基于核主成分分析与SVM的岩爆烈度组合预测模型

doi:10.11872/j.issn.1005-2518.2020.04.019

摘要/Abstract

摘要：

为了更好地预测岩土工程中的岩爆烈度，建立了基于多类型核函数的主成分分析方法与遗传算法或粒子群优化算法（GA/PSO）优化的支持向量机（SVM）相结合的组合预测模型。选取围岩最大切向应力 $σ θ$ 、岩石单轴抗拉强度 $σ t$ 、岩石单轴抗压强度 $σ c$ 、应力集中系数 $S C F$ 、脆性指数 $B 1$ 和 $B 2$ 以及弹性应变能指数 $W e t$ 共7个指标构成岩爆预测指标体系。基于统计的246个国内外岩爆实例数据，分别运用主成分分析和基于线性核函数、RBF核函数以及MLP核函数的主成分分析对数据进行预处理，得到2～4个线性无关的主成分。再将降维后的数据输入GA/PSO优化的SVM模型进行训练和预测。经测试，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，为岩土工程中的岩爆烈度预测提供了一种可靠的方法。

关键词: 核主成分分析, 岩爆烈度预测, 遗传算法, 粒子群优化算法, 支持向量机, 组合预测模型

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 $σ θ$ ，rocks’ uniaxial compressive strength $σ t$ ，rocks’ uniaxial tensile strength $σ c$ ，stress concentration coefficient $S C F$ ，rock brittleness coefficient $B 1$ and $B 2$ ，and elastic energy index $W e t$ 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.

Key words: kernel principal component analysis, prediction of rockburst intensity, genetic algorithm, particle swarm optimization algorithm, support vector machine, combination prediction model

中图分类号:

TU45

许瑞, 侯奎奎, 王玺, 刘兴全, 李夕兵. 基于核主成分分析与SVM的岩爆烈度组合预测模型[J]. 黄金科学技术, 2020, 28(4): 575-584.

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

图/表 12

图1

表1

部分岩爆样本原始数据"

序号	$σ θ$ /MPa	$σ c$ /MPa	$σ t$ /MPa	SCF	B₁	B₂	$W e t$	岩爆烈度
1	90.00	170.00	11.30	0.53	15.04	0.88	9.00	M
2	90.00	220.00	7.40	0.41	29.73	0.93	7.30	L
3	62.60	165.00	9.40	0.38	17.53	0.89	9.00	L
4	55.40	176.00	7.30	0.32	24.11	0.92	9.30	M
5	30.00	88.70	3.70	0.34	23.97	0.92	6.60	M
6	48.75	180.00	8.30	0.27	21.69	0.91	5.00	M
$?$	$?$	$?$	$?$	$?$	$?$	$?$	$?$	$?$
243	126.72	189.70	8.95	0.67	21.20	0.91	5.43	L
244	57.97	125.37	7.74	0.67	21.20	0.46	2.86	L
245	57.97	96.16	3.77	0.46	16.20	0.20	2.53	L
246	57.97	70.68	4.19	0.60	25.51	0.19	2.87	L

表1

图2

表2

岩爆评价指标的相关系数"

指标	$σ θ$ /MPa	$σ c$ /MPa	$σ t$ /MPa	SCF	B₁	B₂	$W e t$
$σ θ$ /MPa	1.000	0.034	0.334	0.918	-0.248	-0.219	0.468
$σ c$ /MPa	0.034	1.000	0.422	-0.265	0.076	0.234	0.193
$σ t$ /MPa	0.334	0.422	1.000	0.164	-0.625	-0.471	0.329
SCF	0.918	-0.265	0.164	1.000	-0.258	-0.252	0.329
B₁	-0.248	0.076	-0.625	-0.258	1.000	0.526	-0.108
B₂	-0.219	0.234	-0.471	-0.252	0.526	1.000	-0.082
$W e t$	0.468	0.193	0.329	0.329	-0.108	-0.082	1.000

表2

表3

原始数据标准化处理结果"

序号	$σ θ$ /MPa	$σ c$ /MPa	$σ t$ /MPa	SCF	B₁	B₂	$W e t$
1	0.5917	1.3704	0.9878	-0.0869	-0.3864	0.1446	0.9237
2	0.5917	2.5425	0.0553	-0.2655	0.6451	0.6570	0.5147
3	0.0850	1.2532	0.5335	-0.3101	-0.2116	0.2470	0.9237
4	-0.0482	1.5111	0.0314	-0.3994	0.2505	0.5545	0.9959
5	-0.5179	-0.5353	-0.8294	-0.3697	0.2407	0.5545	0.3463
6	-0.1711	1.6049	0.2705	-0.4738	0.0805	0.4520	-0.0387
$?$	$?$	$?$	$?$	$?$	$?$	$?$	$?$
243	1.2708	1.8322	0.4259	0.1215	0.0461	0.4520	0.0648
244	-0.0006	0.3243	0.1366	0.1215	0.0461	-4.1597	-0.5536
245	-0.0006	-0.3604	-0.8126	-0.1911	-0.3050	-6.8242	-0.6330
246	-0.0006	-0.9577	-0.7122	0.0173	0.3488	-6.9267	-0.5512

表3

图3

图4

表4

核参数及主成分的选择"

核函数类型	核函数表达式	核参数	第一主成分贡献率/ $%$	主成分个数
主成分分析	-	-	40.20	4
线性核函数	$K x i, x j = x i ? x j$	-	59.19	2
高斯核函数	$K x i, x j = e x p ? - x i - x j 2 2 σ 2$	$σ = 890$	58.52	3
多层感知器核函数	$K x i, x j = t a n h ? v x i ? x j + c$	$v = 1 × 10 - 5, c = - 5$	61.59	3

表4

图5

表5

模型参数及模型训练集和测试集准确率"

模型		SVM参数		训练集准确率/ $%$	测试集准确率/ $%$
模型		$C$	$g$	训练集准确率/ $%$	测试集准确率/ $%$
PCA	GA-SVM	81.4710	56.6212	96.8	84.6
PCA	PSO-SVM	97.6345	118.4431	98.2	84.6
KPCA1	GA-SVM	50.5654	890.2415	94.6	73.1
KPCA1	PSO-SVM	51.3095	586.1588	89.6	76.9
KPCA2	GA-SVM	3.1284	256.1905	91.4	88.5
KPCA2	PSO-SVM	31.2537	145.4178	94.6	92.3
KPCA3	GA-SVM	73.1933	282.2821	93.2	80.8
KPCA3	PSO-SVM	82.0614	491.9322	97.7	88.5

表5

图6

图7

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