Prediction of water inrush source of coal seam floor based on Fisher discriminant model
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摘要: 针对传统矿井突水水源判别方法对矿井煤层底板突水水源判别准确率低的问题，以城郊煤矿二2煤层为例，建立了Fisher矿井底板突水水源判别分析模型。城郊煤矿二2煤层具有突水威胁的含水层分别为煤系砂岩含水层和底板太原组岩溶裂隙含水层，考虑到水化学离子的重要性及数据的有效性，采用煤层底板有突水威胁的砂岩水、太灰水和混合水3类水样分析资料作为样本，选取Ca2+，Mg2+，Na++K+，HCO3−，Cl−，SO42−这6种离子含量和矿化度作为矿井突水水源判别分析的变量。利用SPSS软件求得2个典型Fisher判别函数（第1和第2判别函数），计算出典型判别函数在3类水样类别的中心值，通过比较待判水样函数值与这3类水样类别的中心值距离即可判别样本归属哪一类别。利用回代估计法对Fisher矿井底板突水水源判别分析模型进行检验，结果表明：该模型的判别正确率达93.3%，判别结果可信度高。利用该模型对城郊煤矿二2煤层10个已知水样进行分类，得出10个水样的判别结果与实际情况吻合，判别正确率为100%。Abstract: In order to solve the problems of low accuracy mine water inrush source discriminant method for mine floor water inrush source discrimination, taking the second level coal seam of suburban coal mine as an example, the Fisher mine floor water inrush source discriminant model is established. The aquifers with the threat of water inrush in the second level coal seam of suburban coal mine are the coal-measure sandstone aquifer and the karst fractured aquifer of the Taiyuan Formation in the floor. Considering the importance of hydrochemical ions and the validity of the data, three kinds of water quality analysis data of sandstone water, limestone water and mixed water with water inrush threat in the coal seam floor are used as samples. The content and mineralization of six kinds of ions, Ca2+, Mg2+, Na++K+, HCO3−, Cl− and SO42−, are selected as the discriminant analysis variables for the identification of mine inrush water sources. Two typical Fisher discriminant functions (the first and the second discriminant functions) are obtained by SPSS software. The central values of the typical discriminant functions in the three water quality groups are calculated. By comparing the distance between the function values of the water samples to be discriminated and the central values of the three water quality groups, it is able to determine which group the samples belong to. The back substitution estimation method is used to test the Fisher mine floor water inrush source discriminant model. The results show that the discriminant accuracy rate of the model is 93.3%, and the discriminant results are highly reliable. The model is used to classify 10 known water samples in the second level of suburban coal mine. The results show that the discriminant effect of 10 water samples is consistent with the actual situation, and the discriminant accuracy rate is 100%.
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图 2 第1和第2判别函数分组结果
Figure 2. Grouping results of the first and second discriminant functions
表 1 训练样本
Table 1. Training sample
