Integrated Safety Management of Russian Oil and Gas Enterprises Using the Complex Number Method


The use of the method of complex numbers for solving problems of managing the integrated safety system at the enterprises of the oil and gas complex of Russia is substantiated. A formalized description is presented related to the sequence of processing data taken from the statistics of accidents and fires at the enterprises under consideration.

The mathematical apparatus of complex numbers was successfully used in various fields — for example, to determine the magnitude of the deviation of characteristics (current from voltage) in electrical engineering. It is possible to represent the instantaneous value of the characteristic under study on the plane through the proven connection between trigonometric functions and the exponent using the method of complex numbers. The use of this method in the integrated safety of enterprises allows to compactly state the sequence in the growth and development of conditions for the occurrence of hazardous events (accidents and fires) that cause damage (material and economic, sanitary, and irretrievable losses of the personnel and third parties).

The figures allow to represent the complex value of the influence of factors causing damage from hazardous events (accidents and fires) in the form of vectors directed towards the area of primary and secondary factors and having a deviation from each other by an angle φ. This angle is used in the calculations for the equivalent determination of the impact of damage caused by hazardous events.

The example is presented that proves in practice the adequacy of using the method of complex numbers for solving problems in managing the integrated safety system of enterprises in the oil and gas complex of Russia.

1. Gvozdev E.V. The use of digitalization elements in the presentation of statistics on the occurrence of accidents and fires at the enterprises of the oil and gas complex of Russia. Problemy bezopasnosti i chrezvychaynykh situatsiy = Safety and Emergencies Problems. 2023. № 1. pp. 58–66. (In Russ.). DOI: 10.36535/0869-4176-2023-01-6 
2. Gvozdev E.V. On the Formation of a Scientific and Methodological Apparatus for Assessing the Factors Affecting the Integrated Safety of the Enterprises of Oil and Gas Complex of Russia. Bezopasnost Truda v Promyshlennosti = Occupational Safety in Industry. 2022. № 10. pp. 21–26. (In Russ.). DOI: 10.24000/0409-2961-2022-10-21-26 
3. Odintsov B.E., Berzin D.V. Structure and Scheme of Subject-oriented Banking Information Systems. Proceedings of 2018 11th International Conference «Management of Large-Scale System Development» (MLSD 2018). Moscow: V.A. Trapeznikov Institute of Control Sciences Moscow, 2018. P. 8551872. DOI: 10.1109/MLSD.2018.8551872 
4. Massel A.G., Pesterev D.V. Transformation of cognitive models into knowledge base of production expert system. Proceedings of the 19th International Workshop оn Computer Science and Information Technologies (CSIT 2017). Baden-Baden, 2017. Vol. 1. pp. 121–124. 
5. Kennedy W.G., van Vugt M.K., Banks A.P. Editors’ Introduction: Cognitive Modeling at ICCM: Advancing the State of the Art. Topics in Cognitive Science. 2018. Vol. 10. Iss. 1. pp. 140–143. DOI: 10.1111/tops.12321
6. Avdotin V.P., Akimov V.A., Plyushchikov V.G. Interdisciplinary research on technosphere safety: Russian and foreign experience. Мoscow: Rossiyskiy universitet druzhby narodov, 2021. 248 p. (In Russ.).
7. Khagram S., Nicholas K.A., Bever D.M., Warren J., Richards E.H., Oleson K., Kitzes J., Katz R., Hwang R., Goldman R., Funk J., Brauman K.A. Thinking about knowing: Conceptual foundations for interdisciplinary environmental research. Environmental Conservation. 2010. Vol. 37. Iss. 4. pp. 388–397. DOI: 10.1017/S0376892910000809
8. Sudha S., Gnanam A. Complex Method on Octagonal Number. International Journal of Recent Technology and Engineering. 2019. Vol. 8. Iss. 4S5. pp. 11–13. DOI: 10.35940/ijrte.D1005.1284S519
9. Benardete D.M. Complex Methods for Bounds on the Number of Periodic Solutions with an Application to a Neural Model. The American Mathematical Monthly. 2020. Vol. 129. Iss. 2. pp. 133–150. DOI: 10.1080/00029890.2022.2005389  
10. Filonenko T.P., Makarov Ya.V. Using the complex numbers in the kinematics and dynamics.  Nauka i proizvodstvo Urala = Science and production of the Urals. 2016. № 12. pp. 137–140. (In Russ.).
11. Garfunkel J. Solving Problems in Geometry by Using Complex Numbers. The Mathematics Teacher. 1967. Vol. 60. Iss. 7. pp. 731–734. DOI: 10.5951/mt.60.7.0731
12. Lessons learned from accidents. Available at: (accessed: March 24, 2023). (In Russ.).
13. Gvozdev E.V., Migalchinskiy N.M., Koldin T.E., Sinyakin D.S. Certificate of the state registration of the computer program № 2023611653 Russian Federation. Former of rating data for the assessment of industrial and fire safety at the enterprises of oil and gas complex of Russia № 2023610660. Applied: January 16, 2023. Published: January 24, 2023. (In Russ.).
DOI: 10.24000/0409-2961-2023-5-46-51
Year: 2023
Issue num: May
Keywords : oil and gas complex integrated safety and security system complex number method cognitive model influence coefficient
  • Gvozdev E.V.
    Gvozdev E.V.
    Cand. Sci. (Eng.), Assoc. Prof.,, National Research Moscow State University of Civil Engineering, Moscow, Russian Federation