基于稀少样本数据的地应力场反演重构方法
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摘要
地应力测量昂贵的成本限制了测点数量,稀少样本实测数据难以对区域地应力场进行全面的描述与表达。如何依据稀少样本地应力实测数据准确地构建地质体内部地应力场分布状态,一直是岩土工程关心的重点问题,尤其随着深部工程的建设,掌握地应力场的分布规律是进行工程安全设计和防灾工作的基础。提出的GMDH(批数据处理)神经网络算法,结合地应力场分布随埋深的非线性特征及局部地质构造处地应力场的非连续性特点,构建出形成复杂地质体地应力场的边界条件模式,并基于现场的稀少样本测点数据进行复杂边界条件的生成,拟合出边界载荷非线性表达式。通过Matlab编程构建GMDH神经网络算法平台,该平台具有结构最优性和全局性等优势,克服了传统神经网络方法假设过多(网络结构假设)和网络结构过于简单等缺点,实现复杂地质体边界载荷表达式与实测点应力值的非线性映射,从而获取了较为合理的地应力场分布。为了验证算法的有效性,构建二维急倾斜地层地质区域模型,分别选取15个、12个、9个及6个测点数据进行地应力场反演。结果表明:随测点数量的减少,GMDH神经网络算法反演精度均大于83%,特别是6个测点稀少样本数据中,GMDH神经网络算法反演精度为84%,BP神经网络算法反演精度为76%,说明GMDH神经网络算法在稀少样本测点数据下具有较高的反演精度。另外,对稀少样本测点数据下的杏山铁矿地应力场进行反演和重构,结果显示,GMDH神经网络算法反演精度达到84%,绝大多数测点应力分量反演误差小于10%。因此,GMDH神经网络算法在稀少样本测点数据的反演计算中,具有良好的泛化性和非线性数据预测性,可为今后日益复杂的工程设计和施工提供有效的理论依据。
The high cost of in-situ stress measurement limits the number of measuring points. It is difficult to describe and express regional in-situ stress field comprehensively with limited sample measured data. How to accurately construct the distribution state of the in-situ stress field within the geological body based on the limited samples of measured in-situ data has always been a key issue of geotechnical engineering concern. Especially with the construction of deep engineering project,the understanding on the distribution law of in-situ stress field is the basis of engineering safety design and disaster prevention work. The GMDH(Group Modeling of Data Handing) neural network algorithm proposed in this paper combined the non-linearity of in-situ stress field distribution with burial depth and the discontinuity of in-situ stress field in local geological structure,constructed a boundary condition model for the formation of complex geological body in-situ stress field,and generated complex boundary conditions based on a limited sample of measured data in the field,and fitted the non-linear expression of boundary load. The GMDH neural network algorithm platform was constructed by MATLAB programming,which has the advantages of structural optimization and global optimization,and it overcame the shortcomings of traditional neural network method such as too many assumptions(network structure assumptions) and too simple network structure. It realized the non-linear mapping between the boundary load expression of complex geological body and the stress values of measured points,so as to obtain a more reasonable distribution of in-situ stress field. In order to verify the effectiveness of the method,a two-dimensional geological regional model of steeply inclined layer was constructed. Fifteen,twelve,nine and six measuring points were selected for in-situ stress field inversion. The results showed that with the decrease of the number of measuring points,the inversion accuracy of GMDH neural network algorithm was more than 83%. Especially in the limited sample data of six measuring points,the inversion accuracy of GMDH neural network algorithm was 84%,and BP neural network algorithm was76%. It showed that GMDH neural network algorithm has a higher inversion accuracy in the limited sample data. In addition,the in-situ stress field of Xingshan iron mine was inversely calculated and reconstructed based on limited sample data. The results showed that the inversion accuracy of GMDH neural network algorithm reached 84%,and the inversion error of stress component of most measuring point was less than 10%. Therefore,GMDH neural network algorithm has a good generalization and non-linear data predictability in the inversion calculation of limited sample measuring data,which could provide an effective theoretical basis for future increasingly complex engineering design and construction.
