METHOD OF RECURSIVE CHORD SEARCH FOR CALCULATION OF RELIABILITY SCHEMES

Abstract

The current issue of chord search is considered with the aim of further using the research results in developing a method for calculating the reliability of radial and ring circuits based on the proposed equilibrium balancing methodology. Chord search methods for reliability circuits are considered and analyzed. One of the approaches to determining a chord in a circuit is the possibility of using the method of recursively searching for it among the branches that form an independent circuit.

The article uses a matrix of fault-free operation of the branches of the scheme, which takes into account not only the direct probabilities of the branches, but also the mutual influence exerted by the branches of the selected and neighboring circuits of the reliability scheme. Mathematical models of the method of recursive chord search are formed on the basis of a logical-mathematical apparatus, which is proposed for algorithmization of tasks and processes with their subsequent automation for the purpose of developing information and software modules. A step-by-step method for searching for chords in reliability schemes represented by independent circuits has been developed. It consists in using algorithms for searching through the nodes of the circuit until a node that has already participated in the search process is repeated, which, in turn, corresponds to the elements of the matrix of the probability of failure-free operation of the circuit elements, symmetric with respect to the main diagonal. The process of searching for elements of the reliability uptime matrix is ​​illustrated, which performs a transition through non-zero elements of this matrix, which characterizes the inclusion of a new node in the desired circuit, the last branch of which is identified as a chord. Before the next iteration of the alternate search for the remaining chords of the reliability scheme, both symmetric elements according to the main diagonal of the probability matrix are set to zero. Logical-mathematical, as well as functional and algorithmic models were created, which were used to automate the process of software development for the method of recursive chord search for reliability schemes. The software is implemented in PHP using the Apache2 web server. The adequacy and operability of the developed models, algorithms and programs are illustrated, and the reliability of the obtained results is confirmed.