THE CONCEPT OF MODERN APPROACHES TO THE LEVELS OF DESCRIBING THE AGING PROCESSES OF STRUCTURALLY AND FUNCTIONALLY COMPLEX CRITICAL SYSTEMS WITH LONG PERIODS OF ACTIVE EXISTENCE

Abstract

Background. Traditional methods for assessing and analyzing the indicators of the durability of equipment of complex systems are based on the description of systems in time at the level of trajectories of behavior, and are idealizations, since they do not take into account changes in the structure of the phase space. It should be recognized that these methods and existing techniques based on the theory of long-term strength are provided with appropriate standards. At the same time, over the past 40-50 years, new theoretical developments have appeared that take into account the finer structure of time in dynamics and thermodynamics. These works show that modern approaches to dynamics and thermodynamics can significantly increase the reliability of calculations of equipment durability indicators for structurally and functionally complex systems at all stages of their life cycle. Therefore, the goals of this article are to analyze the existing approaches and methods for describing the aging processes of equipment (blocks, subsystems) and their further development in the theory of the durability of complex systems, which is especially important for critical systems with long periods of active existence. Materials and methods. The physical and mathematical essence of new modern approaches to the levels of describing the aging processes of equipment of structurally and functionally complex systems, taking into account the achievements of classical mechanics and thermodynamics, is as follows: 1. Wide application of the language of the theory of operators of functional analysis in classical mechanics, which means replacing the description of systems at the level of studying the trajectory by researching their distribution functions. 2. Introduction to the description of systems of simpler equations that take into account the specifics of irreversible processes. 3. Mandatory application of the theory of random processes. Results and conclusions. 1. It has been proved that, since the fundamental theoretical basis of the new approach in describing the aging levels of equipment in the theory of the durability of structurally and functionally complex systems, taking into account the asymmetry of time, are unstable and irreversible processes, then for solving theoretical and applied problems of assessing and analyzing durability indicators it is necessary to use eigenfunctions and eigenvalues of the Leeouville and Hamilton operators, transformation entropy and internal time. 2. A new methodology for the concept of an integrated approach to the levels of description of indicators of durability and the sequence of research is proposed.

Keywords

• operators of microscopic entropy
• transformation and internal time
• "age" of the system
• indicators of durability