Sensitivity of inverse advection–diffusion–reaction to sensor and control: A low computational cost tool

A two-dimensional (2D) concentration field may be reconstructed using inverse advection–diffusion–reaction based on pointwise sensor outputs. The studied reconstruction process consists in defining fictitious boundaries and identifying the optimal concentrations on these boundaries that minimize the data misfit. The minimization is performed by means of the adjoint method. The reconstruction process is observed to fail for some sets of sensor placements. Therefore, in this paper, we aim to develop a low computational cost framework that can be used to identify badly placed sensors and to reveal potentially optimal sensor placement. From this framework, we have derived a sensitivity tool that can predict, for a given set of sensors, which boundary concentrations are easy or difficult to identify using the inverse method. This tool only requires the resolution of an adjoint problem. It is compared with the “sensitivity-to-observation” method in a 2D water pipe junction with 2⋅103 Reynolds number and 103 Peclet number. The compared methods do produce similar quantitative and qualitative results.