序号 判别指标含量/（mg·L−1） 类别 Ca2+ Mg2+ Na++ K+ HCO3− Cl− SO42− M 1 95.13 31.92 1 941.1 289.58 131.16 4 230.10 6 739.90 砂岩水 2 225.70 81.84 2 171.0 266.83 109.90 4 836.41 7 698.30 砂岩水 3 133.07 55.43 2 206.8 300.67 140.03 4 428.37 7 286.80 砂岩水 4 30.84 24.19 1 463.6 406.93 287.14 2 454.08 4 680.81 砂岩水 5 40.30 23.45 1 485.0 405.42 297.78 2 749.76 5 019.32 砂岩水 6 23.49 11.54 1 843.9 524.47 235.74 3 221.08 5 868.13 砂岩水 7 60.72 25.04 1 665.9 302.45 251.70 3 094.96 5 423.65 砂岩水 8 73.75 31.46 1 613.5 328.19 274.74 3 117.44 5 453.08 砂岩水 9 38.49 13.52 1 724.6 424.72 265.88 3 156.29 5 654.40 砂岩水 10 58.76 23.35 1 757.2 470.46 280.06 2 952.35 5 560.64 砂岩水 11 66.86 31.95 1 649.0 276.94 274.74 2 903.79 5 243.07 砂岩水 12 62.81 18.43 1 920.0 437.09 210.93 3 603.03 6 260.54 砂岩水 13 200.40 81.44 736.4 350.78 177.25 1 964.43 3 517.73 太灰水 14 173.15 28.69 688.0 0 202.06 1 469.72 2 605.20 太灰水 15 99.40 36.95 1 129.6 400.90 191.43 2 065.29 3 938.47 太灰水 16 136.27 34.03 686.0 0 198.52 1 421.69 2 515.40 太灰水 17 133.70 63.72 1 350.0 316.97 251.34 2 925.84 5 050.99 太灰水 18 229.26 0 1 398.0 255.46 246.38 2 065.29 4 347.13 太灰水 19 138.28 0 1 503.0 133.43 249.92 2 276.62 4 438.26 太灰水 20 192.38 85.09 919.9 336.47 203.84 2 046.08 3 794.84 太灰水 21 214.43 88.73 913.6 332.89 200.29 2 113.32 3 869.80 太灰水 22 320.64 106.96 489.6 304.25 219.79 1 719.47 3 168.75 太灰水 23 194.31 77.34 669.0 193.29 207.38 1 600.84 2 948.84 太灰水 24 184.37 80.71 906.0 322.15 209.16 1 988.44 3 694.47 太灰水 25 183.57 79.49 927.1 325.73 205.61 2 094.11 3 823.36 太灰水 26 186.21 79.80 901.2 318.57 207.38 1 969.52 3 667.63 太灰水 27 215.63 90.43 823.1 329.31 210.93 1 911.59 3 585.55 太灰水 28 199.60 86.79 929.1 322.15 209.16 2 074.90 3 830.01 太灰水 29 157.11 74.87 958.6 300.67 200.29 2 209.38 3 905.09 太灰水 30 198.36 85.44 896.2 332.89 203.84 1 998.62 3 554.19 太灰水 31 201.59 86.43 894.8 332.89 203.84 2 008.33 3 566.52 太灰水 32 202.40 85.94 889.7 340.05 200.29 2 037.43 3 590.25 太灰水 33 201.59 87.65 878.0 332.89 202.06 1 979.22 3 520.03 太灰水 34 203.21 87.41 889.2 340.05 198.52 2 027.73 3 580.54 太灰水 35 204.43 85.94 891.3 340.05 198.52 2 047.13 3 602.18 太灰水 36 202.40 85.44 888.8 332.89 202.06 1 988.92 3 539.53 太灰水 37 202.40 87.90 906.6 336.47 202.06 2 076.24 3 647.83 太灰水 38 206.45 85.94 886.6 336.47 202.06 2 095.64 3 649.20 太灰水 39 202.40 87.90 903.9 336.47 200.29 2 047.13 3 614.31 太灰水 40 331.94 116.26 428.05 345.42 215.36 1 474.71 2 742.29 混合水 41 246.93 168.43 408.50 338.88 218.90 1 455.31 2 671.18 混合水 42 332.75 116.38 429.60 309.69 220.68 1 541.66 2 799.16 混合水 43 344.09 117.36 381.0 311.18 221.56 1 523.22 2 746.15 混合水 44 331.94 114.42 434.30 311.18 222.27 1 538.75 2 800.68 混合水 45 238.03 102.39 1 068.40 287.36 176.36 2 580.75 4 315.95 混合水 
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表 2 典型判别函数系数项和常数项
Table 2. Coefficient term and constant term of typical discriminant function
变量 第1判别函数 第2判别函数 Ca2+ −0.013 10 0.017 2 Mg2+ −0.018 80 0.006 9 Na++K+ −0.003 40 0.002 1 HCO3− 0.001 40 0.003 4 Cl− 0.020 80 0.041 7 SO42− 0.004 70 0.008 6 M −0.000 37 −0.005 2 常数项 −7.175 40 −14.165 5
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表 3 判别函数方差
Table 3. Variance of discriminant function
判别函数 特征值 方差贡献率/% 累积方差贡献率/% 典型相关系数 第1判别 8.514 92.8 92.8 0.946 第2判别 0.660 7.2 100.0 0.631
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表 4 典型判别函数在各类别的中心值
Table 4. Center value of typical discriminant function in each category
类别 判别函数 第1判别函数 第2判别函数 砂岩水 4.509 0.343 太灰水 −1.230 −0.542 混合水 −3.481 1.751
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表 5 回代估计结果
