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Session S08 - Inverse Problems and Applications

Thursday, July 15, 18:20 ~ 18:50 UTC-3

Combination of SEM and Light Scattering Data for the Inverse Estimation of Particle Size Distribution using a Bayesian Approach

Fernando Otero

Universidad Nacional de Mar del Plata, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Particle systems are morphologically characterized through their particle size distribution (PSD). It can define various final properties of the material, which is why it is of fundamental importance to obtain an estimate as accurate and precise as possible. However, there is no single experimental technique capable of providing us with a complete description of PSD . This reason motivates the present talk, which is to analyze the optimization of combining measurements from different techniques in a process that is known as data fusion. We analyze various elements of the process of data fusion to optimize the performance of the PSD estimation applied to the Combination of SEM (Scanning Electron Microscopy) micrographs with SLS (Static Light Scattering) scattered light measurements.

The scheme applied here is to solve an inverse problem using a Bayesian inference where the prior information is deduced from the SEM micrographs and measurements are data from SLS. For this purpose we propose two Bayesian schemes (one parametric and another non-parametric) to solve the stated light scattering problem and take advantage of the obtained results to summarize some features of the Bayesian approach within the context of inverse problems.

The features presented in this talk include the improvement of the results when some useful prior information from an alternative experiment is considered instead of a non-informative prior as it occurs in a deterministic maximum likelihood estimation. This improvement will be shown in terms of accuracy and precision in the corresponding results and also in terms of minimizing the effect of multiple minima by including significant information in the optimization. Both Bayesian schemes are implemented using Markov Chain Monte Carlo methods. They have been developed on the basis of the Metropolis– Hastings (MH) algorithm using Matlab® and are tested with the analysis of simulated and experimental examples of concentrated and semi-concentrated particles. In the simulated examples, SLS measurements were generated using a rigorous model, while the inversion stage was solved using an approximate model in both schemes and also using the rigorous model in the parametric scheme. Priors from SEM micrographs were also simulated and experimental, where the simulated ones were obtained using a Monte Carlo routine and Monte Carlo-based statistical tools are also employed to assess the quality of these priors.

In addition to the presentation of these features of the Bayesian approach, some other topics will be discussed, such as regularization and some implementation issues of the proposed schemes, among which we remark the selection of the parameters used in the MH algorithm.

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