Three-dimensional fatigue crack quantification using densely connected convolutional network-assisted ultrasonic guided waves

Linear and nonlinear ultrasonic guided wave (UGW)-based methods are available for fatigue crack detection and quantification. However, linear methods usually fail to detect undersized cracks, while nonlinear methods struggle to assess cracks once they have extended to a certain degree. The fusion of linear and nonlinear UGW features offers a new opportunity to enhance evaluation precision and effectiveness, yet it necessitates highly complex modeling. Motivated by this, a regression model is proposed based on the famed densely connected convolutional network, DenseNet, for three-dimensional (3D) fatigue crack quantification in both crack initiation and growth stages. Via the continuous wavelet transform (CWT), the spectra of UGW signals embracing both linear and nonlinear features of UGW are obtained. Subsequently, DenseNet is adopted to extract implicit features of spectra images. Finally, the last fully connected layer of DenseNet is modified as a regression layer to estimate the length and depth of 3D fatigue cracks. A dataset comprising 500 UGW signals is created for validating the proposed model. The results demonstrate that the model can characterize the length and depth of 3D cracks in both initiation and growth stages, establishing it as a promising proof-of-concept for the deep learning-based quantification of 3D fatigue cracks.