砂土液化势评价的Bayes判别分析法及其应用
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摘要
为了给砂土地震液化的数量化研究提供参考,基于多元统计分析理论,建立砂土地震液化判别与液化势分类的Bayes判别分析模型。模型选用震级、地面加速度最大值、标准贯入击数、比贯入阻力、相对密实度、平均粒径和地下水位等7个指标作为判别因子;将砂土液化势分为严重液化、中等液化、轻微液化和未液化4个级别,并作为Bayes判别分析的4个正态总体;以17个砂土实测数据作为训练样本,建立Bayes线性判别函数,以Bayes线性判别函数的最大值对应的总体作为样品所归属的总体;最后将建立的模型对训练样本进行回判,以回代估计误判率对模型进行检验。研究表明,对训练样本的回代误判率为0,对另外20个砂土样本的判别正确率为90%。
To provide reference for the quantitative study on seismic liquefaction of sandy soil,Bayes discriminant model(BDM)for identification and classification of seismic liquefaction potential of sandy soil was established based on multivariate statistical analysis theory.According to the analysis of some influencing factors of sand liquefaction,seven parameters including earthquake magnitude,peak ground acceleration,the value of standard penetration test,specific penetration resistance,relative compaction,mean particle diameter,and underground water table were selected as the indexes for synthetic evaluation of the seismic liquefaction of sandy soil.The seismic liquefaction potential of sandy soil was divided into four grades,i.e.,serious liquefaction,medium liquefaction,slight liquefaction and non-liquefaction,and regarded as four normal collectivities in Bayes discriminant analysis.Bayes discriminant functions obtained through training 17 sandy soil samples were employed to compute the Bayes function values of samples,and the maximal function value was used to judge which collectivity the sample belongs to.The established Bayes discriminant analysis model was used to back-discriminate the training samples,and verified by the ratio of mistake-discrimination.The study indicates that the ratio of mistake-discrimination of training samples is zero.The other twenty sets of sand samples regarded as testing samples were assessed by BDM and the correct rate is 90%.
To provide reference for the quantitative study on seismic liquefaction of sandy soil,Bayes discriminant model(BDM)for identification and classification of seismic liquefaction potential of sandy soil was established based on multivariate statistical analysis theory.According to the analysis of some influencing factors of sand liquefaction,seven parameters including earthquake magnitude,peak ground acceleration,the value of standard penetration test,specific penetration resistance,relative compaction,mean particle diameter,and underground water table were selected as the indexes for synthetic evaluation of the seismic liquefaction of sandy soil.The seismic liquefaction potential of sandy soil was divided into four grades,i.e.,serious liquefaction,medium liquefaction,slight liquefaction and non-liquefaction,and regarded as four normal collectivities in Bayes discriminant analysis.Bayes discriminant functions obtained through training 17 sandy soil samples were employed to compute the Bayes function values of samples,and the maximal function value was used to judge which collectivity the sample belongs to.The established Bayes discriminant analysis model was used to back-discriminate the training samples,and verified by the ratio of mistake-discrimination.The study indicates that the ratio of mistake-discrimination of training samples is zero.The other twenty sets of sand samples regarded as testing samples were assessed by BDM and the correct rate is 90%.
引文
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[8]薛新华,陈群.基于GRNN的砂土液化危害等级评价模型研究[J].四川大学学报:工程科学版,2010,42(1):42-47.XUE Xinhua,CHEN Qun.Study on hazard degree evaluation of sand liquefaction based on the generalized regression neural network[J].Journal of Sichuan University(Engineering Science Edition),2010,42(1):42-47.(in Chinese).
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[10]刘勇健.饱和砂土地震液化判别的可拓聚类预测方法[J].岩土力学,2009,30(7):1939-1944.LIU Yongjian.Extension clustering prediction method for evaluation of seismic liquefaction of saturated sandy soil[J].Rock and Soil Mechanics,2009,30(7):1939-1944.(in Chinese).
[11]SAMOI P.Seismic liquefaction potential assessment by using relevance vector machine[J].Earthquake Engineering and Engineering Vibration,2007,6(4):331-336.
