Development of a hybrid artillery fire control system based on neural networks and uncertainty quantification methods

Authors

DOI:

https://doi.org/10.15587/2706-5448.2026.357488

Keywords:

ballistic modelling, hybrid ballistic pipeline, ballistic dataset, neural networks, uncertainty quantification

Abstract

The object of research is the process of controlling the fire of artillery installations in a hybrid ballistic modeling system. The problem addressed lies in the lack of comprehensive studies of systems that combine neural network forecasting with physical iterative refinement and stochastic assessment of projectile dispersion within a single operational pipeline. This paper examines the specific features of developing a hybrid artillery fire control system based on the integration of neural networks, numerical refinement of aiming angles, and methods for quantifying the uncertainty of the ballistic model. A modular system architecture is proposed and investigated, integrating a ballistic simulator with a 4-DOF model in accordance with NATO STANAG 4355. The system is supplemented by a neural network, which generates an initial approximation of the aiming angles. For the subsequent calculation of the aiming angles, an algorithm was implemented using iterative elevation angle refinement via the Brent method and gradient azimuth correction. To assess uncertainty, polynomial chaos expansion (PCE) and Monte Carlo methods were integrated. A synthetic ballistic dataset consisting of 121107 records was generated based on 24 configurations of artillery systems. Validation of the neural network demonstrated a narrowing of the search space for aiming angles to a corridor of ±3–5°, ensuring further rapid convergence of the iterative refinement algorithm. Testing for the 2S22 “Bohdana” artillery system at a range of 20 km showed a deterministic error of 0.68 m. The PCE method achieved an error of 0.47 m, outperforming the Monte Carlo method (5.28 m) by a factor of 11.2. Analysis using the PCE method revealed anisotropic projectile dispersion: σx = 168.85 m, σz = 80.84 m, CEP50 = 147.3 m. The viability of the hybrid system has been demonstrated under ballistic simulation conditions, laying the groundwork for further validation with real-world firing data.

