Regression-Based Stochastic Study of Electromagnetic Fields Due to Lightning Strikes

Electromagnetic (EM) fields triggered by lightning strikes are likely to display non-negligible variability in practice, with an apparent effect on various quantities of interest, such as induced voltages on transmission lines. This paper investigates the stochastic properties of lightning-generated fields, when the latter are affected by random ground parameters and/or nondeterministic lightning base current. In essence, the EM components are represented herein by truncated series of orthogonal polynomials, according to the generalized polynomial-chaos theory, and their expansion coefficients are computed via a regression approach. The necessary samplings of the random spaces are constructed with either tensor-based or sparse grids, and their performance is validated and compared. It is shown that reliable calculations of the expectation can be conducted with low-order polynomial approximations, while at least third-order expansions are required for the standard deviation. In addition, we conclude that nontrivial variability is induced in lightning-produced pulses, when variations of the considered stochastic parameters are taken into account.