Inverse source problem in a forced network
Optimization and Control
2019-05-22 v2
Abstract
We address the nonlinear inverse source problem of identifying a time-dependent source occurring in one node of a network governed by a wave equation. We prove that time records of the associated state taken at a strategic set of two nodes yield uniqueness of the two unknown elements: the source position and the emitted signal. We develop a non-iterative identification method that localizes the source node by solving a set of well posed linear systems. Once the source node is localized, we identify the emitted signal using a deconvolution problem or a Fourier expansion. Numerical experiments on a node graph confirm the effectiveness of the approach.
Cite
@article{arxiv.1803.04895,
title = {Inverse source problem in a forced network},
author = {J. G. Caputo and A. Hamdi and A. Knippel},
journal= {arXiv preprint arXiv:1803.04895},
year = {2019}
}