基于高斯过程机器学习算法的矿柱稳定性分析
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摘要
矿柱是地下矿山支撑顶板围岩、维持采场稳定的关键结构要素。为迅速准确地判别矿柱稳定性,选取矿柱宽度、矿柱高度、矿柱宽高比、矿岩单轴抗压强度和矿柱承受载荷作为影响指标,利用高斯过程机器学习算法建立矿柱状态与其主要影响因素之间的非线性映射关系,进而提出一种基于高斯过程二元分类(GPC)的矿柱状态识别模型。结合工程实例,以40组样本数据进行训练,以10组样本数据对该模型进行检验,并与ANN和SVM进行对比。结果表明,矿柱状态识别的高斯过程模型是科学可行的,该模型具有参数自适应化获取、分类精度高、计算复杂度低等优点,还可对矿柱状态判别结果的不确定性或可信度进行定量化评价。
This paper is aimed at introducing a new analysis method for pillar stability in the underground mine based on the Gaussian Process for binary classification( GPC). As is known,it is the pillar that serves as the key structural components in sustaining the weight of the roof rock mass and keeping the stability of the stope in the underground situation. In order to predict the stability of the pillars as efficiently and precisely as possible,we have established a recognition model by taking the advantage of the GPC. In order to construct the recognition model,we have first of all analyzed the contributive factors of the pillars' failure and chosen five indexes as the influential indictors,that is,the width,height,ratio of the width of the pillar to its height,the uniaxial compressive strength of the rock and the pillar stress.Then,it has been made easy to establish the nonlinear mapping relationship between the pillar's state and influential indictors via the Gaussian Process for Machine Learning model. Last of all,the recognition model for pillar's status-in-situ has been set up based on the Gaussian Process for Binary Classification. As a result,the Gaussian Process model of pillar's state recognition has been proven scientific and feasible,with the right-recognition rate turning out to be 90%,when combined with the engineering practice and tested with 40 sets of pillar samples for training and 10 sets for testing samples. Thus,we have been able to develop the two different iso-probability contours for the stable pillars,respectively,in the space of the pillar's radio between width-to-height and that between stress-to-UCS through comparison and contrast making based on the proposed model and the model for logistic regression. Furthermore,when compared with the artificial neural networks( ANN) and the supporting vector machines( SVM),it can be found that the proposed model enjoys advantages of self-adaptive parameters determination,higher classification precision but lower computational complexity,thus,it can be expected to provide more reasonable and higher reliable classification results and likely quantitative evaluations with the probabilistic meaning,which doesn't seem possible to be done via the previous model.
This paper is aimed at introducing a new analysis method for pillar stability in the underground mine based on the Gaussian Process for binary classification( GPC). As is known,it is the pillar that serves as the key structural components in sustaining the weight of the roof rock mass and keeping the stability of the stope in the underground situation. In order to predict the stability of the pillars as efficiently and precisely as possible,we have established a recognition model by taking the advantage of the GPC. In order to construct the recognition model,we have first of all analyzed the contributive factors of the pillars' failure and chosen five indexes as the influential indictors,that is,the width,height,ratio of the width of the pillar to its height,the uniaxial compressive strength of the rock and the pillar stress.Then,it has been made easy to establish the nonlinear mapping relationship between the pillar's state and influential indictors via the Gaussian Process for Machine Learning model. Last of all,the recognition model for pillar's status-in-situ has been set up based on the Gaussian Process for Binary Classification. As a result,the Gaussian Process model of pillar's state recognition has been proven scientific and feasible,with the right-recognition rate turning out to be 90%,when combined with the engineering practice and tested with 40 sets of pillar samples for training and 10 sets for testing samples. Thus,we have been able to develop the two different iso-probability contours for the stable pillars,respectively,in the space of the pillar's radio between width-to-height and that between stress-to-UCS through comparison and contrast making based on the proposed model and the model for logistic regression. Furthermore,when compared with the artificial neural networks( ANN) and the supporting vector machines( SVM),it can be found that the proposed model enjoys advantages of self-adaptive parameters determination,higher classification precision but lower computational complexity,thus,it can be expected to provide more reasonable and higher reliable classification results and likely quantitative evaluations with the probabilistic meaning,which doesn't seem possible to be done via the previous model.
