M.V. Horodetskyi, PhD student, Іu.V. Sydorenko, PhD (Eng. sc.)
National Technical University of Ukraine
«Igor Sikorsky Kyiv Polytechnic Institute»,
Ukraine, 03056, Kyiv, Pr-t Peremohy, 37
E–mail: This email address is being protected from spambots. You need JavaScript enabled to view it.; This email address is being protected from spambots. You need JavaScript enabled to view it.

Èlektron. model. 2025, 47(3):03-11

https://doi.org/10.15407/emodel.47.03.003

ABSTRACT

The application of polypoint transformations to modeling the deformation of three-dimensional triangular meshes is considered. Three methods for representing the mesh geometry are proposed and analyzed: the intersection of the planes of a triangle and its normals, orthogonal pla­nes for each vertex, and the intersection of the planes of adjacent triangles. An experimental study was conducted to evaluate the efficiency of each method in modeling two types of nonlinear deformations: twisting around the Z-axis and nonlinear volume expansion.

The accuracy of shape recovery after deformation and the performance of the algorithms were evaluated. The research results showed that the best balance between accuracy and speed is achieved by the method of defining vertices through the intersection of the planes of adjacent triangles. At the same time, its limitations were analyzed, particularly its dependence on the non-parallelism of planes, and the use of the Moore-Penrose pseudoinverse matrix was pro­posed to resolve ambiguities in the transformations.

KEYWORDS

polycoordinate mappings, polypoint transformations, polygonal geometry, transformation basis, transformation object.

REFERENCES

1. Cheng, S.-W., Dey, T.K., & Shewchuk, J. (2016). Delaunay Mesh Generation. CRC Press. https://books.google.com.ua/books?id=oJ3SBQAAQBAJ
   https://doi.org/10.1201/b12987
2. Badaev, Y. & Sidorenko, Y. (2020). Geometric modeling of complex objects on the basis of tile mapping displays of direct cuts. Modern problems of modeling, (16), 17-24. Doi: 10.33842/2313-125X/2019/16/17/24.
   https://doi.org/10.33842/2313-125X/2019/16/17/24
3. Kolot, O.L. & Badaev, Y. (2019). Geometric modeling of complex objects based on point-based three-dimensional transformations of triangles. Modern problems of modeling, (13), 76-83. https://magazine.mdpu.org.ua/index.php/spm/article/view/2647
4. Badaiev, Y.I. & Hannoshyna, I.M. (2016). Design of a spatial curve, taking into account curvature and difficulties in nodes of interpolation method. Visnyk of Vinnytsia Poli­technical Institute, (4), 80-83 https://visnyk.vntu.edu.ua/index.php/visnyk/article/view/1953
5. Ausheva, N. & Humennyi, A. (2021). Modeling of fundamental splines in the form of quaternion curves. Modern problems of modeling, (20), 20-27. Doi: 10.33842/22195203/2021/20/20/27
   https://doi.org/10.33842/22195203/2021/20/20/27
6. Badayev, Y. & Lagodina, L. (2020). Interpolation by rational surfases of bezier and nurbs-sur­fases. Modern problems of modeling, (19), 11-16. Doi: 10.33842/2313-125X/2020/19/11/16
   https://doi.org/10.33842/22195203/2020/19/11/16
7. Badayev, Y.I. & Lagodina, (2020). Approximation by rational surfases of bezier and nurbs-surfases. Modern problems of modeling, (18), 11-17. Doi: 10.33842/22195203/2020/18/11/17
   https://doi.org/10.33842/22195203/2020/18/11/17
8. Sydorenko,V., Kaleniuk, O.S. & Horodetskyi M.V. (2024). Polypoint Transformation Dependency on the Polyfiber Configuration. Control Systems and Computers, 4 (308), 3-9. Doi: 10.15407/csc.2024.04.003
   https://doi.org/10.15407/csc.2024.04.003
9. Dokmanić, I., Kolundžija, M. & Vetterli, M., (2013). Beyond Moore-Penrose: Sparse pseudoinverse. 2013 IEEE International Conference on Acoustics, Speech and Signal Processing, 26-31. Doi: 10.1109/ICASSP.2013.6638923
   https://doi.org/10.1109/ICASSP.2013.6638923
10. Mohamed M. Selim, Roy P. Koomullil & Ahmed S. Shehata. (2017). Incremental approach for radial basis functions mesh deformation with greedy algorithm. Journal of Computational Physics, 340, 556-574. Doi: 10.1016/j.jcp.2017.03.037
    https://doi.org/10.1016/j.jcp.2017.03.037

