QQ群聊

• CN 62-1112/TF
• ISSN 1005-2518
• 创刊于1988年

## Research on Prediction of Rock Mass Blastability Classification Based on PCA-SVM Model

HAN Chaoqun,, CHEN Jianhong,, ZHOU Zhiyong, YANG Shan

School of Resources and Safety Engineering，Central South University，Changsha 410083，Hunan，China

 基金资助: 国家自然科学基金项目“地下金属矿采掘计划可视化优化方法与技术研究”.  51374242“基于属性驱动的矿体动态建模及更新方法研究”.  51504286中南大学中央高校基本科研业务费专项资金.  2018zzts741

Received: 2019-01-28   Revised: 2019-03-25   Online: 2019-12-20

Abstract

The accurate evaluation of the classification of rock mass blast ability is of great significance to the design of blasting excavation and the safety and stability of geotechnical engineering.At present，scholars at home and abroad in the field of blasting have not reached a consensus on the evaluation method of rock blast ability.The factors affecting rock blasting are very complex，and the research indicators adopted by different scholars are different.By comprehensively considering the influence of the inherent properties of the rock mass and the actual blasting effect on the rock mass blast ability，six kinds of attributes including acoustic wave and wave impedance of rock mass，volume of blasting funnel，percentage of large blocks，percentage of small blocks and average eligibility rate were selected to predict the classification of rock mass blast ability.Considering the complex and varied geological conditions of engineering rock masses，according to the actual situation of several mines，55 sample data were selected，which cover quartzite，magnetite，skarn，diorite, gneiss,the lithology of marble，granite，limestone，metamorphic schist，dolomite，sandstone，etc..The sample raw data are from many rock mass engineering with different geographical locations and different geological conditions，which are representative.The PCA-SVM model and the SVM model were used to compare and analyze the explosive rock prediction results.Firstly，the same random seeds were used to ensure that the number of ore samples of the two models is the same as that of the training set and forecast set.Then，according to the data extracted by the principal component analysis and the raw data that have not been processed，the SVM models were established respectively，and the 11 prediction results were compared and analyzed.In the 11 randomized trials，the accuracy of PCA-SVM model was 100% at one time，there were 8 cases where one sample was misjudged,and 2 cases where two samples were misjudged.The number of misjudgments in the PCA-SVM model in a single random experiment is less than or equal to the SVM model.The average prediction accuracy of the PCA-SVM model is 90.1%，which was significantly higher than the SVM model.The results show that：（1） The prediction model based on principal component analysis and support vector machine eliminates the information overlap between the impact indicators and extracts four principal components which contain 98.38% of the original information.Compared with the standard SVM model，the PCA-SVM model not only reduces the dimension of the data，but also improves the accuracy of the rock explode grade from 78.5% to 90.1%.（2） The prediction results of PCA-SVM model are in good agreement with the actual situation.A small number of misjudgments mainly occur between some rock samples with small differences in characteristics.（3）The PCA-SVM prediction model based on the stratified random sampling technique ensures the randomness and difference of the sample data between the training set and the test set.This method is more scientific and reasonable than the general research model，and has a certain reference significance for the research of similar engineering.

Keywords： rock mass blastability ; inherent properties of the rock mass ; blasting effect ; principal component analysis ; support vector machine ; random sampling ; grade prediction

HAN Chaoqun, CHEN Jianhong, ZHOU Zhiyong, YANG Shan. Research on Prediction of Rock Mass Blastability Classification Based on PCA-SVM Model[J]. Gold Science and Technology, 2019, 27(6): 879-887 doi:10.11872/j.issn.1005-2518.2019.06.879

### 1.1 主成分分析基本原理

PCA（Principal Component Analysis）即为主成分分析，其主要思想是将之前相关程度较强的P个指标，经过线性变换后组合成新的互相无关的综合指标，同时最大程度上保持原有数据集的信息。主成分分析主要用于数据降维工作[15]。其基本流程如图1所示。

### 图1

Fig.1   Process of principal component analysis

（1）原始指标的标准化，假设矿岩可爆性影响指标为P维随机变量$X=(X1,X2,⋯,XP)T$，共有n个矿岩研究样本(n>P)，采用下式对原始矩阵进行标准化变换。

