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 Particle Size Distribution (PSD) in terms of experimental features. The corresponding data fusion is implemented using 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 specific problem by means of solving an inverse problem. Furthermore, low levels of volume fraction and a PSD represented by log-normal distributions are considered in order to reduce processing and model errors due to ill-posedness. The prior statistics corresponding to the SEM micrographs have been achieved by means of the Jackknife procedure used as a resampling technique. The likelihood term considers iid normal measurements generated from the Local Monodisperse Approximation (LMA) and also makes use of the same model as forward linear model, in an inversion case known as inverse crime. However, it has been proved that the LMA performs well in practice for low fraction volume systems as considered here. The PSD retrieval is measured in terms of improvement in precision with respect to one of the log-normal parameters in SEM micrographs, i.e., the desirability. Estimates are expressed as a function of a typical system parameter such as polydispersity, as well as experimental variables, i.e., number of particles per micrograph (PPM) and noise level $\varepsilon$ in the SLS measurements. These estimations are then analyzed by means of the Box-Behnken (BB) design and the response surface methodology (RSM) in order to generate a surrogate model from which rules for the optimization of the experiment are made when desirability is maximized. Finally, a Rule-Based System (RBS) is proposed for future use.

It-Based Filter for a Sequential Monte Carlo Inversion Strategy

“…A statistical methodology for solving an inverse problem in the form of a Fredholm integral equation was proposed in [6]. This methodology is basically a Sequential Monte Carlo (SMC) technique which can be described as a three-step Sampling-Mapping-Filtering (SMF) strategy to building a posterior histogram for the parameters of interest.…”

“…The optimization involved in the PRI can be treated as a regularization procedure with a regularization parameter to be chosen. Here, we are concerned with the analysis of the results of applying a simplified version of this optimization scheme in numerical examples similar to the ones studied in [6]. These examples correspond to a spherical particle size distribution (PSD) estimation problem posed as a data fusion from two experimental sources: Scanning Electron Microscopy (SEM) and Static Light Scattering (SLS) measurements.…”