Leak localisation with a measure source convection-diffusion model

TL;DR

This paper presents a method for accurately localizing gas leaks by solving an inverse convection-diffusion problem with sparsity regularization, jointly estimating physical parameters and source locations.

Contribution

It introduces a stability analysis for the convection-diffusion model and a semi-grid-free optimization approach for source reconstruction, advancing gas leak detection techniques.

Findings

Accurate localization of gas sources demonstrated in experiments.

Joint estimation of physical parameters improves source identification.

Stability analysis provides theoretical guarantees for the inverse problem.

Abstract

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.