Deformation estimation procedure for monitoring engineering facilities

Spatial data processing is discussed with a view to estimating results of deformation monitoring. The finite deformations are approached by testing the conformity between the geometrical parameters of a test object (monitoring) and a generalized model. Building of a deformation pattern by the direct juxtaposition of sets composed of fixed positions of deformation network points from different observation cycles is discussed. This principle of spatial deformation pattern is applicable in case of both buildings and structures and different aggregates such as skip or cage hoists, equipment of processing factories, as well as various machines, including mining facilities. The calculation algorithm is presented in a general form (without connection to any specific type of test objects), and the mathematical framework for the strategies of the method implementation using various computational approaches is described. The results of the analysis are compared after implementation using the existing software program and two computational methods: the parametric method and the direct search method with a varied pitch in the general conformity testing in processing of cyclic observations of a monitoring object.

Mustafin M. G., Zubov A. V., Vasiljev G. E. Deformation estimation procedure for monitoring engineering facilities. MIAB. Mining Inf. Anal. Bull. 2025;(8):92-113. [In Russ]. DOI: 10.25018/0236_1493_2025_8_0_92.

M.G. Mustafin¹, Dr. Sci. (Eng.), Assistant Professor, e-mail: Mustafin_MG@pers.spmi.ru, ORCID ID: 0000-0001-9416-2358,
A.V. Zubov¹, Cand. Sci. (Eng.), Assistant Professor, e-mail: zaw@pers.spmi.ru, ORCID ID: 0000-0002-1848-3405,
G.E. Vasiljev¹, Graduate Student, e-mail: g.vasiljev@promgeo.com, ORCID ID: 0000-0003-1065-203X,
¹ Empress Catherine II Saint-Petersburg Mining University, 199106, Saint-Petersburg, Russia.

G.E. Vasiljev, e-mail: g.vasiljev@promgeo.com.

1. Vystrchil M. G., Gusev V. N., Sukhov A. K. A method of determining the errors of segmented GRID models of open-pit mines constructed with the results of unmanned aerial photogrammetric survey. Journal of Mining Institute. 2023, vol. 262, pp. 562—570. [In Russ].

2. Kuzin A. A., Filippov V. G. Forecasting landslide displacement values based on geodetic data. Sustainable Development of Mountain Territories. 2024, vol. 16, no. 3, pp. 1176—1191. [In Russ]. DOI: 10.21177/1998-4502-2024-16-3-1176-1191.

3. Palkin P. O., Kuzin A. A. Using high accuracy geodetic measurements to fix the main bases of the ship in shipbuilding and ship-repairing. Journal of Physics: Conference Series. 2021, vol. 1728, no. 1, article 012015. DOI: 10.1088/1742-6596/1728/1/012015.

4. Tsareva O. S. Metod otsenki prostranstvennykh deformatsiy pri geodezicheskom monitoringe pamyatnikov kul'turnogo naslediya [Methodology for estimation of spatial deformations of cultural heritage objects], Candidate’s thesis, Saint-Petersburg, 2020, 20 p.

5. Buzik V. V., Buzik G. B. Calibration of industrial equipment by high-precision geodetic methods using laserabsolute trackers leica. Geodeziya, kartografiya, geoinformatika i kadastry. Nauka i obrazovanie: sb. materialov III Vserossiyskoy nauchno-prakticheskoy konferentsii [Geodesy, cartography, geoinformatics and cadastre. Science and education: collection of abstracts of the III Russian Conference of Applied Science], Saint-Petersburg, 2019, pp. 146—151. [In Russ].

6. Kuzin A. A., Palkin P. O. Coordinate method for determining position in geodetic monitoring of cracks. Journal of Physics Conference Series. 2021, vol. 1728, no. 1, article 012010. DOI: 10.1088/ 1742-6596/1728/1/012010.

7. Murzincev P. P., Polianskiy А. V., Serdakov L. E. On optimization of geodetic reference networks of accelerators using laser trackers. Geodesy and cartography. 2017, no. 5, pp. 2—6. [In Russ]. DOI: 10.22389/0016-7126-2017-923-5-2-6.

8. Dyachkova I., Bykowa E., Dudina V., Banikevich T. An assessment of the impact of the protection zone regime for cultural heritage sites on the value of land for individual housing construction in the context of a low-activity market. Heritage. 2024, vol. 6, no. 7, pp. 2682—2708. DOI: 10.3390/ heritage7060128.

