ANALYSIS OF THE APPROACHES TO THE DEVELOPMENT OF THE MATHEMATICAL MODEL FOR THE MONITORING OF NATURAL AND ANTHROPOGENIC SYSTEMS ON THE BASIS OF DETERMINATION OF GRADUAL FAILURES PROBABILITY

The approaches for creating a mathematical model for monitoring natural and technogenic systems (PTS) and emergency situations (ES) based on the probability of gradual failures are outlined. The monitoring of the NAS and ES provides for comprehensive monitoring of changes in the natural and anthropogenic environment and its components. The complexity of this process is determined mainly by the complexity of the diagnostics of the monitoring objects and the precise measurement of a large number of indicators that determine the conditions and factors of the state of the NAS, environmental pollution, etc. The practical solution of this problem is possible on the basis of the use of modern mathematical and geo-information methods of modeling that provide a comprehensive reflection of heterogeneous and multi-linked processes of formation and development of emergency situations of different origins, which can not be achieved with the use of traditional technologies. To describe the functioning of monitoring systems, it is worth building a mathematical model of the research object. The most complete state of the object of the study is characterized by its mathematical functional and statistical model. However, a more complete description of the static and dynamic state of the monitoring object is a probabilistic description of the state of objects with the help of distribution laws of the probabilities of the parameters of the input influences elements, output parameters and vector-operators. Since the probabilities of sudden bounces are determined by known formulas of the reliability theory, the main attention is drawn to the determination of the probability of the gradual failures occurrence.It is established that three mathematical models may be applied to determine the probability of gradual failures (a mathematical model based on the integration of differential equations; a mathematical model based on the Monte Carlo method; a mathematical model based on the quasilinear disturbances method). The results show, that the proposed method of research may use to simulate various scenarios of flooding in the territories of the Chernihiv region.