Rock burst hazard evaluation of coal mining face based on a Gaussian mixture model
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摘要:目的
深入了解声发射或微震能量分布所蕴含的概率学信息，对于工作面回采过程中的冲击危险性评价具有重要意义。
方法以陕西大佛寺煤矿4号煤层40111工作面作为工程背景，运用物理相似模拟实验、理论分析、现场监测等相关方法进行分析，研究了声发射监测数据在回采过程中的演化规律，阐明了声发射能量概率分布呈现波动性的物理意义，提出了基于高斯混合模型(Gaussian minture model，GMM)及置信区间的冲击危险性评价指标模型，并由现场微震数据进行验证。
结果和结论结果表明：回采过程中上覆岩层周期性垮落并伴随声发射能量的集中释放。总能量的概率密度函数呈现多自由度的非对称分布，通过对比残差平方和等多项拟合效果指标，确定高斯混合模型为最佳拟合模型。基于EM(expectation maximization)算法的GMM聚类分析，将声发射事件总能量分布划分为两类：高频低能型和低频高能型，其中低频高能型与冲击事件的突发性和高能量破坏特征一致。依据概率−能量梯度变化特征，对工作面开采过程中冲击危险性进行了评估。研究成果为采煤工作面冲击危险性评价提供了概率学上的创新思路，具有在冲击地压监测预警及后续防治中的潜在应用价值。
Abstract:ObjectiveDeep insights into the probabilistic information contained in the energy distribution of acoustic emission (AE) or microseismic events are significant for the rock burst hazard evaluation of coal mining face.
MethodsThis study investigated No.40111 mining face of the No.4 coal seam at the Dafosi Coal Mine in Shaanxi Province. Using physical simulation experiments with similar materials, theoretical analysis, and on-site monitoring, this study investigated the evolutionary patterns of AE monitoring data during coal mining and illustrated the physical meaning of fluctuations in the probability distribution of AE energy. Accordingly, this study proposed an index model for the rock burst hazard evaluation based on a Gaussian mixture model (GMM) and confidence intervals and validated the proposed model based on field microseismic data.
Results and ConclusionsThe results indicate that the overlying strata collapsed periodically during mining, with the collapse being accompanied by intensive release of AE energy. The probability density function (PDF) of the total energy exhibited a multi-degree-of-freedom asymmetric distribution. The comparison of multiple indices of fitting effects, such as the residual sum of squares, reveals that the GMM is the optimal fitting model. As indicated by the GMM clustering analysis based on the expectation-maximization (EM) algorithm, the total energy distribution of AE events can be categorized into two types, namely the high-frequency/low-energy and low-frequency/high-energy AE signals, with the latter type consistent with the sudden occurrence and high-energy destruction of rock burst events. This study conducted a rock burst hazard evaluation of the mining face based on the probability-energy gradient variations, providing a novel probabilistic approach for the rock burst hazard evaluation of coal mining face. The new assessment method based on probabilistic information has the potential to be applied in the monitoring, early warning, and subsequent prevention of rock bursts.
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图 2 地层柱状图及岩层模拟材料配比
Fig. 2 Stratigraphic column and ratio of materials for rock layer simulation
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图 4 40111工作面回采全过程声发射特征
Fig. 4 AE characteristics during the mining of the No.40111 mining face
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图 5 40111工作面第一次周期来压能量随时间变化
Fig. 5 Time-varying energy during the first periodic weighting of the No.40111 mining face
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图 6 40111工作面声发射能量概率分布规律
Fig. 6 Probability distribution pattern of the total energy of AE events in the No.40111 mining face
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图 7 单一分布函数拟合效果对比
Fig. 7 Comparison of fitting effects of single distribution functions
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图 10 回采全过程声发射总能量概率密度分布特征
Fig. 10 Probability density distribution of the total energy of AE events during mining
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图 11 基于声发射事件总能量的冲击危险性评价
Fig. 11 Rock burst risk assessment based on the total energy of AE events
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图 12 基于现场微震事件能量的冲击危险性评价
Fig. 12 Rock burst risk assessment based on the energy of field microseismic events
表 1 工作面参数
Table 1 Parameters of the mining face
煤层 工作面名称 走向长/m 斜长/m 采高/m 4上 41106 1810 190 3.0 4号 40111 1860 220 11.5 
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表 2 声发射监测设定参数
Table 2 Parameters of AE monitoring
参数 参数值 采集频率/MHz 10 参数间隔/μs 2 000 峰值间隔/μs 1000 波形门阀/dB 45 参数门阀/dB 40 滤波频率/kHz 20~100
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表 3 典型单一分布的拟合效果指标值
Table 3 Fitting effect index values of the typical single distribution
分布类型 ESS/10−9 ERMS/10−6 R Ra 威布尔分布 2.66 5.16 0.45 0.44 t分布 1.49 3.86 0.69 0.69 广义极值分布 1.33 3.64 0.73 0.72 正态分布 2.85 5.34 0.41 0.41
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表 4 5阶高斯混合模型的参数值
Table 4 Parameter values of the fifth-order Gaussian mixture model
阶数 ai/10−6 bi ci 1 1.831 −1.0510 0.1570 2 3.436 −0.9350 0.1787 3 7.856 −1.1460 0.2105 4 0.339 − 0.7118 0.1311 5 6.229 − 0.6419 1.0400
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表 5 2阶与5阶高斯混合模型的拟合效果指标值
Table 5 Fitting effect index values of the 2-component and 5-component Gaussian mixture models
模型 ESS/10−10 ERMS/10−6 R Ra 2阶 8.91 3.13 0.79 0.77 5阶 4.49 2.29 0.90 0.90
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表 6 二维高斯混合模型的参数
Table 6 Parameters of the two-dimensional Gaussian mixture model
类别 ${\textit{π}} $ $ {\text{μ}} $/104 $ {\boldsymbol{\varSigma}} $/108 1 0.7374 $ \left[ {\begin{array}{*{20}{c}} {0.153\;3} \\ {3.126\;1} \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} {0.000\;1}&{0.004\;7} \\ {0.004\;7}&{1.354\;6} \end{array}} \right] $ 2 0.2626 $ \left[ {\begin{array}{*{20}{c}} {0.140\;7} \\ {6.884\;9} \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} {0}&{ - 0.002\;7} \\ { - 0.002\;7}&{7.388\;1} \end{array}} \right] $
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表 7 二维高斯混合模型的参数
Table 7 Parameters of the two-dimensional Gaussian mixture model
类别 $ \textit{π} $ ${\text{μ}} $/103 $ {\boldsymbol{\varSigma}} $/105 1 0.9686 $ \left[ {\begin{array}{*{20}{c}} {0.860\;1} \\ {1.126\;7} \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} {0.287\;8}&{0.371\;3} \\ {0.371\;3}&{3.879\;2} \end{array}} \right] $ 2 0.0314 $ \left[ {\begin{array}{*{20}{c}} {1.184\;2} \\ {3.555\;5} \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} {0.097\;2}&{ - 0.172\;7} \\ { - 0.172\;7}&{9.316\;1} \end{array}} \right] $
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