膨胀土判别与分类的Bayes判别分析法
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摘要
基于Bayes判别分析法以建立膨胀土判别与胀缩等级分类的Bayes判别分析模型.模型选用液限,胀缩总率,塑性指数,天然含水率,自由膨胀率等5个指标作为判别因子;将膨胀土的胀缩性分为极强、强、中、弱4个等级并作为Bayes判别分析的4个正态总体;以训练样本建立Bayes线性判别函数,以该函数计算待判样品的Bayes判别函数值,以最大值对应的总体作为样品的归属;以刀切法对判别准则进行评价.研究表明,该模型以刀切法计算的误判率为13.3%.
Based on the principle of Bayes discriminant analysis,a Bayes discriminant model for evaluating expansive soil is established.Five indexes,including the liquid limit,the overall rate of expansion and contrac- tion,plastic index,moisture content,free expansion rate,are selected as the factors for synthetic evaluation of expansive soil.The shrink and expansion is divided into four grades as four normal populations in Bayes discriminant analysis.Bayes discriminant functions obtained through training a set of expansive soil samples are used to compute the Bayes function values of the evaluating samples,and the maximal function value is used to judge which population the evaluating sample belongs to.The usefulness of the proposed model is verified by Jackknife method.The study shows that the average prediction accuracy is 13.3%.
Based on the principle of Bayes discriminant analysis,a Bayes discriminant model for evaluating expansive soil is established.Five indexes,including the liquid limit,the overall rate of expansion and contrac- tion,plastic index,moisture content,free expansion rate,are selected as the factors for synthetic evaluation of expansive soil.The shrink and expansion is divided into four grades as four normal populations in Bayes discriminant analysis.Bayes discriminant functions obtained through training a set of expansive soil samples are used to compute the Bayes function values of the evaluating samples,and the maximal function value is used to judge which population the evaluating sample belongs to.The usefulness of the proposed model is verified by Jackknife method.The study shows that the average prediction accuracy is 13.3%.
引文
1张欣海．膨胀土胀缩等级划分的新途径．地震地质，1991，13(2)：126～128(Zhang Xinhai.A new method for dividing the expansibilities of swelling soils.Seismology and Geology, 1991,13(2):126～128(in Chinese))
2黄卫，钟理，钱振东．路基膨胀土胀缩等级的模糊评判．岩土工程学报，1999，21(4)：408～413(Huang Wei，Zhong Li，Qian Zhendong.Fuzzy judgment about the grade of shrink and expansion for the expansive soil in the subgrade.Chinese Journal of Geotechnical Engineering,1999,21(4):408～413 (in Chinese))
3郭昱葵，熊友山，姚海林等．模糊数学在当宜高速公路膨胀土判别和分类中的应用．岩土力学，1999，20(3)：61～65(Guo Yukui，Xiong Youshan,Yao Hailin,et al.Application of fuzzy mathematics in classification of expansive soils for express- way from dangyang to yichang.Rock and Soil Mechanics, 1999,20(3):61～65(in Chinese))
4蔡奕，王宝军，施斌等．GIS环境下膨胀土胀缩等级的模糊数学评判．工程勘察，2002，(2)：1～4(Cai Yi，Wang Baojun，Shi Bin,et al.To judge the swell and shrink grades of ex- pansive soil under GIS environment by fuzzy mathematics. Geotechnical Investigation & Surveying,2002,(2):1～4(in Chinese))
