Meniailov Y. Mathematical models and methods for solving problems of improvement of technical systems under conditions of uncertainty of input data

The object of research is the processes of improving complex technical systems under conditions of a priori uncertainty of input data. The goal is to increase the efficiency of the search processes for rational design solutions while improving technical systems using the example of aviation facilities through the development of mathematical models, computational methods and computer systems that implement them, under conditions of input data uncertainty. Methods - methods of systems analysis and decision making theory; approaches and methods of the theory of interchangeability and standardization, probability theory, mathematical statistics; methods of the theory of inverse problems and mathematical programming; models and methods of the theory of artificial intelligence. Results - a systematic mathematical model for the synthesis of solutions to multicriteria stochastic optimization problems has been developed; the method of synthesis of scalar convolutions of objective functions for optimization and decision-making problems has been improved; the method for solving nonlinear multicriteria modification problems in an evolutionary way has been improved using the adaptation procedure when choosing parameters in the process of finding solutions; an evolutionary method for the synthesis of solutions to multicriteria modification problems in deterministic and stochastic formulations; the theory of construction of computer decision support systems was further developed on the basis of the proposed mathematical models and methods for solving problems of improving complex technical systems in a deterministic and stochastic formulation. Introduced - in Motor Sich Joint Stock Company (Zaporozhye) when optimizing a two-stage axial compressor, due to which the efficiency of the stages increased (without reducing the reserves of gas-dynamic stability) at the design air flow rate and design speed; in the educational process of the Department of Mathematical Modeling and Artificial Intelligence of the National Aerospace University, Ministry of Education and Science of Ukraine.