IDENTIFICATION OF BOUNDARY CONDITIONS ON A STAR-SHAPED GEOMETRIC GRAPH OF FOUR STRINGS
A star-shaped geometric graph of four wires with one common vertex at zero is considered. Dead ends of the graph are grounded through the parallel-connected concentrated self-induction and concentrated capacitance of the capacitor. The positive direction of the axis on the wire is the direction from the common vertex of the graph (the point) to the dead end of the graph. The problem is to determine the unknown concentrated self-induction and concentrated capacitance from the first natural oscillation frequencies of the alternating current voltage in the accessible section of one of the wires. It is shown that if the lengths of the strings are the same, then the concentrated self-inductions and capacitances are up to permutations by their places (i.e., ambiguously). If the lengths of the strings are different, then the concentrated self-inductions and capacitances are uniquely determined. If the strings are of unequal length, it is necessary to use the number of natural frequencies greater than the number of unknown parameters for unique determination of these unknown parameters. It is shown that if the number of natural frequencies coincides with the number of unknown parameters, then the parameters are determined ambiguously. The given examples show that if four unknown parameters (one in each boundary condition) are reconstructed at four natural frequencies, then six solutions are obtained. The results of the study can be applied to diagnose the grounding conditions of wires in areas not accessible for visual inspection, according to the natural frequencies of AC voltage fluctuations in the wire section accessible for measurement.