$zij=(xij-xj¯)/sj$

$xj¯=∑i=1nxij/n$$sj2=∑i=1n(xij-xj¯)/(n-1)$i=1,2,$⋯$,nj=1,2,$⋯$,p）。

（2）求解标准化矩阵Z的相关系数矩阵R

$Rij=cov(Zi,Zj)si*sj=E(zji-zi¯)*(zij-zj¯)si*sj=E(zji-zi¯)*(zij-zj¯)$

（3）求解相关系数矩阵R的特征值与特征向量

$R-λIp=0$

（4）提取前m个主成分信息，并对m个主成分进行综合评价。

### 1.2 支持向量机基本原理

SVM（Support Vector Machine）即为支持向量机，本文对于矿岩可爆性分级预测模型的研究，主要是借助SVM中核函数的线性变换功能，将复杂的矿岩可爆性问题转变为高维度空间中的线性问题，最终求解最优分类超平面[16,17,18]

$ω·xi+b=0$

$min12(ω·ω)+C∑i=1nεi=0$

$L(ω,ε,b,α,β)=12(ω·ω)+C∑i=1nεi-∑i=1nαiyi(ω·xi+b)-1+εi-∑i=1nβi·εi$

Lagrange函数L()在鞍点处是关于$ω$b、ε的极小点，此时通过对$ω$b、ε分别求偏导，再整理Lagrange函数L()可得出研究问题对应的对偶问题如下：

$maxQ(a)=L(ω,ε,b,α,β)=∑i=1nαi-12∑i=1n∑i=1nαi·αj·yi·yj·ψ(xi)·ψ(xj)$
$=∑i=1nαi-12∑i=1n∑i=1nαi·αj·yi·yi·K(xi,xj)$
$s.t$$∑i=1nαi·yi=0$$αi≥0$

$f(x)=sgn∑i=1nαi·yi·K(xi,xj)+b$

### 图2

Fig.2   Flow chart for the prediction model of rock mass blastability

## 2 样本数据来源与指标选取

Table 1  Sample data for rock blastability classification prediction

1薄层灰岩3 1288.433.931.511.50.387
2灰白色白云岩3 6809.911.467.17.20.246
3角砾岩2 9277.716.749.311.40.414
4米黄色白云岩3 83010.02.781.25.40.293
5紫色含矿白云岩2 8217.39.956.711.10.395
6紫色不含矿白云岩3 2198.412.852.711.50.765
7青灰色白云岩3 3108.511.255.011.30.359
8角闪斜长片麻岩5 37314.960.68.210.40.17
9黄铜闪锌黄铁矿4 07413.445.820.211.40.12
10致密石榴石矽卡岩5 21517.443.58.615.90.023
11闪长岩4 85412.635.010.718.10.122
12大理岩4 77613.016.214.223.20.204
13磁铁矿4 45014.747.830.07.40.188
14混合岩3 1408.542.228.09.90.483
15绿泥片岩2 0505.310.068.07.30.508
16千枚岩1 9845.211.675.04.50.918
171870细粒大理岩5 53314.529.426.214.80.075
18矽卡岩4 96312.977.96.55.20.093
$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$
551825含矿浅色砂岩4 00410.565.334.50.10.021

### 3.1 PCA-SVM矿岩可爆性模型建立

Table 2  Relevant coefficient matrix of blastability impact index on rock mass

Table 3  Variance contribution of principal components and their eigenvalues

PC12.615943.6043.60
PC21.376922.9566.55
PC31.205820.1086.64
PC40.703911.7398.38
PC50.07291.2299.59
PC60.02460.41100.00

$PC1=-0.482*X1-0.509*X2-0.338*X3+0.446*X4-0.216*X5+0.385*X6$
$PC2=0.397*X1+0.313*X2+0.171*X3+0.454*X4-0.698*X5+0.146*X6$
$PC3=-0.330*X1-0.317*X2+0.729*X3-0.342*X4-0.376*X5-0.007*X6$
$PC4=0.100*X1+0.210*X2+0.129*X3-0.251*X4+0.205*X5+0.910*X6$

