MATHEMATICAL SOFTWARE FOR PROCESSING EXPERIMENTAL DATA IN DETERMINING THE PARAMETERS OF AN INACCESSIBLE POINT OF A CONSTRUCTION OBJECT

Abstract

The article addresses the problem of determining the parameters of inaccessible points of construction objects based on the processing of experimental geodetic data. The relevance of the research is driven by the need for automated acquisition of geometric parameters of buildings and structures during reconstruction, restoration, and the creation of building information models in the context of BIM implementation and the transition to parametric standardization. This task is particularly important in the survey of cultural heritage sites and emergency structures, where direct access to certain structural elements is impossible or unsafe.

The shortcomings of classical geometric models based on intersecting sighting rays are analyzed. It is shown that, under real measurement conditions, errors cause such rays to become skew lines, resulting in ambiguity of solutions and the appearance of multiple possible coordinate values for the target point. To overcome this contradiction, a combined three-dimensional geometric model is proposed. The model considers the most general location of the surveyed object relative to geodetic equipment and enables the determination of parameters of points situated above, below, or at the level of the reference horizontal plane.

Mathematical support for processing experimental data has been developed. The proposed approach is based on optimization procedures for determining the coordinates of inaccessible points. The problem is reduced to finding the minimum distance between skew lines corresponding to sighting rays, followed by solving the resulting system of equations using Cramer’s method. A mathematical and algorithmic framework consisting of seven interconnected blocks is proposed, including the determination of initial point coordinates, localization of inaccessible points, calculation of coordinates and target parameters, estimation of absolute and relative errors, adaptive correction of measurement parameters, and registration of results. A distinctive feature of the developed algorithm is its ability to adaptively control errors by refining angular parameters within permissible measurement tolerances.

An example of applying the developed mathematical support to determine the coordinates of two inaccessible points located on the same perpendicular to the horizontal plane is presented. The obtained results confirm the universality, stability, and uniqueness of the proposed approach compared with traditional methods. The practical significance of the research lies in providing a theoretical basis for the automation of geodetic measurements, integration of results into CAD/BIM systems, and support for modern processes of digital transformation in the construction industry.

Keywords: construction object; inaccessible point; combined geometric model; skew sighting rays; mathematical software; optimization approach; adaptive algorithm; BIM.