Full text: PDF

A.V. Voloshko

Èlektron. model. 2025, 47(3):12-27

https://doi.org/10.15407/emodel.47.03.012

ABSTRACT

A numerical model of the formation of the main indicators of power quality distortion and the generation of multistage and combined distortions is presented. The formation of power quality distortions is carried out in two stages. In the first stage, one of the main parameters of electri­city quality is modeled with a graphical representation and numerical values of its characteristics. In the second stage, the influence of electricity consumers is determined: starting a powerful induction motor, switching compensating devices, and connecting significant single-phase loads on the characteristics of the electricity quality parameter modeled in the first stage. For this purpose, the generated function of the main parameter is modulated by the corresponding function of additional events. The results of such modeling are given in graphical representation and corresponding numerical values. The proposed model can be used in the field of automatic detection and classification of power quality distortions, and verification of the accuracy and reliability of existing algorithms and equipment that perform automatic identification and classification of power quality distortions. All this will contribute to the rapid development of automatic detectors and classifiers of power quality distortions.

KEYWORDS

modeling, quality of electric energy, generation of distortions of the quality of electric energy.

REFERENCES

1. Tejashree G., More, Pooja R. Asabe, Sandeep Chawda. (2014). Power Quality Issues and It’s Mitigation Techniques. Int. Journal of Engineering Research and Applications. Vol 4. No. 4 (Version 4), Pp. 170-177.
2. Adeoye, O.S., Folayan,B. (2019). Power Quality Indices and Mitigation Techniques: A Review. International Journal of Latest Engineering Science (IJLES). Vol. 02. No. 02. Pp. 66-71.
3. Ajinkya Sinkar, Huanfeng Zhao, Bolin Qu, Aniruddha M. Gole. (2021). A Comparative Study of Electromagnetic Transient Simulations using Companion Circuits, and Descriptor State-space Equations. Electric Power Systems Research. 198. Pp. 20-26.
   https://doi.org/10.1016/j.epsr.2021.107360
4. Dommel, H.W. Digital Computer Solution of Electromagnetic Transients in Single and Multiphase Networks, IEEE Transactions on Power Apparatus and Systems, PAS-88, 1969. No. 4, Pp. 388-
   https://doi.org/10.1109/TPAS.1969.292459
5. Kok Wai Chan1, Rodney,G. Tan, Mok, V.H. Simulation of Power Quality Distur­bances Using PSCAD. Applied Mechanics and Materials Submitted. 2014. Vol. 785, pp. 373-378. 
   https://doi.org/10.4028/www.scientific.net/AMM.785.373
6. Gheorghe CÂR0IN, Gheorghe GRIGORA, Elena-Crengu. Power system analysis using matlab toolboxes. 6^th International Conference on Electromechanical and Power Systems, 4-6. 2007. Pp. 305-308.
7. Federico Milano. Power System Analysis Toolbox Quick Reference Manual for PSAT version 2.1.2, June 26, 2008. 105 p.
8. User’s Guide. Hydro-Québec and MathWorks. Inc. 2012. 411 p.
9. Schoder, , Hasanovic, A., Feliachi, A. (2002). PAT: A Power Analysis Toolbox for MATLAB/Simulink. IEEE Power Engineering Review. Vol. 22. Issue: 11. 
   https://doi.org/10.1109/MPER.2002.4311828
10. Saini, M.K., Kapoor, R. (2012). “Classification of power quality events — A review”, International Journal of Electrical Power & Energy Systems, vol. 43(1), pp. 11-19.
    https://doi.org/10.1016/j.ijepes.2012.04.045
11. Deokar, S.A., Waghmare, L.M. (2014). “Integrated DWT–FFT approach for detection and classification of power quality disturbances”, Electrical Power and Energy Systems, vol. 61, pp. 594-605, 
    https://doi.org/10.1016/j.ijepes.2014.04.015
