The Bézier curve and neural network model of the time-domain transient signals

Abstract

The discussion is for the memory of Oleg Alexandrovich Tretyakov. In the discussion, one characteristic of the signal transfer of Professor Tretyakov's Evolutionary Approach to the Electromagnetics method is presented. Theoretically, the problem of the signal generated by a time-domain signal in a waveguide is addressed. The theoretic propagation is realized-exemplified through the actual TEC (TECU) map estimating by the Bézier curve and neural network. The striking aspect of the segmented prototype established with the Bézier approach is its adaptability. This mechanical curve, which does not need any preliminary preparation, is framed on differential geometric invariants. In the essay, a time-dependent complete set of magnetic waveguide modes is remembered. While the Dirichlet and Neumann eigenvalue problems determine the vector functions of the modes, the behavior of the time-evolving amplitudes is given by the Klein-Gordon equation. Examples of current data are discussed with the TEC map for the 2017 year. While the actual fluctuation of the interpolated CODE TEC atlas is illustrated, the mechanical Bézier curve family (untouched before) and the neural network introduce time-domain estimations to the reader. The parametric curve approach governs the Bézier model. The curve, which is C0 class segmented continuously, models on its way with new hourly components every twelve hours. The network model employs the solar wind parameters for the TEC atlas estimation. The reliability and consistency of the models are exhibited by the R correlation ratio, absolute error, and mean squared error. As a result, the R coefficient of the curve and network models vary around 91.2% and 98.8%, respectively. One can note the error of the network model falls to 1.1308 TECU. The outcomes are compatible with the former discussions.