Table 4  Input factor data after main component extraction

1薄层灰岩0.8423610.3150030.4229270.162393
2灰白色白云岩1.5393611.699857-1.110430-0.97020
3角砾岩1.7974040.438431-0.451760-0.14860
4米黄色白云岩2.0723452.252531-1.640230-1.087060
5紫色含矿白云岩2.1779120.490495-0.765810-0.401240
6紫色不含矿白云岩2.2393570.837842-0.8403901.106790
7青灰色白云岩1.6573650.709957-0.957150-0.378490
8角闪斜长片麻岩-2.4214601.4871380.7088590.404729
9黄铜闪锌黄铁矿-1.1765200.8314470.376829-0.201160
10致密石榴石矽卡岩-2.8037200.707335-0.5400100.077760
11闪长岩-1.687660-0.103580-0.5411500.124458
12大理岩-1.348350-0.800030-1.7324600.441841
13磁铁矿-1.0979601.8719130.331022-0.105220
14混合岩0.7956590.5874270.9164040.556719
15绿泥片岩3.3835370.822144-0.275600-0.462640
16千枚岩4.2814481.549846-0.1190000.812629
171870细粒大理岩-1.7659001.004592-1.188400-0.228400
18矽卡岩-2.2291101.8996902.110488-0.067380
$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$
551825含矿浅色砂岩-0.5005202.4348661.986787-1.178260

### 3.2 模型预测结果对比分析

Table 5  Comparison of the prediction results between PCA-SVM and SVM model

4米黄色白云岩Ⅲ*Ⅲ*
7青灰色白云岩Ⅲ*
8角闪斜长片麻岩
16千枚岩
21三层铁
33-160 m西四层铁
37+1 600 m底板紫色砂岩
42+1 620 m顶板长石石英砂岩
48+1 845 m矿体浅色砂岩
49+1 860 m底板紫红色沙哑
52+331 m浅色含矿砂岩Ⅳ*

### 图3

Fig.3   Distribution diagram of classification of rock mass blastability in PCA-SVM model

### 3.3 模型可靠性对比分析

Table 6  Comparison of prediction results of 11 randomized trial models

11831（90.9）2（81.8）
22081（90.9）3（72.7）
32791（90.9）1（90.9）
43041（90.9）3（72.7）
54060（100.0）1（90.9）
64241（90.9）4（63.6）
75141（90.9）2（81.8）
86212（81.8）4（63.6）
97241（90.9）1（90.9）
107662（81.8）2（81.8）
118101（90.9）3（72.7）

## 4 结语

（1）矿岩可爆性等级受岩体固有属性与爆破效果的多重作用，避免重要信息的遗漏，尽可能地考虑与其相关联的信息，综合考虑了岩体声波、波阻抗、爆破漏斗体积、大块率、小块率和平均合格率6类指标，对55个矿岩样本建立了基于PCA-SVM的矿岩可爆性预测模型。

（2）利用主成分分析方法，得到包含原始数据集98.38%信息的4个主成分。通过对比PCA-SVM模型与原始SVM模型预测结果可知：改进后的模型不仅降低了数据的维度，同时使得矿岩可爆性等级预测准确率从78.5%提高至90.1%，验证了该模型在矿岩可爆性等级预测中具有较高的准确度。

（3）利用R语言，实现了基于分层随机抽样技术的PCA-SVM矿岩可爆性预测模型的程序化。该方法针对研究指标维数较多且部分指标间相关性较强的数据模型具有较强的适用性，同时对相似工程的研究具有一定的借鉴意义。

## 参考文献 原文顺序 文献年度倒序 文中引用次数倒序 被引期刊影响因子

[D].长沙中南大学2012.

Jiang Fuliang.

The Evaluation of Ore-rock’s Blastability in Metal Mine and the Theoretical and Experimental Study of Deep-hole Blasting Parameters’ Optimization in Underground Stope

[D].ChangshaCentral South University2012.

[J].爆破，2016331）：19-2583.

Zhang QinliLiu WeijunYang Weiet al.

Study on rock mass blastability based on combined PCA and improved BP predicting model

[J].Blasting2016331）：19-2583.

[J].黄金科学技术，2018263）：349-356.

Hu GuiyingLiu KeweiDu Xinet al.