12. Moises Vidal Ribeiro, Jose Luiz Rezende Pereira. (2007). Classification of Single and Multiple Disturbances in Electric Signals, EURASIP Journal on Advances in Signal Processing. P 1-18.
    https://doi.org/10.1155/2007/56918
13. Manimala, K., Selvi, K., Ahila, R. (2012). “Optimization techniques for improving power quality data mining using wavelet packet based support vector machine”, Neurocomputing, vol. 77, pp. 36-47, 
    https://doi.org/10.1016/j.neucom.2011.08.010
14. Naderian S., Salemnia, A. (2016). “An implementation of type‐2 fuzzy kernel based support vector machine algorithm for power quality events classification”, International Transactions on Electrical Energy Systems, vol. 27(5), 
    https://doi.org/10.1002/etep.2303
15. Lazzaretti, A.E., Ferreira, V.H., Vieira, H. (2016). “New trends in power quality event analysis: novelty detection and unsupervised classification”, Journal of Control, Automation and Electrical Systems, vol. 27(6), pp. 718-727.
    https://doi.org/10.1007/s40313-016-0265-z
16. Eristi, H., Yıldırım, Ö., Eristi, B., Demir, Y. (2013). “Optimal feature selection for classification of the power quality events using wavelet transform and least squares support vector machines”, Electrical Power and Energy Systems, vol. 49, pp. 95-103.
    https://doi.org/10.1016/j.ijepes.2012.12.018
17. Khokhar, S., Zin, A.A.M., Mokhtar, A.S., Ismail, N. (2014). “MATLAB/Simulink based modeling and simulation of power quality disturbances”, in IEEE Conf. on Energy Conversion (CENCON), Johor Bahru, pp. 445-450.
    https://doi.org/10.1109/CENCON.2014.6967545
18. Lee, C.Y., Shen, Y.X. (2011). “Optimal Feature Selection for Power-Quality Disturbances Classification”, IEEE Transactions on Power Delivery, vol. 26(4).
    https://doi.org/10.1109/TPWRD.2011.2149547
19. Kanirajan, P., Kumar, V.S. (2015). “Power quality disturbance detection and classification using wavelet and RBFNN”, Applied Soft Computing, vol. 35, pp. 470-481,
    https://doi.org/10.1016/j.asoc.2015.05.048
20. Saxena, D., Singh, S.N., Verma K.S. (2011). Wavelet based denoising of power quality events for characterization. International Journal of Engineering, Science and Technology, 3. No. 3. Pp. 119-132. 
    https://doi.org/10.4314/ijest.v3i3.68429
21. Pengfei Wei, Yonghai Xu, Yapen Wu, Chenyi Li. Research on classification of voltage sag sources based on recorded events. 24th International Conference & Exhibition on Electricity Distribution (CIRED) 12-15 June 2017. Is. 1. Pp. 846- 
    https://doi.org/10.1049/oap-cired.2017.0907
22. Math H. Bollen. (2000). Understanding Power Quality Problems: Voltage Sags and Interruptions. Wiley-IEEE Press. 672 p.
23. Pavan Kumar Singh, Vahadood Hasan. (2018). Effect of voltage sag of induction motor. International journal of engineering sciences & research technology. Vol. 7(6). Pp. 11- DOI: 10.5281. Pp. 11-23.
24. Rodney, H.G., Tan, Ramachandaramurthy, V.K. (2010). Numerical Model Framework of Power Quality Events. European Journal of Scientific Research. Vol. 43 No. 1. Pp. 30-47.

Full text: PDF

O.V. Sirotkin, M.S. Yaroshynskyi, D.P. Sinko, S.B. Hunko, D.O. Manoliuk

Èlektron. model. 2025, 47(3):28-45

https://doi.org/10.15407/emodel.47.03.028

ABSTRACT

An approach to numerical modeling is considered, which suggests the representation of states (points) of the phase space in the form of sub-states. In the future, this approach will simplify the parallelization of calculations of numerical models. The definition of the modeled object, the set of states of the object, the model and the simulation of the model are given. The method of decomposition of each state of the object into several sub-states is shown.

