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

## 基于核主成分分析与SVM的岩爆烈度组合预测模型

1.中南大学资源与安全工程学院，湖南 长沙 410083

2.山东黄金集团深井开采实验室，山东 莱州 261442

## Combined Prediction Model of Rockburst Intensity Based on Kernel Principal Component Analysis and SVM

XU Rui,1, HOU Kuikui2, WANG Xi2, LIU Xingquan2, LI Xibing,1

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

2.Deep Mining Laboratory of Shandong Gold Group Co. ，Ltd. ，Laizhou 261442，Shandong，China

 基金资助: 国家自然科学基金项目“开采扰动下深部工程结构的动态响应机理”.  11972378“考虑非平稳、强噪声信号到时差拾取的硬岩矿山微震定位方法研究”.  51904335

Received: 2019-12-25   Revised: 2020-04-22   Online: 2020-08-27

Abstract

Rockburst is a relatively dangerous engineering geological disaster in underground hard rock engineering constructed in high geostress area.Due to the re-distribution of the stress in surrounding rocks during the excavation of underground engineering，the elastic strain energy is released suddenly and abruptly，causing rock fragments to eject from the rock.And then，the casualties and equipment damage are often happened，which make the rockburst become one of the worldwide difficulties in underground engineering.Therefore，the prediction of possibility of rockburst and its intensity is a problem that must be solved in underground engineering construction.For predicting rock-burst intensity effectively，a combined prediction model based on kernel principal component analysis （KPCA） of multiple types and the support vector machine （SVM） optimized by genetic algorithm or particle swarm optimization algorithm （GA/PSO） was established.According to the characteristics and causes of rockburst，rocks’ maximum tangential stress $σθ$，rocks’ uniaxial compressive strength $σt$，rocks’ uniaxial tensile strength $σc$，stress concentration coefficient $SCF$，rock brittleness coefficient $B1$ and $B2$，and elastic energy index $Wet$ were chosen to form the rockburst prediction indexes system.Based on 246 groups of typical rockburst cases at home and abroad，the data were preprocessed through the principal component analysis and the principal component analysis based on linear kernel function，radial basis function （RBF） kernel function and multi-layer perceptron （MLP） kernel function.On the basis of ensuring the amount of information in the original data，2 to 4 linearly independent principal components are obtained，which reduces the correlation between the indicators and the input parameters of the SVM model，and simplifies the training process.Then input the dimensionality-reduced data into GA/PSO optimized SVM model for training and prediction.To improve classification accuracy and generalization ability of the SVM，GA/PSO were adopted to automatically determine the parameters for support vector machine，and the optimal values of parameters $C$ and $g$ were determined by the method of 10 fold cross validation，which avoided the blindness of manually providing parameters.In this study，220 rockburst samples were randomly selected as the training set，and the remaining 26 samples were selected as the test set.After testing，the optimal parameters，the training set and test set accuracy of the 8 combined models were obtained.The prediction accuracy of the model based on the combination of the principal component analysis method of RBF kernel function and PSO-SVM reached 92.3%，which was the optimal combination model.It demonstrated that the combined prediction model can accurately deal with the complex non-linear relationship between various factors affecting the rockburst intensity，and the model has strong engineering practicability in the prediction of rockburst intensity.

Keywords： kernel principal component analysis ; prediction of rockburst intensity ; genetic algorithm ; particle swarm optimization algorithm ; support vector machine ; combination prediction model

XU Rui, HOU Kuikui, WANG Xi, LIU Xingquan, LI Xibing. Combined Prediction Model of Rockburst Intensity Based on Kernel Principal Component Analysis and SVM[J]. Gold Science and Technology, 2020, 28(4): 575-584 doi:10.11872/j.issn.1005-2518.2020.04.019

