Multi-sensors source inversion algorithm based on remote measurement and domain of dependence

Identification of passive scalar sources from remote measurements raised serious challenges due to the combined effect of molecular diffusion and turbulent dispersion. To enable fast identification, the adjoint operator is adopted to exploit the sensitivity of remote measurements to source locations. This sensitivity is also coined as the measurement's domain of dependence (DoD). Our work utilizes measurements and the DoDs of a multi-sensor system to identify the source location and provide its confidence interval swiftly. The algorithm is tested in a turbulent channel flow with Reynolds number $Re_\tau=180$. The forward-adjoint duality relation shows that the time-averaged measurement and mean adjoint field are related by a proportionality equal to the source strength, where uncertainty is embedded in the finite window of length $T$ used for the time average. We quantify this averaging uncertainty represented by Gaussian random variables and add to the duality relation, which is then used to estimate the confidence interval of the source location. The standard deviation of the Gaussian variable scales with $1/\sqrt{T}$, and depends on the wall-normal location of the source-sensor pair. These trends are presented and discussed in the current research.