Optimal emission control and identification of an unknown pollution source

Abstract

The advection-diffusion-reaction equation is used for describing the dispersion of a quasi-passive contaminant from industrial point sources in a limited area. The conditions established on the open boundary ensure that the problem is correct in the sense of Hadamard, that is, its solution exists, is unique, and is stable to initial perturbations. The Lagrange identity is used to construct the adjoint operator and formulate an adjoint problem. Equivalent direct and adjoint estimates are derived to assess the concentration of the pollutant at monitoring sites of the area. Formulas obtained on the basis of adjoint estimates are useful in analysing the sensitivity of the model to both variations in the intensity of pollution sources and variations in the initial distribution of the pollutant concentration in the area. New optimal emission control strategies based on using the adjoint estimates are developed in order to prevent violations of existing sanitary standards by timely reduction of emission rates of operating sources. Optimal control here lies in minimizing these reductions. In addition, this control is primarily aimed at reducing the intensity of emissions from sources that most pollute the monitoring site. Also, new methods are proposed for identifying the main parameters of an unknown point source that arose as a result of a dangerous incident (accident, explosion, etc.). These methods allow determining the location and intensity of a constant or non-stationary point source, as well as the moment of emission of a pollutant in the case of an instantaneous point source. This helps to quickly assess the scale of the incident and its consequences. Numerical results show the effectiveness of the methods.