Estimation of position and intensity of a pollutant source in channel flow using transmittance functions (Q2888760)

This paper considers the one-dimension linear advection-diffusion equation with constant coefficients for a transient pollutant point source. The linear transport equation is first presented with the convolution structure of its solution, which gives rise to transfer functions of two different types: an impedance relates an observed sensor response to the intensity of the source while a transmittance relates a concentration response at a given location to a reference concentration that is the first to depart from its initial zero value. The concentration solution of the corresponding state model, in a one-dimension transient advection and diffusion case, is obtained analytically in the Laplace domain. Once the direct analytical solution of the dual form mass transfer model is established, this model is rewritten in its transmittance form for noisy measurements at the location of all the virtual detectors in order to obtain an estimation of its two structural parameters, the flow velocity and the diffusion coefficient. A nonlinear fixed point method based on least-squares estimation based on noisy concentration responses and using truncated singular value decomposition regularization is implemented to determinate gaseous contaminant source locations and strengths.