Quasi-Monte Carlo, Monte Carlo, and regularized gradient optimization methods for source characterization of atmospheric releases

An inversion technique based on MC/QMC search and regularized gradient optimization was developed to solve the atmospheric source characterization problem. The Gaussian Plume Model was adopted as the forward operator and QMC/MC search was implemented in order to find good starting points for the gradient optimization. This approach was validated on the Copenhagen Tracer Experiments. The QMC approach with the utilization of clasical and scrambled Halton, Hammersley and Sobol points was shown to be 10-100 times more efficient than the Mersenne Twister Monte Carlo generator. Further experiments are needed for different data sets. Computational complexity analysis needs to be carried out

Source characterization of atmospheric releases using quasi-random sampling and regularized gradient optimization

technical reportIn the present work, an inversion technique to solve the atmospheric source characterization problem is described. The inverse problem comprises characterizing the source (x, y and z coordinates and the source strength) and the meteorological conditions (wind speed and wind direction) at the source, given certain receptor locations and the concentration values at these receptor locations. A simple Gaussian plume dispersion model for continuous point releases has been adopted as the forward model. The solution methodology for this nonlinear inverse problem consists of Qausi-Monte Carlo (QMC) sampling of the model parameter space and the subsequent application of gradient optimization. The purpose of conducting QMC sampling is to provide the gradient scheme a good initial iterate to converge to the final solution. A new misfit functional that computes the L?-norm of the ratio of the observed and predicted data has been developed and was used in the QMC search stage. It has been demonstrated that the misfit functional developed, guides the inversion algorithm to the global minimum. Quasi-random sampling was performed using the Hammersley point-set in its original, scrambled and randomized form. Its performance was evaluated against the Mersenne-Twister uniform pseudo-random number generator in terms of the speed and quality of the initial iterate provided. Regularized Newton?s method with quadratic line-search was employed for gradient optimization. The standard Tikhonov stabilizing functional was used for regularization and the regularization parameter was updated adaptively during inversion. The proposed approach has been validated against both synthetic and field experiment data. Results obtained indicate that the proposed approach performs exceedingly well for inverse-source problems with the Gaussian dispersion equation as the forward operator. Also, the work presented highlights the advantages of using deterministic low-discrepancy sampling compared to the conventional pseudo-random sampling to solve the sourceinversion proble

Doctor of Philosophy

dissertationThe present work focuses on developing a holistic understanding of flow and dispersion in urban environments. Toward this end, ideas are drawn from the fields of physical modeling, inverse modeling, and optimization in urban fluid dynamics. The physical modeling part of the dissertation investigates flow in the vicinity of tall buildings using wind tunnel two-dimensional particle image velocimetry (PIV) measurements. The data obtained have been used to evaluate and improve urban wind and dispersion models. In the inverse modeling part of the dissertation, an event reconstruction tool is developed to quickly and accurately characterize the source parameters of chemical / biological / radiological (CBR) agents released into the atmosphere in an urban domain. Event reconstruction is performed using concentration measurements obtained from a distributed sensor network in the city, where the spatial coordinates of the sensors are known a priori. Source characterization comprises retrieving several source parameters including the spatial coordinates of the source, the source strength, the wind speed, and wind direction at the source, etc. The Gaussian plume model is adopted as the forward model, and derivative-based optimization is chosen to take advantage of its simple analytical nature. The solution technique developed is independent of the forward model used and is comprised of stochastic search with regularized gradient optimization. The final part of the dissertation is comprised of urban form optimization. The problem of identification of urban forms that result in the best environmental conditions is referred to as the urban form optimization problem (UFOP). The decision variables optimized include the spatial locations and the physical dimensions of the buildings and the wind speed and wind direction over the domain of interest. For the UFOP, the quick urban and industrial complex (QUIC) dispersion model is used as the forward model. The UFOP is cast as a single optimization problem, and simulated annealing and genetic algorithms are used in the solution procedure