Uncertainty quantification for damage detection in 3D printed auxetic structures based on ultrasonic guided-wave using Flipout probabilistic convolutional neural network

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Abstract The auxetic structure is widely used in aviation, bio-engineering, automation, and other industries due to its outstanding properties, such as being lightweight, high strength-to-weight ratio, and absorbing energy. Neural network methods have been popularly used for auxetic structures’ structural health monitoring. However, the performance of neural network methods in unknown areas is limited. To increase the reliability of the network model, more comprehensive uncertainty quantification is needed for damage detection in unknown areas. This paper introduces a comprehensive framework for health diagnosis and uncertainty quantification in 3D-printed auxetic structures made of polylactic acid. The framework involves quasi-static uniaxial compression and ultrasonic tests conducted simultaneously to capture ultrasonic signals at different deformation states. Critical damage deformation is identified based on observed deformation patterns and variations in signal energy. Using the Hilbert transform, two damage-sensitive features—envelope and phase—are extracted. These features serve as input data for the Flipout probabilistic convolutional neural network (FPCNN) model, which integrates pseudo-independent weight perturbations and a Gaussian probabilistic layer within the visual geometry group 13 architecture to predict structural deformations and associated uncertainties. The uncertainty quantification framework, based on variational inference and the conditional covariance law, effectively separates and quantifies the predictive variance of the network model into aleatoric and epistemic uncertainty. This framework’s feasibility is demonstrated through compression and ultrasonic tests, utilizing the FPCNN. This showcases the uncertainty quantification capabilities of the FPCNN model.