### 1.1 基于核函数的主成分分析

$1n∑j=1nxjTxj$

$Φx→F$

$K=ΦXTΦX=kxi,xjn×n$

$kxi,xj=ΦxiT,Φxj=ΦxiTΦxj$

$C=1n∑j=1nΦxjTΦxj$

$λV=CV$

$λΦxk⋅V=Φxk⋅CV(k=1,2,⋯,n)$

$V=∑i=1nαiΦxi$

$nλα=Kα$

### 1.2 GA/PSO优化的支持向量机分类预测原理

$fx=sgn∑i=1nαi*yjxixiT+b*$

$max-12∑i=1n∑j=1nαiαjyiyjKxi,xj+∑i=1nαis.t.∑i=1nαiyj=0,0≤αi≤C,i=1,2,⋯,n$

$fx=sgn∑i=1nαi*yjKxi,x+b*$

SVM的性能主要取决于核参数$g$和惩罚因子$C$的值，为了提升支持向量机的性能，采用遗传算法和粒子群算法设定RBF核偏差$g$和惩罚因子$C$的值。

$vk+1=c0vk+c1r1pbest-xk+c2r2gbest-xk$
$xk+1=xk+vk+1$

### 图1

Fig.1   Flowchart of the rockburst intensity forecasting model

### 2.2 原始数据分析

Table 1  Partial raw data of rockburst samples

190.00170.0011.300.5315.040.889.00M
290.00220.007.400.4129.730.937.30L
362.60165.009.400.3817.530.899.00L
455.40176.007.300.3224.110.929.30M
530.0088.703.700.3423.970.926.60M
648.75180.008.300.2721.690.915.00M
$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$
243126.72189.708.950.6721.200.915.43L
24457.97125.377.740.6721.200.462.86L
24557.9796.163.770.4616.200.202.53L
24657.9770.684.190.6025.510.192.87L

### 图2

Fig.2   Boxplot obtained for raw data of the rockburst samples

### 2.3 核主成分分析

Table 2  Correlation coefficient of rockburst evaluation indexes

$σθ$/MPa1.0000.0340.3340.918-0.248-0.2190.468
$σc$/MPa0.0341.0000.422-0.2650.0760.2340.193
$σt$/MPa0.3340.4221.0000.164-0.625-0.4710.329
SCF0.918-0.2650.1641.000-0.258-0.2520.329
B1-0.2480.076-0.625-0.2581.0000.526-0.108
B2-0.2190.234-0.471-0.2520.5261.000-0.082
$Wet$0.4680.1930.3290.329-0.108-0.0821.000

Table 3  Results for the standardized processing of raw data

10.59171.37040.9878-0.0869-0.38640.14460.9237
20.59172.54250.0553-0.26550.64510.65700.5147
30.08501.25320.5335-0.3101-0.21160.24700.9237
4-0.04821.51110.0314-0.39940.25050.55450.9959
5-0.5179-0.5353-0.8294-0.36970.24070.55450.3463
6-0.17111.60490.2705-0.47380.08050.4520-0.0387
$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$$⋮$
2431.27081.83220.42590.12150.04610.45200.0648
244-0.00060.32430.13660.12150.0461-4.1597-0.5536
245-0.0006-0.3604-0.8126-0.1911-0.3050-6.8242-0.6330
246-0.0006-0.9577-0.71220.01730.3488-6.9267-0.5512

### 图3

Fig.3   Relationship between the first principal component contribution rate and the kernel parameters in the RBF kernel

### 图4

Fig.4   Comparisons of accumulation contribution rate

Table 4  Selection of kernel parameters and principal components

### 图5

Fig.5   Data visualization of dimensionality reduction results

### 2.4 GA/PSO-SVM模型训练和岩爆烈度预测

Table 5  Results for the SVM parameters，training set accuracy and test set accuracy

$C$$g$
PCAGA-SVM81.471056.621296.884.6
PSO-SVM97.6345118.443198.284.6
KPCA1GA-SVM50.5654890.241594.673.1
PSO-SVM51.3095586.158889.676.9
KPCA2GA-SVM3.1284256.190591.488.5
PSO-SVM31.2537145.417894.692.3
KPCA3GA-SVM73.1933282.282193.280.8
PSO-SVM82.0614491.932297.788.5

### 图6

Fig.6   Fitness curves of the optimal parameters selected by the generated models

### 图7

Fig.7   Partial prediction results for the test samples of generated models

## 3 结论

（1）综合考虑了影响岩爆发生及其烈度的7个指标，采用基于不同核函数的主成分分析法对样本数据进行非线性特征提取，将影响岩爆的7个指标缩减为2~4个综合预测指标，减少了各指标之间的相关性，同时减少了SVM模型的输入参数，简化了训练过程，提升了模型的预测精度和效率。

（2）SVM参数的选择对预测结果有很大影响，因此采用遗传算法和粒子群优化算法对SVM的参数寻优，通过十折交叉检验的方法确定参数$C$$g$的最优值，提高了模型的泛化能力，避免了人工提供参数的盲目性。

（3）将基于不同核的主成分分析与GA/PSO优化的SVM相结合，建立岩爆烈度的组合预测模型，并对国内外246组岩爆实例进行训练、学习、预测和评估。结果表明：基于RBF核函数的主成分分析方法与PSO-SVM相结合的模型预测准确率达到了92.3%，为最佳组合模型，说明构建的组合预测模型能够准确地处理影响岩爆烈度的各因素之间的复杂非线性关系，将该模型用于岩爆烈度的预测方面有较强的工程实用性。

http://www.goldsci.ac.cn/article/2020/1005-2518/1005-2518-2020-28-4-575.shtml

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