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Bayesian Inference in Inverse Problem
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Bayesian Inference in Inverse Problem

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Mechanical Engineering".

Deadline for manuscript submissions: closed (30 January 2021) | Viewed by 11000

Special Issue Editors

Prof. Emmanuelle Abisset-Chavanne

E-Mail Website
Guest Editor
Ecole Nationale Supérieure d'Arts et Métiers (ENSAM), Institut de Mécanique et Ingénierie de Bordeaux, I2M BORDEAUX, Université de Bordeaux, Gradignan, France
Interests: inverse method; numerical simulations
Prof. Battaglia Jean-Luc

E-Mail Website
Guest Editor
Department of Science and Technology, I2M, Université de Bordeaux, Gradignan, France

Special Issue Information

Dear Colleagues,

With the development of digital applications in engineering applications, the questions of data assimilation and model parameter inference have risen to primary importance.
Various methods exist to tackle these challenging problems, which are more or less adapted to the physics content involved within either the model or the system.

Among them, Bayesian inference is a powerful statistical method based on the well-known equation of conditional probability established by Bayes in the 1930s. Nevertheless, this method implies a sampling within the parameters domain that is very time consuming for complex systems. Moreover, this method has evolved to include new efficient techniques from different communities and applications.

In this Special Issue, we invite the scientific community to publish their works dealing with operational applications of the Bayesian inference in different uses of this method depending on the physics involved and the final application.

The following suggested subtopics are of particular interest:

- System numerical twin using Bayesian inference;
- Inverse method and model identification;
- Bayesian experimental design;
- Maximum entropy and choice of prior distributions;
- Bayesian modeling and inference;
- High-performance computing for Bayesian data analysis;
- Bayesian methods for the analysis of big data.

Prof. Emmanuelle Abisset-Chavanne
Prof. Battaglia Jean-Luc
Guest Editors

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Keywords

  • Bayesian inference
  • inverse method
  • digital twin
  • big data
  • numerical methods

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Published Papers (5 papers)