Author Biographies

Yurii Rubel, Lviv Polytechnic National University

PhD Student, Assistant

Department of Software

Yurii Hrytsiuk, Lviv Polytechnic National University

Doctor of Technical Sciences, Professor

Department of Software

References

  1. Xie, J., Yang, G., Wang, L., Li, L. (2024). Multi-Stage Multidisciplinary Design Optimization Method for Enhancing Complete Artillery Internal Ballistic Firing Performance. Computer Modeling in Engineering & Sciences, 140 (1), 793–819. https://doi.org/10.32604/cmes.2024.048174
  2. Baranowski, L., Szymonik, J., Majewski, P. (2024). Dynamic calculation of the fire zone for anti-aircraft artillery. Journal of Theoretical and Applied Mechanics, 62 (4), 787–798. https://doi.org/10.15632/jtam-pl/194401
  3. Masluk, L., Havalko, V., Dzhygomon, S. (2022). Main problematic questions and ways of their solution in the development of automated management systems for rocket troops and artillery. Modern Information Technologies in the Sphere of Security and Defence, 45 (3), 63–68. https://doi.org/10.33099/2311-7249/2022-45-3-63-68
  4. Budaretskiy, Y., Schavinskiy, Y. (2016). Synthesis of structure and optimization of algorithms of work of the decision support system of at a fire-control artillery subdivisions of tactical link. 2016 13th International Conference on Modern Problems of Radio Engineering, Telecommunications and Computer Science (TCSET). Lviv: IEEE, 312–316. https://doi.org/10.1109/tcset.2016.7452043
  5. Li, D., Guo, L. H. (2012). The application of digital signal processing (DSP) for the real time solving of artillery fire control exterior trajectory. 2012 IEEE International Conference on Computer Science and Automation Engineering. Beijing: IEEE, 32–35. https://doi.org/10.1109/icsess.2012.6269399
  6. Hao, B., Tegang, L., Zhengzheng, Y., Sheng, Z., Wufan, S. (2024). Design of a Software-Defined Artillery System Architecture. Journal of Physics: Conference Series, 2891 (11), 112009. https://doi.org/10.1088/1742-6596/2891/11/112009
  7. Rothe, H., Kuhrt, A., Schroeder, S., Trebing, S.; Sánchez-Gálvez, V., Brebbia, C. A., Motta, A. A., Anderson, C. E. (Eds.) (2005). Fire control algorithms and software for the modular naval artillery concept (MONARC) of the German navy. Computational Ballistics II. WIT Press, 40, 406–416. Available at: https://www.witpress.com/elibrary/wit-transactions-on-modelling-and-simulation/40/14941
  8. Qian, L., Chen, G., Tong, M., Tang, J. (2022). General design principle of artillery for firing accuracy. Defence Technology, 18 (12), 2125–2140. https://doi.org/10.1016/j.dt.2022.09.001
  9. Bragado, A. C., Solera-Rico, A., Gómez, M. A. (2023). Implementation of Trajectory Propagator for Artillery Projectiles Based on Artificial Neural Networks. New Technologies and Developments in Unmanned Systems, 187–192. https://doi.org/10.1007/978-3-031-37160-8_29
  10. Liu, H., Shan, G., Mei, W. (2014). Analysis on the kill probability of two Shooting Modes for fire control system of antiaircraft artillery. Proceedings of the 33rd Chinese Control Conference. Nanjing: IEEE, 9075–9081. https://doi.org/10.1109/chicc.2014.6896529
  11. Pan, W., Sun, Y., Jing, Y. (2016). Artillery firepower selection based on chaos genetic algorithm. 2016 Chinese Control and Decision Conference (CCDC). Yinchuan: IEEE, 1588–1593. https://doi.org/10.1109/ccdc.2016.7531237
  12. Papp, Z., Rožnjik, A.; Kovács, T. A., Nyikes, Z., Fürstner, I. (Eds.) (2022). A Method for Approximating Circular Error Probable. Security-Related Advanced Technologies in Critical Infrastructure Protection. Dordrecht: Springer, 29–42. https://doi.org/10.1007/978-94-024-2174-3_3
  13. Ghosh, A. K., Prakash, O. (2004). Neural Models for Predicting Trajectory Performance of an Artillery Rocket. Journal of Aerospace Computing, Information, and Communication, 1 (2), 112–115. https://doi.org/10.2514/1.3398
  14. Gao, Z., Zhang, D., Yi, W. (2025). Projectile trajectory and launch point prediction based on CORR-CNN-BiLSTM-Attention model. Expert Systems with Applications, 275, 127045. https://doi.org/10.1016/j.eswa.2025.127045
  15. Roux, A., Changey, S., Weber, J., Lauffenburger, J.-P. (2023). LSTM-Based Projectile Trajectory Estimation in a GNSS-Denied Environment. Sensors, 23 (6), 3025. https://doi.org/10.3390/s23063025
  16. Wang, L., Chen, Z., Yang, G. (2021). An Uncertainty Analysis Method for Artillery Dynamics with Hybrid Stochastic and Interval Parameters. Computer Modeling in Engineering & Sciences, 126 (2), 479–503. https://doi.org/10.32604/cmes.2021.011954
  17. Herbut, A., Brząkała, W. (2024). Polynomial chaos expansion vs. Monte Carlo simulation in a stochastic analysis of wave propagation. Wave Motion, 130, 103390. https://doi.org/10.1016/j.wavemoti.2024.103390
  18. Wang, M., Qian, L., Chen, G., Lin, T., Shi, J., Zhou, S. (2024). High-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer based on probability density evolution method. Defence Technology, 32, 209–221. https://doi.org/10.1016/j.dt.2023.03.004
  19. Jacewicz, M., Lichota, P., Miedziński, D., Głębocki, R. (2022). Study of Model Uncertainties Influence on the Impact Point Dispersion for a Gasodynamicaly Controlled Projectile. Sensors, 22 (9), 3257. https://doi.org/10.3390/s22093257
  20. Ilg, M., Rogers, J., Costello, M. (2011). Projectile Monte-Carlo Trajectory Analysis Using a Graphics Processing Unit. AIAA Atmospheric Flight Mechanics Conference. https://doi.org/10.2514/6.2011-6266
  21. Du, A. (2021). A comparative study between 6 degree-of-freedom trajectory model and modified point mass trajectory model of spinning projectiles. [Master’s thesis; Embry-Riddle Aeronautical University]. Available at: https://commons.erau.edu/edt/594/
  22. Baranowski, L. (2013). Feasibility analysis of the modified point mass trajectory model for the need of ground artillery fire control systems. Journal of Theoretical and Applied Mechanics, 51 (3), 511–522. Available at: http://www.ptmts.org.pl/jtam/index.php/jtam/article/view/v51n3p511
