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

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

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.

Inversion analysis is an important part of the closed⁃loop system of on⁃site monito⁃ring,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 displace⁃ments 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 con⁃vexity of the objective function,thereby to identify whether the constructed convex program⁃ming 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 ma⁃trix 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.