基于模糊理论与SVM的边坡地震失稳规模贝叶斯网络评估方法
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摘要
由于历史边坡样本数量不足,使用传统机器学习方法进行边坡稳定性评估往往会出现过拟合问题。以贝叶斯网络为框架,结合模糊理论与支持向量机,建立一种边坡地震失稳规模评估新方法。采用模糊理论求解贝叶斯网络参数的先验分布,同时采用支持向量机求解贝叶斯网络参数的实际样本潜在分布;利用贝叶斯估计方法将先验分布与实际样本潜在分布结合,以得到既满足基本规律又体现样本非线性与随机性的边坡地震失稳规模贝叶斯网络。利用建立好的贝叶斯网络对32个实际边坡样本进行失稳规模评估,正确率为81.25%。通过与基于先验知识的贝叶斯网络、基于实际样本的支持向量机进行对比,可以看出,提出的方法解决了样本不足带来的过拟合问题,正确率有很大提升。并且,该方法在边坡属性不完整的情况下也能对失稳规模作出有效评估。
Due to the insufficiency of historical slope samples,there are frequently over-fitting problems when using traditional machine learning method to assess the stability of slope. Based on Bayesian network,this paper combines fuzzy theory with support vector machine to propose a new method for slope seismic instability scale assessment. The method utilizes fuzzy theory to solve the prior distribution of the Bayesian network parameter.Meanwhile,support vector machine is applied to solve the actual sample potential distribution of the Bayesian network parameter. Then Bayesian estimation method is used to combine the prior distribution with the actual sample potential distribution to obtain the Bayesian network of slope instability scale. This Bayesian network satisfies both the basic law and the sample nonlinearity and randomness. Using the established Bayesian network to evaluate the instability scale of 32 actual slope samples,the correct rate is 81.25%. By comparing with Bayesian network based on prior knowledge and support vector machine based on actual sample,it can be seen that the proposed method solves the over-fitting problem caused by insufficiency of samples,and the accuracy is greatly improved. Moreover,this method can also effectively assess the instability scale when the slope properties are incomplete.
Due to the insufficiency of historical slope samples,there are frequently over-fitting problems when using traditional machine learning method to assess the stability of slope. Based on Bayesian network,this paper combines fuzzy theory with support vector machine to propose a new method for slope seismic instability scale assessment. The method utilizes fuzzy theory to solve the prior distribution of the Bayesian network parameter.Meanwhile,support vector machine is applied to solve the actual sample potential distribution of the Bayesian network parameter. Then Bayesian estimation method is used to combine the prior distribution with the actual sample potential distribution to obtain the Bayesian network of slope instability scale. This Bayesian network satisfies both the basic law and the sample nonlinearity and randomness. Using the established Bayesian network to evaluate the instability scale of 32 actual slope samples,the correct rate is 81.25%. By comparing with Bayesian network based on prior knowledge and support vector machine based on actual sample,it can be seen that the proposed method solves the over-fitting problem caused by insufficiency of samples,and the accuracy is greatly improved. Moreover,this method can also effectively assess the instability scale when the slope properties are incomplete.
引文
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[6]王如宾,徐卫亚,孟永东,等.锦屏一级水电站左岸坝肩高边坡长期稳定性数值分析[J].岩石力学与工程学报,2014,33(增1):3 105-3 113.(WANG Rubin,XU Weiya,MENG Yongdong,et al.Numerical analysis of long-term stability of left bank abutment high slope at Jinping I Hydropower Station[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(Supp.1):3 105-3 113.(in Chinese))
[7]舒苏荀,龚文惠.二维随机场下边坡稳定性的径向基函数神经网络分析法[J].岩土力学,2015,36(4):1 205-1 210.(SHU Suxun,GONG Wenhui.Radial basis function neural network-based method for slope stability analysis under two-dimensional random field[J].Rock and Soil Mechanics,2015,36(4):1 205-1 210.(in Chinese))
[8]KANG F,XU Q,LI J.Slope reliability analysis using surrogate models via new support vector machines with swarm intelligence[J].Applied Mathematical Modelling,2016,40(11-12):6 105-6 120.
[9]ZHAO H,YIN S,RU Z.Relevance vector machine applied to slope stability analysis[J].International Journal for Numerical and Analytical Methods in Geomechanics,2012,36(5):643-652.