5陈新民，李生林．膨胀土判别与分类的灰关联分析法．岩土力学，1996,17(4):30～34(Chen Xinming,Li Shenglin.A new ap- proach for identification and classification of expansive soil with grey correlation analysis.Rock and Soil Mechanics, 1996,17(4):30～34(in Chinese))
6李玉花，冯晓腊，严应征．灰色聚类法在膨胀土分类中的应用．岩土力学，2003，24(2)：304～306(Li Yuhua，Feng Xiaola，Yan Yingzheng.Application of gray clustering procedure to classification of expansive soils.Rock and Soil Mechan- ics,2003,24(2):304～306(in Chinese))
7易顺民，晏同珍．膨胀土判别与分类的人工神经网络方法．地质科技情报，1995，14(3)：91～94(Yi Shunmin，Yan Tongzhen．Man-made neural network method for discrimination and classification of expansion soil.Geological Science and Technology Information,1995,14(3):91～94(in Chinese))
8傅鹤林，范臻辉，刘宝琛．利用人工神经网络模型判定膨胀土等级．中国铁道科学，2002，23(5)：118～120(Fu Helin，Fan Zhenhui,Liu Baochen.Determination of expanded clay with artificial neutral network model.China Railway Sci- ence,2002,23(5):118～120(in Chinese))
9汪明武，金菊良，李丽．可拓学在膨胀土胀缩等级评判中的应用．岩土工程学报，2003，25(6)：754～757(Wang Mingwu，Jin Juliang,Li Li.Application of extension method to the evaluation of the grade of shrinkage and expansion for the expansive soil.Chinese Journal of Geotechnical Engineer- ing,2003,25(6):754～757(in Chinese))
10王广月，马华月，刘健．路基膨胀土胀缩等级的物元可拓识别模型．公路交通科技，2005，22(11)：30～33(Wang Guangyue，Ma Huayue,Liu Jian.Matter-element extension model of expansive soils'expansive scale in embankments.Jour- nal of Highway and Transportation Research and Develop- ment,2005,22(11):30～33(in Chinese))
11马文涛．支持向量机方法在膨胀土分类中的应用．岩土力学，2005,26(11):1790～1792(Ma Wentao.Application of support vector machine to classification of expansive soils. Rock and Soil Mechanics,2005,26(11):1790～1792(in Chi- nese))
12宫凤强，李夕兵．膨胀土胀缩等级分类中的距离判别分析法．岩土工程学报，2007，29(3)：463～466(Gong Fengqiang，Li Xibing.Distance discriminant analysis to the classification of the grade of shrink and expansion for the expansive soils. Chinese Journal of Geotechnical Engineering,2007,29(3): 463～466(in Chinese))
13余颂，陈善雄，余飞等．膨胀土判别与分类的Fisher判刖分析方法．岩土力学，2007，28(3)：499～504(Yu Song，Chen Shanx- iong,Yu Fei,et al.Fisher's discriminant analysis method for identification and classification of expansive soil.Rock and Soil Mechanics,2007,28(3):499～504(in Chinese))
14文畅平．潭邵高速公路膨胀土的判别实践．重庆建筑大学学报，2007，29(3)：70～74(Wen Changping．The practice of ex- pansive soil judgment in Xiangtan-Shaoyang Expressway. Journal of Chongqing Yianzhu University,2007,29(3): 70～74(in Chinese))
15梅长林，周家良．实用统计方法．北京：科学出版社，2002．85～110
16张尧庭、方开泰．多元统计分析引论．北京：科学出版社，2003．155～184
2黄卫，钟理，钱振东．路基膨胀土胀缩等级的模糊评判．岩土工程学报，1999，21(4)：408～413(Huang Wei，Zhong Li，Qian Zhendong.Fuzzy judgment about the grade of shrink and expansion for the expansive soil in the subgrade.Chinese Journal of Geotechnical Engineering,1999,21(4):408～413 (in Chinese))
3郭昱葵，熊友山，姚海林等．模糊数学在当宜高速公路膨胀土判别和分类中的应用．岩土力学，1999，20(3)：61～65(Guo Yukui，Xiong Youshan,Yao Hailin,et al.Application of fuzzy mathematics in classification of expansive soils for express- way from dangyang to yichang.Rock and Soil Mechanics, 1999,20(3):61～65(in Chinese))
