MATHEMATICAL MODELING OF OPTIMAL HEIGHTS OF EXTERNAL GEODESIC SIGNS

• O. Voronkov O.M. Beketov National University of Urban Economy in Kharkiv
• O. Baistryk O.M. Beketov National University of Urban Economy in Kharkiv
• A. Danylyuk O.M. Beketov National University of Urban Economy in Kharkiv
Keywords: geodetic sign, optimization, modeling.

Abstract

Due to the great importance of geodetic networks for the formation of a unified coordinate system on the territory of Ukraine, external geodetic signs have been established, which need to be restored and further developed. At the design stage, the calculation of the heights of geodetic signs is performed on topographic maps. The cost of erection of geodetic signs on average is 50 - 60% of the total cost of creating a geodetic network, so there is a need to pay close attention to the choice of places to build signs that provide their optimal height. The article presents a methodical approach  to  determining  the  heights  of  external  geodetic  signs,  based  on  the  mathematical apparatus used for modeling and solving optimization problems. The principle of construction of the optimization model of the problem during the design of external geodetic signs in the conditions when their direct visibility should be provided is considered. The article considers in detail the types and structures of external geodetic signs, identifies the features of their location and construction. The resulting optimization model includes objective function, which is a quadratic form, and line restriction. This model is a model of quadratic programming, that belongs to a class of nonlinear programming models, but have their particular case and the simplest of nonlinear. This is because property quadratic model, which consists in the fact that since the problem of quadratic programming set of feasible solutions is convex, then, if the objective function is concave, any local maximum is global, and if the objective function is convex, then any local minimum is also global. The necessity of solving the problem of optimizing the heights of geodetic signs is substantiated, which is still connected with the financial costs for their construction and reconstruction. It is concluded that the approach to determining the heights of external geodetic signs presented in the article, which uses a mathematical apparatus for solving optimization problems, is an effective and efficient approach, and allows to numerically justify the minimum required and sufficient height of external geodetic signs. Using the present approach to the determination of geodetic heights external signs to optimize the financial costs of their construction, which is essential.

Author Biographies

O. Voronkov, O.M. Beketov National University of Urban Economy in Kharkiv

PhD, Associate Professor, Associate Professor of the Department

O. Baistryk, O.M. Beketov National University of Urban Economy in Kharkiv

Student

A. Danylyuk, O.M. Beketov National University of Urban Economy in Kharkiv

Student

References

Kushtin I.F. Geodeziya : ucheb.-prakt. pos. – Moskva : «Izdatel'stvo PRIOR», 2001. – 448 s.

Derzhavna heodezychna merezha Ukrainy [Elektronnyi resurs] / Derzhavna sluzhba Ukrainy z pytan heodezii, kartohrafii ta kadastru. Naukovo-doslidnyi instytut heodezii i kartohrafii. – Rezhym dostupu: http://dgm.gki.com.ua/

Romanyshyn P.O. Rozvytok astronomo-heodezychnoi merezhi Ukrainy / P.O. Romanyshyn, A.O. Teliatnyk, I.M. Zaiets // Visnyk heodezii ta kartohrafii. – Kyiv, 1994. – № 1.

Bondar A.L. Stan ta osnovni napriamy rozvytku derzhavnoi heodezychnoi merezhi Ukrainy / A.L. Bondar, I.M. Zaiets, O.V. Kucher // Visnyk heodezii ta kartohrafii. – Kyiv, 2001. – № 3.

Pro derzhavnyi zemelnyi kadastr : Zakon Ukrainy vid 16.10.2012 r. № 5462–VI // Vidomosti Verkhovnoi Rady Ukrainy. – 2012. – № 8. – st. 61.

Zaiets I. Osoblyvosti zahalnoho vyrivniuvannia derzhavnoi heodezychnoi merezhi Ukrainy / I. Zaiets // Heodeziia i heodynamika: Suchasni dosiahnennia heodezychnoi nauky ta vyrobnytstva. – Lviv, 2013. – Vyp. 1 (25). – S. 43–50.

Monitorynh stanu punktiv heodezychnoi merezhi Ukrainy z vykorystanniam sotsialnykh merezh [Elektronnyi resurs]. – Rezhym dostupu : http://ena.lp.edu.ua/bitstream/ntb/34313/1/06_35-37.pdf

Michal, Ondrej. (2016). OPTIMIZATION METHODS IN GEODETIC NETWORKS / 16th International Multidisciplinary Scientific GeoConference SGEM 2016, www.sgem.org, SGEM2016 Conference Proceedings, ISBN 978-619-7105-59-9 / ISSN 1314-2704, June 28 - July 6, 2016, Book2 Vol. 2, 479–486 pp.

Heodezychnyi entsyklopedychnyi slovnyk / Za redaktsiieiu V. Litynskoho. – Lviv: Yevrosvit, 2001. – 668 s.

Instruktsiia z topohrafichnoho znimannia u masshtabakh 1:5 000, 1:2 000, 1:1 000 ta 1:500, (HKNTA-2.04-02-98) / Ukrheodezkartohrafiia, 1999 r. Dokument z0393-98, potochna redaktsiia. – Rezhym dostupu : https://zakon.rada.gov.ua/laws/show/z0393-98/

Ehkonomiko-matematicheskie metody : ehl. ucheb. [Elektronnyi resurs]. – Rezhym dostupu : http://www.math.mrsu.ru/text/courses/method/kvadratichnoe_programmirovanie.htm

Teoriya i metody resheniya zadach nevypuklogo kvadratichnogo programmirovaniya. [Elektronnyi resurs]. – Rezhym dostupu : https://www.rfbr.ru/rffi/ru/project_search/o_73804

Tatarenko S.I. Linejnoe reshenie zadachi kvadratichnogo programmirovaniya / S.I. Tatarenko // Programmnye produkty i sistemy. – 2014. – № 3(107), S. 36–40. – Rezhym dostupu : https://cyberleninka.ru/article/n/lineynoe-reshenie-zadachi-kvadratichnogo-programmirovaniya

Published
2021-03-26
How to Cite
VoronkovO., BaistrykO., & DanylyukA. (2021). MATHEMATICAL MODELING OF OPTIMAL HEIGHTS OF EXTERNAL GEODESIC SIGNS. Municipal Economy of Cities, 1(161), 109-115. Retrieved from https://khg.kname.edu.ua/index.php/khg/article/view/5722
Section
статьи