[10]覃光华,李祚泳.BP网络过拟合问题研究及应用[J].武汉大学学报:工学版,2006,(6):55-58.(QIN Guanghua,LI Zuoyong.Over-fitting of BP NN research and its application[J].Engineering Journal of Wuhan University,2006,(6):55-58.(in Chinese))
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[12]谢洪涛.基于故障贝叶斯网的边坡垮塌事故风险评估方法研究[J].安全与环境学报,2012,12(6):237-241.(XIE Hongtao.Fault Bayesian network based method for risk assessment of slope collapse accident[J].Journal of Safety and Environment,2012,12(6):237-241.(in Chinese))
[13]郑霞忠,李华飞,魏雄伟,等.贝叶斯网络在岩质边坡开挖风险概率评估中的应用[J].水电能源科学,2013,31(7):130-132.(ZHENGXiazhong,LI Huafei,WEI Xiongwei,et al.Application of Bayesian network in probability assessment of risk for rocky slope excavation[J].Water Resources and Power,2013,31(7):130-132.(in Chinese))
[14]SONG Y Q,GONG J H,GAO S,et al.Susceptibility assessment of earthquake-induced landslides using Bayesian network:a case study in Beichuan,China[J].Computers and Geosciences,2012,42(5):189-199.
[15]LI X Y,ZHANG L M,ZHANG S.Efficient Bayesian networks for slope safety evaluation with large quantity monitoring information[J].Geoscience Frontiers,2017,9(1):1-9.
[16]ZADEH L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353.
[17]CORTES C,VAPNIK V.Support-vector networks[J].Machine Learning,1995,20(3):273-297.
[18]BENOV D M.The Manhattan project,the first electronic computer and the Monte Carlo method[J].Monte Carlo Methods and Applications,2016,22(1):73-79.
[19]苏永华,何满潮,孙晓明.岩体模糊分类中隶属函数的等效性[J].北京科技大学学报,2007,29(7):670-675.(SU Yonghua,HEManchao,SUN Xiaoming.Equivalent characteristic of membership function type in rock mass fuzzy classification[J].Journal of University of Science and Technology Beijing,2007,29(7):670-675.(in Chinese))
[20]PLATT J C.Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods[J].Advances in Large Margin Classifiers,1999,10(4):61-74.
[21]PRICE D,KNERR S,PERSONNAZ L,et al.Pairwise neural network classifiers with probabilistic outputs[C]//International Conference on Neural Information Processing Systems.[S.l.]:MIT Press,1994:1 109-1 116.
[22]张连文,郭海鹏.贝叶斯网引论[M].北京:科学出版社,2006:31-74.(ZHANG Lianwen,GUO Haipeng.An introduction to Bayesian networks[M].Beijing:Science Press,2006:31-74.(in Chinese))
[23]陈乐生.汶川地震公路震害调查.路基[M].北京:人民交通出版社,2012:63-372.(CHEN Lesheng.Seismic damage investigation for highway in Wenchuan earthquake.Subgrade[M].Beijing:China Communications Press,2012:63-372.(in Chinese))
[24]李家春,田伟平,陈建壮.公路边坡水毁灾害等级快速评估方法[J].长安大学学报,2006,26(2):27-30.(LI Jiachun,TIAN Weiping,CHEN Jianzhuang.Rapid assessment of highway slope disaster caused by rainfall[J].Journal of Chang'an University,2006,26(2):27-30.(in Chinese))
[25]王余庆,辛鸿博,高艳平,等.预测岩土边坡地震崩滑的综合指标法研究[J].岩土工程学报,2001,23(3):311-314.(WANG Yuqing,XIN Hongbo,GAO Yanping,et al.Study on comprehensive index method for predicting earthquake-induced landslides[J].Chinese Journal of Geotechnical Engineering,2001,23(3):311-314.(in Chinese))
[26]中华人民共和国国家标准编写组.GB/T 50218-2014工程岩体分级标准[S].北京:中国计划出版社,2014.(The National Standards Compilation Group of People?s Republic of China.GB/T 50218-2014Standards for engineering classification of rock mass[S].Beijing:China Planning Press,2014.(in Chinese))
[27]庄建琦,崔鹏,葛永刚,等.“5·12”汶川地震崩塌滑坡危险性评价:以都汶公路沿线为例[J].岩石力学与工程学报,2010,29(增2):3 735-3 742.(ZHUANG Jianqi,CUI Peng,GE Yonggang,et al.Risk assessment of collapses and landslides caused by 5·12Wenchuan earthquake:a case study of Dujiangyan-Wenchuan highway[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(Supp.2):3 735-3 742.(in Chinese))
[28]LAM W,BACCHUS F.Learning Bayesian belief networks:an approach based on the MDL principle[J].Computational Intelligence,1994,10(3):269-293.