4蔡奕，王宝军，施斌等．GIS环境下膨胀土胀缩等级的模糊数学评判．工程勘察，2002，(2)：1～4(Cai Yi，Wang Baojun，Shi Bin,et al.To judge the swell and shrink grades of ex- pansive soil under GIS environment by fuzzy mathematics. Geotechnical Investigation & Surveying,2002,(2):1～4(in Chinese))
5陈新民，李生林．膨胀土判别与分类的灰关联分析法．岩土力学，1996,17(4):30～34(Chen Xinming,Li Shenglin.A new ap- proach for identification and classification of expansive soil with grey correlation analysis.Rock and Soil Mechanics, 1996,17(4):30～34(in Chinese))
6李玉花，冯晓腊，严应征．灰色聚类法在膨胀土分类中的应用．岩土力学，2003，24(2)：304～306(Li Yuhua，Feng Xiaola，Yan Yingzheng.Application of gray clustering procedure to classification of expansive soils.Rock and Soil Mechan- ics,2003,24(2):304～306(in Chinese))
7易顺民，晏同珍．膨胀土判别与分类的人工神经网络方法．地质科技情报，1995，14(3)：91～94(Yi Shunmin，Yan Tongzhen．Man-made neural network method for discrimination and classification of expansion soil.Geological Science and Technology Information,1995,14(3):91～94(in Chinese))
8傅鹤林，范臻辉，刘宝琛．利用人工神经网络模型判定膨胀土等级．中国铁道科学，2002，23(5)：118～120(Fu Helin，Fan Zhenhui,Liu Baochen.Determination of expanded clay with artificial neutral network model.China Railway Sci- ence,2002,23(5):118～120(in Chinese))
9汪明武，金菊良，李丽．可拓学在膨胀土胀缩等级评判中的应用．岩土工程学报，2003，25(6)：754～757(Wang Mingwu，Jin Juliang,Li Li.Application of extension method to the evaluation of the grade of shrinkage and expansion for the expansive soil.Chinese Journal of Geotechnical Engineer- ing,2003,25(6):754～757(in Chinese))
10王广月，马华月，刘健．路基膨胀土胀缩等级的物元可拓识别模型．公路交通科技，2005，22(11)：30～33(Wang Guangyue，Ma Huayue,Liu Jian.Matter-element extension model of expansive soils'expansive scale in embankments.Jour- nal of Highway and Transportation Research and Develop- ment,2005,22(11):30～33(in Chinese))
11马文涛．支持向量机方法在膨胀土分类中的应用．岩土力学，2005,26(11):1790～1792(Ma Wentao.Application of support vector machine to classification of expansive soils. Rock and Soil Mechanics,2005,26(11):1790～1792(in Chi- nese))
12宫凤强，李夕兵．膨胀土胀缩等级分类中的距离判别分析法．岩土工程学报，2007，29(3)：463～466(Gong Fengqiang，Li Xibing.Distance discriminant analysis to the classification of the grade of shrink and expansion for the expansive soils. Chinese Journal of Geotechnical Engineering,2007,29(3): 463～466(in Chinese))
13余颂，陈善雄，余飞等．膨胀土判别与分类的Fisher判刖分析方法．岩土力学，2007，28(3)：499～504(Yu Song，Chen Shanx- iong,Yu Fei,et al.Fisher's discriminant analysis method for identification and classification of expansive soil.Rock and Soil Mechanics,2007,28(3):499～504(in Chinese))
14文畅平．潭邵高速公路膨胀土的判别实践．重庆建筑大学学报，2007，29(3)：70～74(Wen Changping．The practice of ex- pansive soil judgment in Xiangtan-Shaoyang Expressway. Journal of Chongqing Yianzhu University,2007,29(3): 70～74(in Chinese))
15梅长林，周家良．实用统计方法．北京：科学出版社，2002．85～110
16张尧庭、方开泰．多元统计分析引论．北京：科学出版社，2003．155～184
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