The high cost of in-situ stress measurement limits the number of measuring points. It is difficult to describe and express regional in-situ stress field comprehensively with limited sample measured data. How to accurately construct the distribution state of the in-situ stress field within the geological body based on the limited samples of measured in-situ data has always been a key issue of geotechnical engineering concern. Especially with the construction of deep engineering project,the understanding on the distribution law of in-situ stress field is the basis of engineering safety design and disaster prevention work. The GMDH(Group Modeling of Data Handing) neural network algorithm proposed in this paper combined the non-linearity of in-situ stress field distribution with burial depth and the discontinuity of in-situ stress field in local geological structure,constructed a boundary condition model for the formation of complex geological body in-situ stress field,and generated complex boundary conditions based on a limited sample of measured data in the field,and fitted the non-linear expression of boundary load. The GMDH neural network algorithm platform was constructed by MATLAB programming,which has the advantages of structural optimization and global optimization,and it overcame the shortcomings of traditional neural network method such as too many assumptions(network structure assumptions) and too simple network structure. It realized the non-linear mapping between the boundary load expression of complex geological body and the stress values of measured points,so as to obtain a more reasonable distribution of in-situ stress field. In order to verify the effectiveness of the method,a two-dimensional geological regional model of steeply inclined layer was constructed. Fifteen,twelve,nine and six measuring points were selected for in-situ stress field inversion. The results showed that with the decrease of the number of measuring points,the inversion accuracy of GMDH neural network algorithm was more than 83%. Especially in the limited sample data of six measuring points,the inversion accuracy of GMDH neural network algorithm was 84%,and BP neural network algorithm was76%. It showed that GMDH neural network algorithm has a higher inversion accuracy in the limited sample data. In addition,the in-situ stress field of Xingshan iron mine was inversely calculated and reconstructed based on limited sample data. The results showed that the inversion accuracy of GMDH neural network algorithm reached 84%,and the inversion error of stress component of most measuring point was less than 10%. Therefore,GMDH neural network algorithm has a good generalization and non-linear data predictability in the inversion calculation of limited sample measuring data,which could provide an effective theoretical basis for future increasingly complex engineering design and construction.
引文
[1]张社荣,胡安奎,王超,等.基于SLR-ANN的地应力场三维智能反演方法研究[J].岩土力学,2017,38(9):2737-2745.ZHANG Sherong,HU Ankui,WANG Chao,et al.Three-dimensional intelligent inversion method for in-situ stress field based on SLR-ANN algorithm[J].Rock and Soil Mechanics,2017,38(9):2737-2745.
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[3]程远平,张晓磊,王亮.地应力对瓦斯压力及突出灾害的控制作用研究[J].采矿与安全工程学报,2013,30(3):408-414.CHENG Yuanping,ZHANG Xiaolei,WANG Liang.Controlling effect of ground stress on gas pressure and outburst disaster[J].Journal of Mining&Safety Engineering,2013,30(3):408-414.
[4]袁海平,王金安,蔡美峰.复杂地应力场几何跨尺度反演与重构方法研究[J].采矿与安全工程学报,2011,28(4):589-595.YUAN Haiping,WANG Jinan,CAI Meifeng.Geometric cross-scale back-analysis and reconstruction method for complicated geo-stress field[J].Journal of Mining&Safety Engineering,2011,28(4):589-595.
[5]陈章华,陈磊,纪洪广.基于偏最小二乘法的地应力场拟合[J].北京科技大学学报,2013,35(1):1-7.CHEN Zhanghua,CHEN Lei,JI Hongguang.Geo-stress field fitting based on the partial least square method[J].Journal of University of Science and Technology Beijing,2013,35(1):1-7.
[6]张乐文,张德永,邱道宏.径向基函数神经网络在地应力场反演中的应用[J].岩土力学学报,2012,33(3):799-804.ZHANG Lewen,ZHANG Deyong,QIU Daohong.Application of radial basis function neural network to geostress field back analysis[J].Rock and Soil Mechanics,2012,33(3):799-804.
[7]叶智峰,曹青.极限学习机在初始地应力场反演中的应用[J].水电能源科学,2016,34(6):158-160,157.YE Zhifeng,CAO Qing.Application of extreme learning machine in back analysis of initial geostress field[J].Water Resources and Power,2016,34(6):158-160,157.
[8]裴启涛,丁秀丽,卢波,等.考虑地应力分布形式的坝址区初始应力场二次反演方法[J].岩土力学,2016,37(10):2961-2970.PEI Qitao,DING Xiuli,LU Bo,et al.Two-stage back analysis method of initial geostress field in dam areas considering distribution characteristics of geostress[J].Rock and Soil Mechanics,2016,37(10):2961-2970.
[9]杨志强,高谦,翟淑花,等.复杂工程地质体地应力场智能反演[J].哈尔滨工业大学学报,2016,48(4):154-160.YANG Zhiqiang,GAO Qian,ZHAI Shuhua,et al.Intelligent inversion method of in-situ stress field for a complicated engineering geological body[J].Journal of Harbin Institute of Technology,2016,48(4):154-160.