[29]LAURITZEN S L,SPIEGEHALTER D J.Local computations with probabilities on graphical structures and their application to expert systems[J].Journal of the Royal Statistical Society,1988,50(2):157-224.
[2]邓东平,李亮.基于滑动面应力假设下的三维边坡稳定性极限平衡法研究[J].岩土力学,2017,38(1):189-196.(DENG Dongping,LI Liang.Three-dimensional limit equilibrium method for slope stability based on assumption of stress on slip surface[J].Rock and Soil Mechanics,2017,38(1):189-196.(in Chinese))
[3]刘子振,言志信.降雨入渗非饱和黏土边坡稳定性的极限平衡条分法研究[J].岩土力学,2016,37(2):350-356.(LIU Zizhen,YANZhixin.Limit equilibrium slice method for unsaturated clay slope under rainfall infiltration[J].Rock and Soil Mechanics,2016,37(2):350-356.(in Chinese))
[4]卢坤林,朱大勇,甘文宁,等.一种边坡稳定性分析的三维极限平衡法及应用[J].岩土工程学报,2013,35(12):2 276-2 282.(LUKunlin,ZHU Dayong,GAN Wenlin,et al.Generalized 3Dlimit-equilibrium method for slope stability analysis and its application[J].Chinese Journal of Geotechnical Engineering,2013,35(12):2 276-2 282.(in Chinese))
[5]李典庆,肖特,曹子君,等.基于高效随机有限元法的边坡风险评估[J].岩土力学,2016,37(7):1 994-2 003.(LI Dianqing,XIAOTe,CAO Zijun,et al.Slope risk assessment using efficient random finite element method[J].Rock and Soil Mechanics,2016,37(7):1 994-2 003.(in Chinese))
[6]王如宾,徐卫亚,孟永东,等.锦屏一级水电站左岸坝肩高边坡长期稳定性数值分析[J].岩石力学与工程学报,2014,33(增1):3 105-3 113.(WANG Rubin,XU Weiya,MENG Yongdong,et al.Numerical analysis of long-term stability of left bank abutment high slope at Jinping I Hydropower Station[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(Supp.1):3 105-3 113.(in Chinese))
[7]舒苏荀,龚文惠.二维随机场下边坡稳定性的径向基函数神经网络分析法[J].岩土力学,2015,36(4):1 205-1 210.(SHU Suxun,GONG Wenhui.Radial basis function neural network-based method for slope stability analysis under two-dimensional random field[J].Rock and Soil Mechanics,2015,36(4):1 205-1 210.(in Chinese))
[8]KANG F,XU Q,LI J.Slope reliability analysis using surrogate models via new support vector machines with swarm intelligence[J].Applied Mathematical Modelling,2016,40(11-12):6 105-6 120.
[9]ZHAO H,YIN S,RU Z.Relevance vector machine applied to slope stability analysis[J].International Journal for Numerical and Analytical Methods in Geomechanics,2012,36(5):643-652.
[10]覃光华,李祚泳.BP网络过拟合问题研究及应用[J].武汉大学学报:工学版,2006,(6):55-58.(QIN Guanghua,LI Zuoyong.Over-fitting of BP NN research and its application[J].Engineering Journal of Wuhan University,2006,(6):55-58.(in Chinese))
[11]JUDEA P.Causality:models,reasoning,and inference[M].New York:Cambridge University Press,2000:53-639.
