oa Analysis of the Stability of High-Rise Base Points using the Linear Programming Method

The paper proposes a solution to the problem of determining the probable values of subsidence/release of the height base references based on the results of repeated leveling cycles to analyze their stability using the linear programming method. The algorithm of the simplex method allows to automatically exclude the references that have received the maximum displacements and thus establishes the most stable reference of the height base. The purpose of the study is also to identify the most effective approach to the mathematical processing of leveling results in the conditions of free geodetic networks, which are characterized by a high risk of erroneous identification of stable points. This is related to the problem of initial selection of the reference surface, relative to which it is necessary to calculate the marks of the references and their vertical displacements, as well as the assessment of the stability of the references. The results of the study provide useful information to ensure the accuracy of monitoring deformations of building structures. Using the example of a leveling network for the 21st excess between 17 references, which form 4 closed polygons with 8 leveling cycles of the leveling network of the II class of an industrial site, a reliable assessment of the stability of the height base references was obtained.