Interpretable and Explainable Machine Learning for Ultrasonic Defect Sizing

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Despite its popularity in literature, there are few examples of machine learning (ML) being used for industrial nondestructive evaluation (NDE) applications. A significant barrier is the ‘black box’ nature of most ML algorithms. This paper aims to improve the interpretability and explainability of ML for ultrasonic NDE by presenting a novel dimensionality reduction method: Gaussian feature approximation (GFA). GFA involves fitting a 2D elliptical Gaussian function an ultrasonic image and storing the seven parameters that describe each Gaussian. These seven parameters can then be used as inputs to data analysis methods such as the defect sizing neural network presented in this paper. GFA is applied to ultrasonic defect sizing for inline pipe inspection as an example application. This approach is compared to sizing with the same neural network, and two other dimensionality reduction methods (the parameters of 6 dB drop boxes and principal component analysis), as well as a convolutional neural network applied to raw ultrasonic images. Of the dimensionality reduction methods tested, GFA features produce the closest sizing accuracy to sizing from the raw images, with only a 23% increase in RMSE, despite a 96.5% reduction in the dimensionality of the input data. Implementing ML with GFA is implicitly more interpretable than doing so with principal component analysis or raw images as inputs, and gives significantly more sizing accuracy than 6 dB drop boxes. Shapley additive explanations (SHAP) are used to calculate how each feature contributes to the prediction of an individual defect’s length. Analysis of SHAP values demonstrates that the GFA-based neural network proposed displays many of the same relationships between defect indications and their predicted size as occur in traditional NDE sizing methods.
Original languageEnglish
Pages (from-to)277-290
Number of pages14
JournalIEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
Issue number4
Publication statusPublished - 24 Feb 2023

Bibliographical note

Funding Information:
This work was supported by the Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/L015587/1 through the Research Centre for Non-Destructive Evaluation (RCNDE), with additional funding provided by Baker Hughes, Cramlington, UK.

Publisher Copyright:
© 1986-2012 IEEE.


  • Interpretability
  • machine learning
  • ultrasound
  • defect characterisation
  • neural network
  • plane wave imaging
  • simulation


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