Unconditionally-stable time-domain approach for uncertainty assessment in transmission lines

Abstract

Uncertainties characterizing the per-unit-length parameters of transmission lines (TL) may have a significant impact on the properties of the propagating voltage and current waves that deterministic models tend to overlook. In this paper, we present an unconditionally-stable finite-difference time-domain (FDTD) algorithm that calculates the statistics of the involved field quantities, provided that the variability of the line characteristics is known. Being free from time-step restrictions, the proposed scheme is an extension of the standard stochastic FDTD method and exhibits better efficiency, esp. in densely discretized computational domains. Indicative results verify that uncertainty quantification in TL problems is possible in a reliable manner, even when larger than usual time-steps are selected.

A Short Review of FDTD‐Based Methods for Uncertainty Quantification in Computational Electromagnetics

“…However, the additional computational burden is compensated for by the reduced number of iterations, thanks to the larger values of time steps. The numerical results in [17] verify that the statistics of wave phenomena along transmission lines that display uncertainty in their per-unit parameters can be successfully assessed even with large time step, provided that a sufficient spatial resolution is ensured.…”

“…Unconditionally stable methods based on special temporal updating, such as the locally-onedimensional (LOD) approach, are not restricted by stability requirements and allow the utilization of any time-step size (of course, the larger the time step, the higher the numerical errors). A LOD-based Stochastic FDTD method is presented in [17], which is suitable for the solution of the telegraph equations for transmission-line problems. Similar to the deterministic algorithm, the updates for the mean values and standard deviations of the involved variables (voltages and currents) are implicit and require the solution of tridiagonal systems at each time step.…”

A Stochastic Finite-Difference Time-Domain (FDTD) Method for Assessing Material and Geometric Uncertainties in Rectangular Objects

“…The work in [9] introduced a novel S-FDTD scheme, which is free from time-step stability restrictions. This method utilizes the locally one-dimensional approach (hence named S-LOD-FDTD) and is useful for cases with dense grids.…”

Application of Stochastic FDTD to Holland's Thin-Wire Method

“…Corresponding author email: salva@ugr.es statistical parameters from the simulation of a set of problems (often several thousand) with material properties randomly generated. The stochastic methodology has been extended to deal with transmission lines [11], to the finite difference frequency domain method [12], etc.…”