﻿ 矿井突水水源的多元统计分析判别

# 矿井突水水源的多元统计分析判别Multivariate Statistical Analysis and Discrimination of Water Inrush Source in Mine

Abstract: Accurately distinguishing the source of water inrush is the primary task of water prevention and control. In order to solve this problem, the hydrogeological data of a mine in Anhui are collected and sorted out. Based on the results of water quality analysis and hydrogeochemistry, seven main ions are selected as discriminant indexes. Based on SPSS software, 30 hydrochemical data of different aquifers are taken as training samples and 6 as prediction samples. Cluster analysis and Bayesian stepwise discriminant analysis in multivariate statistical analysis method establish discriminant models for water inrush source, and compare the two methods. The results show that both cluster analysis and Bayesian stepwise discriminant analysis can accurately discriminate the source of water inrush in this mine; Ward method is the most accurate method in cluster analysis; Bayesian stepwise discriminant eliminates duplicate information, and the accuracy rate of discriminant results reaches 100%, which is the preferred method to discriminate the source of water inrush in this mine. It can provide a new way to distinguish the source of mine water inrush.

1. 引言

2. 矿井概况

3. 突水水源的多元统计分析判别

Table 1. Water sample data table (unit: mg/L)

3.1. 突水水源的系统聚类判别分析

Figure 1. The dendrogram of the nearest distance method

Figure 2. Tree diagram of the connection method between groups

Ward法聚类效果最好，从图3可以看到，只有15号样品与21~30号样品划分成一组，不同于实际情况，其它样品均划分正确，且联接清晰，易区分，基本无链状连接情况。

Figure 3. Ward method tree

3.2. 突水水源的Bayes逐步判别分析

Bayes逐步判别法的前提是已知全部样本划分为几类，然后对一个未知类别的样本进行统计分析，并根据Bayers判别准则予以类别判定。判别过程中选用的Bayes准则要求具有多个总体(3个及以上)。设N (N ≥ 3)类样本为N个总体T1T2，……，TN (所有总体满足正态分布)，假设某预判样品YX1X2，……，Xn等n个判定变量，接着根据Wilks准则，从n个变量中挑选出极具代表性与判别能力强的变量作为判别函数因子，构建判别函数。比较样本Y代入哪一判别函数所得函数值最大，就归为哪一类(或比较Y属于哪一总体的后验概率最大，就归入哪一类)。

Table 2. Correlation coefficient matrix

Table 3. Identify the input variables step by step

Table 4. Classification function coefficients

$\left\{\begin{array}{l}{Y}_{1}=-101.425+0.356{X}_{2}+0.881{X}_{3}+0.161{X}_{6}\\ {Y}_{2}=-30.138+0.443{X}_{2}+0.878{X}_{3}+0.081{X}_{6}\\ {Y}_{3}=-67.572+1.596{X}_{2}+1.985{X}_{3}+0.055{X}_{6}\end{array}$

Table 5. The judgment result of sample back generation

4. 判别模型的应用

Table 6. Water samples to be judged

4.1. 系统聚类判别模型的应用

4.2. Bayes逐步判别模型的应用

Figure 4. Density diagram of centroid method

Figure 5. Ward method tree

Table 7. Bayes step-by-step discrimination results of samples

5. 结论

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