岩土工程问题参数反演的可辨识性研究

The Research of Differentiability of Parameter in the Back Analysis of Geotechnical Engineering

针对岩土工程问题参数反分析过程中,采用逆反分析法以及最小二乘法、遗传算法等作为优化方法反演参数,对未知参数的可辨识性进行了理论证明:当量测信息量小于未知参数量时,无法唯一确定未知量;当量测信息量等于未知量时,当且仅当未知参数的系数矩阵K∈Rm×rr(m,r为正整数)时,参数可唯一确定;而当量测信息量大于未知量时,未知参数的唯一可辨识性条件也是未知参数的系数矩阵K∈Rm×rr(m,r为正整数).

In the back analysis of stress field parameter in the geotechnical engineering, the differentiability of the parameter, which is made up of the measure information matrix, the unknown quality matrix and modulus matrix, while using the invertible back analysis and some optimization methods, such as least double multiplication and genetic algorithms, is proved to be one and only under the condition that the matrix of K~ T K is nonsingular matrix and the rank of matrix K is greater than half of the number of column of the matrix, the matrix K∈R^(m×r)_r,m,r are positive integers. If the total number of measure information is greater than the unknown quality, the differentiability of the parameter is still proved to be one and only.