Imaging cracks in orthotropic steel decks based on guided wave and variational Bayesian robust principal component analysis

This study proposes a novel crack imaging method based on guided waves, by incorporating variational Bayesian robust principal component analysis (VBRPCA) into delayed imaging to achieve high resolution and contrast. The performance of the conventional delay-and-sum imaging method becomes worse when the time-delayed array contains overlapping wave packets and significant measurement noise. The VBRPCA-based delayed imaging method reduces the rank of the time-delayed subarray to mitigate the effects of noise and overlapping wave packets. Principal components and their singular values are then obtained and used as the pixel value of crack imaging. The maximum singular value of the time-delayed subarray which focused on crack is much larger than that of crack-free position because the former subarray only contains the crack-reflected wave packets with consistent phase alignment while crack-free subarray contains other unrelated wave packets resulting in phase misalignment. Therefore, the maximum singular value is an effective indicator for crack imaging. The performance of the proposed approach was validated through multiple numerical simulations and an experimental study on a simplified orthotropic steel deck, demonstrating its effectiveness and robustness in imaging cracks under challenging conditions.