Розроблення гібридної системи управління артилерійським вогнем на підставі нейронних мереж та методів квантифікації невизначеності

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.