KEYWORDS

modeling, state space, phase space, model, numerical simulation.

REFERENCES

1. Contributors to Wikimedia projects. Subject and object (philosophy) — Wikipedia. Wikipedia, the free encyclopedia. URL: https://en.wikipedia.org/wiki/Subject_and_object_ (philosophy) (date of access: 12.03.2025).
2. Achinstein, P. (1965). Theoretical models. The British Journal for the Philosophy of Science, 16(62), 102-120.
   https://doi.org/10.1093/bjps/XVI.62.102
3. Banks, J. (2001). Discrete-event system simulation(3-тє вид.). Prentice Hall. 5 p.
4. Babbie, E.R. (2020). Practice of social research. Cengage Learning. 14-18
5. Myshkis A.D. (1994). Elements of the theory of mathematical models. 8-9
6. Nolte, D.D. (2010). The tangled tale of phase space. Physics Today, 63(4), 33-38.
   https://doi.org/10.1063/1.3397041
7. SWRS/Python/scripts/mixing_example/function_set_representation.py at master AlexCAB/ SWRS. GitHub. https://github.com/AlexCAB/SWRS/blob/master/Python/scripts/mixing_ example/function_set_representation.py
8. SWRS/Python/scripts/mixing_example/sub_state_set_representation.py at master AlexCAB/ SWRS. GitHub. https://github.com/AlexCAB/SWRS/blob/master/Python/scripts/mixing_ example/sub_state_set_representation.py
9. SWRS/Python/scripts/mixing_example/function_set_interactive_simulation.py at master AlexCAB/SWRS. GitHub. https://github.com/AlexCAB/SWRS/blob/master/Python/scripts/ mixing_example/function_set_interactive_simulation.py

Full text: PDF

V. Kharchenko, H. Fesenko, I. Kliushnikov, E. Brezhniev, S. Stirenko, V. Mokhor

Èlektron. model. 2025, 47(3):46-65

https://doi.org/10.15407/emodel.47.03.046

ABSTRACT

The list of types of unmanned (crewless) vehicles that can form a heterogeneous unmanned system in various combinations is determined. A classification of heterogeneous unmanned systems and scenarios of their use is presented. Examples of such scenarios for heterogeneous unmanned systems consisting of three types of unmanned (crewless) vehicles are given, with the functions of each of these types detailed. The definition of a dangerous space is given and examples of it with one and three types of threats (multi-dangerous space) are given. The main operational tasks of overcoming dangerous spaces are formulated and the roles of heterogeneous unmanned systems and unmanned mobile depots in their implementation are shown. The ways to achieve situational awareness of dangerous spaces are formulated and the roles of heterogeneous unmanned systems and unmanned mobile depots in their implementation are shown. The correlation between the ways of achieving situational awareness of dangerous space and the tasks of overcoming it is presented. Directions for further research are formulated.

KEYWORDS

heterogeneous unmanned system, unmanned (crewless) vehicle, unmanned mobile depot, dangerous space, situational awareness

