基于支持向量机回归的岩体变形模量预测
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摘要
岩体变形模量是表征岩体变形特性的最重要参数之一,其获取手段有室内试验与现场试验法、经验关系法、数值模拟法、人工智能预测方法等。人工智能预测方法中常用的是神经网络方法,但神经网络易陷入局部极小值和过学习而导致低精度,支持向量机回归(SVR)方法能有效地避免神经网络的以上缺陷,并在小样本、非线性预测方面具有较大优势,但目前SVR应用于岩体变形模量预测的研究较少。以某水电站坝址区英安岩的试验数据为依托,采用灰色关联分析筛选出与变形模量最相关的纵波波速作为输入变量。在此基础上,以3个国内的水电站为例,分别建立相应的以实测纵波波速作为输入变量的粒子群算法优化-支持向量机回归(PSO-SVR)变形模量预测模型,同时,通过与BP神经网络(BP-NN)、RBF神经网络(RBF-NN)2种预测方法进行对比,对比分析表明SVR模型具有更高的预测精度,预测效果较好,说明PSO-SVR方法更适用于岩体变形模量预测。
The deformation modulus is one of the most important parameters for characterization of rock mass deformation.It can be obtained by laboratory and field experiments,empirical relation method,numerical simulation method and intelligent nonlinear methods.In these methods,the artificial neural network method is the most widely used intelligent nonlinear method,such as back propagation neural network(RBF-NN)and radial basis functionneural network(RBF-NN).But the structure of neural network is difficult to determine,and the disadvantage of local minimization and over learning leads to low prediction accuracy.While support vector machine regression(SVR)method has more advantages in small samples and nonlinear prediction,but there are few researches in prediction of rock mass modulus with SVR method currently.With experimental data from dacite of a hydropower station dam area,this paper selects the optimal input variable using grey relational analysis(GRA)as the input variables of particle swarm optimization(PSO)algorithm optimized SVR model to predict the deformation modulus of rock mass.In order to reveal its supremacy of the PSO-SVR model over its comparison objects,i.e.,BP-NN,RBF-NN models,in-situ test data of longitudinal wave velocity and deformation modulus from 3 hydropowers are obtained to develop the corresponding PSO-SVR model,BP-NN model and RBF-NN model.It turns out that the PSO-SVR prediction model has higher prediction accuracy,and is more suitable for the prediction of rock mass deformation modulus.The simulation results proved the presented method to be applicable,and the obtained results confirm the superiority of the PSO-SVR in modeling of deformation modulus of rock mass.
The deformation modulus is one of the most important parameters for characterization of rock mass deformation.It can be obtained by laboratory and field experiments,empirical relation method,numerical simulation method and intelligent nonlinear methods.In these methods,the artificial neural network method is the most widely used intelligent nonlinear method,such as back propagation neural network(RBF-NN)and radial basis functionneural network(RBF-NN).But the structure of neural network is difficult to determine,and the disadvantage of local minimization and over learning leads to low prediction accuracy.While support vector machine regression(SVR)method has more advantages in small samples and nonlinear prediction,but there are few researches in prediction of rock mass modulus with SVR method currently.With experimental data from dacite of a hydropower station dam area,this paper selects the optimal input variable using grey relational analysis(GRA)as the input variables of particle swarm optimization(PSO)algorithm optimized SVR model to predict the deformation modulus of rock mass.In order to reveal its supremacy of the PSO-SVR model over its comparison objects,i.e.,BP-NN,RBF-NN models,in-situ test data of longitudinal wave velocity and deformation modulus from 3 hydropowers are obtained to develop the corresponding PSO-SVR model,BP-NN model and RBF-NN model.It turns out that the PSO-SVR prediction model has higher prediction accuracy,and is more suitable for the prediction of rock mass deformation modulus.The simulation results proved the presented method to be applicable,and the obtained results confirm the superiority of the PSO-SVR in modeling of deformation modulus of rock mass.
引文
[1]王新峰,梁杏,刘蕴,等.裂隙岩体局域离散模型构建及参数敏感性分析:以锦屏一级水电站坝区为例[J].地质科技情报,2013,32(6):195-200.
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[5]王昌硕,梁烨,王亮清,等.基于三维结构面网络模拟的岩体变形模量确定方法[J].煤田地质与勘探,2016,44(3):97-102.
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[12]赵渊,王亮清,周鹏.基于改进RBF神经网络的硬岩岩体变形模量预测[J].人民长江,2015,46(3):38-41.
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[15]王昌硕,王亮清,葛云峰,等基于统计参数的二维节理粗糙度系数非线性确定方法[J].岩土力学,2017,38(2):565-573.
[16]仝跃,陈亮,黄宏伟.基于PSO-SVM算法的高放废物处置北山预选区岩爆预测[J].长江科学院院报,2017,34(5):68-74.
[17]董辉,陈家博,杨果岳,等.工程先验知识辨识下的滑坡非平稳变形支持向量机预测[J].岩土力学,2012,33(8):2366-2372,2382.
[18]彭磊,黄张裕,凌晨阳,等.基于PSO-SVM模型的深基坑变形预测研究[J].工程勘察,2011,39(3):82-85.
[19]万智,董辉,刘宝琛.基于正交设计下SVM滑坡变形时序回归预测的超参数选择[J].岩土力学,2010,31(2):503-508,515.