9. Jaafar H. A., Meng X., Sowter A., Bryan P. New approach for monitoring historic and heritage buildings: Using terrestrial laser scanning and generalised Procrustes analysis. Structural Control and Health Monitoring. 2017, vol. 24, no. 11, article 1987. DOI: 10.1002/stc.1987.

10. Gusev V. N., Blishchenko A. A., Sannikova A. P. Study of a set of factors influencing the error of surveying mine facilities using a geodesic quadcopter. Journal of Mining Institute. 2022, vol. 254, pp. 173—179. [In Russ]. DOI: 10.31897/PMI.2022.35.

11. Kuzin A. A., Filippov V. G. Method for determining the plan view coordinates and height of the working benchmark on a landslide with forced inclinations of the pole from the plumb position. Geodesy and cartography. 2024, no. 9, pp. 2—11. [In Russ]. DOI: 10.22389/0016-7126-2024-10119-2-11.

12. Bryn M. Ya., Lobanova Yu. V., Afonin D. A., Shevchenko G. G. Evaluating the accuracy of determining the points’ position by free stationing method. Geodesy and cartography. 2021, no. 5, pp. 2—9. [In Russ]. DOI: 10.22389/0016-7126-2021-971-5-2-9.

13. Sušić Z. Geometric deformation analysis in free geodetic networks: Case study for Fruska Gora in Serbia. Acta Geodynamica et Geomaterialia. 2017, vol. 14, pp. 341—355. DOI: 10.13168/ AGG.2017.0017.

14. Filipiak-Kowszyk D., Kamiński W. Determination of vertical displacements in relative monitoring networks. Archives of Civil Engineering. 2020, vol. 66, no. 1, pp. 309—326.

15. Tsareva O. Estimation of absolute deformations by changes in distances between the reference points and deformation marks. MATEC Web Conferences. 2018, vol. 245, article 04013. DOI: 10.1051/matecconf/201824504013.

16. Markuze Yu. I., Le Anh Cuong. Investigation of an algorithm for analyzing deformations of geodetic points when observing horizontal displacements of hydraulic structures. Geodesy and cartography. 2017, no. 7, pp. 23—30. [In Russ]. DOI: 10.22389/0016-7126-2017-925-7-23-30.

17. Nowel K. Specification of deformation congruence models using combinatorial iterative DIA testing procedure. Journal of Geodesy. 2020, vol. 94, no. 12, pp. 1—23. DOI: 10.1007/s00190-02001446-9.

18. Yang L., Shen Y. Robust M estimation for 3D correlated vector observations based on modified bifactor weight reduction model. Journal of Geodesy. 2020, vol. 94, pp. 31. DOI: 10.1007/s00190020-01351-1.

19. Nowel K., Kamiński W. Robust estimation of deformation from observation differences for free control networks. Journal of Geodesy. 2014, vol. 88, no. 8, pp. 749—764. DOI: 1007/s00190014-0719-7.

20. AbdAllah A. A. G., Wang Z. Optimizing the geodetic networks based on the distances between the net points and the project border. Scientific Reports. 2022, vol. 12, no. 1, article 647. DOI: 10.1038/ s41598-021-04566-0.

21. Lehmann R. Transformation model selection by multiple hypotheses testing. Journal of Geodesy. 2014, vol. 88, no. 12, pp. 1117—1130. DOI: 10.1007/s00190-014-0747-3.

22. Teunissen P. J. G. Distributional theory for the DIA method. Journal of Geodesy. 2018, vol. 92, pp. 59—80. DOI: 10.1007/s00190-017-1045-7.

23. Wiśniewski Z., Zienkiewicz M. Shift-Msplit estimation in deformation analyses. Journal of Surveying Engineering. 2016, vol. 142, no. 4, article 04016015. DOI: 10.1061/(ASCE)SU.1943-5428.0000183.

24. Shendrik N. K. Methodology for determining Helmert's consistent parameters for local territories. Vestnik SGUGiT. 2021, vol. 26, no. 5, pp. 63—74. [In Russ]. DOI: 10.33764/2411-1759-202126-5-63-74.

25. Herrmann C., Lösler M., Bähr H. Comparison of spatialanalyzer and different adjustment programs. The 1st International Workshop on the Quality of Geodetic Observation and Monitoring Systems (QuGOMS'11). 2011, vol. 140, pp. 79—84. DOI: 10.1007/978-3-319-10828-5_12.