Bayesian approach to the inverse problem in a light scattering application

Otero, Fernando; Orlande, Helcio R. B.; Frontini, Gloria L.; Eliçabe, Guillermo E.

doi:10.1080/02664763.2014.993370

Cited by 10 publications

(5 citation statements)

References 38 publications

(49 reference statements)

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“…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 [26] 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 [25].…”

Section: Physical Problem: Sem and Sls Modellingmentioning

confidence: 99%

“…In this sense, there are several methodologies within the framework of MSIF techniques, with the only requisite of expressing information in a statistical manner, through a probability density function (pdf). For example, several articles have successfully applied Bayesian approaches to the PSD retrieval such as [7,26]. Nevertheless, an effective employment of typical Bayesian methodologies such as Monte Carlo Markov Chain (MCMC) and Sequential Monte Carlo (SMC) methods to realistic cases often implies a large computational cost, mostly because in such Monte Carlo algorithms is the need to numerically evaluate the posterior distribution, up to a normalisation constant, commonly many thousands or millions of times [33].…”

Section: Introductionmentioning

confidence: 99%

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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.

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Section: Physical Problem: Sem and Sls Modellingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…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%

“…In this sense, there are several methodologies within the framework of MSIF techniques, with the only requisite of expressing information in a statistical manner, through a probability density function (pdf). For example, several articles have successfully applied Bayesian approaches to the PSD retrieval such as [2,3]. Nevertheless, an effective employment of typical Bayesian methodologies such as Monte Carlo Markov Chain (MCMC) and Sequential Monte Carlo (SMC) methods to realistic cases often implies a large computational cost, mostly because in such Monte Carlo algorithms is the need to numerically evaluate the posterior distribution, up to a normalisation constant, commonly many thousands or millions of times [4].…”

Section: Introductionmentioning

confidence: 99%

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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“…Measurements based on magnetic properties are introduced for the inversion of the magnetic diameter distribution. Commonly used methods include maximum likelihood estimation [19], Bayesian method [20], nonlinear method [21], and regularization method [22], however, noise in the data causes oscillations during parameter estimation. The temperature exerts a significant influence on the volume of the magnetic core, resulting in alterations to the magnetic diameter at both high and low temperatures.…”

Section: Introductionmentioning

confidence: 99%

Inversion of magnetic diameter distribution of magnetic fluids under high and low temperatures

Xue,

Yang,

Zhang

et al. 2024

Nanotechnology

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The magnetic diameter is a crucial factor affecting the magnetic properties of magnetic fluid. The magnetic diameter distribution can be estimated based on the magnetic properties. However, the magnetic dipole interaction of magnetic nanoparticles (MNPs) and the variation of the magnetic diameter with temperature have received relatively little attention in previous research. Hence, this research proposes the AP-MMF1-L method to inverse the magnetic diameter which considers the magnetic dipole interaction and derives the magnetic diameter at different temperatures. Firstly the AP-MMF1-L uses the least square method between the first-order modified mean-field Langevin function (MMF1-L) and the measured magnetization curve as the objective function. Meanwhile, the hybrid Artificial bee colony-Particle swarm (AP) optimization algorithm is introduced to inverse the optimal magnetic diameter distribution. Secondly, the hydrodynamic diameter distribution experimental values are compared with the theoretical values, demonstrating the AP-MMF1-L method obtains accurate inversion results of the magnetic diameter distribution when compared to other models. Finally, the arithmetic mean of the magnetic diameter at different temperatures is investigated, revealing a decreasing trend as the temperature rises, approximately following a linear distribution. The AP-MMF1-L provides a novel and effective tool for accurately determining the magnetic diameter of the MNPs across various temperatures.

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Bayesian approach to the inverse problem in a light scattering application

Cited by 10 publications

References 38 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

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

Inversion of magnetic diameter distribution of magnetic fluids under high and low temperatures

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