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.

This study presents a comparative analysis of the novel guided-wave-based imaging method that integrates variational Bayesian principal component analysis with time-delay strategy for detecting internal and external defects in plate-like structures. The performance of the conventional delay-and-sum imaging method deteriorates when the signal-to-noise ratio of signals is low or when other wave packets overlap with the defect scattering signal. The imaging method based on variational Bayesian principal component analysis analyzes the principal components and corresponding singular values of the time-delayed signal array, and the maximum singular value represents the contribution of the most principal component, serving as an indicator of the coherent defect-related wave packets. Thus, the defect can be highlighted by accounting for the effect of noise and wave packet interference on the time-delayed signal array. However, when defects are located outside the sensor network, the limited information available may reduce the imaging performance. Numerical simulations and experimental studies conducted on plate-like structures demonstrate the proposed method achieves higher imaging clarity and localization accuracy for the internal defect compared with the external defect, with the former exhibiting mm-level absolute localization errors.