Research on smooth-cutting method and its application in tunnel excavation

[J].Gold Science and Technology2018263）：349-356.

[J].黄金科学技术，2018263）：365-371.

Lu FuranChen Jianhong.

Rock burst prediction method based on AHP and entropy weight TOPSIS model

[J].Gold Science and Technology2018263）：365-371.

[J].爆破，2010274）：43-47.

Zhang DemingWang XinminZheng Jingjinget al.

Blastability classification of rock and mine based on fuzzy comprehensive evaluation

[J].Blasting2010274）：43-47.

[J].爆破，2013304）：20-2431.

Zhao GuoyanYu PeipeiZhou Li.

Classification of rock mass blastability based on unascertained measurement theory

[J].Blasting2013304）：20-2431.

[J].黄金科学技术，2017254）：87-92.

Li JinlingWang LiguanChen Xin.

Complex blasting network detonation simulation and effect prediction for open pit mine

[J].Gold Science and Technology2017254）：87-92.

[J].黄金科学技术，2016243）：1-8.

Li QiyueWei JiaruiLi Yiet al.

Application of technology improvement of construction scheme in deep hole blasting of a gold mine

[J].Gold Science and Technology2016243）：1-8.

[J].爆破，2017344）：80-84105.

Peng YaxiongCheng YaoWu Liet al.

Assessment for ore-bearing rock mass blastability based on AHP-TOPSIS

[J].Balsting2017344）：80-84105.

[J].武汉科技大学学报（自然科学版），2016393）：200-203.

Ma KangZhang QunSheng Jianlonget al.

GCRN-based model for classification of ore-bearing rock-mass blastability and its application

[J].Journal of Wuhan University of Science and Technology（Natural Science Edition）2016393）：200-203.

[J].中国安全科学学报，2015257）：68-73.

Shao LiangshanZhao LinlinWen Tingxinet al.

Assessment of rock mass blastability based on fuzzy multiple linear regression model

[J].China Safety Science Journal2015257）：68-73.

[J].昆明理工大学学报（自然科学版），2017422）：34-3762.

Wang ChaoXu HongleiLi Xianglonget al.

A distance discriminant analysis method for orebody blastability classification and its application

[J].Journal of Kunming University of Science and Technology （Natural Science Edition）2017422）：34-3762.

[J].世界科技研究与发展，2016385）：946-949.

Deng HongweiChen ChaoqunZhang Yanan.

Random forest model of rock mass blastability grading and R language implementation

[J].World Sci-Tech R&D2016385）：946-949.

[J].工程爆破，2006121）：7-10.

Xin MingyinQu ShijieChen Xuannianet al.

A new method of rock-mass blastability classification and its application in Nan-fen open pit iron mine engineering balsting

[J].Engineering Blasting2006121）：7-10.

[J].矿冶工程，2014344）：16-19.

Liu ZhixiangGuo HuqiangLan Ming.

Study on PCA-SVM model for evaluation of gob hazards in metal mine

[J].Mining and Metallurgical Engineering2014344）：16-19.

[J].电测与仪表，2015529）：6-1040.

Zhan ChangjieZhou Buxiang.

The medium and long term power load forecasting model based on PCA-SVM

[J].Electrical Measurement and Instrumentation2015529）：6-1040.

[J].岩石力学与工程学报，2005241）：144-148.

Luo ZhanyouYang XiaojunGong Xiaonan.

Support vector machine model in slope stability evaluation

[J].Chinese Journal of Rock Mechanics and Engineering2005241）：144-148.

[J].中国地质灾害与防治学报，2018294）：64-69.

Zhang ManChen JianhongZhou Zhiyong.

Grading prediction model of rock burst based on SVM and its R language description

[J].The Chinese Journal of Geological Hazard and Control2018294）：64-69.

[J].金属矿山，198412）：2-8.

Niu QiangLong LingxiaoWang Minglin.

Experimental study on rock blasting classification in China

[J].Metal Mine198412）：2-8.

[J].现代矿业，20173312）：59-63.

Han LupengXiao MinLiu Jie.

Study on prediction of rock mass blastability classification based on fisher discriminant analysis method and R language

[J].Modern Mining20173312）：59-63.

/

 〈 〉