A novel in silico Monte Carlo approach to optimize a PSD estimation problem. Generation of data fusion experiment rules

Abstract

This article analyzes the performance of combining information from Scanning Electron Microscopy(SEM) micrographs with Static Light Scattering (SLS) measurements for retrieving the so-called ParticleSize Distribution (PSD) in terms of experimental features. The corresponding data fusion is implementedusing a novel Monte Carlo-based method consisting in a SMF (Sampling-Mapping-Filtering) approach.This approach provides an important reference to assess the strategy of the experiment for this specificproblem by means of solving an inverse problem. Furthermore, low levels of volume fraction and a PSDrepresented by log-normal distributions are considered in order to reduce processing and model errors dueto ill-posedness. The prior statistics corresponding to the SEM micrographs have been achieved by meansof the Jackknife procedure used as a resampling technique. The likelihood term considers iid normalmeasurements generated from the Local Monodisperse Approximation (LMA) and also makes use of thesame model as forward linear model, in an inversion case known as inverse crime. However, it has beenproved that the LMA performs well in practice for low fraction volume systems as considered here. ThePSD retrieval is measured in terms of improvement in precision with respect to one of the log-normalparameters in SEM micrographs, i.e., the desirability. Estimates are expressed as a function of a typicalsystem parameter such as polydispersity, as well as experimental variables, i.e., number of particles permicrograph (PPM) and noise level ε in the SLS measurements. These estimations are then analyzed bymeans of the Box-Behnken (BB) design and the response surface methodology (RSM) in order to generatea surrogate model from which rules for the optimization of the experiment are made when desirability ismaximized. Finally, a Rule-Based System (RBS) is proposed for future use.