OPTIMAL STRUCTURAL RESERVATION OF TECHNICAL SYSTEMS

Abstract

Purpose. The purpose of the article is to give designers of highly reliable technical systems that do not have special knowledge in the field of optimization and programming skills, a simple and accessible mathematical tool for choosing the optimal solution for structural redundancy of systems. Methodology. The article poses the problem of optimal structural redundancy of technical systems. Two typical redundancy schemes are considered: a) a separate "hot" backup scheme; b) a separate "cold" backup scheme. The computational models for estimating the reliability of redundant systems are formulated. We offer optimization models that allow us to find a rational option for reserving a system that is being designed, taking into account conflicting requirements for its reliability and cost. These models are numerically implemented in the operating environment of the Excel spreadsheet as applied to the main object, consisting of 7 elements. The optimal variants of reserving this object according to the "hot" and "cold" separate reservation schemes are given. Findings. Calculated models for estimating reliability, as well as models for optimizing the systems reserved for the "hot" and "cold" separate backup schemes, have been developed. With the use of the Excel spreadsheet, the optimal options for reserving 7 element objects are found for separate "hot" and "cold" backups. Originality. New computational models for estimating the reliability of redundant systems are proposed, as well as optimization models developed on the basis of these, which are formulated using the decomposition of unknown initial problem of structural redundancy into binary components. In this case, the obtained optimization models belong to the class of problems of non-linear mathematical programming with binary variables, for the numerical solution of which (even for a sufficiently large dimension) well-known packages of applied computer programs, in particular, the MS Excel spreadsheet, are well adapted. Thus, the process of solving the initially very complicated problem of optimal structural redundancy is much simpler and reduced to performing elementary actions in the corresponding software interfaces. Practical value. The proposed calculation models for estimating the reliability of redundant systems, models for optimal structural redundancy, and the methodology for their formation, in order to simplify further numerical implementation, can be useful in solving problems of ensuring the reliability of technical systems in the early stages of their design.