State Estimation of the Size Distribution and Underlying Physical Processes of Aerosols

Abstract

Aerosols, a system of solid or liquid particles in a gas, are a harmful form of air pollution that play a key role in climate change and public health. To understand its effects, it is paramount to study its size distribution, which in turn is dependent on the physical processes of condensation growth, coagulation, nucleation, and deposition. These processes drive the time-evolution of the size distribution of aerosol populations. Measurements of the size distribution are obtained using a differential mobility particle sizer, however there are no direct measurements on the physical processes mentioned above. The simultaneous estimation of the size distribution and these physical processes based only on measurements of the size distribution is a nonstationary ill-posed inverse problem. In this thesis we use the state estimation framework to simultaneously estimate the size distribution and the physical processes of condensation growth, nucleation, and deposition. Specifically, we use the extended Kalman filter as an estimator, which requires the development of a model for the time-varying size distribution and processes, and a model to relate the measurements to the size distribution and processes. We use the general dynamic equation of aerosols to model the time evolution of the size distribution which is based on the physical processes of condensation growth, coagulation, nucleation, and deposition. This is a integro-partial differential equation that is nonlinear with respect to the size distribution. We use the Petrov-Galerkin finite element method to obtain approximate solutions of the size distribution based on the general dynamic equation. We also use the method of characteristics combined with the finite element method to obtain approximate solutions. To model the evolution of the underlying physical processes of condensation growth, nucleation, and deposition, we use random walk and autoregressive processes. These models were tested with simulated measurements and obtained feasible estimates. The main contribution of this thesis is showing that state estimation is a feasible framework for estimating the size distribution of aerosols and the underlying physical processes, and in particular, the extended Kalman filter is a feasible approximation to the sequential filtering problem.