混凝土重力坝多参数弹性位移反演分析不唯一性理论探讨

黄耀英; 殷晓慧; 李春光

doi:10.21656/1000-0887.400164

混凝土重力坝多参数弹性位移反演分析不唯一性理论探讨

doi: 10.21656/1000-0887.400164

¹三峡大学水利与环境学院, 湖北宜昌 443002;²中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室, 武汉 430071

基金项目: 国家自然科学基金(51779130)

详细信息

作者简介:
黄耀英(1977—)，男，教授，博士(通讯作者. E-mail: huangyaoying@sohu.com).

中图分类号: TV31|O302
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出版历程
- 收稿日期: 2019-05-09
- 修回日期: 2019-05-31
- 刊出日期: 2020-02-01

Theoretical Study on Multi-Parameter Inversion Non-Uniqueness Based on Elastic Displacements of Concrete Gravity Dams

¹College of Hydraulic & Environmental Engineering, China Three Gorges University, Yichang, Hubei 443002, P.R.China;²State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, P.R.China

Funds: The National Natural Science Foundation of China(51779130)

摘要

摘要: 反演分析是现场监测-反演分析-工程实践检验-正演分析及预测的闭环系统的重要环节，而参数反分析是工程实践中研究最多的反分析问题.针对混凝土重力坝多参数反演分析是否具有唯一性，基于均质地基上重力坝在水压力作用下的位移解析解建立目标函数，进而以目标函数和非空凸集构建一个凸规划问题，然后通过分析目标函数的Hesse矩阵是否是正定矩阵，验证目标函数是否是严格凸函数，从而辨识构建的凸规划问题是否具有唯一全局极小点.对坝体和岩基弹性参数的不同组合方案分析表明，当采用理论值与实测值的差值的l₁范数作为目标函数时，目标函数的Hesse矩阵均不能保证为正定矩阵，即混凝土重力坝多参数弹性位移反演分析凸规划问题不具有唯一全局极小点，反演分析不唯一.
- 多参数反演 /
- 位移反演 /
- 凸规划问题 /
- Hesse矩阵 /
- 唯一性
Abstract: Inversion analysis is an important part of the closed-loop system of on-site monitoring, inversion analysis, engineering practice test, forward analysis and prediction, and the back analysis problem in engineering practice mainly involves the parameter back analysis. Aimed at the uniqueness of multi-parameter inversion analysis on concrete gravity dams, the objective functions were established based on the theoretical solution of gravity dam displacements on homogeneous foundation under water pressure, and a convex programming problem was constructed with the objective function and the non-empty convex set. Then the positive definiteness of the Hessian matrix of the objective function was analyzed to verify the strict convexity of the objective function, thereby to identify whether the constructed convex programming problem has a unique global minimum. The analysis on different combinations of elastic constants of dams and rock foundations shows that, when the l₁ norm of the difference between the theoretical value and the measured value is used as the objective function, the Hessian matrix of the objective function cannot be guaranteed to be a positive definite matrix, that is, the multi-parameter elastic displacement inversion analysis of concrete gravity dams does not have a unique global minimum point.
- multi-parameter inversion /
- inversion based on displacement /
- convex programming problem /
- Hessian matrix /
- uniqueness

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参考文献(20)