REFERENCES

1. Huang, Y., Li, W., Ning, J., & Li, Z. (2023). Formation Control for UAV-USVs Heterogeneous System with Collision Avoidance Performance. Journal of Marine Science and Engineering, 11(12). 
   https://doi.org/10.3390/jmse11122332
2. Wu, J., Li, R., Li, J., Zou, M., & Huang, Z. (2023). Cooperative unmanned surface vehicles and unmanned aerial vehicles platform as a tool for coastal monitoring activities. Ocean and Coastal Management, 232, 106421 
   https://doi.org/10.1016/j.ocecoaman.2022.106421
3. Wang, Y., Liu, W., Liu, J., & Sun, C. (2023). Cooperative USV-UAV marine search and rescue with visual navigation and reinforcement learning-based control. ISA Transactions, 137, 222- 
   https://doi.org/10.1016/j.isatra.2023.01.007
4. Santos, M.C., Bartlett, B., Schneider, V.E., Brádaigh, F.O., Blanck, B., Santos, P.C., Trslic P., Riordan J., Dooly, G. (2024). Cooperative Unmanned Aerial and Surface Vehicles for Extended Coverage in Maritime Environments. IEEE Access, 12, 9206- 
   https://doi.org/10.1109/ACCESS.2024.3353046
5. Li, Y., Li, S., Zhang, Y., Zhang, W., & Lu, H. (2023). Dynamic Route Planning for a USV-UAV Multi-Robot System in the Rendezvous Task with Obstacles. Journal of Intelligent and Robotic Systems: Theory and Applications, 107(4). 
   https://doi.org/10.1007/s10846-023-01830-5
6. Liao, Y., Chen, X., Liu, J., Han, Y., Xu, N., & Yuan, Z. (2024). Cooperative UAV-USV MEC Platform for Wireless Inland Waterway Communications. IEEE Transactions on Consumer Electronics, 70(1), 3064-3076 
   https://doi.org/10.1109/TCE.2023.3327401
7. Ennong, T., Ye, L., Teng, M., Yulei, L., Yueming, L., & Jian, C. (2024). Design and experiment of a sea-air heterogeneous unmanned collaborative system for rapid inspection tasks at sea. Applied Ocean Research, 143. 
   https://doi.org/10.1016/j.apor.2023.103856
8. Shirakura, N., Kiyokawa, T., Kumamoto, H., Takamatsu, J., & Ogasawara, T. (2021). Collection of Marine Debris by Jointly Using UAV-UUV with GUI for Simple Operation. IEEE Access, 9, 67432-67443 
   https://doi.org/10.1109/ACCESS.2021.3076110
9. Nordin, M.H., Sharma, S., Khan, A., Gianni, M., Rajendran, S., & Sutton, R. (2022). Collaborative Unmanned Vehicles for Inspection, Maintenance, and Repairs of Offshore Wind Turbines. Drones, 6(6), 137. 
   https://doi.org/10.3390/drones6060137
10. Hu, D., Gan, V.J.L., Wang, T., & Ma, L. (2022). Multi-agent robotic system (MARS) for UAV-UGV path planning and automatic sensory data collection in cluttered environments. Building and Environment, 221. 
    https://doi.org/10.1016/j.buildenv.2022.109349
11. Battistoni, P., Cantone, A.A., Martino, G., Passamano, V., Romano, M., Sebillo, M., & Vitiello, G. (2023). A Cyber-Physical System for Wildfire Detection and Firefigh­ting. Future Internet, 15(7), 237. 
    https://doi.org/10.3390/fi15070237
12. Chen, P., Luo, L., Guo, D., Luo, X., Li, X., & Sun, Y. (2024). Secure Task Offloading for Rural Area Surveillance Based on UAV-UGV Collaborations. IEEE Transactions on Vehicular Technology, 73(1), 923-937 
    https://doi.org/10.1109/TVT.2023.3307443
13. Munasinghe, I., Perera, A., & Deo, R.C. (2024). A Comprehensive Review of UAV-UGV Collaboration: Advancements and Challenges. Journal of Sensor and Actuator Networks, 13(6), 81. 
    https://doi.org/10.3390/jsan13060081
14. Dinelli, C., Racette, J., Escarcega, M., Lotero, S., Gordon, J., Montoya, J., Dunaway, C., And­roulakis, V., Khaniani, H., Shao, S., Roghanchi, P., & Hassanalian, M. (2023). Configurations and Applications of Multi-Agent Hybrid Drone/Unmanned Ground Vehicle for Underground Environments: A Review. Drones, 7(2), 136. 
    https://doi.org/10.3390/drones7020136
15. Ke, C., Chen, H., & Xie, L. (2023). Cross-Domain Fixed-Time Formation Control for an Air-Sea Heterogeneous Unmanned System with Disturbances. Journal of Marine Science and Engineering, 11(7). 1336. 
