Numerical Analysis of a Transmission Line Illuminated by a Random Plane-Wave Field Using Stochastic Reduced Order Models

Abstract

A novel nonintrusive statistical approach, known as the stochastic reduced order model (SROM) method, is applied to efficiently estimate the statistical information of the terminal response (i.e., the induced current) in transmission lines excited by a random incident plane-wave field. The idea of the SROM method is conceptually simple, i.e., to represent the uncertain input space dimensioned by random variables using the SROM-based input model. This input model consists of a very small number of selected samples with assigned probabilities. Thus, only these input samples in the model need to be evaluated using the deterministic solver. The SROM-based output model can be constructed to approximate the propagated uncertainty to the real output response with elementary calculation. The efficiency and accuracy of the SROM method to obtain the statistics of the induced current are analyzed using two examples, where the complexity of the uncertain input space gradually increases. The performance of the SROM method is compared with that of the traditional Monte Carlo (MC) method. The stochastic collocation (SC) method based on sparse grid sampling strategy computed via the Smolyak algorithm is also implemented to fairly evaluate the SROM performance. The result shows that the SROM method is much more efficient than the MC method to obtain accurate statistics of the induced current, and even shows a faster convergence rate compared with that of the SC method in the examples considered. Therefore, the SROM method is a suitable approach to investigate the variability of radiated susceptibility in electromagnetic compatibility problems with a random incident wave.