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The methodological aspects of fractal structured account of meteorological conditions for functioning of aviation systems

Keywords:

V.V. Mikhailov – Dr.Sc. (Eng.), Professor, Head of Hydrometeorological Department, Military Educational Research Centre of Air Force «Air Force Academy named after professor N.E. Zhukovsky and Y.A. Gagarin» (Voronezh). E-mail: mvv987@pochta.ru
S.L. Kirnosov – Ph.D. (Eng.), Doctoral Candidate, Military Educational Research Centre of Air Force «Air Force Academy named after professor N.E. Zhukovsky and Y.A. Gagarin» (Voronezh)


Development of methodological aspects of fractal structured account of meteorological conditions for functioning of aviation systems in the article made on the basis of a systematic approach to the process of fulfilling the objectives of aviation. Under this approach, used the main provisions of deterministic chaos theory and functional analysis. In particular, the isolated system «pilot – aircraft – environment». Internal elements of the system are formalized data on the qualifications of the pilot and the technical capabilities of the aircraft. External parameters that influence the system under consideration are weather conditions and other external impacts associated with the state of the aerodrome ground landing system readiness, training entities of operational control and so on. This system is an open, dynamic and nonlinear. Its operation is subject to complex cause-and-effect relationships between the internal elements of the system itself and with the external environment, which leads to the need to find sustainable and safe modes of operation of the system based on the use of quantitative and qualitative methods of the theory of deterministic chaos. The article shows the relationship universal scale similarity of the bifurcation diagram Verhulst and Mandelbrot fractal. Established universal laws governing the transition to dynamic chaos in the doubling of the period of oscillations were experimentally confirmed for a wide class of mechanical, hydrodynamic, chemical and other systems. In this paper, the following conclusions are made. When building a control system for meteorological service possible and appropriate use of quantitative and qualitative methods of deterministic chaos theory and elements of complex dynamics. Search for stable and safe modes of operation of aviation systems must be based on the analysis of invariant sets (attractors), which are areas of attraction in the phase space characteristics of functioning. Analysis of one-dimensional nonlinear discrete maps and endomorphisms on the complex plane shows, first, their relationship universal scale similarity, and secondly – the presence of both the first and second cases of stable structures – fractals. Such structures are hypersensitive to external influences, resulting in a need to visualize them for later use in making management decisions. Delineation of attractors is a critical task, since in practice it is the set of possible states controlled aviation system after stabilization.
References:

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