[10]杨风威,房敬年,杨继华,等.兰州水源地工程超长输水隧洞初始地应力反演研究[J].水电能源科学,2018,36(8):94-97,73.YANG Fengwei,FANG Jingnian,YANG Jihua,et al.initial geostress inversion of ultralong water transport tunnel in water source area of Lanzhou[J].Water Resources and Power,2018,36(8):94-97,73.
[11]史佳欢.露天转地下开采上覆岩体变形机理及其灾害预测[D].北京:北方工业大学,2015:4.SHI Jiahuan.Deformation mechanism and disaster analysis of overlying rock in mining with transition from pit to underground[D].Beijing:North China University of Technology,2015:4.
[12]孙世国,苗子臻,龚之淇,等.杏山铁矿冲击地压预测的优化GM(1,1)模型[J].金属矿山,2017(1):165-168.SUN Shiguo,MIAO Zizhen,Gong Zhiqi,et al.Optimized GM(1,1)model for prediction of rock burst in Xingshan Tron Mine[J].Metal Mine,2017(1):165-168.
[13]戴荣,李仲奎.三维地应力场BP反分析的改进[J].岩石力学与工程学报,2005,24(1):83-88.DAI Rong,LI Zhongkui.Modified BP back analysis of 3D in-situ stresses[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(1):83-88.
[14]王金安,李飞.复杂地应力场反演优化算法及研究最新进展[J].中国矿业大学学报,2015,44(2):189-205.WANG Jinan,LI Fei.Review of inverse optimal algorithm of in-situ stress field and new achievement[J].Journal of China University of Mining and Technology,2015,44(2):189-205.
[15]穆成林,裴向军,路军富.基于多层次灰色理论围岩稳定性评价研究[J].地下空间与工程学报,2016,12(1):220-226.MU Chenglin,PEI Xiangjun,LU Junfu.Study on evaluation of surrounding rock stability based on muti-hierarchy gray theory[J].Chinese Journal of Underground Space and Engineering,2016,12(1):220-226.
[16]朱兵,贺昌政,肖进.基于GMDH方法的四川民用汽车保有量预测研究[J].现代管理科学,2006(6):20-21.ZHU Bing,HE Changzheng,XIAO Jin.Study on the prediction of Sichuan civil automobile ownership based on GMDH method[J].Modern management science,2006(6):20-21.
[17]徐玲.基于GMDH神经网络的轮胎硫化温度预测[J].橡胶工业,2013,60(5):301-304.XU Ling.Tire vulanization temperature prediction based on gmdh neural network[J].Rubber Industry,2013,60(5):301-304.
[18]李牡丹,王印松.基于灰色GMDH网络组合模型的风速预测[J].可再生能源,2017,35(4):522-527.LI Mudan,WANG Yinsong.Wind speed prediction based on grey GMDH network combined model[J].Renewable Energy Resources,2017,35(4):522-527.
[19]顾洁,李雪亮,牛新生,等.基于GMDH的中长期电力负荷组合预测模型[J].电力科学与技术学报,2012,27(1):54-58.GU Jie,LI Xueliang,NIU Xinsheng,et al.Study on combination forecasting model for mid-long term power load based on GMDH[J].Jounal of Eiectric Power Science and Technology,2012,27(1):54-58.
[20]PHAM D T,LIU X.Modelling and prediction using GMDH networks of Adalines with nonlinear preprocessors[J].International Journal of Systems Science,1994,25(11):1743-1759.
[21]崔霞,高建华.基于GMDH神经网络的组合预测模型[J].小型微型计算机系统,2016,37(6):1164-1167.CUI Xia,CAO Jianhua.Combined prediction model based on gmdh neuro network[J].Journal of Chinese Computer Systems,2016,37(6):1164-1167.
[22]黄克智,薛明德,陆明万.张量分析(第2版)[M].北京:清华大学出版社,2003.
[23]邱海涛,黄正均,任奋华.杏山铁矿露天转地下开采边坡变形分析[J].矿冶,2011,20(2):1-4,9.QIU Haitao,HUANG Zhengjun,REN Fenhua.Deformation analysis of the slope during the process from open-pit to underground mining in Xingshan iron mine[J].Mining&Metallurgy,2011,20(2):1-4,9.
[24]王金安,黄琨,张然.高陡复杂露天矿边坡地应力场分区非线性反演分析[J].岩土力学,2013,34(S2):214-221.WANG Jinan,HUANG Kun,ZHANG Ran.Sub-regional nonlinear in-situ stress inversion analysis of complex high steep slope of open pit[J].Rock and Soil Mechanics,2013,34(S2):214-221.