引文
[1]LUO Zhouquan(罗周全),PENG Dong(彭东),SU Hanyu(苏汉语),et al.Analysis of pillar stability based on orthogonal design and principal component regression[J].The Chinese Journal of Geological Hazard and Control(中国地质灾害与防治学报),2015,26(4):51-55.
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[5]MUSA A I,DAVID S,ERLING N.Stochastic assessment of pillar stability at Laisvall mine using artificial neural network[J].Tunnelling and Underground Space Technology,2015,49:307-319.
[6]DENG Jian(邓建),LI Xibing(李夕兵),GU Desheng(古德生).Reliability analysis on pillar structure using a new monte-carlo finite element method[J].Chinese Journal of Rock Mechanics and Engineering(岩石力学与工程学报),2002,21(4):459-465.
[7]ZHAO Kui(赵奎),CAI Meifeng(蔡美峰),RAO Yunzhang(饶运章),et al.Study on fuzzy random reliability analysis for block stability in caved area[J].Rock and Soil Mechanics(岩土力学),2003,24(6):988-990.
[8]LUO Hui(罗辉),YANG Shijiao(杨仕教),TAO Ganqiang(陶干强),et al.Stability analysis of ore pillar and application using concept of dynamic fuzzy reliability based on finite element method-artificial neural network-Monte Carlo simulation[J].Journal of China Coal Society(煤炭学报),2010,35(4):551-554.
[9]CAUVIN M,VERDEL T,SALMON R.Modeling uncertainties in mining pillar stability analysis[J].Risk Analysis,2009,29(10),1371-1380.
[10]MONJEZI M,SEYED M H,MANOJ K.Superiority of neural networks for pillar stress prediction in bord and pillar method[J].Arabian Journal of Geosciences,2011,4(5):845-853.
[11]ZHOU Jian,LI Xibing,MITRI H S.Comparative performance of six supervised learning methods for the development of models of hard rock pillar stability prediction[J].Natural Hazards,2015,79(1):291-316.
[12]NICKISCH H,RASMUSSEN C E.Approximations for binary gaussian process classification[J].Journal of Machine Learning Research,2008,9:2035-2078.
[13]YAO Futian(姚伏天).Gaussian processes based classification for hyperspectral imagery(基于高斯过程的高光谱图像分类研究)[D].Hangzhou:Zhejiang University,2011.
[14]RASMUSSEN C E,WILLIAMS C K I.Gaussian processes for machine learning[M].Massachusetts:Massachusetts Institute of Technology Press,2006.
[15]YIN Shenghua(尹升华),WU Aixiang(吴爱祥),LI Xiwen(李希雯),et al.Orthogonal polar difference analysis for sensitivity of the factors influencing the ore pillar stability[J].Journal of China Coal Society(煤炭学报),2012,37(S):48-52.
[16]YAO Gaohui(姚高辉),WU Aixiang(吴爱祥),WANG Yiming(王贻明),et al.Stability analysis of stope retention pillars in broken rock conditions[J].Journal of University of Science and Technology Beijing(北京科技大学学报),2011,33(4):401-405.
[17]LI Jianling(李坚玲).Stope pillar stability and sensitivity analysis of effect factors in overall mining method[J].Nonferrous Metals(有色金属),2010,62(5):6-8.
[18]JIA Pengpeng(贾朋朋).Research on Gaussian process for classification(用于分类的高斯过程研究)[D].Tianjin:Hebei University of Technology,2012.
[19]WATTIMENA R K,KRAMADIBRATA S,SIDI I D,et al.Developing coal pillar stability chart using logistic regression[J].International Journal of Rock Mechanics&Mining Sciences,2013,58(1):55-60.
