Neural Network Based Calculation of Load Resistances Taking into Account the Multiport Input-to-Output Ratio Invariant Properties

Abstract

The invariant properties of a multiport input-output ratio as a model of unstable two- and three-wire power supply lines of power loads or resistive sensors are considered. The fractional linear expressions typical for the electrical circuit theory are interpreted as projective transformations in the sense of projective geometry. Projective transformations preserve an invariant: a cross ratio or a duplicate proportion of four samples of variable resistance and the corresponding values of currents in different sections of the circuit. In this way, it becomes possible to calculate the load resistances from the measured current samples at the circuit input and their known base or test values; in doing so, the circuit parameters are not explicitly used. In turn, the base load values can also vary or are known with some uncertainty. To eliminate the influence of the variable parameters, neural networks are used for the calculation. For training the neural network, a set of possible values of the base resistances, loads, and the variable resistance of the multiport itself is specified. The corresponding set of input currents forms a training vector, and the load values are components of the target vector. Numerical experiments carried out in the Deep Learning package of the MATLAB system with one and two loads show the control calculation accuracy for the trained shallow neural network at a level of one to two percent.