  23. Šilinger, K., Blaha, M. (2017). The New Automated Fire Control System for Artillery Units based on Interoperability and Standards. Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics. Madrid, 332–337. https://doi.org/10.5220/0006468003320337
  24. Shchavinskyi, Y. V. (2015). Vidpratsiuvannia alhorytmiv rozrakhunku danykh dlia pidvyshchennia efektyvnosti vohnevoho urazhennia velykorozmirnykh tsilei. Bionika intelektu, 2 (85), 120–126. Available at: http://nbuv.gov.ua/UJRN/bioi_2015_2_21
  25. Majstrenko, O. V., Makeev, V. I., Prokopenko, V. V., Andreiev, І. М., Kamentsev, S. Y., Onofriychuk, A. Y. (2024). An improved mathematical model of the method of fully preparing the determination of firing units for hitting the information and calculation component of the automated fire control system of combat vehicles of reactive artillery. Radio Electronics, Computer Science, Control, 4, 195–209. https://doi.org/10.15588/1607-3274-2024-4-19
  26. Maksymova, O., Boltyonkov, V., Gultsov, P., Maksymov, O. (2023). Improvement of the model and method of artillery installation target damage control with minimal combat capability loss. Odes’kyi Politechnichnyi Universytet Pratsi, 2 (68), 98–115. https://doi.org/10.15276/opu.2.68.2023.11
  27. Rubel, Y., Hrytsiuk, Y. (2025). Intelektualne koryhuvannia strilby v avtomatyzovanykh systemakh upravlinnia vohnem artyleriiskykh ustanovok. 1st International Scientific and Practical Conference “Science and Technology: New Horizons of Development”. Prague, 192–198. Available at: https://isu-conference.com/wp-content/uploads/2025/07/Prague_Czech-Republic_14.05.25.pdf
  28. Rubel, Y., Hrytsiuk, Y. (2025). Current state of automated fire control systems for artillery systems. Herald of Khmelnytskyi National University. Technical Sciences, 355 (4), 520–530. https://doi.org/10.31891/2307-5732-2025-355-73
  29. Rubel, Y., Hrytsiuk, Y. (2026). Arkhitekturnyi pidkhid do realizatsii hibrydnoi systemy upravlinnia vohnem artylerii. 4th International Scientific and Practical Conference. International Scientific Unity, 125–130. https://doi.org/10.70286/isu-14.01.2026.006
  30. Katalinić, I. (2021). Implementation of MPMM ballistic model for calculation of differential coefficients for TFTs according to NATO STANAG 4119. Strategos, 5 (1), 169–196. Available at: https://hrcak.srce.hr/en/file/379956
  31. ISO 2533:1975 Standard Atmosphere (2024). International Organization for Standardization. Available at: https://www.iso.org/standard/7472.html
  32. Stull, R. B. (Ed.) (1988). An Introduction to Boundary Layer Meteorology. Dordrecht: Springer, 670. https://doi.org/10.1007/978-94-009-3027-8
  33. Tobin, J., Fong, R., Ray, A., Schneider, J., Zaremba, W., Abbeel, P. (2017). Domain randomization for transferring deep neural networks from simulation to the real world. 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems, 23–30. https://doi.org/10.48550/arXiv.1703.06907
  34. Dormand, J. R., Prince, P. J. (1980). A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics, 6 (1), 19–26. https://doi.org/10.1016/0771-050x(80)90013-3
  35. Hairer, E., Norsett, S. P., Wanner, G. (1993). Solving Ordinary Differential Equations I: Nonstiff Problems. Heidelberg: Springer Berlin, 528. https://doi.org/10.1007/978-3-540-78862-1
  36. Brent, R. P. (2013). Algorithms for Minimization Without Derivatives. Dover Publications, 208. Available at: https://www.perlego.com/book/111565/algorithms-for-minimization-without-derivatives-pdf
  37. Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P. (2007). Numerical recipes: The art of scientific computing. Cambridge University Press, 1235. Available at: https://numerical.recipes/
  38. Xiu, D., Karniadakis, G. E. (2002). The Wiener – Askey Polynomial Chaos for Stochastic Differential Equations. SIAM Journal on Scientific Computing, 24 (2), 619–644. https://doi.org/10.1137/s1064827501387826
  39. Eldred, M., Burkardt, J. (2009). Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification. 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. https://doi.org/10.2514/6.2009-976
  40. Yaro, A. S., Maly, F., Prazak, P. (2023). Outlier Detection in Time-Series Receive Signal Strength Observation Using Z-Score Method with Sn Scale Estimator for Indoor Localization. Applied Sciences, 13 (6), 3900. https://doi.org/10.3390/app13063900
  41. Goodfellow, I., Bengio, Y., Courville, A. (2016). Deep Learning. MIT Press book. Available at: http://www.deeplearningbook.org
  42. Zhao, Q., Tang, Q., Han, J., Yang, M., Chen, Z. (2019). Efficient Method of Firing Angle Calculation for Multiple Launch Rocket System Based on Polynomial Response Surface and Kriging Metamodels. Mathematical Problems in Engineering, 2019 (1), 1–15. https://doi.org/10.1155/2019/7689860
  43. Gao, Z., Yi, W. (2025). Prediction of projectile impact points and launch conditions based on extreme learning machine. Measurement, 252, 117308. https://doi.org/10.1016/j.measurement.2025.117308
  44. Sivaprasad, G., Mathur, G., Rajesh, G. (2025). Physics informed neural network (PINN) for trajectory estimation of artillery shells from target location. 34th International Symposium on Ballistics. Jacksonville. https://doi.org/10.12783/ballistics25/37082
Development of a hybrid artillery fire control system based on neural networks and uncertainty quantification methods

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Published

2026-04-30

How to Cite

Rubel, Y., & Hrytsiuk, Y. (2026). Development of a hybrid artillery fire control system based on neural networks and uncertainty quantification methods. Technology Audit and Production Reserves, 2(2(88), 98–105. https://doi.org/10.15587/2706-5448.2026.357488

Issue

Vol. 2 No. 2(88) (2026): Information and control systems

Section

Systems and Control Processes

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Copyright (c) 2026 Yurii Rubel, Yurii Hrytsiuk

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