A-optimal Bayesian experiment design for identification of an initial gas distribution in an urban flow simulation

Abstract

This thesis presents a method for determining an optimal experiment design (A-optimal experiment design) for the identification of pollutant sources. A well-known formulation for the determination of an A-optimal design is extended so that it can be applied to a real scenario, such as the release of pollutants in a chemical park. The solution of an incompressible Navier-Stokes equation system enables the determination of a wind simulation, which is then used to create a valid flow model for the pollutant transport with the help of the linear advection-diffusion equation. Using this model, it is possible to characterize the source of the pollutant, given by the initial condition of the advection-diffusion problem, by means of discrete pollutant measurements in space and time. Since sensor measurements are typically subject to a certain amount of noise, the use of a Bayesian formulation is advantageous, by means of which an adequate approximation of the original pollutant concentration can be derived in the form of a random distribution. This model ultimately results in a measure for the inaccuracies of the resulting system, which is dependent on the sensor positions. This measure can then be used to develop the A-optimal design. The work includes the mathematical modeling and the numerical implementation of an efficient solution to this problem.