Quantification of microcracks by physics-guided neural network-assisted nonlinear ultrasonic technique.

Quantifying microcracks whose dimensions are considerably smaller than the ultrasonic wavelength remains a formidable challenge in nondestructive testing, as linear ultrasonic techniques are constrained by the ratio of wavelength to defect size, while nonlinear ultrasonic techniques (NUT) often suffer from difficulties in decoupling multiple damage parameters. To address these challenges, this study proposes a physics-guided convolutional neural network (PGCNN)-assisted nonlinear ultrasonic technique for the quantitative characterization of microcracks. The proposed PGCNN incorporates a phenomenological damage indicator (DI) model defined in terms of the crack aspect ratio, which is explicitly embedded into the multi-task learning loss function. This physics-based regularization guides the network to remain consistent with nonlinear ultrasonic mechanisms, thereby enabling effective decoupling of crack length and width from a single set of nonlinear Rayleigh wave signals. Experimental validation is performed on torsion shaft specimens containing surface microcracks with varying geometries. The results demonstrate that the proposed PGCNN achieves superior robustness and generalization performance compared with conventional convolutional neural networks. Notably, under data-poor conditions using only 40% of the training dataset, the PGCNN achieves an improvement of more than 15% in the coefficient of determination (R2) and reductions greater than 33% in mean absolute error (MAE) for both crack length and width prediction.