[20]罗战友,杨晓军,龚晓南.基于支持向量机的边坡稳定性预测模型[J].岩石力学与工程学报,2005,24(1):144-148.
[21]陆有忠,杨有贞,张会林.边坡工程可靠性的支持向量机估计[J].岩石力学与工程学报,2005,24(1):149-153.
[22]白春华,周宣赤,林大超,等.消除EMD端点效应的PSO-SVM方法研究[J].系统工程理论与实践,2013,33(5):1298-1306.
[23]邓聚龙.灰色系统理论的关联空间[J].模糊数学,1985(2):1.
[24]Barton N.Some new Q-value correlations to assist in-site characterisation and tunnel design[J].International Journal of Rock Mechanics&Mining Sciences,2002,39(2):185-216.
[25]赵明阶,徐蓉.岩石声学特性研究现状及展望[J].重庆交通学院学报,2000,19(2):79-85.
[26]周洪福,聂德新,王春山.水电工程坝基玄武岩体波速与变形模量关系[J].地球科学:中国地质大学学报,2015,40(11):1904-1912.
[2]董学晟.水工岩石力学[M].北京:中国水利水电出版社,2004.
[3]何娇,王亮清,杨国俊.基于纵波波速值的岩体质量分级及变形模量估算[J].人民长江,2012,43(增刊2):14-16.
[4]李维树,黄志鹏,谭新.水电工程岩体变形模量与波速相关性研究及应用[J].岩石力学与工程学报,2010,29(增刊1):2727-2733.
[5]王昌硕,梁烨,王亮清,等.基于三维结构面网络模拟的岩体变形模量确定方法[J].煤田地质与勘探,2016,44(3):97-102.
[6]Panthee S,Singh P K,Kainthola A,et al.Comparative study of the deformation modulus of rock mass[J].Bulletin of Engineering Geology&the Environment,2018,77(2):751-760.
[7]Shen X,Chen M,Lu W,et al.Using P wave modulus to estimate the mechanical parameters of rock mass[J].Bulletin of Engineering Geology&the Environment,2016,76(4):1-10.
[8]杨超,黄达,张永兴.基于Copula理论岩体质量Q值及波速与变形模量多变量相关性研究[J].岩石力学与工程学报,2014,33(3):507-513.
[9]朱雷,王小群,聂德新,等.基于随机模型溶蚀岩体强度参数研究[J].工程地质学报,2014,22(6):1034-1038.
[10]冯夏庭,王泳嘉.用于岩体质量评价的神经网络专家系统[J].有色金属,1994,46(4):1-7.
[11]张楠,王亮清,葛云峰,等.基于因子分析的BP神经网络在岩体变形模量预测中的应用[J].工程地质学报,2016,24(1):87-95.
[12]赵渊,王亮清,周鹏.基于改进RBF神经网络的硬岩岩体变形模量预测[J].人民长江,2015,46(3):38-41.
[13]Gholami M,Bodaghi A.A robust approach through combining optimized neural network and optimized support vector regression for modeling deformation modulus of rock masses[J].Modeling Earth Systems&Environment,2017,3(1):22.
[14]Vapnik V N.The nature of statistical learning theory[J].IEEE Transactions on Neural Networks,2002,8(6):1564-1564.
[15]王昌硕,王亮清,葛云峰,等基于统计参数的二维节理粗糙度系数非线性确定方法[J].岩土力学,2017,38(2):565-573.
[16]仝跃,陈亮,黄宏伟.基于PSO-SVM算法的高放废物处置北山预选区岩爆预测[J].长江科学院院报,2017,34(5):68-74.
[17]董辉,陈家博,杨果岳,等.工程先验知识辨识下的滑坡非平稳变形支持向量机预测[J].岩土力学,2012,33(8):2366-2372,2382.
[18]彭磊,黄张裕,凌晨阳,等.基于PSO-SVM模型的深基坑变形预测研究[J].工程勘察,2011,39(3):82-85.
[19]万智,董辉,刘宝琛.基于正交设计下SVM滑坡变形时序回归预测的超参数选择[J].岩土力学,2010,31(2):503-508,515.
[20]罗战友,杨晓军,龚晓南.基于支持向量机的边坡稳定性预测模型[J].岩石力学与工程学报,2005,24(1):144-148.
[21]陆有忠,杨有贞,张会林.边坡工程可靠性的支持向量机估计[J].岩石力学与工程学报,2005,24(1):149-153.
[22]白春华,周宣赤,林大超,等.消除EMD端点效应的PSO-SVM方法研究[J].系统工程理论与实践,2013,33(5):1298-1306.
[23]邓聚龙.灰色系统理论的关联空间[J].模糊数学,1985(2):1.
[24]Barton N.Some new Q-value correlations to assist in-site characterisation and tunnel design[J].International Journal of Rock Mechanics&Mining Sciences,2002,39(2):185-216.
[25]赵明阶,徐蓉.岩石声学特性研究现状及展望[J].重庆交通学院学报,2000,19(2):79-85.
[26]周洪福,聂德新,王春山.水电工程坝基玄武岩体波速与变形模量关系[J].地球科学:中国地质大学学报,2015,40(11):1904-1912.