[12]谢洪涛.基于故障贝叶斯网的边坡垮塌事故风险评估方法研究[J].安全与环境学报,2012,12(6):237-241.(XIE Hongtao.Fault Bayesian network based method for risk assessment of slope collapse accident[J].Journal of Safety and Environment,2012,12(6):237-241.(in Chinese))
[13]郑霞忠,李华飞,魏雄伟,等.贝叶斯网络在岩质边坡开挖风险概率评估中的应用[J].水电能源科学,2013,31(7):130-132.(ZHENGXiazhong,LI Huafei,WEI Xiongwei,et al.Application of Bayesian network in probability assessment of risk for rocky slope excavation[J].Water Resources and Power,2013,31(7):130-132.(in Chinese))
[14]SONG Y Q,GONG J H,GAO S,et al.Susceptibility assessment of earthquake-induced landslides using Bayesian network:a case study in Beichuan,China[J].Computers and Geosciences,2012,42(5):189-199.
[15]LI X Y,ZHANG L M,ZHANG S.Efficient Bayesian networks for slope safety evaluation with large quantity monitoring information[J].Geoscience Frontiers,2017,9(1):1-9.
[16]ZADEH L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353.
[17]CORTES C,VAPNIK V.Support-vector networks[J].Machine Learning,1995,20(3):273-297.
[18]BENOV D M.The Manhattan project,the first electronic computer and the Monte Carlo method[J].Monte Carlo Methods and Applications,2016,22(1):73-79.
[19]苏永华,何满潮,孙晓明.岩体模糊分类中隶属函数的等效性[J].北京科技大学学报,2007,29(7):670-675.(SU Yonghua,HEManchao,SUN Xiaoming.Equivalent characteristic of membership function type in rock mass fuzzy classification[J].Journal of University of Science and Technology Beijing,2007,29(7):670-675.(in Chinese))
[20]PLATT J C.Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods[J].Advances in Large Margin Classifiers,1999,10(4):61-74.
[21]PRICE D,KNERR S,PERSONNAZ L,et al.Pairwise neural network classifiers with probabilistic outputs[C]//International Conference on Neural Information Processing Systems.[S.l.]:MIT Press,1994:1 109-1 116.
[22]张连文,郭海鹏.贝叶斯网引论[M].北京:科学出版社,2006:31-74.(ZHANG Lianwen,GUO Haipeng.An introduction to Bayesian networks[M].Beijing:Science Press,2006:31-74.(in Chinese))
[23]陈乐生.汶川地震公路震害调查.路基[M].北京:人民交通出版社,2012:63-372.(CHEN Lesheng.Seismic damage investigation for highway in Wenchuan earthquake.Subgrade[M].Beijing:China Communications Press,2012:63-372.(in Chinese))
[24]李家春,田伟平,陈建壮.公路边坡水毁灾害等级快速评估方法[J].长安大学学报,2006,26(2):27-30.(LI Jiachun,TIAN Weiping,CHEN Jianzhuang.Rapid assessment of highway slope disaster caused by rainfall[J].Journal of Chang'an University,2006,26(2):27-30.(in Chinese))
[25]王余庆,辛鸿博,高艳平,等.预测岩土边坡地震崩滑的综合指标法研究[J].岩土工程学报,2001,23(3):311-314.(WANG Yuqing,XIN Hongbo,GAO Yanping,et al.Study on comprehensive index method for predicting earthquake-induced landslides[J].Chinese Journal of Geotechnical Engineering,2001,23(3):311-314.(in Chinese))
[26]中华人民共和国国家标准编写组.GB/T 50218-2014工程岩体分级标准[S].北京:中国计划出版社,2014.(The National Standards Compilation Group of People?s Republic of China.GB/T 50218-2014Standards for engineering classification of rock mass[S].Beijing:China Planning Press,2014.(in Chinese))
[27]庄建琦,崔鹏,葛永刚,等.“5·12”汶川地震崩塌滑坡危险性评价:以都汶公路沿线为例[J].岩石力学与工程学报,2010,29(增2):3 735-3 742.(ZHUANG Jianqi,CUI Peng,GE Yonggang,et al.Risk assessment of collapses and landslides caused by 5·12Wenchuan earthquake:a case study of Dujiangyan-Wenchuan highway[J].Chinese Journal of Rock Mechanics and Engineering,2010,29(Supp.2):3 735-3 742.(in Chinese))
[28]LAM W,BACCHUS F.Learning Bayesian belief networks:an approach based on the MDL principle[J].Computational Intelligence,1994,10(3):269-293.
[29]LAURITZEN S L,SPIEGEHALTER D J.Local computations with probabilities on graphical structures and their application to expert systems[J].Journal of the Royal Statistical Society,1988,50(2):157-224.