Usenko V. Geometric models of structural reliability of reserved engineering networks

Chapter 1 reveals the problematic issues of research on the maintenance of the efficiency of engineering infrastructure networks. Scientific research of these objects stimulates further development of methods of modeling and definition of a new direction of development of applied geometry and engineering graphics, the realization of the results obtained in other industries. Chapter 2 analyzes the network objects of engineering infrastructure from the positions of structural form-forming. Geometric tasks are solved at all stages of the existence of systems associated with the processes of their design, construction and operation. Therefore, geometric modeling forms a unified basis for other technical branches of science in solving set tasks. The form, component dimensions and their placement in higher-level entities significantly depend on the set of combinations in the structure of the system. The geometric model of the probability of the connection of the structure of the system takes into account its form and the law of distribution of the element’s development. It helps to predict the system time and reliability, depending on the system of connections in the structure. Chapter 3 deals with geometric structural modeling. The structure of systems is classified as hierarchical objects of various dimensions for their reservation. An invariant was obtained in this paper, which allows quantifying the ratio of parallel and sequential combinations in the structure of the system to determine its probability of connectivity. Variable parameters of the reliability of structural elements form a multiplicity as a geometric model in the space of states of the object of study. To solve the problems of analysis and synthesis, the method of configuration change is proposed by structural projection. The educed property of position importance represents the influence of location of elements on distribution of its reliability in the structure of the technical system for the optimization tasks solving of its creating. In chapter 4, the geometric interpretation of the process of functioning of the system is proposed, which extends the approach to optimal control of the system with a visual representation of this process. On the basis of the study of the process of functioning of the system of multidimensional space, the means of controlling its reliability in the form of boundary hypersurfaces are proposed. Approximation of permissible space implements geometric modeling in the study of complex network structures for prediction and optimization of reliability.