PSD retrieval by Bayesian data fusion via metropolis-hastings and the Jackknife procedure

Otero, Fernando; Frontini, Gloria L.; Eliçabe, Guillermo E.

doi:10.23919/rpic.2017.8214311

Cited by 3 publications

(11 citation statements)

References 16 publications

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“…The SEM micrographs are the result of a direct microscopy measurement technique and allow capturing details from the structure on the surface of the particles. However, they are experimentally expensive and the electron beam may distort the results [10]. Electron microscopy methods have been widely simulated using the MC method.…”

Section: Physical Problem: Sem and Sls Modellingmentioning

confidence: 99%

“…For reasons of simplicity, the complete process of SEM microscopic imaging has not been simulated here. This work uses a simplified random sampling MC routine as described in a previous article [3] and is applied to a sample of a low number of particles, that is far below the several hundreds needed in order to make a reliable statistics per se [10].…”

Section: Physical Problem: Sem and Sls Modellingmentioning

confidence: 99%

“…(2). Relations between these parameters and the mean and variance of the PSD can be seen in [10]. It is worthy to point out that this article has followed the parameterization of the PSD applied in [10], that is, representing the PSD by the two parameters 0 and * = ln ( )…”

Section: Physical Problem: Sem and Sls Modellingmentioning

confidence: 99%

“…The Jackknife procedure, formerly formulated by Quenouille [17], applied to this specific case can be considered the preprocessing stage and it basically consists in generating n resamples of n-1 particles each one, obtained from the micrograph, where every resample is achieved by deleting a different particle at each time. From these resamples, approximate normal distributions are drawn for 0 and * with means ( 0 ) and ( * ) (the original sample averages using the total number of PPM) and standard deviations ( 0 ) = √ 0 and ( * ) = √ * where 0 2 and * 2 are the variances of each parameter obtained by resampling the micrograph with Jackknife [10] After this procedure and corresponding drawing of normal distributions, the actual three stages in the SMF methodology are performed. These are shortly presented from sections 4.2. to 4.4.…”

Section: The Jackknife Proceduresmentioning

confidence: 99%

“…The examples considered in this paper follows the previous article [10] and they belong to a typical range of polymeric systems such as the ones studied for a solid polymer matrix in [35]. Three values of PSD standard deviation of 0.02, 0.05 and 0.10 µm for a mean radius of 0.25 µm as well as three values for SLS noise levels of additive normal distribution of 0.1%, 1% and 10% from the measurement peak, and three values of PPM (50, 80 and 100 particles).…”

Section: Computational Implementation and Examplesmentioning

confidence: 99%

See 4 more Smart Citations

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

Otero¹

2021

Preprint

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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.

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Section: Physical Problem: Sem and Sls Modellingmentioning

confidence: 99%

Section: Physical Problem: Sem and Sls Modellingmentioning

confidence: 99%

Section: Physical Problem: Sem and Sls Modellingmentioning

confidence: 99%

Section: The Jackknife Proceduresmentioning

confidence: 99%

Section: Computational Implementation and Examplesmentioning

confidence: 99%

See 3 more Smart Citations

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

Otero¹

2021

Preprint

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It-Based Filter for a Sequential Monte Carlo Inversion Strategy

Otero¹,

Ghlam²,

Managó³

2023

Preprint

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In this article, we propose and develop an information-theoretic filter for a three-step Sequential Monte Carlo(SMC) inversion procedure. The last stage in this procedure corresponds to a filter, which selects/rejects samplesaccording to a noise level, only known approximately up to a certain order of magnitude. Therefore, we have designedan information-theoretic (IT)-based filter which selects this noise level instead of choosing an approximate but stillarbitrary value for it. A cut-off level is calculated using an optimization scheme based on the principle of relevantinformation (PRI). The PRI has been used to balance the minimization of the entropy of the prior PDF with thediscrepancy between the original data and the solution found by the SMC procedure. Finally, we briefly analyze theperformance of the filter for the computation of both solution and approximate noise level in simulated cases of anapplication inverse problem.

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A Novel In Silico Monte Carlo Approach to Optimize a PSD Estimation Problem. Generation of Data Fusion Experiment Rules

Otero

Frontini

2022

TCAM

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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.

show abstract

PSD retrieval by Bayesian data fusion via metropolis-hastings and the Jackknife procedure

Cited by 3 publications

References 16 publications

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

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

It-Based Filter for a Sequential Monte Carlo Inversion Strategy

A Novel In Silico Monte Carlo Approach to Optimize a PSD Estimation Problem. Generation of Data Fusion Experiment Rules

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