[12]刘年平,王宏图,袁志刚,等.砂土液化预测的Fisher判别模型及应用[J].岩土力学,2012,33(2):554-557.LIU Nianping,WANG Hongtu,YUAN Zhigang,et al.Fisher discriminant analysis model of sand liquefaction and its application[J].Rock and Soil Mechanics,2012,33(2):554-557.(in Chinese).
[13]颜可珍,刘能源,夏唐代.基于判别分析法的地震砂土液化预测研究[J].岩土力学,2009,30(7):2049-2052.YAN Kezhen,LIU Nengyuan,XIA Tangdai.Discriminant analysis model for prediction of sand soil liquefaction during earthquake[J].Rock and Soil Mechanics,2009,30(7):2049-2052.(in Chinese).
[14]金志仁.基于距离判别分析法的砂土液化预测模型及应用[J].岩土工程学报,2008,30(5):776-780.JIN Zhiren.Prediction of sand liquefaction based on distance discriminant analysis and its application[J].Chinese Journal of Geotechnical Engineering,2008,30(5):776-780.(in Chinese).
[15]陈国兴,胡庆兴,刘雪珠.关于砂土液化判别的若干意见[J].地震工程与工程振动,2002,22(1):141-151.CHEN Guoxing,HU Qingxing,LIU Xuezhu.Some comments on methodologies for estimating liquefaction of sandy soils[J].Earthquake Engineering and Engineering Vibration,2002,22(1):141-151.(in Chinese).
[16]陈国兴,李方明.基于径向基函数神经网络模型的砂土液化概率判别方法[J].岩土工程学报,2006,28(3):301-305.CHEN Guoxing,LI Fangming.Probabilistic estimation of sand liquefaction based on neural network model of radial basis function[J].Chinese Journal of Geotechnical Engineering,2006,28(3):301-305.(in Chinese).
[17]梅长林,周家良.实用统计方法[M].北京:科学出版社,2002.
[18]张尧庭,方开泰.多元统计分析引论[M].北京:科学出版社,2003.
[19]文畅平.岩体质量分级的Bayes判别分析方法[J].煤炭学报,2008,33(4):395-399.WEN Changping.Bayes discriminant analysis method of rock-mass quality classification[J].Journal of China Coal Society,2008,33(4):395-399.(in Chinese).
[20]张晓晖,吴亚萍,尚伟宏,等.利用模糊神经网络进行砂土液化势评判[J].工程地质学报,2001,9(2):209-213.ZHANG Xiaohui,WU Yaping,SHANG Weihong,et al.Using fuzzy neural network to evaluate sand liquefaction potential[J].Journal of Engineering Geology,2001,9(2):209-213.(in Chinese).
[2]赵艳林,杨绿峰,吴敏哲.砂土液化的灰色综合评判[J].自然灾害学报,2000,9(1):72-79.ZHAO Yanlin,YANG Lyufeng,WU Minzhe.Grey synthetical evaluation of liquefaction of sands[J].Journal of Natural Disaster,2000,9(1):72-79.(in Chinese).
[3]薛新华,张我华,刘红军.砂土地震液化的模糊综合评判法[J].重庆建筑大学学报,2006,28(1):55-58.XUE Xinhua,ZHANG Wohua,LIU Hongjun.Comprehensive fuzzy evaluation method for sand liquefaction[J].Journal of Chongqing Jianzhu University,2006,28(1):55-58.(in Chinese).
[4]BAZIAR M H,NILIPOUR N.Evaluation of liquefaction potential using neural-networks and CPT results[J].Soil Dynamics and Earthquake Engineering,2003,23(7):631-636.
[5]刘勇健,刘义健.人工神经网络在砂土液化评价中的应用[J].勘察科学技术,1999,17(1):3-5,41.LIU Yongjian,LIU Yijian.Application of artificial neural network to the assessment of sand liquefaction[J].Site Investigation Science and Technology,1999,(1):3-5,41.(in Chinese).
[6]赵胜利,赵红英,刘燕.基于SOFM神经网络的砂土液化评价[J].华中科技大学学报:城市科学版,2005,22(2):23-26.ZHAO Shengli,ZHAO Hongying,LIU Yan.Evaluation of sand liquefaction potential based on SOFM neural network[J].Journal of HUST(Urban Science Edition),2005,22(2):23-26.(in Chinese).
