Structural and functional simulation of interaction in the field of aviation safety by using matrices

Abstract

Purpose: The conducted research was aimed at constructing a structural and functional model for the interaction of bodies providing aviation safety during crisis management. Design/methodology/approach: The methods of mathematical simulation and the graph theory, the methods comparison and formalization have been applied to study the process of interaction between the bodies assuring aviation safety. Using methods of the linear algebra allowed constructing a mathematical model for the functional structure of the interaction process that contains description of this process by the main methods of interaction. Findings: It has been proved that the interaction process has a certain functional properties that reflect the functional relations between the modes of violator actions, the modes of using the response forces and the modes of interaction. A structural and functional model of interaction in semantic, algebraic forms and in the form of graphs has been created. using typical operations with incidence matrices, the possibility of obtaining the physical interpretation of the simulation results within the introduced algebra of functional structure models has been justified. Research limitations/implications: Discusses interactions between the bodies that assure aviation safety and at the same time, the possibility of a crisis situation is taken into account. Practical implications: The developed models allow reflecting the current state of the functional system and the elements of the process of interaction rather completely. It makes a structural and functional analysis of interaction possible and allows defining the priority directions of its organization, simulating the options and methods of interaction in solving relevant tasks by the bodies that assure aviation safety. Originality/value: That allowed not only describing the formal relations between the methods of interaction and interacting units, between the interacting units and the modes of violator actions, but also considering the influence of the interaction process on the current state of the functional system.