The problem of estimating the statistics of the distributed parameters of a transmission line which are random functions of time and spatial location is addressed in this paper. The main idea is to transform the spatial–temporal PDE (partial differential equation) problem into a purely temporal problem using spatial test functions and then apply first-order perturbation theory to express the random components of the line voltage and current as linear functional of the random distributed parameters. We then evaluate the line voltage and current statistical correlations in terms of the distributed parameters correlations. Simulation studies are carried out for variance estimation of the resistance per unit length, and appropriate results are obtained.

本文解决了估计传输线分布参数的统计量的问题，这些分布参数是时间和空间位置的随机函数。主要思想是利用空间测试函数将时空 PDE（偏微分方程）问题转化为纯时间问题，然后应用一阶微扰理论将线路电压和电流的随机分量表示为随机分布参数。然后，我们根据分布参数相关性评估线路电压和电流统计相关性。对单位长度电阻的方差估计进行了仿真研究，得到了适当的结果。