Uncertainty quantification for damage detection in 3D-printed auxetic structures using ultrasonic guided waves and a probabilistic neural network

Auxetic structures hold significant potential for applications due to their outstanding properties. Ultrasonic waves and neural networks are the popular technologies used for structural health monitoring (SHM). To increase the reliability of the neural network output for SHM, comprehensive uncertainty quantification is needed for damage detection in unknown areas of auxetic structures. This paper presents the first comprehensive framework for health diagnosis and uncertainty quantification based on ultrasonic guided waves in two 3D-printed star hourglass honeycomb auxetic structures. The proposed framework integrates in- plane compression with simultaneous ultrasonic testing to receive ultrasonic signals across various deformation states. Additionally, fully elastic and elasto-plastic finite element simulations are conducted to analyze wave energy variations and mechanical responses in auxetic structure. Critical damage deformation is identified based on observed deformation patterns and variations in signal energy. The Hilbert transform is used to extract two damage-sensitive features, namely envelope and phase. 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 UQ framework effectively separates and quantifies the predictive variance of the FPCNN model into aleatoric and epistemic uncertainty. The framework's effectiveness is demonstrated through the comprehensive approach, combining compression and ultrasonic tests, finite element simulation, and the FPCNN technique.