Table 5. Back substitution estimation results
序号 第1判
别函数值距砂岩水
中心值
距离距太灰水
中心值
距离距混合水
中心值
距离回代
判别实际
类别序号 第1判
别函数值距砂岩水
中心值
距离距太灰水
中心值
距离距混合水
中心值
距离回代
判别实际
类别1 5.205 0.696 6.435 8.686 砂岩水 砂岩水 24 −1.269 5.778 0.039 2.212 太灰水 太灰水 2 3.831 0.678 5.061 7.312 砂岩水 砂岩水 25 −0.921 5.430 0.309 2.560 太灰水 太灰水 3 4.317 0.192 5.547 7.798 砂岩水 砂岩水 26 −1.382 5.891 0.152 2.099 太灰水 太灰水 4 3.536 0.973 4.766 7.017 砂岩水 砂岩水 27 −1.863 6.372 0.633 1.618 太灰水 太灰水 5 4.849 0.340 6.079 8.330 砂岩水 砂岩水 28 −1.301 5.810 0.071 2.180 太灰水 太灰水 6 4.902 0.393 6.132 8.383 砂岩水 砂岩水 29 −0.222 4.731 1.008 3.259 太灰水 太灰水 7 4.331 0.178 5.561 7.812 砂岩水 砂岩水 30 −1.504 6.013 0.274 1.977 太灰水 太灰水 8 4.824 0.315 6.054 8.305 砂岩水 砂岩水 31 −1.519 6.028 0.289 1.962 太灰水 太灰水 9 5.319 0.810 6.549 8.800 砂岩水 砂岩水 32 −1.438 5.947 0.208 2.043 太灰水 太灰水 10 4.188 0.321 5.418 7.669 砂岩水 砂岩水 33 −1.644 6.153 0.414 1.837 太灰水 太灰水 11 3.779 0.730 5.009 7.260 砂岩水 砂岩水 34 −1.553 6.062 0.323 1.928 太灰水 太灰水 12 5.027 0.518 6.257 8.508 砂岩水 砂岩水 35 −1.465 5.974 0.235 2.016 太灰水 太灰水 13 −1.598 6.107 0.368 1.883 太灰水 太灰水 36 −1.610 6.119 0.380 1.871 太灰水 太灰水 14 −2.083 6.592 0.853 1.398 太灰水 太灰水 37 −1.336 5.845 0.106 2.145 太灰水 太灰水 15 −0.055 4.564 1.175 3.426 太灰水 太灰水 38 −1.195 5.704 0.035 2.286 太灰水 太灰水 16 −1.961 6.470 0.731 1.520 太灰水 太灰水 39 −1.490 5.999 0.260 1.991 太灰水 太灰水 17 3.046 1.463 4.276 6.527 砂岩水 太灰水 40 −4.204 8.713 2.974 0.723 混合水 混合水 18 −1.177 5.686 0.053 2.304 太灰水 太灰水 41 −4.007 8.516 2.777 0.526 混合水 混合水 19 0.533 3.976 1.763 4.014 太灰水 太灰水 42 −3.867 8.376 2.637 0.386 混合水 混合水 20 −1.357 5.866 0.127 2.124 太灰水 太灰水 43 −3.919 8.428 2.689 0.438 混合水 混合水 21 −1.481 5.990 0.251 2.000 太灰水 太灰水 44 −3.814 8.323 2.584 0.333 混合水 混合水 22 −3.050 7.559 1.820 0.431 混合水 太灰水 45 −1.076 5.585 0.154 2.405 太灰水 混合水 23 −2.330 6.839 1.100 1.151 太灰水 太灰水
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表 6 煤层底板突水水源判别分析模型指标数值
Table 6. Indicator value of mine floor water inrush source discrminant model
序号 判别指标含量/（mg·L−1） 实际类别 Ca2+ Mg2+ Na++ K+ HCO3− Cl− SO42− M 1 86.43 35.36 1706.6 373.70 214.47 3333.65 5768.76 砂岩水 2 76.76 31.04 1681.9 320.31 235.740 3085.40 5447.14 砂岩水 3 88.03 36.77 1536.0 347.00 245.67 3144.77 5412.92 砂岩水 4 206.45 85.94 900.6 336.47 200.29 2076.24 3647.26 太灰水 5 207.26 82.50 900.8 325.73 198.52 2037.43 3596.87 太灰水 6 209.69 83.97 888.1 336.47 200.29 2018.03 3572.50 太灰水 7 208.48 87.16 883.1 329.31 202.06 2008.33 3561.56 太灰水 8 210.5 85.94 868.8 336.47 200.29 2056.84 3594.60 太灰水 9 327.89 115.40 403.5 299.27 217.66 1534.87 2752.40 混合水 10 323.85 112.08 404.0 284.38 219.79 1533.90 2743.50 混合水
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表 7 各水样的Fisher判别结果
Table 7. Fisher discrimination results of each water sample
序号 第1判别
函数值距砂岩水
中心值距离距太灰水
中心值距离距混合水
中心值距离判别结果 1 3.914 0.595 5.144 7.395 砂岩水 2 3.523 0.986 4.753 7.004 砂岩水 3 4.285 0.224 5.515 7.766 砂岩水 4 −1.422 5.931 0.192 2.059 太灰水 5 −1.584 6.093 0.354 1.897 太灰水 6 −1.632 6.141 0.402 1.849 太灰水 7 −1.674 6.183 0.444 1.807 太灰水 8 −1.441 5.950 0.211 2.040 太灰水 9 −3.830 8.339 2.600 0.349 混合水 10 −3.694 8.203 2.464 0.213 混合水
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