Numerical analysis of a calibration problem for simulating electric fault arc tests

Abstract

In this article, we present a mathematical model and a numerical approach for a computer-based simulation of electric fault arc tests including the solution of corresponding direct and inverse problems. In particular, we replace the complicated initial-boundary value problem of heat transfer in arc tests by a one-dimensional model based on a purely time-dependent temperature function G(t) of hot gas in a neighborhood of the arc. We analyse the forward problem with respect to its well-posedness and suggest an appropriate numerical approximation. However, we are especially interested in the ill-posed nonlinear inverse problem of identifying (calibrating) the important parameter function G from temperature measurements at a defined distance to the arc during some time interval, where a simplified test procedure is exploited for obtaining temperature data. We present a least-squares solution indicating the ill-posedness effect by strong oscillations and compare a solution from Tikhonov regularization with a solution from a descriptive regularization approach.