[1]	吴中如. 水工建筑物安全监控理论及其应用[M]. 北京: 高等教育出版社, 2003.(WU Zhongru. Safety Monitoring Theory & Its Application of Hydraulic Structures [M]. Beijing: Higher Education Press, 2003.(in Chinese))
[2]	姜弘道, 陈国荣, 赵洪臣, 等. 岩土工程中的反分析方法及其应用[J]. 工程力学, 1998,15(S): 87-99.(JIANG Hongdao, CHEN Guorong, ZHAO Hongchen, et al. Back analysis method in geotechnical engineering and its application[J]. Engineering Mechanics,1998,15(S): 87-99.(in Chinese))
[3]	KAVANAGH K T, CLOUGH R W. Finite element application in the characterization of elastic solids[J]. International Journal of Solids Structures,1971,7(1): 11-13.
[4]	GIODA G, MAIER G. Direct search solution of an inverse problem in elastoplasticity: identification of cohesion, friction angle and in situ stress by pressure tunnel tests[J]. International Journal for Numerical Methods in Engineering,1980,15(11): 1823-1848.
[5]	冯夏庭, 周辉, 李邵军, 等. 岩石力学与工程综合集成智能反馈分析方法及应用[J]. 岩石力学与工程学报, 2007,26(9): 1737-1744.(FENG Xiating, ZHOU Hui, LI Shaojun, et al. Integrated intelligent feedback analysis of rock mechanics and engineering problems and its applications[J]. Chinese Journal of Rock Mechanics and Engineering,2007,26(9): 1737-1744.(in Chinese))
[6]	孙钧. 岩石流变力学及其工程应用研究的若干进展[J]. 岩石力学与工程学报, 2007,26(6): 1081-1106.(SUN Jun. Rock rheological mechanics and its advance in engineering applications[J]. Chinese Journal of Rock Mechanics and Engineering,2007,26(6): 1081-1106.(in Chinese))
[7]	顾冲时, 李波, 虞鸿, 等. 碾压混凝土坝力学参数的反分析[J]. 中国科学: 技术科学, 2010,40(6): 651-656.(GU Chongshi, LI Bo, YU Hong, et al. Back analysis of mechanical parameters of roller compacted concrete dam[J]. Scientia Sinica: Technologica,2010,40(6): 651-656.(in Chinese))
[8]	张涛, 卢玫, 李博汉, 等. 用于寻源导热反问题的自适应蚁群算法研究[J]. 应用数学和力学, 2014,35(7): 823-830.(ZHANG Tao, LU Mei, LI Bohan, et al. Research on self-adaptive ant colony algorithm for inverse problem of sourcing heat conduction[J]. Applied Mathematics and Mechanics,2014,35(7): 823-830.(in Chinese))
[9]	周焕林, 严俊, 余波, 等. 识别含热源瞬态热传导问题的热扩散系数[J]. 应用数学和力学, 2018,39(2): 160-169.(ZHOU Huanlin, YAN Jun, YU Bo, et al. Identification of thermal diffusion coefficients for transient heat conduction problems with heat sources[J]. Applied Mathematics and Mechanics,2018,39(2): 160-169.(in Chinese))
[10]	吕爱钟. 巷道围岩参数及地应力可辨识性的探讨[J]. 岩石力学与工程学报, 1988,7(2): 155-164.(L Aizhong. Discussion of identifiability for parameters of the surrounding rock of a tunnel and in situ stress[J]. Chinese Journal of Rock Mechanics and Engineering,1988,7(2): 155-164.(in Chinese))
[11]	张路青, 贾正雪. 弹性位移反分析对地应力、弹模的反演唯一性[J]. 岩土工程学报, 2001,23(2): 172-177.(ZHANG Luqing, JIA Zhengxue. Inversion uniqueness of elastic displacement back-analysis for ground stress, elastic modulus and Poisson’s ratio[J]. Chinese Journal of Geotechnical Engineering,2001,23(2): 172-177.(in Chinese))
[12]	赵同彬, 谭云亮, 张玉明, 等. 巷道工程位移反分析的可反演性评价研究[J]. 采矿与安全工程学报, 2006,23(2): 224-227, 232.(ZHAO Tongbin, TAN Yunliang, ZHANG Yuming, et al. Invertibility evaluation of back-analysis of roadway displacement[J]. Journal of Mining & Safety Engineering,2006,23(2): 224-227, 232.(in Chinese))
[13]	王建, 岑威钧, 张煜. 邓肯-张模型参数反演的不唯一性[J]. 岩土工程学报, 2011,33(7): 1054-1057.(WANG Jian, CEN Weijun, ZHANG Yu. Non-uniqueness of back-analyzed parameters of Duncan-Chang model[J]. Chinese Journal of Geotechnical Engineering,2011,33(7): 1054-1057.(in Chinese))
[14]	郭科, 陈聆, 魏友华. 最优化方法及其应用[M]. 北京: 高等教育出版社, 2007.(GUO Ke, CHEN Ling, WEI Youhua. Optimization Method and Its Application [M]. Beijing: Higher Education Press, 2007.(in Chinese))
[15]	袁亚湘, 孙文瑜. 最优化理论与方法[M]. 北京: 科学出版社, 2001.(YUAN Yaxiang, SUN Wenyu. Optimization Theory and Method [M]. Beijing: Science Press, 2001.(in Chinese))
[16]	张光澄, 王文娟, 韩会磊, 等. 非线性最优化计算方法[M]. 北京: 高等教育出版社, 2005.(ZHANG Guangcheng, WANG Wenjuan, HAN Huilei, et al. Nonlinear Optimization Calculation Method [M]. Beijing: Higher Education Press, 2005.(in Chinese))
[17]	孙文瑜, 徐成贤, 朱德通. 最优化方法 [M]. 2版. 北京: 高等教育出版社, 2010.(SUN Wenyu, XU Chengxian, ZHU Detong. Optimization Method [M]. 2nd ed. Beijing: Higher Education Press, 2010.(in Chinese))
[18]	韦增欣, 陆莎. 非线性优化算法[M]. 北京: 科学出版社, 2016.(WEI Zengxin, LU Sha. Nonlinear Optimization Algorithm [M]. Beijing: Science Press, 2016.(in Chinese))
[19]	《数学手册》编写组. 数学手册[M]. 北京: 高等教育出版社, 1979.( Mathematics Manual Writing Group. Mathematics Manual [M]. Beijing: Higher Education Press, 1979.(in Chinese))
[20]	黄耀英, 沈振中, 王润富, 等. 水荷载引起混凝土重力坝位移的理论研究[J]. 力学与实践, 2010,32(1): 33-36.(HUANG Yaoying, SHEN Zhenzhong, WANG Runfu, et al. Theoretical study on concrete gravity dam’s displacement with water load[J]. Mechanics in Engineering,2010,32(1): 33-36.(in Chinese))