[7]董贤哲,张军平.补偿模糊神经网络在砂土液化势评价中的应用[J].地球科学与环境学报,2008,30(1):64-68.DONG Xianzhe,ZHANG Junping.Application of compensative fuzzy neural network in assessment of sand liquefaction potential[J].Journal of Earth Sciences and Environment,2008,30(1):64-68.(in Chinese).
[8]薛新华,陈群.基于GRNN的砂土液化危害等级评价模型研究[J].四川大学学报:工程科学版,2010,42(1):42-47.XUE Xinhua,CHEN Qun.Study on hazard degree evaluation of sand liquefaction based on the generalized regression neural network[J].Journal of Sichuan University(Engineering Science Edition),2010,42(1):42-47.(in Chinese).
[9]刘勇健.基于聚类-二叉树支持向量机的砂土液化预测模型[J].岩土力学,2008,29(10):2764-2768.LIU Yongjian.Support vector machine model for predicting sand liquefaction based on clustering binary tree algorithm[J].Rock and Soil Mechanics,2008,29(10):2764-2768.(in Chinese).
[10]刘勇健.饱和砂土地震液化判别的可拓聚类预测方法[J].岩土力学,2009,30(7):1939-1944.LIU Yongjian.Extension clustering prediction method for evaluation of seismic liquefaction of saturated sandy soil[J].Rock and Soil Mechanics,2009,30(7):1939-1944.(in Chinese).
[11]SAMOI P.Seismic liquefaction potential assessment by using relevance vector machine[J].Earthquake Engineering and Engineering Vibration,2007,6(4):331-336.
[12]刘年平,王宏图,袁志刚,等.砂土液化预测的Fisher判别模型及应用[J].岩土力学,2012,33(2):554-557.LIU Nianping,WANG Hongtu,YUAN Zhigang,et al.Fisher discriminant analysis model of sand liquefaction and its application[J].Rock and Soil Mechanics,2012,33(2):554-557.(in Chinese).
[13]颜可珍,刘能源,夏唐代.基于判别分析法的地震砂土液化预测研究[J].岩土力学,2009,30(7):2049-2052.YAN Kezhen,LIU Nengyuan,XIA Tangdai.Discriminant analysis model for prediction of sand soil liquefaction during earthquake[J].Rock and Soil Mechanics,2009,30(7):2049-2052.(in Chinese).
[14]金志仁.基于距离判别分析法的砂土液化预测模型及应用[J].岩土工程学报,2008,30(5):776-780.JIN Zhiren.Prediction of sand liquefaction based on distance discriminant analysis and its application[J].Chinese Journal of Geotechnical Engineering,2008,30(5):776-780.(in Chinese).
[15]陈国兴,胡庆兴,刘雪珠.关于砂土液化判别的若干意见[J].地震工程与工程振动,2002,22(1):141-151.CHEN Guoxing,HU Qingxing,LIU Xuezhu.Some comments on methodologies for estimating liquefaction of sandy soils[J].Earthquake Engineering and Engineering Vibration,2002,22(1):141-151.(in Chinese).
[16]陈国兴,李方明.基于径向基函数神经网络模型的砂土液化概率判别方法[J].岩土工程学报,2006,28(3):301-305.CHEN Guoxing,LI Fangming.Probabilistic estimation of sand liquefaction based on neural network model of radial basis function[J].Chinese Journal of Geotechnical Engineering,2006,28(3):301-305.(in Chinese).
[17]梅长林,周家良.实用统计方法[M].北京:科学出版社,2002.
[18]张尧庭,方开泰.多元统计分析引论[M].北京:科学出版社,2003.
[19]文畅平.岩体质量分级的Bayes判别分析方法[J].煤炭学报,2008,33(4):395-399.WEN Changping.Bayes discriminant analysis method of rock-mass quality classification[J].Journal of China Coal Society,2008,33(4):395-399.(in Chinese).
[20]张晓晖,吴亚萍,尚伟宏,等.利用模糊神经网络进行砂土液化势评判[J].工程地质学报,2001,9(2):209-213.ZHANG Xiaohui,WU Yaping,SHANG Weihong,et al.Using fuzzy neural network to evaluate sand liquefaction potential[J].Journal of Engineering Geology,2001,9(2):209-213.(in Chinese).
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