On the problem of building adequate mathematical models of risk management in the operation of complex unique responsible systems

The paper describes a mathematical model for control risks arising in the course of the operation of complex technical systems of responsible purpose in the context of incompleteness and uncertainty of information about parameters and phase state. The aim of the study is to develop an individual optimal strategy for control risk events arising during the operation of complex technical systems, involving minimization of the magnitude of damage associated with risks, as well as the smallest amount of costs arising from preventive and control and measurement work during the entire period of operation. The objectives of the study are to build a mathematical model of risk management in the operation of complex dynamic technical systems of critical purpose in the conditions of interval uncertainty about parameters and phase state, as well as the development of methods for individual forecast of the state change of the considered class of systems. The article gives a comparative characteristic of the effectiveness of using the mathematical apparatus of the theory of emissions of random processes and the method of individual forecasting when solving the problem of control risks arising from the operation of complex technical systems for critical purposes in conditions of uncertainty. Based on the methods of statistics of interval data, a mathematical model of risk control is created, which takes into account possible errors in measuring the values of the parameters of the considered class of complex systems on all control windows during the period of operation. The scientific novelty of the proposed approach consists in the application of statistics of interval data, which make it possible to most accurately take into account possible errors associated with measuring the values of parameters of the technical systems under study at all stages of control. The mathematical model of risk management built in the course of the research carried out during the operation of complex technical systems for critical purposes makes it possible to select the optimal risk management strategy for the operation of objects of the class under consideration. Along with this, an algorithm for predicting changes in the state of a technical system during the entire period of operation was built on the basis of the apparatus of statistics of interval data, which allows taking into account errors in measuring the main parameters of the system under consideration at all stages of control.