Markov Chain Monte Carlo Posterior Density Approximation for a Groove-Dimensioning Purpose

Vargas, José Ismael De la Rosa; Fleury, Gilles; Osuna, S.E.; Davoust, M.‐E.

doi:10.1109/tim.2005.861495

Cited by 7 publications

(5 citation statements)

References 24 publications

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“…In consequence, the parameter inversion results should be more biased because of those. 19 From Fig. 6, we also see that the likelihood remains nearly the same after warming-up.…”

Section: Mcmc Parameter Estimation Resultsmentioning

confidence: 65%

“…7, we see that estimating the sizes of a single flaw is simple, and the estimated 1D marginal distributions are close to Gaussian ones. We also see that flaw depth and width are 19 highly correlated, with ρ(w, d) = −0.97.…”

Section: Mcmc Parameter Estimation Resultsmentioning

confidence: 69%

“…Markov Chain Monte Carlo (MCMC) methods [24,31,45] have been used in ECT for Bayesian analysis [19,36]. However, they are not widely used for solving ECT inversion problems because of high computational cost.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Metamodel-based Markov-Chain-Monte-Carlo parameter inversion applied in eddy current flaw characterization

Cai

Miorelli

Lambert

et al. 2018

NDT & E International

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Flaw characterization in eddy current testing usually requires to solve a non-linear inverse problem. Due to high computational cost, Markov Chain Monte Carlo (MCMC) methods are hardly employed since often needing many forward evaluations. However, they have good potential in dealing with complicated forward models and they do not reduce to only providing the parameters sought. Here, we introduce a computationally-cheap surrogate forward model into a MCMC algorithm for eddy current flaw characterization. Due to the use of a database trained off-line, we benefit from the MCMC algorithm for getting more information and we do not suffer from the computational burden. Numerous experiments are carried out to validate the approach. The results include not only the estimated parameters, but also standard deviations, marginal densities and correlation coefficients between two parameters of interest.

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“…In consequence, the parameter inversion results should be more biased because of those. 19 From Fig. 6, we also see that the likelihood remains nearly the same after warming-up.…”

Section: Mcmc Parameter Estimation Resultsmentioning

confidence: 65%

Section: Mcmc Parameter Estimation Resultsmentioning

confidence: 69%

See 1 more Smart Citation

Metamodel-based Markov-Chain-Monte-Carlo parameter inversion applied in eddy current flaw characterization

Cai

Miorelli

Lambert

et al. 2018

NDT & E International

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show abstract

“…In Non-Destuctive Testing (NDT), our main research area, there are many demands for joint model choice and parameter estimation. Take the flaw detection and characterization problem [1,2,3,4] for example, it will be very useful if the method can tell automatically what kind of flaw, a hole or a crack, that we are dealing with and what are the corresponding dimensions if it is a crack. The former is a model choice problem while the later is a parameter estimation problem.…”

Section: Introductionmentioning

confidence: 99%

Efficient model choice and parameter estimation by using nested sampling applied in Eddy-Current Testing

Cai

Rodet

Lambert

2015

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In many applications, such as Eddy-Current Testing (ECT), we are often interested in the joint model choice and parameter estimation. Nested Sampling (NS) is one of the possible methods. The key step that reflects the efficiency of the NS algorithm is how to get samples with hard constraint on the likelihood value. This contribution is based on the classical idea where the new sample is drawn within a hyper-ellipsoid, the latter being located from Gaussian approximation. This sampling strategy can automatically guarantee the hard constraint on the likelihood. Meanwhile, it shows the best sampling efficiency for models which have Gaussian-like likelihood distributions. We apply this method in ECT. The simulation results show that this method has high model choice ability and good parameter estimation accuracy, and low computational cost meanwhile.

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“…However, the training samples are often difficult to obtain for real industrial applications and there are obvious errors when a sample has never been contained in training set. Recently, there has been much interest in use of probability density function estimation and Bayesian estimation methods for quantitative evaluation of defects [25][26][27]. These methods employ sampling techniques such as Markov Chain Monte Carlo (MCMC) and Bootstrap methods, for probability density function estimation of defect characteristic parameters to obtain not only the quantity but also the uncertainty characterization of the measurand.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian Network Method for Quantitative Evaluation of Defects in Multilayered Structures from Eddy Current NDT Signals

Shu

Cao

et al. 2014

Mathematical Problems in Engineering

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Accurate evaluation and characterization of defects in multilayered structures from eddy current nondestructive testing (NDT) signals are a difficult inverse problem. There is scope for improving the current methods used for solving the inverse problem by incorporating information of uncertainty in the inspection process. Here, we propose to evaluate defects quantitatively from eddy current NDT signals using Bayesian networks (BNs). BNs are a useful method in handling uncertainty in the inspection process, eventually leading to the more accurate results. The domain knowledge and the experimental data are used to generate the BN models. The models are applied to predict the signals corresponding to different defect characteristic parameters or to estimate defect characteristic parameters from eddy current signals in real time. Finally, the estimation results are analyzed. Compared to the least squares regression method, BNs are more robust with higher accuracy and have the advantage of being a bidirectional inferential mechanism. This approach allows results to be obtained in the form of full marginal conditional probability distributions, providing more information on the defect. The feasibility of BNs presented and discussed in this paper has been validated.

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Markov Chain Monte Carlo Posterior Density Approximation for a Groove-Dimensioning Purpose

Cited by 7 publications

References 24 publications

Metamodel-based Markov-Chain-Monte-Carlo parameter inversion applied in eddy current flaw characterization

Metamodel-based Markov-Chain-Monte-Carlo parameter inversion applied in eddy current flaw characterization

Efficient model choice and parameter estimation by using nested sampling applied in Eddy-Current Testing

A Bayesian Network Method for Quantitative Evaluation of Defects in Multilayered Structures from Eddy Current NDT Signals

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