Clustering elements of electronic circuits as part of preventive diagnosis: prediction of electronic equipment degradation by percolation theory
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Abstract
Among the problems that are solved by specialists in the operation of electronic equipment, including marine, diagnostic and prevention questions of electronic circuits operability are always relevant. These are complex and non-trivial tasks, the solution of which at a satisfactory level is not always possible. This article proposes another algorithmized way to solve such a problem, namely, a method based on the percolation theory. Percolation theory is known to study the structure and properties of the connected regions or groups of similar (same type) elements. The article deals with the clusters formed on the hybrid grid by the elements of the transformed functional scheme of the electric circuit. The assortment and distribution of clusters by size, that is, the cluster system of the lattice determines its properties. A method for diagnosing complex electronic circuits based on such a concept is proposed. The method has two components. The first is intended for practical use, does not require the use of the mathematical apparatus of the theory, and is reduced to converting basic electronic circuits into parallel and serial connections of the same type of circuit elements. This leads to the spontaneous creation of a cluster system of elements, and allows finding elements that are located close to the faulty one and therefore have a reduced service life. The second component is intended for further study of the circuits. To do this, it is necessary to use the percolation analysis of reformatted circuits. Such an analysis allows, in addition to geometric parameters, investigating the electrical conductivity of circuits [4], obtaining the critical power index, and also calculating the fractal and chemical dimensions of the skeleton of an infinite cluster and its lacunarity. The purpose of further research is to identify of the percolation type dependencies between the structure and properties of electronic devices circuits.
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