A MODIFIED NUMERICAL METHOD OF DETERMINING HYDRAULIC SYSTEM PARAMETERS FOR THE DEVELOPMENT OF MATHEMATICAL MODELS AND INFORMATION COMPLEXES OF COMPUTER SIMULATION MODELS FOR INDUSTRIAL CHEMICAL PRODUCTION

The paper introduces a modified numerical method for determining the parameters of hydraulic systems used in mathematical modeling and simulation-based computer systems for industrial chemical production. It explores the dynamics of fluids, gases, and their mixtures as they traverse pipelines equipped with valves, compressors, and other complex components. Traditional methods for solving nonlinear equation systems often face limitations, including sensitivity to initial approximations and the need for relaxation coefficient adjustments, which complicate simulation processes. The proposed method converts nonlinear equations into an optimization problem, us- ing the Nelder-Mead algorithm to minimize deviations between initial estimates and comput- ed parameters. This derivative-free approach employs a simplex geometric transformation, overcoming issues associated with iterative methods and delivering high accuracy, stable convergence, and computational efficiency. Its adaptability makes it suitable for handling in- tricate hydraulic systems. To validate the method, a practical example involving a pipeline system with multiple restricting devices is analyzed. The mathematical model includes equations for pressures and flow rates, supplemented by material balance constraints at branching points. Numerical ex- periments evaluate how input pressure influences system parameters, demonstrating the mod- el's robustness and precision. The results confirm that the method accurately simulates system parameters under steady-state conditions and identifies critical optimization points. This innovative approach offers significant advantages for designing and managing industrial chemical facilities. By simplifying model construction, enhancing reliability, and accelerating simulation processes, the method provides a powerful tool for optimizing the op- eration and control of complex technological systems.