Nonstationary approximation error approach to imaging of three-dimensional pipe flow: experimental evaluation

Abstract

In this paper, we consider nonstationary estimation in imaging of three-dimensional fluid flow. More specifically, we experimentally evaluate the feasibility of a recently invented approximation error method to recovering from modelling errors in imaging of nonstationary targets. In nonstationary estimation, both the observations and the time evolution of the target distribution are modelled, and the image reconstruction problem is written in the form of a state estimation problem. The state estimates rely on these models and the observations carried out during the evolution of the target. If the associated modelling errors are not accounted for, state estimation can lead to heavily biased reconstructions. In the approximation error approach, the model inaccuracies and uncertainties are modelled statistically. In this experimental study, we consider a case of rapidly moving fluid in a pipeline, and model the target with the convection–diffusion equation. Electrical impedance tomography (EIT) is used as the imaging modality. In the nonstationary approximation error scheme, we model the errors due to truncation of the computational domain, discretization, unknown contact impedances of electrodes used in EIT measurements and partly unknown boundary conditions in the convection–diffusion model. The results verify that enhancing the state-space representation with the approximation error models can yield a significant improvement in the reconstructions.