SDE-based variance simulation in transmission line models with random excitations

This paper is focused on the development of a method to determine variances of the stochastic responses in transmission line models with random excitations. It is based on the theory of stochastic differential equations (SDE), namely a system of vector linear SDEs with additive noise is formulated to be prepared to simulate respective stochastic trajectories. One possibility to get the moments of the stochastic process is to determine sample statistics from a set of individual trajectories. This is, however, rather time consuming, and it´s benefit when compared to common methods is not so obvious. In this paper differential equations for getting directly the first two stochastic response moments of transmission line models under randomly varying excitations are formulated and solved. A verification is performed via the above stated approach, while the Student´s t-distribution can directly be used to determine respective confidence intervals in case of an additive noise. All simulations have been performed in a Matlab language environment.