[25]朱权洁,王胜开,田昭军,等.MATLAB在复杂地质区域地应力场反演中的应用[J].工业安全与环保,2017,43(7):24-28.ZHU Quanjie,WANG Shengkai,TIAN Zhaojun,et al.Application of MATLAB in the in-situ stress inverse analysis[J].Industrial Safety and Environmental Protection,2017,43(7):24-28.
[26]张龙飞,许英霞,高孝敏,等.冀东杏山沉沉积变质型铁矿床富铁矿成因探讨[J].地质与斟探,2015,51(3):405-413.ZHANG Longfei,XU Yingxia,GAO Xiaomin,et al.Genesis of high-grade ores in the Xingshan sedimentary metamorphic iron deposit of eastern Hebei Province[J].Geology and Exploration 2015,51(3):405-413.
[2]LI Qingfeng,ZHU Quanqu.Control technology and coordination deformation mechanism of rise entry group with high ground stress[J].International Journal of Mining Science and Technology,2012,22(3):429-435.
[3]程远平,张晓磊,王亮.地应力对瓦斯压力及突出灾害的控制作用研究[J].采矿与安全工程学报,2013,30(3):408-414.CHENG Yuanping,ZHANG Xiaolei,WANG Liang.Controlling effect of ground stress on gas pressure and outburst disaster[J].Journal of Mining&Safety Engineering,2013,30(3):408-414.
[4]袁海平,王金安,蔡美峰.复杂地应力场几何跨尺度反演与重构方法研究[J].采矿与安全工程学报,2011,28(4):589-595.YUAN Haiping,WANG Jinan,CAI Meifeng.Geometric cross-scale back-analysis and reconstruction method for complicated geo-stress field[J].Journal of Mining&Safety Engineering,2011,28(4):589-595.
[5]陈章华,陈磊,纪洪广.基于偏最小二乘法的地应力场拟合[J].北京科技大学学报,2013,35(1):1-7.CHEN Zhanghua,CHEN Lei,JI Hongguang.Geo-stress field fitting based on the partial least square method[J].Journal of University of Science and Technology Beijing,2013,35(1):1-7.
[6]张乐文,张德永,邱道宏.径向基函数神经网络在地应力场反演中的应用[J].岩土力学学报,2012,33(3):799-804.ZHANG Lewen,ZHANG Deyong,QIU Daohong.Application of radial basis function neural network to geostress field back analysis[J].Rock and Soil Mechanics,2012,33(3):799-804.
[7]叶智峰,曹青.极限学习机在初始地应力场反演中的应用[J].水电能源科学,2016,34(6):158-160,157.YE Zhifeng,CAO Qing.Application of extreme learning machine in back analysis of initial geostress field[J].Water Resources and Power,2016,34(6):158-160,157.
[8]裴启涛,丁秀丽,卢波,等.考虑地应力分布形式的坝址区初始应力场二次反演方法[J].岩土力学,2016,37(10):2961-2970.PEI Qitao,DING Xiuli,LU Bo,et al.Two-stage back analysis method of initial geostress field in dam areas considering distribution characteristics of geostress[J].Rock and Soil Mechanics,2016,37(10):2961-2970.
[9]杨志强,高谦,翟淑花,等.复杂工程地质体地应力场智能反演[J].哈尔滨工业大学学报,2016,48(4):154-160.YANG Zhiqiang,GAO Qian,ZHAI Shuhua,et al.Intelligent inversion method of in-situ stress field for a complicated engineering geological body[J].Journal of Harbin Institute of Technology,2016,48(4):154-160.
[10]杨风威,房敬年,杨继华,等.兰州水源地工程超长输水隧洞初始地应力反演研究[J].水电能源科学,2018,36(8):94-97,73.YANG Fengwei,FANG Jingnian,YANG Jihua,et al.initial geostress inversion of ultralong water transport tunnel in water source area of Lanzhou[J].Water Resources and Power,2018,36(8):94-97,73.
[11]史佳欢.露天转地下开采上覆岩体变形机理及其灾害预测[D].北京:北方工业大学,2015:4.SHI Jiahuan.Deformation mechanism and disaster analysis of overlying rock in mining with transition from pit to underground[D].Beijing:North China University of Technology,2015:4.
[12]孙世国,苗子臻,龚之淇,等.杏山铁矿冲击地压预测的优化GM(1,1)模型[J].金属矿山,2017(1):165-168.SUN Shiguo,MIAO Zizhen,Gong Zhiqi,et al.Optimized GM(1,1)model for prediction of rock burst in Xingshan Tron Mine[J].Metal Mine,2017(1):165-168.
