Deep learning uncertainty quantification for ultrasonic damage identification in composite structures

In this paper, three state-of-the-art deep learning uncertainty quantification (UQ) methods - Flipout probabilistic convolutional neural network (CNN), deep ensemble probabilistic CNN, and Bayesian probabilistic CNN - based on the Visual Geometry Group 13 architecture are proposed. They are compared with a traditional Bayesian inference approach for localizing delamination damage in composite. The law of conditional covariance is used to separate and quantify the predictive variance of the three networks into aleatoric and epistemic uncertainty. The network models' performance is enhanced through hyperparameter optimization using Hyperband and warm-up optimization algorithms. The performance of the three networks in measuring the uncertainty is assessed on an out -of -distribution (OOD) dataset and validated on an in -distribution (ID) dataset for localization of composite delamination damage. Results indicate high accuracy in predicting damage locations for all methods on the ID dataset. On the OOD dataset, the Flipout and deep ensemble network have better performance, stably measuring aleatoric uncertainty in both trained and untrained areas, while the Bayesian network's aleatoric uncertainty shows a discernible change across both areas. All three networks effectively measure epistemic uncertainty. Overall in both ID and OOD datasets, the Flipout network provides an optimal balance among training efficiency, UQ effectiveness and accuracy in predicting damage locations.