Probabilistic approaches to compute uncertainty intervals and sensitivity factors of ultrasonic simulations of a weld inspection

Rupin, Fabienne; Blatman, Géraud; Lacaze, Sylvain; Fouquet, Thierry; Chassignole, Bertrand

doi:10.1016/j.ultras.2013.12.006

Cited by 14 publications

(16 citation statements)

References 24 publications

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“…A first study [46] has been realized with an inspection configuration aiming to detect a manufactured volumic defect located in a 40 mm thick V grooveweld made of 316L steel ( Figure 6). The weld material reveals a heterogeneous and anisotropic structure.…”

Section: Industrial Applicationmentioning

confidence: 99%

“…The scalar output variable of the model is the amplitude of the defect echoes resulting from an ultrasonic inspection (maximum value on a so-called Bscan). Uncertainty and sensitivity analysis (based on polynomial chaos expansion [19]) have then been applied from 6000 Monte Carlo simulations of ATHENA2D in [46]. The sensitivity analysis has shown that almost all inputs are influential (only one input has a total Sobol' index smaller than 5%), that the interaction effects are non-negligible (approximately 30% of the total variance) and that the orientations play a major role for explaining the amplitude variability.…”

Section: Industrial Applicationmentioning

confidence: 99%

“…The analysis confirms that an accurate determination of the micro-structure is essential in these simulation studies. Finally, as a perspective of their work, the authors in [46] explain that the real configuration has been strongly simplified by considering independent input random variables. Indeed, due to the welding physical process, a dependence structure exists between the orientations, in particular between two neighboring domains (see Figure 6 right).…”

Section: Industrial Applicationmentioning

confidence: 99%

“…In our study, the probability distributions of all the inputs are considered Gaussian. Their means and standard deviations are unchanged with respect to those of [46]. From physical models of welding process and solidification [47], engineers have been able to estimate the following correlation matrix between the 7 orientations (Or 1 , .…”

Section: Industrial Applicationmentioning

confidence: 99%

See 3 more Smart Citations

Shapley Effects for Sensitivity Analysis With Correlated Inputs: Comparisons With Sobol' Indices, Numerical Estimation and Applications

Iooss

Prieur

2019

Int. J. UncertaintyQuantification

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The global sensitivity analysis of a numerical model aims to quantify, by means of sensitivity indices estimates, the contributions of each uncertain input variable to the model output uncertainty. The so-called Sobol' indices, which are based on functional variance analysis, present a difficult interpretation in the presence of statistical dependence between inputs. The Shapley effects were recently introduced to overcome this problem as they allocate the mutual contribution (due to correlation and interaction) of a group of inputs to each individual input within the group. In this paper, using several new analytical results, we study the effects of linear correlation between some Gaussian input variables on Shapley effects, and compare these effects to classical first-order and total Sobol' indices. This illustrates the interest, in terms of sensitivity analysis setting and interpretation, of the Shapley effects in the case of dependent inputs. For the practical issue of computationally demanding computer models, we show that the substitution of the original model by a metamodel (here, kriging) makes it possible to estimate these indices with precision at a reasonable computational cost.

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Section: Industrial Applicationmentioning

confidence: 99%

Section: Industrial Applicationmentioning

confidence: 99%

Section: Industrial Applicationmentioning

confidence: 99%

Section: Industrial Applicationmentioning

confidence: 99%

See 2 more Smart Citations

Shapley Effects for Sensitivity Analysis With Correlated Inputs: Comparisons With Sobol' Indices, Numerical Estimation and Applications

Iooss

Prieur

2019

Int. J. UncertaintyQuantification

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show abstract

“…In this section, we illustrate the decomposition of the overall error from the estimation of the indices and we consider as examples the additive Gaussian framework and the Ishigami function. We also consider the industrial application of introduced in Rupin et al (2014) and also used in Iooss and Prieur (2017).…”

Section: Numerical Simulations With Kriging Modelmentioning

confidence: 99%

Shapley effects for sensitivity analysis with dependent inputs: bootstrap and kriging-based algorithms

Benoumechiara

Elie-Dit-Cosaque

2019

ESAIM: ProcS

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In global sensitivity analysis, the well known Sobol' sensitivity indices aim to quantify how the variance in the output of a mathematical model can be apportioned to the different variances of its input random variables. These indices are based on the functional variance decomposition and their interpretation become difficult in the presence of statistical dependence between the inputs. However, as there is dependence in many application studies, that enhances the development of interpretable sensitivity indices. Recently, the Shapley values developed in the field of cooperative games theory have been connected to global sensitivity analysis and present good properties in the presence of dependencies. Nevertheless, the available estimation methods don't always provide confidence intervals and require a large number of model evaluation. In this paper, we implement a bootstrap sampling in the existing algorithms to estimate confidence intervals of the indice estimations. We also proposed to consider a metamodel in substitution of a costly numerical model. The estimation error from the Monte-Carlo sampling is combined with the metamodel error in order to have confidence intervals on the Shapley effects. Besides, we compare for different examples with dependent random variables the results of the Shapley effects with existing extensions of the Sobol' indices.

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Model Assisted Probability of Detection Curves: New Statistical Tools and Progressive Methodology

Gratiet¹,

Iooss²,

Blatman³

et al. 2016

J Nondestruct Eval

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The Probability Of Detection (POD) curve is a standard tool in several industries to evaluate the performance of Non Destructive Testing (NDT) procedures for the detection of harmful defects for the inspected structure. Due to new capabilities of NDT process numerical simulation, Model Assisted Probability of Detection (MAPOD) approaches have also been recently developed. In this paper, a generic and progressive MAPOD methodology is proposed. Limits and assumptions of the classical methods are enlightened, while new metamodel-based methods are proposed. They allow to access to relevant information based on sensitivity analysis of MAPOD inputs. Applications are performed on Eddy Current Non Destructive Examination numerical data.

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Probabilistic approaches to compute uncertainty intervals and sensitivity factors of ultrasonic simulations of a weld inspection

Cited by 14 publications

References 24 publications

Shapley Effects for Sensitivity Analysis With Correlated Inputs: Comparisons With Sobol' Indices, Numerical Estimation and Applications

Shapley Effects for Sensitivity Analysis With Correlated Inputs: Comparisons With Sobol' Indices, Numerical Estimation and Applications

Shapley effects for sensitivity analysis with dependent inputs: bootstrap and kriging-based algorithms

Model Assisted Probability of Detection Curves: New Statistical Tools and Progressive Methodology

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