[2]LIU Xuezeng(刘学增),ZHAI Deyuan(翟德元).The reliability design of pillar[J].Chinese Journal of Rock Mechanics and Engineering(岩石力学与工程学报),2000,18(6):85-88.
[3]ZHOU Jian,LI Xibing,SHI Xiuzhi,et al.Predicting pillar stability for underground mine using Fisher discriminant analysis and SVM methods[J].Transactions of Nonferrous Metals Society of China,2011,21(12):2734-2743.
[4]WATTIMENA R K.Predicting the stability of hard rock pillars using multinomial logistic regression[J].International Journal of Rock Mechanics&Mining Sciences,2014,71:33-40.
[5]MUSA A I,DAVID S,ERLING N.Stochastic assessment of pillar stability at Laisvall mine using artificial neural network[J].Tunnelling and Underground Space Technology,2015,49:307-319.
[6]DENG Jian(邓建),LI Xibing(李夕兵),GU Desheng(古德生).Reliability analysis on pillar structure using a new monte-carlo finite element method[J].Chinese Journal of Rock Mechanics and Engineering(岩石力学与工程学报),2002,21(4):459-465.
[7]ZHAO Kui(赵奎),CAI Meifeng(蔡美峰),RAO Yunzhang(饶运章),et al.Study on fuzzy random reliability analysis for block stability in caved area[J].Rock and Soil Mechanics(岩土力学),2003,24(6):988-990.
[8]LUO Hui(罗辉),YANG Shijiao(杨仕教),TAO Ganqiang(陶干强),et al.Stability analysis of ore pillar and application using concept of dynamic fuzzy reliability based on finite element method-artificial neural network-Monte Carlo simulation[J].Journal of China Coal Society(煤炭学报),2010,35(4):551-554.
[9]CAUVIN M,VERDEL T,SALMON R.Modeling uncertainties in mining pillar stability analysis[J].Risk Analysis,2009,29(10),1371-1380.
[10]MONJEZI M,SEYED M H,MANOJ K.Superiority of neural networks for pillar stress prediction in bord and pillar method[J].Arabian Journal of Geosciences,2011,4(5):845-853.
[11]ZHOU Jian,LI Xibing,MITRI H S.Comparative performance of six supervised learning methods for the development of models of hard rock pillar stability prediction[J].Natural Hazards,2015,79(1):291-316.
[12]NICKISCH H,RASMUSSEN C E.Approximations for binary gaussian process classification[J].Journal of Machine Learning Research,2008,9:2035-2078.
[13]YAO Futian(姚伏天).Gaussian processes based classification for hyperspectral imagery(基于高斯过程的高光谱图像分类研究)[D].Hangzhou:Zhejiang University,2011.
[14]RASMUSSEN C E,WILLIAMS C K I.Gaussian processes for machine learning[M].Massachusetts:Massachusetts Institute of Technology Press,2006.
[15]YIN Shenghua(尹升华),WU Aixiang(吴爱祥),LI Xiwen(李希雯),et al.Orthogonal polar difference analysis for sensitivity of the factors influencing the ore pillar stability[J].Journal of China Coal Society(煤炭学报),2012,37(S):48-52.
[16]YAO Gaohui(姚高辉),WU Aixiang(吴爱祥),WANG Yiming(王贻明),et al.Stability analysis of stope retention pillars in broken rock conditions[J].Journal of University of Science and Technology Beijing(北京科技大学学报),2011,33(4):401-405.
[17]LI Jianling(李坚玲).Stope pillar stability and sensitivity analysis of effect factors in overall mining method[J].Nonferrous Metals(有色金属),2010,62(5):6-8.
[18]JIA Pengpeng(贾朋朋).Research on Gaussian process for classification(用于分类的高斯过程研究)[D].Tianjin:Hebei University of Technology,2012.
[19]WATTIMENA R K,KRAMADIBRATA S,SIDI I D,et al.Developing coal pillar stability chart using logistic regression[J].International Journal of Rock Mechanics&Mining Sciences,2013,58(1):55-60.