Leak localisation with a measure source convection-diffusion model
摘要
We study the inverse problem of locating gas leaks from line-of-sight concentration measurements using a convection-diffusion model with the source term a Radon measure. By imposing sparsity-promoting regularisation on this measure, we recover point sources - identifying both their locations and intensities - rather than diffuse approximations. We jointly estimate the underlying physical convection (wind) and diffusion parameters. Our main theoretical contribution is the stability analysis of the convection-diffusion equation with respect to its parameters: the measure, and the convection and diffusion fields. Numerically, we employ a semi-grid-free optimisation approach for reconstructing the source measure. Our experiments demonstrate accurate localisation, highlighting the potential of the method for practical gas emission detection.
引用
@article{arxiv.2605.12095,
title = {Leak localisation with a measure source convection-diffusion model},
author = {Thi Tam Dang and Tuomo Valkonen},
journal= {arXiv preprint arXiv:2605.12095},
year = {2026}
}