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Bayesian Statistics Applied to the Nondestructive Evaluation for the POD and Classification of Flaw Sizes

Ramos, H. ; Baskaran, P. ; Ribeiro, A. L.

Bayesian Statistics Applied to the Nondestructive Evaluation for the POD and Classification of Flaw Sizes, Proc Electromagnetic Nondestructive Evaluation International Workshop on Electromagnetic Nondestructive Evaluation ENDE, Detroit, United States, Vol. Pen drive, pp. 0 - 0, September, 2018.

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Abstract
In the field of Nondestructive Evaluation (NDE), classification of the size of a flaw (crack length) is a critical issue. In this work it is intended to develop a Probability of Detection (POD) model and also characterize the flaws based on their size, by assigning the class conditionals (observations) directly to a bivariate Gaussian distribution. It is known that the non-destructive inspection data (for the flaw length) are heteroscedastic. But for performing any linear regression, the condition of homoscedasticity has to be met. In this paper, the mean and variance of the distribution is directly inferred from the observations, utilizing the Gaussian Mixture Model (GMM). From this model, it is possible to arrive at the classical Hit/Miss model by fixing a minimum threshold. It is also possible to perform risk analysis on the probability of misclassification considering a 0/1 loss function and then making a classification from the posterior estimates within the Bayesian framework. For the analysis, a finite element simulation study has been made for flaws located at the sub-surface of a 10 mm thick stainless steel (SS304) specimen.