基于KPCA-GPC的地震砂土液化预测
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摘要
在砂土液化多指标综合判别法中,采用的判别因子数量一般为5~12,为防止特征冗余,引入核主成分分析(KPCA)对原始样本进行非线性特征提取,同时基于高斯过程分类(GPC)原理,构建了砂土液化预测的KPCA-GPC模型。以唐山地震砂土液化的25个案例为样本,选取平均粒径D50、地下水位dw、标准贯入击数N63.5、砂层埋深ds、地震烈度I、震中距离L、不均匀系数Cu、剪应力与有效上覆应力比τ_d/σ'v共8个指标作为判别因子,对该模型进行验证。研究结果表明:距离判别分析(DDA)、高斯过程分类(GPC)、Seed法的判别准确率分别为83%、83%、67%,而KPCA-DDA和KPCA-GPC的判别准确率均为100%,由此说明消除特征冗余的必要性及KPCA-GPC模型的适用性;同时,与DDA、SVM、BP等确定性判别方法相比,GPC可获得具有概率意义的砂土液化预测结果。
In multi-index comprehensive discrimination method for sand liquefaction, the number of discriminant factors are generally 5 to 12. In order to prevent feature redundancy resulted by too many discriminant factors,kernel principal component analysis( KPCA) was introduced to extract the non-linear feature of raw data,then based on Gaussian process classification( GPC) principle,the prediction model of KPCA-GPC for sand liquefaction was constructed. Combined with 25 cases of sand liquefaction in Tangshan earthquake,eight factors were selected for model verification listed as follows: average particle size D50,groundwater table dw,standard penetration blow count N63. 5,sand depth ds,magnitude I,epicentral distance L,coefficient of non-uniformity Cu,ratio of shearing stress to effective overburden stress τd/σ'v. The results show that the accuracy of DDA( distance discriminant analysis) method,GPC method and Seed method are83%,83% and 67%,respectively. The accuracy of KPCA-DDA method and KPCA-GPC method are all100%,it indicates the necessity of reducing feature redundancy of raw data and the applicability of the KPCAGPC method. Compared to deterministic discrimination method such as DDA,SVM( support vector machine)and BP( neural network),the GPC model can produce the prediction results of sandy soil liquefaction with probability significance which helps people very much in practical engineering.
In multi-index comprehensive discrimination method for sand liquefaction, the number of discriminant factors are generally 5 to 12. In order to prevent feature redundancy resulted by too many discriminant factors,kernel principal component analysis( KPCA) was introduced to extract the non-linear feature of raw data,then based on Gaussian process classification( GPC) principle,the prediction model of KPCA-GPC for sand liquefaction was constructed. Combined with 25 cases of sand liquefaction in Tangshan earthquake,eight factors were selected for model verification listed as follows: average particle size D50,groundwater table dw,standard penetration blow count N63. 5,sand depth ds,magnitude I,epicentral distance L,coefficient of non-uniformity Cu,ratio of shearing stress to effective overburden stress τd/σ'v. The results show that the accuracy of DDA( distance discriminant analysis) method,GPC method and Seed method are83%,83% and 67%,respectively. The accuracy of KPCA-DDA method and KPCA-GPC method are all100%,it indicates the necessity of reducing feature redundancy of raw data and the applicability of the KPCAGPC method. Compared to deterministic discrimination method such as DDA,SVM( support vector machine)and BP( neural network),the GPC model can produce the prediction results of sandy soil liquefaction with probability significance which helps people very much in practical engineering.
引文
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[17]HANNA A M,URAL D,SAYGILI G.Neural network model for liquefaction potential in soil deposits using Turkey and Taiwan earthquake data[J].Soil Dynamics&Earthquake Engineering,2007,27(6):521-540.
[2]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.
[3]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.
[4]胡记磊,唐小微,裘江南.基于贝叶斯网络的地震液化概率预测分析[J].岩土力学,2016,37(6):1745-1752.HU Jilei,TANG Xiaowei,QIU Jiangnan.Prediction of probability of seismic-induced liquefaction based on Bayesian network[J].Rock and Soil Mechanics,2016,37(6):1745-1752.
[5]禹建兵,刘浪.不同判别准则下的砂土地震液化势评价方法及应用对比[J].中南大学学报(自然科学版),2013,44(9):3849-3856.YU Jianbing,LIU Lang.Two multiple discriminant methods to evaluate sand seismic siquefaction potential and its comparison[J].Journal of Central South University(Science and Technology),2013,44(9):3849-3856.
[6]宫凤强,李嘉维.基于PCA-DDA原理的砂土液化预测模型及应用[J].岩土力学,2016,37(S1):448-454.GONG Fengqiang,LI Jiawei.Discrimination model of sandy soil liquefaction based on PCA-DDA principle and its application[J].Rock and Soil Mechanics,37(S1):448-454.
[7]TANG Xiaowei,HU Jilei,QIU Jiang-nan.Identifying significant influence factors of seismic soil liquefaction and analyzing their structural relationship[J].KSCE Journal of Civil Engineering,2016:1-9.
[8]杨胜凯.基于核主成分分析的特征变换研究[D].浙江:浙江大学,2014.YANG Shengkai.Research on feature transformation based on kernel principal component analysis[D].Zhejiang:Zhejiang University,2014.
[9]杨先勇,周晓军,张文斌,等.基于局域波法和KPCA-LSSVM的滚动轴承故障诊断[J].浙江大学学报(工学版),2010,44(8):1519-1524.YANG Xianyong,ZHOU Xiaojun,ZHANG Wenbin,et al.Rolling bearing fault diagnosis based on local wave method and KPCA-LSSVM[J].Journal of Zhejiang University(Engineering Science),2010,44(8):1519-1524.
[10]RASMUSSEN C E,WILLIAMS C K I.Gaussian processes for machine learning[M].Cambridge:MIT Press,2006.
[11]NICKISCH H,RASMUSSEN C E.Approximations for binary Gaussian Process classification[J].Journal of Machine Learning Research,2008(9):2035-2078.
[12]XU Yong,ZHANG David,SONG Fengxi,et al.A method for speeding up feature extraction based on KPCA[J].Neurocomputing,2007,70(4-6):1056-1061.
[13]WANG Quan.Kernel principal component analysis and its applications in face recognition and active shape models[J].Computer Science,2014.
[14]童楚东,史旭华.基于互信息的PCA方法及其在过程监测中的应用[J].化工学报,2015,66(10):4101-4106.TONG Chudong,SHI Xuhua.Mutual information based PCA algorithm with application in process monitoring[J].CIESC Journal,2015,66(10):4101-4106.
[15]RASMUSSEN C E,NICKISCH H.The GPML Toolbox version 4.0[EB/OL].[2016-10-28].http://www.gaussianprocess.org/gpml/code/matlab/doc/manual.pdf.
[16]NHAT D H,DIEU T B.Predicting earthquakeinduced soil liquefaction based on a hybridization of kernel Fisher discriminant analysis and a least squares support vector machine:a multi-dataset study[J].Bulletin of Engineering Geology and the Environment,2016:1-14.
[17]HANNA A M,URAL D,SAYGILI G.Neural network model for liquefaction potential in soil deposits using Turkey and Taiwan earthquake data[J].Soil Dynamics&Earthquake Engineering,2007,27(6):521-540.