Study of uniqueness of multi-parameter inverse analysis of elastic displacement of concrete gravity dam

To study the uniqueness of a multi-parameter inverse analysis of a concrete gravity dam, the present method establishes herein an objective function based on a theoretical solution of the displacement of a gravity dam on a homogeneous foundation, with the dam subjected to water pressure. From this objective function and a non-empty convex set, a convex-programming problem is constructed. To determine whether the objective function is a strictly convex function, whether or not the Hesse matrix of the objective function is positive definite is considered, which could determine whether the constructed convex-programming problem has a unique global minimum. An analysis of various combinations of elastic constants for the dam and rock foundation shows that when the l(1) norm of the difference between the theoretical value and the measured value is used as the objective function, the Hesse matrix is not guaranteed to be positive definite, so the multi-parameter elastic-displacement inverse analysis of the concrete gravity dam gives no unique global minimum.