[13]戴荣,李仲奎.三维地应力场BP反分析的改进[J].岩石力学与工程学报,2005,24(1):83-88.DAI Rong,LI Zhongkui.Modified BP back analysis of 3D in-situ stresses[J].Chinese Journal of Rock Mechanics and Engineering,2005,24(1):83-88.
[14]王金安,李飞.复杂地应力场反演优化算法及研究最新进展[J].中国矿业大学学报,2015,44(2):189-205.WANG Jinan,LI Fei.Review of inverse optimal algorithm of in-situ stress field and new achievement[J].Journal of China University of Mining and Technology,2015,44(2):189-205.
[15]穆成林,裴向军,路军富.基于多层次灰色理论围岩稳定性评价研究[J].地下空间与工程学报,2016,12(1):220-226.MU Chenglin,PEI Xiangjun,LU Junfu.Study on evaluation of surrounding rock stability based on muti-hierarchy gray theory[J].Chinese Journal of Underground Space and Engineering,2016,12(1):220-226.
[16]朱兵,贺昌政,肖进.基于GMDH方法的四川民用汽车保有量预测研究[J].现代管理科学,2006(6):20-21.ZHU Bing,HE Changzheng,XIAO Jin.Study on the prediction of Sichuan civil automobile ownership based on GMDH method[J].Modern management science,2006(6):20-21.
[17]徐玲.基于GMDH神经网络的轮胎硫化温度预测[J].橡胶工业,2013,60(5):301-304.XU Ling.Tire vulanization temperature prediction based on gmdh neural network[J].Rubber Industry,2013,60(5):301-304.
[18]李牡丹,王印松.基于灰色GMDH网络组合模型的风速预测[J].可再生能源,2017,35(4):522-527.LI Mudan,WANG Yinsong.Wind speed prediction based on grey GMDH network combined model[J].Renewable Energy Resources,2017,35(4):522-527.
[19]顾洁,李雪亮,牛新生,等.基于GMDH的中长期电力负荷组合预测模型[J].电力科学与技术学报,2012,27(1):54-58.GU Jie,LI Xueliang,NIU Xinsheng,et al.Study on combination forecasting model for mid-long term power load based on GMDH[J].Jounal of Eiectric Power Science and Technology,2012,27(1):54-58.
[20]PHAM D T,LIU X.Modelling and prediction using GMDH networks of Adalines with nonlinear preprocessors[J].International Journal of Systems Science,1994,25(11):1743-1759.
[21]崔霞,高建华.基于GMDH神经网络的组合预测模型[J].小型微型计算机系统,2016,37(6):1164-1167.CUI Xia,CAO Jianhua.Combined prediction model based on gmdh neuro network[J].Journal of Chinese Computer Systems,2016,37(6):1164-1167.
[22]黄克智,薛明德,陆明万.张量分析(第2版)[M].北京:清华大学出版社,2003.
[23]邱海涛,黄正均,任奋华.杏山铁矿露天转地下开采边坡变形分析[J].矿冶,2011,20(2):1-4,9.QIU Haitao,HUANG Zhengjun,REN Fenhua.Deformation analysis of the slope during the process from open-pit to underground mining in Xingshan iron mine[J].Mining&Metallurgy,2011,20(2):1-4,9.
[24]王金安,黄琨,张然.高陡复杂露天矿边坡地应力场分区非线性反演分析[J].岩土力学,2013,34(S2):214-221.WANG Jinan,HUANG Kun,ZHANG Ran.Sub-regional nonlinear in-situ stress inversion analysis of complex high steep slope of open pit[J].Rock and Soil Mechanics,2013,34(S2):214-221.
[25]朱权洁,王胜开,田昭军,等.MATLAB在复杂地质区域地应力场反演中的应用[J].工业安全与环保,2017,43(7):24-28.ZHU Quanjie,WANG Shengkai,TIAN Zhaojun,et al.Application of MATLAB in the in-situ stress inverse analysis[J].Industrial Safety and Environmental Protection,2017,43(7):24-28.
[26]张龙飞,许英霞,高孝敏,等.冀东杏山沉沉积变质型铁矿床富铁矿成因探讨[J].地质与斟探,2015,51(3):405-413.ZHANG Longfei,XU Yingxia,GAO Xiaomin,et al.Genesis of high-grade ores in the Xingshan sedimentary metamorphic iron deposit of eastern Hebei Province[J].Geology and Exploration 2015,51(3):405-413.
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