	62
︙	︙	︙	︙	︙	︙	︙	︙	︙	︙	︙	︙
34	2.315	3.9	1	112.5	24.36	2.62	30	0.513	0.24	1.95	61.4
35	2.45	1.94	9.5	181	1.66	0.56	110	0.86	0.3	1.8	84
36	5	2	34	114.5	1.66	0.54	4.5	0.63	0.24	1.6	65

计算结果	f	M/m	α/(°)	H/m	D₃/H	D₁/H	h/m
信息熵值	0.966	0.891	0.901	0.908	0.859	0.885	0.829
信息效用值	0.034	0.109	0.099	0.092	0.141	0.115	0.171
权重	0.045	0.144	0.130	0.121	0.185	0.151	0.225

参数	f	M/m	α/(°)	H/m	D₃/H	D₁/H	h/m
q	0.898	0.836	0.820	0.841	0.832	0.818	0.780
b	0.873	0.858	0.799	0.828	0.826	0.809	0.786
tanβ	0.869	0.853	0.790	0.840	0.834	0.815	0.776
θ/(°)	0.900	0.849	0.814	0.849	0.832	0.821	0.784
加权关联度	0.159	0.488	0.419	0.407	0.616	0.491	0.702

工作面序号	采矿地质条件					PIM参数
工作面序号	M/m	α/(°)	H/m	D₃/H	h/m	q	b	tanβ	θ_k
1	7.4	4	548	1.69	155	0.9	0.25	1.6	0.6
2	3.2	11	490	1.72	300	0.86	0.3	2.2	0.3
3	8.7	6	418	2.49	202	0.82	0.33	2.2	1.5
︙	︙	︙	︙	︙	︙	︙	︙	︙	︙
43	3.25	6	1 010	1.29	212	0.82	0.28	1.85	0.5
44	8.72	6	437	6.44	200	0.83	0.27	2.2	0.5
45	5.28	12	450	0.89	400	1	0.28	1.8	0.6

测试次数	BP			GRNN			SAA-GRNN
测试次数	RMSE	MAE	MAPE	RMSE	MAE	MAPE	RMSE	MAE	MAPE
1	0.301 2	0.196 1	0.320 5	0.124 6	0.095 3	0.122 3	0.034 5	0.028 5	0.074 9
2	0.209 8	0.162 4	0.174 6	0.301 2	0.211 8	0.222 2	0.190 4	0.133 9	0.153 6
3	0.234 3	0.168 5	0.114 3	0.213 5	0.152 2	0.106 0	0.160 8	0.091 0	0.051 5
4	0.159 4	0.144 8	0.210 6	0.114 9	0.079 4	0.082 2	0.042 8	0.033 9	0.048 5
5	0.177 1	0.139 9	0.153 9	0.155 3	0.125 5	0.134 4	0.061 9	0.053 2	0.087 7
6	0.076 4	0.058 7	0.060 0	0.092 0	0.059 2	0.057 6	0.024 8	0.021 0	0.033 1
7	0.407 9	0.226 9	0.321 6	0.063 8	0.051 2	0.051 3	0.054 7	0.048 1	0.063 8

基于SAA-GRNN优化模型的厚松散层条件下概率积分法参数求解

Parameter solution of probability integral method under condition of thick loose layer based on SAA-GRNN optimization model

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