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27 pages, 1905 KiB  
Article
On the Use of Structured Prior Models for Bayesian Compressive Sensing of Modulated Signals
by Yosra Marnissi, Yasmine Hawwari, Amadou Assoumane, Dany Abboud and Mohamed El-Badaoui
Appl. Sci. 2021, 11(6), 2626; https://doi.org/10.3390/app11062626 - 16 Mar 2021
Viewed by 1558
Abstract
The compressive sensing (CS) of mechanical signals is an emerging research topic for remote condition monitoring. The signals generated by machines are mostly periodic due to the rotating nature of its components. Often, these vibrations witness strong interactions among two or multiple rotating [...] Read more.
The compressive sensing (CS) of mechanical signals is an emerging research topic for remote condition monitoring. The signals generated by machines are mostly periodic due to the rotating nature of its components. Often, these vibrations witness strong interactions among two or multiple rotating sources, leading to modulation phenomena. This paper is specifically concerned with the CS of this particular class of signals using a Bayesian approach. The main contribution of this paper is to consider the particular spectral structure of these signals through two families of hierarchical models. The first one adopts a block-sparse model that jointly estimates the sparse coefficients at identical or symmetrical positions around the carrier frequencies. The second is a spike-and-slab model where the spike component takes into account the symmetrical properties of the support of non-zero-coefficients in the spectrum. The resulting posterior distribution is approximated using a Gibbs sampler. Simulations show that considering the structure in the prior model yields better noise shrinkage and better reconstruction of small side-bands. Application to condition monitoring of a gearbox through CS of vibration signals highlights the good performance of the proposed models in reconstructing the signal, offering an accurate fault detection with relatively high compression rate. Full article
(This article belongs to the Special Issue Bayesian Inference in Inverse Problem)
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24 pages, 8364 KiB  
Article
Hierarchical Bayesian Models to Estimate the Number of Losses of Separation between Aircraft in Flight
by Rosa María Arnaldo Valdés and Victor Fernando Gómez Comendador
Appl. Sci. 2021, 11(4), 1600; https://doi.org/10.3390/app11041600 - 10 Feb 2021
Cited by 1 | Viewed by 2251
Abstract
Air transport is considered to be the safest mode of mass transportation. Air traffic management (ATM) systems constitute one of the fundamental pillars that contribute to these high levels of safety. In this paper we wish to answer two questions: (i) What is [...] Read more.
Air transport is considered to be the safest mode of mass transportation. Air traffic management (ATM) systems constitute one of the fundamental pillars that contribute to these high levels of safety. In this paper we wish to answer two questions: (i) What is the underlying safety level of ATM systems in Europe? and (ii) What is the dispersion, that is, how far does each ATM service provider deviate from this underlying safety level? To do this, we develop four hierarchical Bayesian inference models that allow us to infer and predict the common rate of occurrence of SMIs, as well as the specific rates of occurrence for each air navigation service provider (ANSP). This study shows the usefulness of hierarchical structures when it comes to obtaining parameters that enable risk to be quantified effectively. The models developed have been found to be useful in explaining and predicting the safety performance of 29 European ATM systems with common regulations and work procedures, but with different circumstances and numbers of aircraft, each managing traffic of differing complexity. Full article
(This article belongs to the Special Issue Bayesian Inference in Inverse Problem)
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24 pages, 7435 KiB  
Article
Understanding Time-Evolving Citation Dynamics across Fields of Sciences
by Minkyoung Kim
Appl. Sci. 2020, 10(17), 5846; https://doi.org/10.3390/app10175846 - 24 Aug 2020
Cited by 1 | Viewed by 2385
Abstract
Scholarly publications draw collective attention beyond disciplines, leading to highly skewed citation distributions in sciences. Uncovering the mechanisms of such disparate popularity is very challenging, since a wide spectrum of research fields are not only interacting and influencing one another but also time-evolving. [...] Read more.
Scholarly publications draw collective attention beyond disciplines, leading to highly skewed citation distributions in sciences. Uncovering the mechanisms of such disparate popularity is very challenging, since a wide spectrum of research fields are not only interacting and influencing one another but also time-evolving. Accordingly, this study aims to understand citation dynamics across STEM fields in terms of latent affinity and novelty decay, which is based upon Bayesian inference and learning of the Affinity Poisson Process model (APP) with bibliography data from the Web of Science database. The approaches shown in the study can shed light on predicting and interpreting popularity dynamics in diverse application domains, by considering the effect of time-varying subgroup interactions on diffusion processes. Full article
(This article belongs to the Special Issue Bayesian Inference in Inverse Problem)
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24 pages, 1577 KiB  
Article
Data Assimilation in Spatio-Temporal Models with Non-Gaussian Initial States—The Selection Ensemble Kalman Model
by Maxime Conjard and Henning Omre
Appl. Sci. 2020, 10(17), 5742; https://doi.org/10.3390/app10175742 - 19 Aug 2020
Cited by 4 | Viewed by 1980
Abstract
Assimilation of spatio-temporal data poses a challenge when allowing non-Gaussian features in the prior distribution. It becomes even more complex with nonlinear forward and likelihood models. The ensemble Kalman model and its many variants have proven resilient when handling nonlinearity. However, owing to [...] Read more.
Assimilation of spatio-temporal data poses a challenge when allowing non-Gaussian features in the prior distribution. It becomes even more complex with nonlinear forward and likelihood models. The ensemble Kalman model and its many variants have proven resilient when handling nonlinearity. However, owing to the linearized updates, conserving the non-Gaussian features in the posterior distribution remains an issue. When the prior model is chosen in the class of selection-Gaussian distributions, the selection Ensemble Kalman model provides an approach that conserves non-Gaussianity in the posterior distribution. The synthetic case study features the prediction of a parameter field and the inversion of an initial state for the diffusion equation. By using the selection Kalman model, it is possible to represent multimodality in the posterior model while offering a 20 to 30% reduction in root mean square error relative to the traditional ensemble Kalman model. Full article
(This article belongs to the Special Issue Bayesian Inference in Inverse Problem)
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13 pages, 1861 KiB  
Article
Bayesian Inference for 3D Volumetric Heat Sources Reconstruction from Surfacic IR Imaging
by Marie-Marthe Groz, Emmanuelle Abisset-Chavanne, Anissa Meziane, Alain Sommier and Christophe Pradère
Appl. Sci. 2020, 10(5), 1607; https://doi.org/10.3390/app10051607 - 28 Feb 2020
Cited by 6 | Viewed by 2148
Abstract
The domain of non-destructive testing (NDT) or thermal characterization is currently often done by using contactless methods based on the use of an IR camera to monitor the transient temperature response of a system or sample warmed by using any heat source. Though [...] Read more.
The domain of non-destructive testing (NDT) or thermal characterization is currently often done by using contactless methods based on the use of an IR camera to monitor the transient temperature response of a system or sample warmed by using any heat source. Though many techniques use optical excitation (flash lamps, lasers, etc.), some techniques use volumetric sources such as acoustic or induction waves. In this paper, we propose a new inverse processing method, which allows for the estimation of 3D fields of heat sources from surface temperature measurements. This method should be associated with volumetric heat source generation. To validate the method, a volumetric source was generated by the Joule effect in a homogeneous PVC sample using an electrical thin cylindrical wire molded in the material. The inverse processing allows us to retrieve the depth of the wire and its geometrical shape and size. This tool could be a new procedure for retrieving 3D defects on NDT. Full article
(This article belongs to the Special Issue Bayesian Inference in Inverse Problem)
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