Uncertainty Quantification for Deep Learning in Ultrasonic Crack Characterization.

Deep learning for nondestructive evaluation (NDE) has received a lot of attention in recent years for its potential ability to provide human level data analysis. However, little research into quantifying the uncertainty of its predictions has been done. Uncertainty quantification (UQ) is essential for qualifying NDE inspections and building trust in their predictions. Therefore, this article aims to demonstrate how UQ can best be achieved for deep learning in the context of crack sizing for inline pipe inspection. A convolutional neural network architecture is used to size surface breaking defects from plane wave imaging (PWI) images with two modern UQ methods: deep ensembles and Monte Carlo dropout. The network is trained using PWI images of surface breaking defects simulated with a hybrid finite element / ray-based model. Successful UQ is judged by calibration and anomaly detection, which refer to whether in-domain model error is proportional to uncertainty and if out of training domain data is assigned high uncertainty. Calibration is tested using simulated and experimental images of surface breaking cracks, while anomaly detection is tested using experimental side-drilled holes and simulated embedded cracks. Monte Carlo dropout demonstrates poor uncertainty quantification with little separation between in and out-of-distribution data and a weak linear fit ( R=0.84 ) between experimental root-mean-square-error and uncertainty. Deep ensembles improve upon Monte Carlo dropout in both calibration ( R=0.95 ) and anomaly detection. Adding spectral normalization and residual connections to deep ensembles slightly improves calibration ( R=0.98 ) and significantly improves the reliability of assigning high uncertainty to out-of-distribution samples.

Domain Adapted Deep-Learning for Improved Ultrasonic Crack Characterization Using Limited Experimental Data.

Deep learning is an effective method for ultrasonic crack characterization due to its high level of automation and accuracy. Simulating the training set has been shown to be an effective method of circumventing the lack of experimental data common to nondestructive evaluation (NDE) applications. However, a simulation can neither be completely accurate nor capture all variability present in the real inspection. This means that the experimental and simulated data will be from different (but related) distributions, leading to inaccuracy when a deep learning algorithm trained on simulated data is applied to experimental measurements. This article aims to tackle this problem through the use of domain adaptation (DA). A convolutional neural network (CNN) is used to predict the depth of surface-breaking defects, with in-line pipe inspection as the targeted application. Three DA methods across varying sizes of experimental training data are compared to two non-DA methods as a baseline. The performance of the methods tested is evaluated by sizing 15 experimental notches of length (1-5 mm) and inclined at angles of up to 20° from the vertical. Experimental training sets are formed with between 1 and 15 notches. Of the DA methods investigated, an adversarial approach is found to be the most effective way to use the limited experimental training data. With this method, and only three notches, the resulting network gives a root-mean-square error (RMSE) in sizing of 0.5 ± 0.037 mm, whereas with only experimental data the RMSE is 1.5 ± 0.13 mm and with only simulated data it is 0.64 ± 0.044 mm.

Deep Learning for Ultrasonic Crack Characterization in NDE.

Machine learning for nondestructive evaluation (NDE) has the potential to bring significant improvements in defect characterization accuracy due to its effectiveness in pattern recognition problems. However, the application of modern machine learning methods to NDE has been obstructed by the scarcity of real defect data to train on. This article demonstrates how an efficient, hybrid finite element (FE) and ray-based simulation can be used to train a convolutional neural network (CNN) to characterize real defects. To demonstrate this methodology, an inline pipe inspection application is considered. This uses four plane wave images from two arrays and is applied to the characterization of cracks of length 1-5 mm and inclined at angles of up to 20° from the vertical. A standard image-based sizing technique, the 6-dB drop method, is used as a comparison point. For the 6-dB drop method, the average absolute error in length and angle prediction is ±1.1 mm and ±8.6°, respectively, while the CNN is almost four times more accurate at ±0.29 mm and ±2.9°. To demonstrate the adaptability of the deep learning approach, an error in sound speed estimation is included in the training and test set. With a maximum error of 10% in shear and longitudinal sound speed, the 6-dB drop method has an average error of ±1.5 mmm and ±12°, while the CNN has ±0.45 mm and ±3.0°. This demonstrates far superior crack characterization accuracy by using deep learning rather than traditional image-based sizing.