岩爆烈度分级预测中的贝叶斯判别分析
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摘要
针对岩爆烈度分级预测中存在诸多不确定因素的问题,应用贝叶斯判别分析法建立岩爆烈度分级预测的评价模型。根据岩爆的特点及成因,选取岩石的弹性能量指数Wet,应力系数σθ/σc及岩石脆性系数σc/σt作为判别因子;将岩爆烈度分为无、弱、中、强4个等级并作为贝叶斯判别分析的4个正态总体;以国内外14组工程岩爆分析初始数据进行分级判别,以训练样本建立贝叶斯线性判别函数,以该函数计算待判样品的贝叶斯判别函数值,以最大值对应的总体作为样品的归属。为进一步考察该模型的有效性与实用性,运用该模型对秦岭隧道工程及凡口铅锌矿的岩爆实例进行分析,并与人工神经网络模型、模糊概率模型的判别结果及实际情况进行比较。研究结果表明,该模型判别预测结果与人工神经网络模型及模糊概率模型的判别结果及实际岩爆情况较吻合。
In view of many uncertain elements in classification and prediction of rockburst intensity,the evaluation model for classification and prediction of rockburst intensity is established by Bayes discriminant analysis.According to the characteristic and cause of rockburst,three factors of the stress coefficient of rock,the brittleness coefficient of rock and the elastic energy index of rock are selected as the discriminant factors.And the intensity of rockburst is divided into 4 grades,denoted as none,inferior,medium and intense,which are taken as the four normal populations in Bayes discriminant analysis.The classification discrimination is carried out based on the initial data for rockburst intensity analysis of 14 rock projects around the world.Bayes linear discriminant function is obtained through the training samples,which is then used to calculate the Bayes function value of the evaluating samples.Meanwhile,the population corresponding to the maximum function value is used to judge which population the evaluating sample belongs to.In order to verify the effectiveness and feasibility of the model,the cases of Qinling Tunnel and Fankou Lead-Zinc Mine are analyzed using the proposed method,and the obtained results are also compared with the results of neural network model,fuzzy probability model and practical conditions.The results show that the results predicted by Bayes model are both in good agreement with the practical conditions and the results obtained from the neural network model and fuzzy probability model.
In view of many uncertain elements in classification and prediction of rockburst intensity,the evaluation model for classification and prediction of rockburst intensity is established by Bayes discriminant analysis.According to the characteristic and cause of rockburst,three factors of the stress coefficient of rock,the brittleness coefficient of rock and the elastic energy index of rock are selected as the discriminant factors.And the intensity of rockburst is divided into 4 grades,denoted as none,inferior,medium and intense,which are taken as the four normal populations in Bayes discriminant analysis.The classification discrimination is carried out based on the initial data for rockburst intensity analysis of 14 rock projects around the world.Bayes linear discriminant function is obtained through the training samples,which is then used to calculate the Bayes function value of the evaluating samples.Meanwhile,the population corresponding to the maximum function value is used to judge which population the evaluating sample belongs to.In order to verify the effectiveness and feasibility of the model,the cases of Qinling Tunnel and Fankou Lead-Zinc Mine are analyzed using the proposed method,and the obtained results are also compared with the results of neural network model,fuzzy probability model and practical conditions.The results show that the results predicted by Bayes model are both in good agreement with the practical conditions and the results obtained from the neural network model and fuzzy probability model.
引文
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[2]王伟,王恩元.岩爆预测技术综述及发展分析[J].矿业安全与环保,2003,30(4):12-15.
[3]郭雷,李夕兵,岩小明.岩爆研究进展及发展趋势[J].采矿技术,2006,6(1):16-21.
[4]徐林生,王兰生,李永林,等.岩爆形成机制与判据研究[J].岩土力学,2002,23(3):300-303.
[5]杨涛,李国维.基于先验知识的岩爆预测研究[J].岩石力学与工程学报,2000,19(4):429-431.
[6]王光远.论未确知性信息及其数学处理[J].哈尔滨建筑工程学院学报,1990,23(4):52-58.
[7]董陇军,李夕兵,宫凤强.膨胀土胀缩等级分类的未确知均值聚类方法及应用[J].中南大学学报:自然科学版,2008,39(5):1075-1080.
[8]董陇军,李夕兵,宫凤强.开采地面沉陷预测的未确知聚类预测模型[J].中国地质灾害与防治学报,2008,19(2):95-99.
[9]宫凤强,李夕兵,董陇军,等.基于未确知测度理论的采空区危险性评价研究[J].岩石力学与工程学报,2008,27(2):323-330.
[10]董陇军,王飞跃.基于未确知测度的边坡地震稳定性综合评价[J].中国地质灾害与防治学报,2007,18(4):74-78.
[11]DONG Longjun,PENG Gangjian,FU Yuhua,et al.Unascertained measurement classifying model of goaf collapse prediction[J].Journal of Coal Science&Engineering,2008,14(2):221-224.
[12]梅长林,周家良.实用统计方法[M].北京:科学出版社,2002.
[13]张尧庭,方开泰.多元统计分析引论[M].北京:科学出版社,2003.
[14]于秀林,任雪松.多元统计分析[M].北京:中国统计出版社,1999.
[15]谢政,基于贝叶斯方法的分类问题研究[D].长沙:中南大学,2008.
[16]白明洲,王连俊,许兆义.岩爆危险性预测的神经网络模型及应用研究[J].中国安全科学学报,2002,12(4):65-69.
[17]王元汉,李卧东,李启光,等.岩爆预测的模糊数学综合评判方法[J].岩石力学与工程学报,1998,17(5):493-501.
[18]谷明成,何发亮,陈成宗.秦岭隧道岩爆的研究[J].岩石力学与工程学报,2002,21(9):1324-1329.
[19]刘章军,袁秋平,李建林.模糊概率模型在岩爆烈度分级预测中的应用[J].岩石力学与工程学报,2008,27(S1):3095-3103.
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