    https://doi.org/10.3390/jmse11071336
16. Li, J., Zhang, G., Jiang, C., & Zhang, W. (2023, October 1). A survey of maritime unmanned search system: Theory, applications and future directions. Ocean Engineering. Elsevier Ltd. 
    https://doi.org/10.1016/j.oceaneng.2023.115359
17. Barilaro, L. (2023). BEA: Overview of a multi-unmanned vehicle system for diver assistance. In Aeronautics and Astronautics. Materials Research Forum LLC.
    https://doi.org/10.21741/9781644902813-53
18. Cao, X., Liu, W., & Ren, L. (2024). Underwater Target Capture based on Heterogeneous Unmanned System Collaboration. IEEE Transactions on Intelligent Vehicles. 
    https://doi.org/10.1109/TIV.2024.3362358
19. Chen, Y., Wang, J., Zhu, S., Gu, Y., Dai, H., Xu, J., Zhu, Y., & Wu, T. (2022). Know­ledge Graph Construction for Foreign Military Unmanned Systems. In Communications in Computer and Information Science(pp. 127-137). Springer Nature Singapore.
    https://doi.org/10.1007/978-981-19-8300-9_14
20. Park, S.-B., Ha, J.-U., & Park, J.-K. (2021). A Study on the Obstacle Collision Avoidance Using Leader-Follower Formation Control Algorithm of Multiple Unmanned Vehicles in Ground Warfare. Journal of the Korean Association of Defense Industry Studies, 28(3), 61- 
    https://doi.org/10.52798/KADIS.2021.28.3.5
21. On Approval of the Rules of Flight Operations by Unmanned Aircraft Systems of the State Aviation of Ukraine, Order of the Ministry of Defense of Ukraine No. 661 (2020) (Ukraine). https://zakon.rada.gov.ua/laws/show/z0031-17#Text
22. Bouraou, N.I., & Zolotarov, Y.O. (2023). Systems of Visualization of The Movement of Unmanned Underwater Apparatus. Scientific notes of Taurida National V.I. Vernadsky University. Series: Technical Sciences, 1(3), 83- 
    https://doi.org/10.32782/2663-5941/2023.3.1/14
23. Moshref-Javadi, M., Hemmati, A., & Winkenbach, M. (2020). A truck and drones model for last-mile delivery: A mathematical model and heuristic approach. Applied Mathematical Modelling, 80, 290-318 
    https://doi.org/10.1016/j.apm.2019.11.020
24. Horbulin, V.P., Hulianytskyi, L.F., & Sergienko, I.V. (2020). Optimization of UAV Team Routes in the Presence of Alternative and Dynamic Depots. Cybernetics and Systems Analysis, 56(2), 195- 
    https://doi.org/10.1007/s10559-020-00235-8
25. Fesenko, H., Illiashenko, O., Kharchenko, V., Kliushnikov, I., Morozova, O., Sachenko, A., & Skorobohatko, S. (2023). Flying Sensor and Edge Network-Based Advanced Air Mobi­lity Systems: Reliability Analysis and Applications for Urban Monitoring. Drones, 7(7), 409.
    https://doi.org/10.3390/drones7070409
26. Kharchenko, V., Kliushnikov, I., Rucinski, A., Fesenko, H., & Illiashenko, O. (2022). UAV Fleet as a Dependable Service for Smart Cities: Model-Based Assessment and Smart Cities, 5(3), 1151-1178. 
    https://doi.org/10.3390/smartcities5030058
27. Illiashenko, O., Kharchenko, V., Babeshko, I., Fesenko, H., & Di Giandomenico, F. (2023). Security-Informed Safety Analysis of Autonomous Transport Systems Conside­ring AI-Powered Cyberattacks and Protection / Entropy. 2023. Vol. 25, no. 8. P. 1123. 
    https://doi.org/10.3390/e25081123
28. Fesenko, H., Illiashenko, O., Kharchenko, V., Leichenko, K., Sachenko, A., & Scislo, L. (2024). Methods and Software Tools for Reliable Operation of Flying LiFi Networks in Destruction Conditions. Sensors, 24(17), 5707. 
    https://doi.org/10.3390/s24175707
29. Fedorenko, G., Fesenko, H., Kharchenko, V., Kliushnikov, I., & Tolkunov, I. (2023) Robotic-biological systems for detection and identification of explosive ordnance: concept, general structure, and models. Radioelectronic and Computer Systems, 2, 143- 
    https://doi.org/10.32620/reks.2023.2.12
30. Munir, A., Aved, A., & Blasch, E. (2022) Situational Awareness: Techniques, Challenges, and Prospects. AI, 3(1), 55-77. 
    https://doi.org/10.3390/ai3010005

Full text: PDF