This thesis aims to provide SMPS users with a methodology to compute uncertainties associated with the estimation of aerosol size distributions. SMPS selects and detects airborne particles with a Differential Mobility Analyser (DMA) and a Condensation Particle Counter (CPC), respectively. The on-line measurement provides particle counting over a large measuring range. Then, recovering aerosol size distribution from CPC measurements yields to consider an inverse problem under uncertainty.
A review of models to represent CPC measurements as a function of the aerosol size distribution is presented in the first chapter showing that competitive theories exist to model the physic involved in the measurement. It shows in the meantime the necessity of modelling parameters and other functions as uncertain. The physical model we established was first created to accurately represent the physic and second to be low time consuming. The first requirement is obvious as it characterizes the performance of the model. On the other hand, the time constraint is common to every large-scale problems for which an evaluation of the uncertainty is sought.
To perform the estimation of the size distribution, a new criterion that couples regularization techniques and decomposition on a wavelet basis is described. Regularization is largely used to solve ill-posed problems. The regularized solution is computed as a trade-off between fidelity to the data and prior on the solution to be rebuilt, the trade-off being represented by a scalar known as the regularization parameter. Nevertheless, when dealing with size distributions showing broad and sharp profiles, an homogeneous prior is no longer suitable. Main improvement of this work is brought when such situations occur. The multi-scale approach we propose for the definition of the new prior is an alternative that enables to adjust the weights of the regularization on each scale of the signal. The method is tested against common regularization with homogeneous smoothness prior and shows improvements.
Last chapter of this thesis deals with the propagation of the uncertainty through the data inversion. Sources of uncertainty are gathered in two different groups, one called the experimental dispersion and the second being the lack of knowledge. Since there is no reference available to evaluate the bias on the final estimate of the size distribution, the lack of knowledge is used here to characterize it. Unlike standard propagation that uses a fixed model for the inversion, we propose to use a random model drawn from random selection of elements of the second group.
The methodology is finally tested on real measurements of an aerosol made of SiO2 droplets and of DEHP droplets (oil). It reveals that the main source of uncertainty arises from the lack of knowledge for the definition of the physical model. Indeed, SMPS measurements are repeatable under controlled laboratory conditions, making the experimental dispersion less influential in terms of the variance of the final estimate.